UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Beta-detected NMR of ⁸Li⁺ in spintronic materials Song, Qun 2012

You don't seem to have a PDF reader installed, try download the pdf

Item Metadata

Download

Media
ubc_2013_spring_song_qun.pdf [ 6.17MB ]
[if-you-see-this-DO-NOT-CLICK]
Metadata
JSON: 1.0073399.json
JSON-LD: 1.0073399+ld.json
RDF/XML (Pretty): 1.0073399.xml
RDF/JSON: 1.0073399+rdf.json
Turtle: 1.0073399+rdf-turtle.txt
N-Triples: 1.0073399+rdf-ntriples.txt
Original Record: 1.0073399 +original-record.json
Full Text
1.0073399.txt
Citation
1.0073399.ris

Full Text

β-Detected NMR of 8Li+ in Spintronic Materials by Qun Song B.Sc., Tianjin University, 2004 M.Sc., The University of British Columbia, 2006 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in The Faculty of Graduate Studies (Physics) THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) November 2012 c© Qun Song 2012Abstract β–detected Nuclear Magnetic Resonance (β-nmr) employs radioactive 8Li+ which is optically spin-polarized, as a local probe to study magnetism in materials via β decay. In this thesis, β-nmr is applied to spintronic ma- terials, including GaAs, Ga1−xMnxAsand Fe/GaAs heterostructures in a depth-controlled manner at TRIUMF. High resolution β-nmr measurements were carried out on GaAs crystals (semi-insulating (SI-GaAs) and heavily doped n-type (n-GaAs)) as a control experiment for β-nmr on Fe/GaAs heterostructures. A small resonance shift was observed and found to be dependent on depth, temperature and doping. The depth dependence is only observed in SI-GaAs and not in n-GaAs. The resonance shift below 150 K in both GaAs is ∼ 100 ppm, on the same order of some Knight shifts of 8Li+ in noble metals. Ga1−xMnxAs is the first β-nmr study on a ferromagnetic material through the ferromagnetic transition. Both spin lattice relaxation (SLR) and reso- nance of 8Li+ were measured. Two resonances were clearly resolved from the nonmagnetic GaAs substrate and the magnetic Ga1−xMnxAs film. The latter one negatively shifts and is linearly proportional to the applied field. The hyperfine coupling constant AHF of 8Li+ in Ga1−xMnxAs is found to be negative. The SLR rate λ does not follow Korringa’s Law and its ampli- tude shows a weak temperature dependence through TC. The behaviors of AHF and λ suggest that the delocalized holes originate from a Mn derived impurity band. No evidence of magnetic phase separation is found. 8Li+ provides a new depth-dependent local probe to detect injected spin polarization. We measured the 8Li+ resonance in Fe/GaAs heterostructures with semi-insulating and heavily doped n-type substrates, with and without injected current. With zero current, no spin polarization at thermal equi- iiAbstract librium is found. A new current injection system was designed and setup to conduct current injection from the thin Fe layer into the n-GaAs substrate. We found effects of local Joule heating and a very small stray field caused by the injected current but no convincing evidence of injected spin polarization. iiiPreface In this thesis, most of the results in Chapter 4 and some of the results in Chapter 3 have been published in journal articles and conference proceedings in which I am listed as first author. The co-authors either helped with data collection or provided the sample. The papers are listed chronologically as follows: • Q. Song, K.H. Chow, R.I. Miller, I. Fan, M.D. Hossain, R.F. Kiefl, S.R. Kreitzman, C.D.P. Levy, T.J. Parolin, M.R. Pearson, Z. Salman, H. Saadaoui, M. Smadella, D. Wang, K.M. Yu, J.K. Furdyna and W.A. MacFarlane. Beta-detected NMR study of the local magnetic field in epitaxial GaAs:Mn. Physica B 404:892, 2009; which has a version of Section 4.3. I carried out all the data analysis. I drafted the manuscript, prepared and presented the associated poster on the 11th µSR International Conference (Tsukuba, Japan, 2008). • Q. Song, K.H. Chow, Z. Salman, H. Saadaoui, M.D. Hossain, R.F. Kiefl, G.D. Morris, C.D.P. Levy, M.R. Pearson, T.J. Parolin, I. Fan, T.A. Keeler, M. Smadella, D. Wang, K.M. Yu, X. Liu, J.K. Furdyna and W.A. MacFarlane. beta-detected NMR of Li in Ga1−xMnxAs. Phys. Rev. B 84:054414, 2011; which contains my analysis and has a version of Section 4.4. I performed the data analysis, conducted the SQUID measurements and wrote the manuscript. • Q. Song, K.H. Chow, R.I. Miller, I. Fan, M.D. Hossain, R.F. Kiefl, G.D. Morris, S.R. Kreitzman, C.D.P. Levy, T.J. Parolin, M.R. Pear- son, Z. Salman, H. Saadaoui, M. Smadella, D. Wang, K.M. Yu, X. Liu, J.K. Furdyna and W.A. MacFarlane. β-Detected NMR Search ivPreface for Magnetic Phase Separation in Epitaxial GaAs:Mn. Physics Proce- dia 30:174-177, 2012; which has a version of Section 4.6. I assisted in the additional data collection, and wrote the manuscript. • Q. Song, K.H. Chow, M.D. Hossain, R.F. Kiefl, G.D. Morris, C.D.P. Levy, H. Saadaoui, M. Smadella, D. Wang, B. Kardasz, B. Heinrich and W.A. MacFarlane. β-detected NMR Study of Semi-Insulating GaAs. Physics Procedia 30:227-230, 2012; which has a version of Sec- tion 3.3. I carried out most of data collection, sample characterization, performed data analysis and wrote the manuscript. I also prepared the associated poster for the 12th µSR International Conference (Cancun, Mexico, 2011). The respective publishers grant permission for this material to be incor- porated into this thesis. The Ga1−xMnxAs sample measured in Chapter 4 was provided and char- acterized by X. Liu and J.K. Furdyna from the University of Notre Dame. The GaAs crystals used in Chapter 3 were provided by B. Kardasz in B. Heinrich’s lab at Simon Fraser University (SFU). The Fe/GaAs samples used in Chapter 5 were epitaxially grown by B. Kardasz in B. Heinrich’s lab at SFU. I designed the contact pattens on the Fe/n-GaAs sample. The gold contacts on both sides of the Fe/n-GaAs sample were thermally evaporated by me to conduct current injection experiment presented in Chapter 5. The sample holder for the thermal evaporator was designed by me and made by P. Dosanjh at AMPEL. In order to carry out the current injection experiment, I designed the system allowing the application of electrical current to a sample during a β- nmr run. The SolidWorks model was initially built by me and later revised by D. Eldridge. I tested the current injection system in liquid Nitrogen and set it up in the β-nmr spectrometer with the help of R. Abasalti. For the data shown in Chapter 5, I did most of the data collection, and performed all of the analysis. vTable of Contents Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi List of Acronyms . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Ferromagnetism . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Ferromagnetic Ga1−xMnxAs and Fe . . . . . . . . . . . . . . 6 1.2.1 Dilute Magnetic Semiconductor: Ga1−xMnxAs . . . . 6 1.2.2 Itinerant Ferromagnetism: Fe . . . . . . . . . . . . . 11 1.3 Ferromagnetic Proximity Effect and Spin Injection . . . . . . 14 1.3.1 Schottky Barrier at the Fe/GaAs Interface . . . . . . 14 1.3.2 Ferromagnetic Proximity Effect . . . . . . . . . . . . 16 1.3.3 Spin Injection . . . . . . . . . . . . . . . . . . . . . . 17 1.4 Organization of This Thesis . . . . . . . . . . . . . . . . . . 18 2 The β-nmr Technique . . . . . . . . . . . . . . . . . . . . . . . 20 2.1 Production of Spin-Polarized 8Li+ . . . . . . . . . . . . . . . 21 2.2 The β-nmr Spectrometer . . . . . . . . . . . . . . . . . . . . 25 viTable of Contents 2.3 β-nmr Ion Implantation Profile . . . . . . . . . . . . . . . . 29 2.4 β-nmr Data Collection . . . . . . . . . . . . . . . . . . . . . 32 2.4.1 β-nmr Resonance Spectra . . . . . . . . . . . . . . . 34 2.4.1.1 Continuous-Wave (CW) Mode . . . . . . . . 37 2.4.1.2 Pulsed RF Mode . . . . . . . . . . . . . . . 41 2.4.2 β-nmr Spin Lattice Relaxation (SLR) Spectra . . . . 44 3 The Local Magnetic Field in Crystalline GaAs . . . . . . . 48 3.1 The Susceptibility of GaAs . . . . . . . . . . . . . . . . . . . 49 3.2 Previous β-nmr Study on Semi-Insulating GaAs . . . . . . . 52 3.3 High Resolution Measurements of β-nmr in GaAs Crystals . 54 3.3.1 Experimental . . . . . . . . . . . . . . . . . . . . . . . 56 3.3.2 Results and Analysis . . . . . . . . . . . . . . . . . . 58 3.3.2.1 Depth Dependence of the Local Magnetic Field in GaAs . . . . . . . . . . . . . . . . . 58 3.3.2.2 Temperature Dependence of the 8Li+ Reso- nance in GaAs . . . . . . . . . . . . . . . . . 61 3.3.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . 61 3.3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . 67 4 β-Detected NMR of Li in Ga1−xMnxAs . . . . . . . . . . . . 69 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 4.2 Sample Preparation and Characterization . . . . . . . . . . . 71 4.3 The Depth Dependence of the Local Magnetic Field in Epi- taxial GaAs:Mn . . . . . . . . . . . . . . . . . . . . . . . . . 72 4.3.1 Results and Analysis . . . . . . . . . . . . . . . . . . 73 4.3.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . 76 4.4 Temperature Dependence of in Ga1−xMnxAs . . . . . . . . . 79 4.4.1 Resonance Spectra . . . . . . . . . . . . . . . . . . . . 80 4.4.2 Spin Lattice Relaxation . . . . . . . . . . . . . . . . . 83 4.4.3 Analysis and Discussion . . . . . . . . . . . . . . . . . 86 4.4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . 93 viiTable of Contents 4.5 The Effect of Magnetic Field on the β-nmr Spectrum of 8Li+ in Ga1−xMnxAs . . . . . . . . . . . . . . . . . . . . . . . . . 93 4.6 Magnetic Phase Separation Problem . . . . . . . . . . . . . . 97 4.6.1 Further Analysis on the Amplitude of the Pulsed RF Resonance . . . . . . . . . . . . . . . . . . . . . . . . 97 4.6.2 CW Mode Resonance . . . . . . . . . . . . . . . . . . 100 4.6.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . 103 5 Ferromagnetic Proximity Effect in Fe/GaAs Heterostruc- tures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 5.1 The MBE Growth and Properties of Fe/GaAs Heterostruc- tures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 5.1.1 The MBE Growth of Fe/GaAs Heterostructures . . . 105 5.1.2 Stopping Distribution of 8Li+ in Fe/GaAs Heterostruc- tures . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 5.1.3 Current-Voltage (IV) Characteristics of Fe/n-GaAs Sam- ples . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 5.1.4 Spin Current through Fe/GaAs Heterostructure Inter- face . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 5.2 β-nmr Study on Zero-Biased Fe/GaAs Heterostructures . . . 114 5.2.1 β-nmr on Fe/Semi-Insulating GaAs . . . . . . . . . . 115 5.2.1.1 β-nmr Resonance Shift of 8Li+ in Fe/SI- GaAs (09-A1) . . . . . . . . . . . . . . . . . 118 5.2.1.2 Resonance Broadening of 8Li+ Resonance in Fe/SI-GaAs (09-A1) . . . . . . . . . . . . . 120 5.2.2 β-nmr on Fe/n-GaAs . . . . . . . . . . . . . . . . . . 122 5.2.2.1 Results and Analysis . . . . . . . . . . . . . 122 5.2.2.2 Discussion . . . . . . . . . . . . . . . . . . . 127 5.3 Spin-Polarized Current Injection Measurement . . . . . . . . 130 5.3.1 Experimental . . . . . . . . . . . . . . . . . . . . . . . 130 5.3.2 Temperature Dependence of 8Li+ Resonance in Fe/n- GaAs with Current Injection . . . . . . . . . . . . . . 134 viiiTable of Contents 5.3.3 Current Dependence of 8Li+ Resonance in Fe/n-GaAs with Current Injection . . . . . . . . . . . . . . . . . 136 5.3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . 141 6 Summary and Future Work . . . . . . . . . . . . . . . . . . . 142 6.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 6.1.1 β-nmr Study of GaAs Crystals . . . . . . . . . . . . 142 6.1.2 β-nmr Study of Ga1−xMnxAs . . . . . . . . . . . . . 143 6.1.3 β-nmr Study of Fe/GaAs Heterostructures . . . . . . 144 6.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 Appendices A List of Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 A.1 Ga1−xMnxAs . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 A.2 GaAs Crystals and Fe/n-GaAs Heterostructures . . . . . . . 164 B SQUID Measurements on Ga1−xMnxAs . . . . . . . . . . . . 168 B.1 SQUID at AMPEL and Sample Descriptions . . . . . . . . . 168 B.2 Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 B.3 Summary of SQUID Measurements . . . . . . . . . . . . . . 173 C Current Injection Experimental Setup . . . . . . . . . . . . 179 D Sample Preparation for Current Injection Experiment . . 183 ixList of Tables 2.1 Some isotopes suitable for β-nmr study. . . . . . . . . . . . . 22 5.1 Fit results of resonance shift as a linear relation to the current at 150 K and 10 K. . . . . . . . . . . . . . . . . . . . . . . . . 139 B.1 Samples used in the SQUID measurements . . . . . . . . . . 172 xList of Figures 1.1 Schematic showing of the spintronic devices . . . . . . . . . . 2 1.2 Diagrams of free electrons with and without exchange inter- action. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 EF positions in different subband structures. . . . . . . . . . 5 1.4 Mn lattice locations in GaAs. . . . . . . . . . . . . . . . . . . 7 1.5 Hole mediated ferromagnetism in Ga1−xMnxAs. . . . . . . . . 8 1.6 Magnetization of iron as a function of temperature. . . . . . . 13 1.7 Diagram of the Schottky Barrier formed when Fe is in contact with n-type GaAs. . . . . . . . . . . . . . . . . . . . . . . . . 15 2.1 Schematic layout of ISAC collinear polarizer. . . . . . . . . . 22 2.2 Optical pumping scheme for the D1 transition of 8Li. . . . . . 23 2.3 Schematic layout of ISAC collinear polarizer and β-nmr spec- trometer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.4 A schematic diagram of β-nmr spectrometer. . . . . . . . . . 26 2.5 The β-nmr spectrometer and the sample holder. . . . . . . . 28 2.6 The graphic interface of the program SRIM. . . . . . . . . . . 29 2.7 A typical SRIM simulation result. . . . . . . . . . . . . . . . . 31 2.8 SRIM underestimates channeling effect. . . . . . . . . . . . . 32 2.9 The angular and energy distribution of 8Li+ β-decay. . . . . . 33 2.10 Incomplete saturation. . . . . . . . . . . . . . . . . . . . . . . 35 2.11 An example of CW mode resonance spectra of 8Li+ in MgO. 39 2.12 An example of rf pulse. . . . . . . . . . . . . . . . . . . . . . 42 2.13 A typical puled rf resonance spectrum of 8Li+ in MgO in pulsed rf mode. . . . . . . . . . . . . . . . . . . . . . . . . . . 44 2.14 Representative SLR spectrum. . . . . . . . . . . . . . . . . . 46 xiList of Figures 3.1 Preliminary β-nmr study on GaAs . . . . . . . . . . . . . . . 51 3.2 Possible sites 8Li+ may take in an analogous 2D lattice. . . . 55 3.3 SRIM simulation of 8Li+ in the GaAs single crystal. . . . . . 57 3.4 Energy dependence of β-nmr spectra in the semi-insulating GaAs (09-B1) and in the heavily doped n-GaAs (09-B2) at ∼5 K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 3.5 Summary of β-nmr spectra measured in GaAs crystals as a function of implantation energy. . . . . . . . . . . . . . . . . . 60 3.6 Temperature dependence of β-nmr spectra with the full beam energy (28 keV). . . . . . . . . . . . . . . . . . . . . . . . . . 62 3.7 Fit results of 8Li+ spectra in the semi-insulating GaAs and n-GaAs with full beam energy 28 keV. . . . . . . . . . . . . . 63 3.8 Diagram of the shift composistion. . . . . . . . . . . . . . . . 66 4.1 Volume magnetization M as a function of temperature at 1.33T. 72 4.2 The 8Li+ implantation profiles of 8Li+ in Ga1−xMnxAs for various energies simulated by SRIM-2006.02. . . . . . . . . . 73 4.3 β-nmr spectrum of 8Li+ in Ga1−xMnxAs as a function of implantation energy at 50 K. . . . . . . . . . . . . . . . . . . 75 4.4 Spin Lattice Relaxation (SLR) spectrum of 8Li+ in Ga1−xMnxAs with different implantation energies at 50 K. . . . . . . . . . 75 4.5 The portion of 8Li+ stopping in GaAs substrate and in the overlayer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 4.6 β-nmr spectra of 8Li+ in Ga1−xMnxAs as a function of tem- perature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 4.7 The analysis result of 8Li+ spectrum in Ga1−xMnxAs as a function of temperature at 8 keV. . . . . . . . . . . . . . . . . 82 4.8 8Li+ relaxation spectrum in Ga1−xMnxAs at 8 keV as a func- tion of temperature. . . . . . . . . . . . . . . . . . . . . . . . 84 4.9 Comparison of Bint and Bcont . . . . . . . . . . . . . . . . . . 89 4.10 The analysis of the 8Li+ resonance in Ga1−xMnxAs as a func- tion of the volume magnetization M . . . . . . . . . . . . . . . 91 4.11 Field dependence of 8Li+ resonance spectra in Ga1−xMnxAs. 94 xiiList of Figures 4.12 The analysis results of β-nmr spectra of 8Li+ for various fields. 95 4.13 The amlitudes of pulsed rf resonance after correction for fast relaxation as a function of temperature. . . . . . . . . . . . . 98 4.14 CW mode β-nmr resonance . . . . . . . . . . . . . . . . . . . 101 5.1 Diagrams of thin film interface. . . . . . . . . . . . . . . . . . 106 5.2 Implantation profile of 8Li in Au/Fe/GaAs simulated by SRIM.108 5.3 Field emission (FE) and thermoionic emission (TFE) tunnel- ing through a Schottky barrier. . . . . . . . . . . . . . . . . . 109 5.4 I-V characteristic curve of Fe/n-GaAs. . . . . . . . . . . . . . 111 5.5 The spin polarization decays exponentially with z¯. . . . . . . 113 5.6 8Li+ spectra in Au/Fe/SI-GaAs as a function of implantation energy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 5.7 The temperature dependence of β-nmr spectra in Au/Fe/GaAs with the implantation energy of 28 keV . . . . . . . . . . . . 117 5.8 The analysis of β-nmr spectra in Au/Fe/GaAs. . . . . . . . . 118 5.9 β-nmr spectra in Au/Fe/n-GaAs and n-GaAs as a function of implantation energy at 300 K. . . . . . . . . . . . . . . . . 123 5.10 Summary of fit results of β-nmr resonance as a function of implantation energy at different temperatures. . . . . . . . . 124 5.11 β-nmr spectra in Fe/n-GaAs and n-GaAs as a function of temperature with implantation energy of 28 keV. . . . . . . . 125 5.12 Analysis of β-nmr spectra in Au/Fe/n-GaAs and n-GaAs as a function of temperature in 2.2 T field. . . . . . . . . . . . . 126 5.13 The geometry of the sample contacts and circuit setup. . . . 130 5.14 The beam view of the sample glued to the sapphire plate with 2 Au pads on it. . . . . . . . . . . . . . . . . . . . . . . . . . 131 5.15 A diagram of the sample resistor network. . . . . . . . . . . . 132 5.16 β-nmr spectra in Au/Fe/n-GaAs (11-A1) as a function of temperature in 2.2 T field. . . . . . . . . . . . . . . . . . . . . 134 5.17 Analysis of β-nmr spectra in Au/Fe/n-GaAs as a function of temperature in 2.2 T field. . . . . . . . . . . . . . . . . . . . . 135 5.18 Resonance spectra as a function of current in 2.2 T. . . . . . 137 xiiiList of Figures 5.19 Depth dependent β-nmr spectra in Au/Fe/n-GaAs at 10 K and 150 K with the current of -400 mA in 2.2 T. . . . . . . . 138 5.20 Analysis of β-nmr spectra in As/Fe/n-GaAs and n-GaAs as a function of current in 2.2 T field. . . . . . . . . . . . . . . . 139 5.21 Resonance shift corrected for current effect. . . . . . . . . . . 140 A.1 Ga1−xMnxAs on semi-insulating GaAs. . . . . . . . . . . . . . 165 A.2 Samples of GaAs crystals. . . . . . . . . . . . . . . . . . . . . 166 A.3 Fe/GaAs samples used in β-nmr with zero bias. . . . . . . . 166 A.4 The n-GaAs sample (10-B1) . . . . . . . . . . . . . . . . . . . 167 A.5 Samples used in 2011. . . . . . . . . . . . . . . . . . . . . . . 167 B.1 Left: the diagram of the pick up coil to measure the longitu- dinal moment. Right: SQUID response. . . . . . . . . . . . . 169 B.2 SQUID holder diagram and magnet drifting. . . . . . . . . . . 171 B.3 Previous SQUID data. . . . . . . . . . . . . . . . . . . . . . . 172 B.4 SQUID samples before and after polising. . . . . . . . . . . . 173 B.5 SQUID measurements of various samples at 1.3 T. . . . . . . 175 B.6 Volume susceptibility of Ga1−xMnxAs as a function temper- ature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176 C.1 Components of the current injection system. . . . . . . . . . . 180 C.2 Comparison of original and new sample holders. . . . . . . . . 181 C.3 The vespel clamp and socket. . . . . . . . . . . . . . . . . . . 182 C.4 The assembled current injection system in the cryostat. . . . 182 D.1 Gold contacts on both sides of Au/Fe/nGaAs sample. . . . . 183 D.2 Thermal evaporator sample holder and masks. . . . . . . . . 184 D.3 Au contacts on the sapphire plate . . . . . . . . . . . . . . . . 185 xivList of Acronyms AMPEL Advanced Materials and Process Engineering Laboratory, the Brimacombe Building at UBC CCD Charge-coupled device CW Continuous Wave DMS Dilute Magnetic Semiconductor DOS Density of States EFG Electric Field Gradient FE Field Emission FM Ferromagnetic/Ferromagnetism FWHM Full Width Half Maximum GMR Giant magnetoresistance IB Impurity Band ISAC Isotope Separator and Accelerator Facility, at TRIUMF MBE Molecular Beam Epitaxial ML Mono-Layer NMR Nuclear Magnetic Resonance PIXE Particle Induced X-ray Emission ppm parts per million xvList of Acronyms RBS Rutherford Backscattering Spectrometry RHEED Reflection High-Energy Electron Diffraction rf radio frequency RKKY stands for Ruderman-Kittel-Kasuya-Yosida. It refers to a coupling mechanism in metal between the nuclear magnetic moment to the spins of conduction electrons[1, 2, 3]. SC semiconductor SFU Simon Fraser University SI Semi-Insulating SLR Spin Lattice Relaxation SQUID Superconducting QUantum Interference Device, a sensitive mag- netometer SRIM Stopping and Range of Ions in Matter, a Monte Carlo code TRIUMF Tri-University Meson Facility, Canada’s national laboratory for nuclear and particle physics research and related sciences TFE Temperature Field Emission UHV Ultra High Vacuum VB Valence Band xviAcknowledgements This thesis could not have been possible without the help of a great number of people. First and foremost, I would like to thank my co-supervisors: Prof. Andrew MacFarlane and Prof. Rob Kiefl for their overall guidance and patience. Their knowledge, expertise and challenge of the experimental and theoretical aspects of our work are crucial for the completion of this thesis, and their enthusiasm for physics have been inspirational and motivating. I would also like to thank other members in my committee: J. Brewer and M. Berciu for reading the thesis and their insightful comments. This thesis has benefited a lot from the help and expertise of Gerald Morris for his design and continual improvement of the β-nmr facility at TRIUMF. Gerald taught me a lot about how to use β-nmr and about spin injection system designing. I would also like to thank Prof. Kim Chow for his dedication to the technique and interest in my projects. His advice was always very helpful. I wish to thank my colleagues in β-nmr group: Terry Paronlin, Hassan Saadaoui, Masrur Hossein, Dong Wang, Oren Ofer, Mike Smadella, Todd Keeler, and others. I’m very grateful for you guys spending many nights tak- ing data, and for the helpful discussions and good times we had together. Special thanks to Terry Paronlin, Hassan Saadaoui for teaching me the first lesson of β-nmr. Their encouragements never stopped even after they grad- uated. Many thanks to Dale Eldridge for improving the design of the spin injection system. I must acknowledge Sarah Dunsiger for her helpful discus- sions on Ga1−xMnxAs. I would also like to acknowledge TRIUMF staffs for their great contributions to the β-nmr experiments: Rahim Abasalti, Phil Levy, M.R. Pearson, Donald Arseneau, Bassam Hitti, and Suzannah Daviel, as well as the ISAC II operators. xviiAcknowledgements I express my acknowledgment to X. Liu and J.K. Furdyna from the University of Notre Dame for providing and characterizing the Ga1−xMnxAs samples, and to B. Kardasz and B. Heinrich at Simon Fraser University for the growing and characterization of Fe/GaAs heterostructures. Many thanks to Pinder Dosanjh, Alina Kulpa, Mario Beaudoin and Mark Greenburg for their great help with e-beam evaporation. It’s my great plea- sure to acknowledge Josh Folk for letting me use his wire bonder and M. Studer who actually did the wire bonding. Finally last but not least, I would like to thank my family, especially my husband Yuan, for their exceptional support over my Ph.D. years. I would also like to say “thank you” to my friends for their support and encouragement. xviiiChapter 1 Introduction Electrons, the elementary constituents of electronic devices, not only have electrical charge but also carry an intrinsic angular momentum known as “spin”. Ever since the discovery of transistors[4], electronics based on the precise manipulation of carrier charges to achieve information processing has been an exceptional success that has revolutionized everyday life, while the electron spin, although it has been known for most of the 20th century, has been generally ignored until the discovery of the giant magneto-resistance (GMR) effect in multilayered ferromagnetic metals in 1988[5, 6]. The new field of spin electronics, or “spintronics”, explores the potential for new de- vices combining both charge and spin degrees of freedom of mobile electrons (Fig. 1.1). It is driven not only by commercial applications, such as low power data processing and storage, new device functionality and integrating magnetic memory and processing, but also by fundamental interest. Numer- ous conceptual spin-based transistors have been proposed[7, 8, 9, 10, 11], and spins in semiconductors are expected to play essential roles in quan- tum computation[12, 13]. These applications require fundamental research to understand the interactions between the electron spin and its solid-state environments, including polarization, transport and detection[14]. As a rapidly emerging field of science and technology, spintronics has shown a significant impact on the electronics. In order to develop spin- tronic technology, it is first necessary to fully explore potential spintronic materials, such as ferromagnetic semiconductors and heterostructures of fer- romagnetic (FM) films on normal semiconductors. The spin polarization of carriers can be generated and detected optically or electronically[14]. Nu- clear Magnetic Resonance (NMR), as a local probe, is also suitable to study the interactions of electronic spins within the materials. However, NMR 1Chapter 1. Introduction Figure 1.1: The combination of the complementary properties of electron charge and magnetic spin is required to create functional spintronic devices. requires typically ∼ 1018 spins for resolvable signals, therefore its applica- tion to thin film materials is limited. In a β-detected NMR experiment, one implants spin-polarized radioactive ions into the material under study and monitors the nuclear magnetic resonance via anisotropic β decay. β-nmr could overcome the signal limitation problem and be used as a local probe to study the spin polarization in spintronic materials. The β-nmr technique is presented in Chapter 2. In this thesis, we focus on β-nmr studies on three potential candidate materials for spintronic application: the ferromagnetic semiconductor Mn doped GaAs (Chapter 4), GaAs crystals (Chapter 3), and Fe/GaAs heterostructures (Chapter 5). As the concept will be important throughout this thesis, first let’s dis- cuss the difference between “Fermi energy EF” and “chemical potential µ”. Electrons follow the Fermi-Dirac distribution. Fermi energy EF is defined as the energy of the topmost filled state at T = 0 K. EF does not vary with temperature. The occupation probability f(E) for a state at energy E is: f(E) = 1 e(E−µ)/kBT + 1 (1.1) where µ the chemical potential is the Gibbs free energy per particle[15] and is a function of temperature. At T = 0 K, f(E) changes discontinuously from 1 to 0 at E = µ, so the chemical potential is equal to the Fermi energy µ = EF . When T 6= 0 K, the chemical potential is determined by the total 21.1. Ferromagnetism number of electrons N : N = ∑ i f(Ei) = ∑ i 1 e(Ei−µ)/kBT + 1 (1.2) indicating the change in the free energy when one more particle is introduced into the system at finite temperature. When the temperature is much less than the Fermi temperature TF ≡ EF /kB, µ ≈ EF [16]. This is valid for metal because of its high EF[15], resulting in a Fermi temperature on the order of 104 K. In semiconductors with wide band gap such as GaAs[15], T  TF is also valid, therefore µ ≈ EF . In this thesis, we still use EF at finite temperature in the discussion, but it is really the chemical potential µ that indicates where Eqn. (1.1) is 1/2. 1.1 Ferromagnetism We first quickly review some fundamentals of ferromagnetism before we proceed. Quantum theory of magnetism has been rooted from two start- ing points: the localized model (localized electron states in real space) and the band model (localized electron states in momentum space)[16, 17]. The localized model mainly deals with magnetism in insulators and rare-earth metals, while the band model provides an insight understanding of ferro- magnetism in transition metals[17]. In a strongly interacting system, the inter-atomic interactions come into play and result in the ferromagnetism. In the localized model, each electron remains localized on an atom. The main contribution of the atomic mag- netic moment is from the spins of electrons in partially filled d or f bands. The exchange Hamiltonian describing the interaction of localized spins on different atoms is: H = − ∑ ij AijSi · Sj (1.3) where Aij is the exchange integral, and Si is the spin operator at the lattice site i. This is the well-known Heisenberg model (direct-exchange interac- tion), which arises from direct Coulomb interactions among the electrons of 31.1. Ferromagnetism Figure 1.2: Left: Band diagrams of free electron band without exchange interaction. Right: The band splitting when the exchange interaction is in play. The energy splitting between spin-up and spin-down subbands is 2∆. g↑↓(E) is the density of states for the spin up and down subbands. Adapted from Ref. [16]. any two magnetic ions. When Aij is positive, spins tend to align parallel, and the material is ferromagnetic in the ground state. When Aij is neg- ative, Si and Sj are anti-parallel in the ground state, and the material is antiferromagnetic. Although the localized model works well for insulating magnetic materi- als and rare-earth metals, both quantitatively and qualitatively, it does not apply to transition metals: Fe, Co and Ni. Here the d electrons are not fully localized and the magnetic moment is not an integer multiple of the Bohr magneton (µB) as it is for magnetic ions. They are itinerant magnets and should be described using the band model. In the band model, the carriers which carry the magnetism are itiner- ant. They move in the average field of the other electrons and ions, and the electron levels form energy bands. Inside one energy band, electrons with different spin polarization form two degenerate subbands (spin-up ↑ and spin-down ↓ subbands) when there’s no exchange interaction. (Fig. 1.2 Left Panel). In the ground state at T=0 K, electrons, following the Fermi-Dirac distribution, fill energy bands up to the Fermi energy (EF). As mentioned 41.1. Ferromagnetism Figure 1.3: Left: EF lies in both ↑ and ↓ subbands. Right: EF lies in only ↓ subband. above, d electrons are partially localized, and Heisenberg exchange interac- tions come into play and compete with the kinetic band energy. The electron transfer near the Fermi energy (EF) from spin-down (↓) subband to spin-up (↑) subband induces an increase in band energy (∆EBand) and a decrease in the magnetic energy(∆EMag). The magnetic order is achieved when the band energy increase is smaller than the magnetic energy loss (∆EBand< ∆EMag). The exchange interaction splits the degenerate subbands (Fig. 1.2 Right Panel). The unbalance of electron occupation between the spin-up (↑) and spin-down (↓) subbands gives rise to a net magnetization M , char- acterized by densities of up and down spins (n↑ 6=n↓): M = µB(n↑ − n↓) (1.4) The position of EF results in different types of itinerant ferromagnetism. As shown in the left panel of Fig. 1.3, EF lies in both ↑ and ↓ subbands – for instance the metal iron (Fe) (more discussion in Section 1.2.2). Electrons occupy both energy subbands. The polarization of electrons at EF is not 100% parallel aligned in the ground state of Fe. In some cases, e.g. nickle (Ni), EF falls in a single spin subband as shown in the right panel of Fig. 1.3. For T = 0 K, the spin-up subband is filled, and its density of states at EF vanishes. The magnetic magnetization is M = µBn↓(E) with n↓(E) is the density of state at energy E. 51.2. Ferromagnetic Ga1−xMnxAs and Fe 1.2 Ferromagnetic Ga1−xMnxAs and Fe Discussion in Section 1.1 on the ferromagnetism provides us with a good start in understanding spintronic materials. This section will review some magnetic properties of the spintronic materials studied in this thesis. Ferromagnetic semiconductors are attractive candidates, offering the op- portunity to integrate information storage and processing into a single ma- terial. Some early discovered ferromagnetic semiconductors, such as EuO, exhibit ferromagnetism below a certain transition temperature TC (Curie temperature), and have been well–studied in the 1960s and 1970s[18, 19]. One way to make a ferromagnetic semiconductor is to dope normal semi- conductors (e.g. GaAs, GaN) with some magnetic ions, such as Mn2+. The transition temperature can be varied by doping density and process condi- tions. We focus our attention on Ga1−xMnxAs, which will be introduced in Section 1.2.1. Another possibility to combine semiconductor with fer- romagnetic materials is to grow ferromagnetic materials on conventional semiconductors, such as Fe/GaAs heterostructures. Fe thin films on GaAs substrates is favored in MBE growth because of their lattice match. The properties of the itinerant ferromagnet iron will be discussed in Section 1.2.2. 1.2.1 Dilute Magnetic Semiconductor: Ga1−xMnxAs Ga1−xMnxAs is one of the most promising and the most extensively-studied ferromagnetic semiconductors. The magnetism in Mn doped GaAs was first discovered by H. Ohno in 1996[20]. The Curie temperature (TC) has been greatly improved, from below liquid nitrogen temperature to above 200 K[21], and even to 250 K by using delta-doping techniques[22]. There are 3 Mn lattice locations in GaAs, which are crucial in determin- ing the magnetic properties[24, 25, 26, 27, 28]. Divalent Mn2+ can occupy the Ga lattice sites (MnGa), forming the Ga1−xMnxAs solid solution with concentrations x as high as several percent. Since one Mn2+ contributes only two electrons to the GaAs host instead of three by the original Ga3+, one substitutional Mn2+ (MnGa), as an acceptor, provides one free hole to medi- ate ferromagnetic interactions between Mn ions. Most Mn2+ ions take MnGa 61.2. Ferromagnetic Ga1−xMnxAs and Fe Figure 1.4: Divalent Mn2+ occupy the Ga lattice sites in GaAs. Such sub- stitutional Mn (MnGa) provides free holes to mediate ferromagnetic inter- actions between Mn2+ local moments. Mn residing in the interstitial sites (MnI) is a double electron donor that compensates the hole doping due to (MnGa). Adapted from Ref. [23]. 71.2. Ferromagnetic Ga1−xMnxAs and Fe Figure 1.5: Schematic diagram of ferromagnetic coupling mechanism in Ga1−xMnxAs mediated by holes. sites. In addition, a small fraction of Mn ( 20%) may reside at interstitial sites (MnI). Here the MnI are double electron donors which compensate the hole doping due to MnGa. Furthermore, the moments of MnI tend to align antiferromagnetically with the MnGa spins, reducing the total magnetic mo- ment. MnI are metastable and can, upon annealing, precipitate out as Mn clusters or inclusions of the MnAs impurity phase (a ferromagnetic metal- lic compound). The MnAs impurity phase may segregate at the surface or interface[29, 30]. Such precipitates will contribute to the overall magnetiza- tion. The third site MnRand is not a well-defined crystallographic site, but represents some distribution over disordered sites. They are not involved in the FM interactions. Fig. 1.4 shows the ideal zinc blende structure of GaAs with Mn atoms in the Ga substitutional position and interstitial position. Only a few percent of Mn may distribute randomly. The relatively shallow Mn acceptors introduce holes which, in turn, me- diate ferromagnetism among the spin 5/2 Mn2+ moments through the indi- rect exchange interaction as shown in Fig. 1.5. When a hole carrier aligns anti-parallel with two Mn2+ cation spins through anti-ferromagnetic cou- pling, it will cause the two Mn2+ spins to align parallel, which is equivalent to a ferromagnetic coupling between the two spin 5/2 magnetic moments. Macroscopic magnetic ordering is then introduced by the propagation of spin-polarized hole-carriers in the bulk semiconductor. 81.2. Ferromagnetic Ga1−xMnxAs and Fe There are two fundamentally opposing theoretical viewpoints on the origin of the holes in Ga1−xMnxAs[31]. First, electronic-structure calcu- lations have argued that the ferromagnetism in Ga1−xMnxAs is driven by impurity-derived states (impurity band (IB) model)[32, 33]. In this pic- ture, the wavefunctions of the carriers mediating ferromagnetism are local- ized and take on the character of the Mn-derived impurity band. Second, the mean-field Zener model takes into account the valence-band structure of zinc-blende semiconductors (valence band (VB) model)[24, 34], assuming that Ga1−xMnxAs is metallic and has a high carrier density p. It argues that the ferromagnetism is mediated by extended hole states and that the Fermi energy locates in the valence band. The Zener model was first proposed in 1950s to explain the ferromagnetism in the transition metals driven by the indirect exchange interaction between carriers and localized spins[35].With this model, the Curie temperature of Ga1−xMnxAs was predicted to be pro- portional to xp1/3, which suggested that a strategy to synthesize high TC materials would be to increase the hole-carrier density and the Mn dopant concentration[24]. In the limit of zero concentration (dilute limit), the Mn impurity states are localized and could not mediate ferromagnetism. In this limit, any de- localized holes would be described by the GaAs valence band picture. How- ever, at much higher concentrations (percent level) relevant for the observed ferromagnetism, the Mn states broaden into a band of delocalized states. Within the impurity band model, it is these states that are the mediators of ferromagnetism. At even higher concentrations, this impurity band is ex- pected to broaden further and merge with the valence band of GaAs. In this regime, one would expect that, again, the holes might be better described by the GaAs valence band, and the VB model of ferromagnetism should ap- ply. The crossover concentration between these two limits is still a matter of debate and is complicated by factors such as the compensating effect of Mn interstitials that compensate the MnGa hole doping. The VB model has been proved successful in explaining many experimen- tal trends observed in dilute magnetic semiconductors (DMS) like Ga1−xMnxAs such as the magnetic anisotropy and the dependence of Curie tempera- 91.2. Ferromagnetic Ga1−xMnxAs and Fe ture on hole concentration[28]. Detailed models of this mechanism involve parametrization of the relevant hole states, e.g. the approximation of the GaAs valence band (valence band model)[36]. There is controversy over which is the appropriate picture for the high- est magnetic transition temperature (TC) compositions well into the metal- lic conduction regime[37, 38]. Optical [39, 40, 41, 42], transport[43, 44] and scanning tunneling microscopy[45] (STM) results favour the impurity band model. Rokhinson et al. attributed the observed negative magne- toresistance in Ga1−xMnxAs at low temperature and low magentic fields to weak localization which strongly suggests impurity band transport[43]. The atomic scale fluctuations in the local electronic density of states at the Fermi level mapped by atomic resolution STM showed features characteristic of the localized limit, that would be absent for more extended states deep in the valence band[45]. Recent channeling measurements on Ga1−xMnxAs with the Mn concentration ranging between 3% and 6.8% infer impurity-band- mediated ferromagnetism[46]. On the other hand, a variety of features are consistent with the valence band model[24, 25, 47, 48, 49]. There is also a debate whether this material is magnetically phase- separated. A Low Energy µSR (LE-µSR) experiment reported that parts of the sample remained in the paramagnetic state below TC[50], which is also supported by the direct magnetization measurement[51]. On the other hand, a systematic study with LE-µSR strictly defines the asymmetry baseline and shows no sign of phase separation[52]. The origin of the holes mediating the ferromagnetism and the magnetic phase separation are problems under debate over a dozen years. Chapter 4 will deal with these two questions in detail. Calculations predict that in the ferromagnetic ground state the hole magnetization is opposite to (and much weaker than) that of the Mn2+ local moments[28]. The delocalized holes play a crucial role in the formation of the magnetic ground state, however, little is known experimentally about their magnetization and its variation with temperature. As the material is intrinsically inhomogeneous, a local probe may also reveal any magnetic inhomogeneity, through broadening and structure of the resonance line, for 101.2. Ferromagnetic Ga1−xMnxAs and Fe example, in the controversial proposal of magnetic phase separation[50, 51, 52]. Nuclear spin lattice relaxation yields information on the low frequency spin dynamics where correlations are expected to play an important role[53]. The β-nmr in Ga1−xMnxAs is presented in Chapter 4 The thermodynamic equilibrium solubility limit of Mn in GaAs is very low, while the required concentration of Mn for ferromagnetism to occur in GaAs is in the few atomic percent range, far beyond the solubility limit[54]. So the production of Ga1−xMnxAs at the high Mn concentrations necessary for ferromagnetism requires non-equilibrium growth in the form of thin films, and bulk samples are not available. Growing Ga1−xMnxAs thin films by molecular beam epitaxy (MBE) at low temperatures of 200-300 ◦C limits Mn diffusion and suppresses the formation of other phases. Post-growth annealing has proven to help remove intersitial Mn atoms therefore increase TC[27]. Preliminary experiments injecting spins from Ga1−xMnxAs into GaAs using a spin-LED structure demonstrated reasonable spin-injection efficiencies[55]. The discovery of ferromagnetic Ga1−xMnxAs and the demonstration of spin injection suggests the feasibility of all-semiconductor spintronic circuits, where magnetic and non-magnetic semiconductors could co-exist to perform spintronic functions, analogous to the integrated circuits. 1.2.2 Itinerant Ferromagnetism: Fe As discussed at the beginning of this section, one candidate to make use of the spin property is the heterostructure of ferromagnetic thin films on conventional semiconductors, such as thin Fe films on GaAs. It is expected that the spin polarization could be injected from the ferromagnetic Fe layer into semiconductor GaAs. Therefore it is useful to review the properties of the itinerant ferromagnet iron (Fe). Iron is a common transition metal with the atomic number 26. It’s also the most commonly-used ferromagnetic material. The electron configuration is [Ar] 3d64s2, with 6 3d electrons. The melting temperature (Tmelting) is 1538 ◦C, and the magnetic ordering temperature (Curie temperature) TC 111.2. Ferromagnetic Ga1−xMnxAs and Fe is 1043 K (770 ◦C) which is much higher than the Ga1−xMnxAs discussed above. Iron is usually in the solid phase with the density 7.874 g/cm3 at room temperature. As an “unsaturated” itinerant ferromagnet, the 3d and 4s bands of iron are partially filled[56]. In the 4s band, a weaker exchange interaction causes an approximately equal distribution of spin-up and spin-down electrons. Therefore the itinerant s electrons are not responsible for the magnetism, but do contribute to the conductivity. On the other hand, the 3d electron wave function is more localized on each atom. The exchange interaction splits the spin-up and spin-down 3d bands leading to an unbalanced electron population and resulting in a net magnetic moment per atom. As shown in the left panel of Fig. 1.3, for T = 0 K, both spin ↑ and ↓ subbands are partially filled (g↑(EF ) 6= 0, g↓(EF ) 6= 0), therefore the magnetic moment per atom is not saturated for Ho = 0. Above TC, iron is paramagnetic, and its susceptibility follows the Curie- Weiss Law, as shown in the top panel of Fig. 1.6. Here the inverse of the susceptibility χ−1 is linearly proportional to the temperature. Iron orders ferromagnetically below TC. As shown in the bottom panel of Fig. 1.6, the reduced magnetization M/Mo increases as the temperature decreases and follows a power law. For our experimental temperature range (300 K – 3 K), M is nearly constant for Fe. The spin polarization of a ferromagnet PFM is defined as the spin asym- metry in the density of states (DOS) at the Fermi level: PFM = g↑(EF )− g↓(EF ) g↑(EF ) + g↓(EF ) (1.5) where g↑(g↓) is the majority (minority) DOS, respectively. In bulk iron, the DOS at the Fermi level is dominated by the spin-split 3d band and a high PFM is expected assuming simple parabolic bands. Since the elec- trons responsible for conduction processes are those close to the Fermi level, this means a current flowing through a ferromagnet is spin polarized with a polarization approximately PFM . The polarization of the electron spin could be conserved and injected into normal semiconductors such as GaAs 121.2. Ferromagnetic Ga1−xMnxAs and Fe Figure 1.6: Fe Magnetization as a function of temperature above (top) and below (bottom) TC. Top: the inverse of the molar susceptibility χ−1 as a function of temperature above TC. Above TC, iron is paramagnetic, and its susceptibility follows the Curie–Weiss Law, (adapted from Ref. [57]). Bottom: the reduced magnetization M/Mo as a function of the reduced temperature T/TC . Fe is ferromagnetic below TC, and its magnetization follows a critical power law as T → TC. Ni, a similar itinerant ferromagnet, is also shown in both panels, (adapted from Ref. [58]). 131.3. Ferromagnetic Proximity Effect and Spin Injection (Chapter 5). An important distinction between Fe and Ga1−xMnxAs is that Fe is a good metal with a high carrier density. This has important consequences at the interface with a semiconductor which we describe in the next section. 1.3 Ferromagnetic Proximity Effect and Spin Injection We have reviewed the properties of the ferromagnetic semiconductor Ga1−xMnxAs (Section 1.2.1) and itinerant ferromagnetic iron (Section 1.2.2). In order to make use of the spin degree of freedom and the mature (nonmagnetic) semi- conductor technology, we expect that the ferromagnetism in a magnetic layer could be “transferred” into a conventional semiconductors, such as GaAs. The ferromagnetic proximity effect and spin injection are possible mechanisms which could achieve the goal. We’ll briefly review the basics of ferromagnetic proximity effect and spin injection in this section and present our β-nmr study on the proximity effect of Fe/GaAs heterostructure in Chapter 5. 1.3.1 Schottky Barrier at the Fe/GaAs Interface First we review the Schottky barrier at a metal/semiconductor interface which may have great influence on the production of spin polarization in the semiconductor. The Schottky barrier is the intrinsic energy barrier which is formed at the interface of most metal/semiconductor junctions. When a metal layer is in contact with GaAs, the conduction band edge of GaAs bends up to make the chemical potentials are equal on both sides in thermal equilibrium. The conduction electrons of the semiconductor, which have higher energy, cross over into the metal and leave the positive ions behind, setting up a static electric field. In the GaAs region near the Fe, this electric field causes the GaAs to be depleted of mobile electrons. Fig. 1.7 shows a schematic energy band diagram of the Fe/GaAs junction for n-type GaAs relevant to the 141.3. Ferromagnetic Proximity Effect and Spin Injection s71s97s65s115 s69 s67 s69 s86 s70s101 Figure 1.7: Diagram of the Schottky Barrier formed when Fe is in contact with n-type GaAs. The conduction band edge of the semiconductor bends up when the chemical potentials µ (Eqn. (1.1)) are equal on both sides (in thermal equilibrium). The conduction band electrons cross over into the metal and leave the positive ions behind, therefore the GaAs region near the Fe is depleted of mobile electrons. The Schottky barrier height φB and depletion width ω are shown. study presented in Chapter 5. In a simple model[16], the depletion width ω at a Schottky barrier can be estimated as ω = √ 20φB ne , (1.6) where e is the electron charge,  is the static dielectric permittivity, φB is the height of the Schottky barrier and n is the carrier concentration. Take the heavily doped GaAs as an example. Assuming that in Fe/n-GaAs heterostructure, the Schottky barrier height eφB is ∼0.72 eV (Ref. [59]),  = 13.18 for GaAs, and the carrier concentration of heavily doped n-GaAs is n ∼ 2× 1018 cm−3, ω is ∼ 23 nm. Ever since the proposal of the spin dependent field effect transistor[7], the interest in spin injection from a ferromagnetic metal into semiconduc- tors has been greatly intensified. The polarized spin can be sourced either from ferromagnetic semiconductors such as Mn doped GaAs[55, 60], or from ferromagnetic metals[61]. The first approach gives excellent results, but the 151.3. Ferromagnetic Proximity Effect and Spin Injection effort to obtain a magnetic semiconductor with a high Curie temperature TC above room temperature is still ongoing. For the latter approach, the con- ductance mismatch between the ferromagnetic metal and the semiconductor prevents the direct injection from a low-resistivity magnetic metal[62], and the Schottky-barrier-induced electric field can cause strong spin relaxation, making spin injection almost negligible beyond the barrier region[63]. 1.3.2 Ferromagnetic Proximity Effect The magnetic proximity effect refers to the induction of magnetism by con- tact with a magnetic material. In the simplest case, a nonmagnetic material may be driven magnetic by contact with a ferromagnet. Early studies on metallic heterostructures[64, 65] found that the coherence length for in- duced magnetization was material dependent and generally small (tens of ˚A), making detailed studies very difficult. This line of inquiry, in the context of multilayer systems, led to the discovery of the interlayer exchange cou- pling and giant magnetoresistance effects recently recognized with the 2007 Nobel Prize in Physics[5, 66]. Within the nonmagnetic metallic layer of such a heterostructure, the magnetic proximity effect induces an oscillating spin polarization in the conduction electrons. Ultrafast optical pump-probe measurements reveal that the coherent electron spin dynamics in the n-type GaAs are strongly modified by the ad- jacent ferromagnetic (FM) layer[67], aligning along the ferromagnet’s mag- netization M . The dominant interaction is hyperfine coupling with nuclear spins in the GaAs[68, 69, 70], not fringe fields or direct exchange interac- tions with the ferromagnet. In the bulk semiconductor, polarized electron spins from the adjacent ferromagnet couple to nuclear spins through the hyperfine interaction. Nonequilibrium electron spins relax to equilibrium by transferring some of their angular momentum to the nuclear spins via the hyperfine interaction, and dynamically polarize the nuclear spins in the bulk semiconductor–“imprinting” the magnetization of the ferromagnetic layer on the nuclear spin in n-type GaAs. The lifetime of the induced spin polariza- tion in a semiconductor is long and the spin polarization can be transported 161.3. Ferromagnetic Proximity Effect and Spin Injection over a long distance. A series of Time-resolved Faraday Rotation (TRFR) experiments[71, 72] show that in GaAs the spin polarization could persist as long as 0.1 µs, and is robust to transport over distances of ∼ 100µm and across heterointerfaces. Epstein et al. [73] found that photoexcited electrons in a n-GaAs layer could be rapidly spin-polarized due to the proximity of an epitaxial ferro- magnetic metal, and that the GaAs nuclear spins are dynamically polarized with a sign determined by the spontaneous electron-spin orientation. In Fe/GaAs, the electron spin polarization is parallel with the magnetization M of the ferromagnet, and the spin-dependent density of states (DOS) near the Fermi level is larger for the majority spins than the minority spins. The electrons cause the dynamic polarization of nuclear spins and the sign of the nuclear-spin polarization depends on the electron-spin orientation rather than M . This effect demonstrates new control of both electron and nuclear spins in a semiconductor by carefully choosing ferromagnetic materials and manipulating the orientation of M . 1.3.3 Spin Injection Spin injection, the intentional introduction of spin polarized carriers by a spin polarized electrical current, is one of the prerequisites for the realization of spintronic devices. For spintronics, it is thus particularly important to introduce spin polarized electrons into a semiconductor such as GaAs to take advantage of the long spin lifetime[72]. Spin injection has been done by optical excitation with polarized light[68] and by tunnelling from a ferromagnetic STM tip[74], but more recently there has been enormous effort to try to inject polarized carriers from an adjacent magnetic material[14, 75]. Spin injection is achieved by electrical current injection through a ferromagnetic contact. Ferromagnetic metals such as Fe have been used, but generally the injection efficiency is small[76] due to the Schottky barrier (depletion layer) at the interface, which may be as thick as hundreds of nanometers. The spin polarization can be detected optically by measuring the cir- 171.4. Organization of This Thesis cular polarization of the recombination electro-luminescence in a quantum well(e.g. Ref. [76, 77, 78]). Crooker et al. used the optical Kerr effect to image the transport and precession of injected spins[79]. The spin polariza- tion can also be detected electrically. All-electrical injection and detection of electrons spins injected were demonstrated in semiconductors[80, 81, 82, 83]. To avoid the difficulties of metal-semiconductor interfaces, there has also been much effort in developing ferromagnetic semiconductors, either of the dilute variety, such as GaAs doped with a few percent Mn[55, 60] (discussed in Section 1.2.1), or dense, such as EuO[84]. The closer conductivity match with the nonmagnetic semiconductor leads to much more efficient spin in- jection, but the transition temperatures are still too low for a useful room temperature device. Spin injection has been demonstrated in metals and semiconductors, such as GaAs, typically using spin-resolved optical or electrical detection of carriers transmitted through a nonmagnetic layer, yielding an overall measure of the effect. While such measurements are very sensitive, a much more detailed understanding could be obtained from a depth profile of the induced spin polarization, which could then be compared to theory. There are few techniques capable of such depth-resolved magnetic measurements on nanometer length scales[85]. We will see that variable energy β-nmr is a sensitive depth-resolved way to probe the distribution of magnetic field in heterostructures (Chapter 2), and we will use this technique to study spin injection from ferromagnetic metals and semiconductors into nonmagnetic semiconductors in Chapter 5. 1.4 Organization of This Thesis This thesis presents β-nmr studies on three spintronic materials: the GaAs crystals, the ferromagnetic semiconductor Mn doped GaAs and Fe/nGaAs heterostructures. The GaAs crystals (semi-insulating and heavily doped n-GaAs) were studied as control experiments. Chapter 2 will give an intro- duction of the technique used in the study–β-detected NMR. Chapter 3 will discuss the local magnetic field in the semiconductor 181.4. Organization of This Thesis GaAs: semi-insulating and heavily doped n-type. This constitutes a “base- line” for the β-nmr studies of thin films grown on GaAs substrates. The beta-detected NMR experiments carried out on both GaAs crystal wafers use the pulsed radio frequency scheme to make high resolution measure- ments. As a control experiment, we investigate the magnetic properties as a function of temperature and depth. The range of depths probed, from ∼140 nm down to ∼20 nm, coincides with the region of electronic band-bending due to the surface. Similar measurements are made on heavily doped n-type GaAs for comparison, whose Schottky barrier width is reduced to ∼ 20 nm because of its high carrier concentration. The β-nmr studies on Mn doped GaAs are presented in Chapter 4. The magnetic properties of a 180 nm thick epitaxial film of the dilute magnetic semiconductor Ga1−xMnxAs with x = 0.054 are investigated using beta de- tected NMR of low energy implanted 8Li+. We follow the temperature de- pendence of the local magnetic field in the Ga1−xMnxAs thin film through the ferromagnetic transition, and discuss the microscopic magnetic phase separation that has been suggested by some low energy muon spin rotation measurements[50]. In Ga1−xMnxAs, the resonance shift and broadening are much larger than in GaAs crystals (Chapter 3). Therefore we can concen- trate on the resonance in the Ga1−xMnxAs layer and neglect the tiny shift in the GaAs substrate. Chapter 5 follows the line of Chapter 3, presenting the β-nmr study on the Fe/GaAs heterostructures. The local field of the GaAs substrate under the effect of the adjacent thin Fe layer due to the proximity effect is probed as a function temperature and implantation depth. In addition, current is injected in the Fe/n−GaAs heterostructure while 8Li beam is continuously injected to detect the local field in situ. Chapter 6 summarizes the results on the β-nmr studies on spintronic materials, and discusses the potential of depth-resolved β-nmr for investi- gating spintronic materials in reduced geometries with the new capability of current injection. 19Chapter 2 The β-nmr Technique β-nmr is a powerful and sensitive tool in condensed matter physics and ma- terial science, but it is not widely known or widely used. It is very specialized with only a few groups worldwide. This technique, similar to conventional NMR, provides a precise local probe to conduct investigations on, e.g. micro structures, local magnetism, hyperfine interactions, spin relaxation, impu- rities and defects. Conventional NMR requires, in general, ∼ 1018 probe nuclei to generate measurable signals, so that it’s generally not applicable to studies on thin films. In contrast, β-nmr needs only ∼ 107 nuclei, as it is much more sensitive than conventional NMR. In β-nmr a beam of highly spin-polarized radioactive probe nuclei (8Li+ in our case) is introduced into the sample under study. Once implanted into the material, the probe nuclei interact with external and internal magnetic fields within the sample until they decay and emit β particles preferentially opposite to the probe nuclear spin direction. The anisotropic angular distribution of the emitted β parti- cle reflects the probe nuclear spin state inside the material at the moment of its decay. Applying an rf field with a frequency matching the spin resonance condition, the spin polarization can be destroyed by rapid precession with random phases, leading to an isotropic emission of β-electrons and thus the asymmetry reduction. In this chapter, we will discuss the generation of spin-polarized 8Li+ (Section 2.1) and the β-nmr spectrometer (Section 2.2), and describe the ion implantation profile (Section 2.3) and β-nmr data collection (Section 2.4). 202.1. Production of Spin-Polarized 8Li+ 2.1 Production of Spin-Polarized 8Li+ The proton beam with 500 MeV energy generated in the TRIUMF cyclotron is used to drive a secondary radioactive ion beam at the Isotope Separator and Accelerator (ISAC) facility. The high energy proton beam bombards a special production target and produces various radioactive ions by nu- clear reactions. The production target, typically tantalum or SiC, usually is heated to ∼ 2500 ◦C, and held at a high positive voltage of 28–30 kV. Thermal ionization at the surface of the target produces isotopes of metals with low ionization energies, such as the alkali metals. After diffusing to the surface and ionizing, the ions are accelerated by the target potential to 28– 30 keV. The desired isotope is selected by a high resolution mass separator. Although many β-emitting isotopes are suitable β-nmr nuclei, a good β- nmr probe needs to meet some basic requirements. The isotope must have high production rate and be able to be efficiently spin polarized. It should have a high β-decay asymmetry and small nuclear spin to keep the spectra simple. Table 2.1 lists some isotopes suitable for β-nmr among which 8Li+ is the easiest to generate with high intensity (∼ 108 ion/s) at ISAC. The ion beam of interest is then focused and steered to the β-nmr experiment station by electrostatic beamline elements. The other two isotopes 11Be and 15O are also suitable for β-nmr, but there are important differences. For instance, 15O is spin 1/2 particle with no quadrupole moment, which sim- plifies its spectrum in complex structures. Also its lifetime (122 s) is much longer than the 8Li+ lifetime, so it could only be used if the relaxation time T1 is very long. The radioactive beam is polarized by optical pumping using circularly polarized light from a single-frequency ring dye laser. A diagram of the polarizer and the spectrometer is shown in Fig. 2.1. The polarization pro- cess includes three steps. First the ion beam 8Li+ is neutralized by passing through a cell of Na vapor, typically held at 480 ◦C. The neutral beam then flows into the optical pumping region (1.9 m long) where a small lon- gitudinal field of 1 mT is present to maintain the polarization axis. The remaining 8Li+ ions that are not neutralized after Na cell are removed by 212.1. Production of Spin-Polarized 8Li+ Isotope Nuclear Spin T1/2 γ β-Decay Production Rate I (s) (MHz/T) Asymmetry (s−1) 8Li 2 0.842 6.3018 0.33 108 11Be 1/2 13.8 22 0.016[86] 106[86] 15O 1/2 122 10.8 0.7[87] 108 Table 2.1: Some isotopes suitable for β-nmr study. Properties listed are nuclear spin I, half life T1/2, gyromagnetic ratio γ, β-decay asymmetry, and production rate. Figure 2.1: A schematic diagram of ISAC collinear polarizer. Adapted from [88]. two electrostatic deflection plates and dumped into a Faraday cup. Optical pumping is carried out by a single frequency dye laser which is pumped by a Nd:YAG laser. The neutral 8Li atoms interact with the counter-propagating laser light which is circularly polarized with respect to the magnetic holding field axis. The laser is tuned to 671 nm, the wavelength of Li D1 transition– the transition from the ground state 2S1/2 to the first excited state 2P1/2. As shown in Fig.2.2, due to the hyperfine coupling be- tween the total electronic angular momentum for 8Li0 atoms (J = 1/2) and the nuclear spin (I = 2), both the ground state 2S1/2 and the first excited state 2P1/2 are split into two hyperfine levels of total angular momentum of 222.1. Production of Spin-Polarized 8Li+ Figure 2.2: Optical pumping scheme with σ+ light for the D1 transition of 8Li. The excitation induced by the laser is shown in heavy arrows, and the spontaneous emission is in thin arrows. After many cycles of optical pumping, all atoms are “pumped” into the fully stretched state (mF=5/2) with full nuclear and electronic polarization, and can’t be pumped out of this state by laser light. Adapted from Ref. [88]. the atom electron J = 1/2 and nuclear spin I = 2 (F = J + I): F = 3/2 and F = 5/2. The splitting is 382 MHz in 2S1/2 state , and 44 MHz in 2P1/2 states. In the presence of a small external holding field (∼ 10 G), the hyperfine levels are further split into 2F+1 almost degenerate sublevels with magnetic quantum number mF (mF = −F,−F + 1, · · · , F − 1, F ). For cir- cularly polarized light with positive helicity (σ+ pumping), the only allowed absorptions are transitions increasing mF by +1, ∆mF = +1, whereas the spontaneous emission can occur with ∆mF = 0,±1. The quantization axis is established by the helicity direction of the laser light and maintained by the small magnetic field. The lifetime for spontaneous fluorescence of the excited state is ∼ 50 ns, much shorter than the transport time through the optical pumping region (∼ µs). Therefore 8Li atoms have gone through multiple pumping cycles when they reach the end of the region, and a high degree of electronic and nuclear spin polarization is achieved. After about 232.1. Production of Spin-Polarized 8Li+ Figure 2.3: A schematic layout of ISAC collinear polarizer and β-nmr spec- trometer. Adapted from Ref. [89]. 10-20 cycles of absorption and emission, the angular momentum carried by the photons is transferred to the 8Li atoms. Thus the atoms are “pumped” towards a state of high atomic spin polarization. For the positive helicity of the laser light, the atoms are pumped to a state of F = 5/2,mF = 5/2 with a high degree of nuclear polarization (70%). Correspondingly the nuclear spin state is mI = +2, and the nuclear spin polarization is antiparallel to the holding field direction. For the negative helicity, 8Li atoms are pumped to the state F = 5/2,mF = −5/2. In this case, mI = −2 and the nuclear spin polarization is parallel to the holding field. The nuclear polarization is defined as: P = 1 I ∑ mI mIpm (2.1) where mI is the magnetic quantum number of the nuclear spin, and pm is the population of the corresponding quantum state. P is defined with respect to the longitudinal holding field which is set as the zˆ direction. The optically-generated nuclear polarization along this direction is the initial nuclear polarization of 8Li+ and denoted as Po. Finally, the beam is re-ionized by passing it through a He gas cell, ion- 242.2. The β-nmr Spectrometer izing the 8Li with an efficiency of ∼ 50%. The spin-polarized and recharged 8Li+ beam is steered through a 45o electrostatic bending element and is de- livered to the low- (β-nqr) or high-field (β-nmr) spectrometers (Fig. 2.3). Any 8Li that are not re-ionized go straight into a neutral beam monitor (NBM) at the end of the polarizer. The nuclear polarization is preserved during the electron stripping process. The polarization of 8Li+ is parallel to the momentum at β-nmr station and perpendicular at the β-nqr spec- trometer. We now have a beam of probe 8Li+ at (28.000 ± 0.001) keV that are spin polarized and they can now be directed onto a sample held in the spectrometer. 2.2 The β-nmr Spectrometer The high field spectrometer is designed with longitudinal geometry. The 8Li+ spin polarization and the external magnetic field are both along the beam axis (Fig. 2.4 Panel a). This is necessary because the incoming ions and outgoing β-electrons are both strongly focused by the magnet at a high magnetic field. In order to detect β-electrons in the backward direction, it is required that the detector be outside the magnet since the β-electrons are confined to the magnet axis while inside the magnet bore. Although the solid angles subtended by the two detectors in zero field are very different, they have similar detection efficiencies in high magnetic fields due to the focusing effect of the solenoid. In the section just before the high field spectrometer, there are three electrostatic Einzel lenses and three adjustable collimators which control the beam spot on the sample. A schematic drawing of the spectrometer is shown in Fig. 2.4 Panel a. The polarized beam enters from the left and passes through a hole in the back detector before entering the last Einzel lens at the entrance to the superconducting solenoid generating a homogeneous magnetic field up to 9 Tesla. 8Li+ beam is focused by the magnetic field on to the sample, and the beam spot at the center of the magnet is a sensitive function of Einzel lens voltage, magnetic field and beam energy. Images of 252.2. The β-nmr Spectrometer Figure 2.4: a: the layout of β-nmr spectrometer at ISAC. The beam incident from the left enters the spectrometer by passing through the hole at the center of the backward scintillation detector, and is focused to the sample by the high magnetic field generated by superconducting solenoid. The emitted β-electrons are detected by forward and backward scintillation detectors centered on the axis of the field. Adapted from Ref. [89] b: the geometry of β-nmr experiment. The sample is sitting on a high- voltage platform. c: a typical beam spot image on a sapphire disk in the high field. Adapted from Ref. [90] 262.2. The β-nmr Spectrometer the 8Li+ beam at the sample position were obtained by using a sapphire scintillator at the sample location and taken by a CCD camera. Fig. 2.4 Panel c shows a typical image of the focused β-nmr beam spot usually of 2-4 mm in diameter depending on the above conditions. As shown in Fig. 2.4 Panel b, the polarization of 8Li+ is along the beam axis, and parallel to the magnetic field Bo =Bozˆ (100 G < Bo < 6.5 T). A small Helmholtz coil is used to apply a transverse radio-frequency (rf) field B1(t) (B1max ∼ 1 G) at frequency ω in the horizontal direction, perpendicular to both the beam and the initial polarization. For a photo of this coil, see Fig. 2.5b). Two plastic scintillators are placed in front and behind the sample to detect the outgoing β-electrons emitted from the 8Li+ β-decay. The emitted β-electrons have an average energy ∼ 6 MeV and thus can easily pass through thin stainless steel windows in the UHV chamber to reach the detectors. The backward detector is located outside the bore of the magnet as mentioned above. The focusing effect of the high magnetic field leads to similar detection efficiencies in both detectors although they have different solid angles as the forward detector is much closer to the sample. The sample is mounted on a UHV cold finger cryostat (Oxford Instruments). UHV is critical to avoid the buildup of residual gases on the surface of the sample at low temperature. The pressure in the main chamber can be reduced to 10−10 torr using differential pumping. Temperatures from 300 K to 3 K are obtained by using a helium gas flow cryostat. The cryostat, connected to a motorized bellows, can be inserted into, or retracted from the bore of the superconducting solenoid (Fig. 2.5 Panel a). This allows us to change the sample through a load-lock without venting the entire UHV chamber. Panel b of Fig. 2.5 shows the end of the cryostat viewed along the axis. When loaded, the sample is at the center of the rf coils. The sample holder port in the cryostat is keyed such that the sample can only be loaded facing the beam. A picture of a typical sample is shown in Panel c of Fig. 2.5. Typically, a β-nmr sample is ∼ 8 mm × 10 mm, 0.5 mm thick. Smaller samples may be attached to a sapphire plate (∼ 8 mm × 10 mm × 0.5 mm) using UHV compatible silver paint, and clamped to the sample holder (made of copper or aluminum) by two clamps fastened 272.2. The β-nmr Spectrometer Figure 2.5: a: The β-nmr spectrometer retracted from the bore of the magnet: 1–superconducting solenoid; 2–sample loadlock; 3–UHV chamber; 4–cryostat bellows. b: Axial view of the end of the cryostat (out of UHV) showing the sample position and the rf coil around it. c: The copper housing with a sample mounted on it. The sample is right in the middle of the rf coil. with M2 screws. We redesigned the sample holder for the current injection experiment. More discussion of this can be found in Appendix C. The whole spectrometer is placed on a high-voltage platform which is electronically isolated from ground and can be biased up to 30 kV. By biasing the platform, the incident 8Li+ must overcome the electrostatic potential barrier generated by the bias voltage before they reach the sample. Therefore the 8Li+ beam is decelerated and injected into the sample with different energies, stopping in the sample at different implantation depths. The bias voltage is thus an adjustable parameter controlling the beam implantation depth and allowing depth-resolved measurements. Depth-resolution is an important capability of the β-nmr spectrometer. The whole platform is caged and interlocked for safety. We will discuss β-nmr implantation profile 282.3. β-nmr Ion Implantation Profile and how it varies with implantation energy in more details in the next session (Section 2.3). 2.3 β-nmr Ion Implantation Profile As mentioned above, the implantation energy of 8Li+ ions can be controlled by adjusting the platform bias voltage, corresponding to different implan- tation depths–from several nanometers to a few hundred nanometers. 8Li+ with a higher implantation energy stop further in the sample, and vice versa. The deceleration of 8Li+ is an important characteristic of the β-nmr spec- trometer, allowing for the depth-controlled surface and interface studies. Figure 2.6: SRIM graphic interface. The ion implantation profile is simu- lated by specifying the probe’s charge, atomic mass and energy as well as the densities of target materials in each layer and their thicknesses[91]. Ion implantation is an inherently random process, with each ion following an individual path as it scatters from atoms in the target. However, due to 292.3. β-nmr Ion Implantation Profile the large numbers of ions involved, it is possible to describe the ion profile statistically. The program Stopping and Range of Ions in Matter (SRIM) can simulate the depth profile of the implanted ions in materials. This program is based on the binary collision approximation model using Monte Carlo algorithms for atomic collision processes in solids[91, 92]. The accuracy in calculating ion range distributions in various materials is well established, and it is routinely used in similar depth controlled experiments such as low- energy µSR[93]. Fig. 2.6 shows the graphic interface of the program SRIM. The implantation profile is simulated by specifying the properties of both the incident beam and the target material, including the beam energy, ion charge and atomic mass for the probe, the number of probe particles, and the composition, density and thickness of each layer of the sample under study. Two parameters of an implantation profile are important in this thesis: projected range and ion straggle[91]. The projected range is the averaged stopping range of 8Li+ in the target, and is referred to as “the implantation depth”. The ion straggle (width) is defined as the standard deviation, which characterizes distribution of the stopping range. As an example of a SRIM simulation result, the left panel of Fig. 2.7 shows the characteristic asym- metric and positively skewed distribution of 8Li+ with the beam energy of 5 keV into a GaAs crystal. At 5 keV, the ion range is ∼ 31 nm. The profile is narrow with a straggle of ∼ 17 nm. The implantation depth and straggle of 8Li+ with different implantation energies is shown in the right panel of Fig. 2.7. The average depth increases from ∼20 nm with the beam energy of 3 keV to ∼140 nm at full beam energy. At low energy, a significant fraction of 8Li+ is backscattered from the sample. The fraction of ions that backscatter is strongly energy dependent, so this is a potentially important systematic effect to consider when compar- ing different implantation energies. If one 8Li+ backscatters as an ion, the high magnetic field will confine it to the magnet axis and it will likely exit the cryostat and stop upstream possibly near the back detector. On the other hand, it is possible that the backscattered ion captures an electron 302.3. β-nmr Ion Implantation Profile Figure 2.7: Left: The SRIM simulation of the implantation profile of 8Li+ with the implantation energy of 5 keV in GaAs. Right: The implantation depth and width (straggle) with various beam energies. and leaves as a neutral atom. The trajectories of such atoms are not af- fected by the magnetic field or the electric field, and these 8Li may stop in the spectrometer in or near the coils in materials such as Cu, Al, ceramic or vespel. Such 8Li may result in a background signal. However, if they are not located near the rf coil, they will not contribute a background reso- nance signal. The effect of backscattering likely causes a systematic energy dependence on the baseline asymmetry defined below (Section 2.4.1). Although SRIM simulation provides a reasonable profile prediction, it does not include channeling effects which may be very important in certain single crystalline materials along specific directions. An example is given in Fig. 2.8 from Ref. [94]. The long tail due to the channeling effect extends up to 6–6.2 µm in the measured depth profile (left panel of Fig. 2.8), but is not accounted for in SRIM simulation (right panel of Fig. 2.8). Channeling of implanted ions occurs for incidence below a critical angle Ψ that is estimated simply as[95] Ψ = √ 2Z1Z2e2 dE (2.2) where Z1, Z2 are the atomic number of the incident particle and the stopping 312.4. β-nmr Data Collection Figure 2.8: An example of the discrepancy of the measured depth profile and SRIM simulation. Left: experimental fluorine depth profile in Si[94]. The random orientation (no channeling) is presented in comparison with the Si(100) and Si(111) channeling orientations for the same accumulated fluence of ∼ 107 atoms/cm2. Right: SRIM-2000 simulation for the random case. Adapted from Ref. [94]. medium, E is the incident energy and d is the distance between lattice atoms along a chain in the channeling direction. The role of channeling in GaAs is considered in Section 4.3. 2.4 β-nmr Data Collection In this section, I will describe the procedure for recording resonance spectra (a function of frequency) in Section 2.4.1 and spin-lattice relaxation spectra (a function of time) in Section 2.4.2. For both types of spectra, we measure the difference between the count rates in the forward and backward counters, the asymmetry A, resulting from the β decay of the 8Li+ which violates parity symmetry. The 8Li nucleus decays into 8Be in an excited state and emits one electron and one antineutrino: 8 3Li −→ 84Be+ e− + νe (2.3) 322.4. β-nmr Data Collection s87s40 s41 s56 s76s105 s43 s61s45s49s47s51 Figure 2.9: The angular (left) and energy (right) distributions of the emitted electrons after 8Li+ β-decay. The asymmetry factor a = −13 . Adapted from Ref. [96] The emitted β-electrons have an average energy of ∼ 6 MeV, with a max- imum (end-point) energy of Eo = 12.5 MeV[97] (Fig. 2.9 left panel). The weak interaction does not conserve parity, and this leads to an angular dis- tribution W (θ) of the emitted electrons (Right panel of Fig. 2.9): W (θ) = 1 + aP v c cosθ (2.4) where v is the average velocity of the electrons emitted from the β-decay, c is the speed of light (at these energies v ≈ c), a = −13 [97] is the asymmetry factor of the β-decay of 8Li+, P is the nuclear polarization (from Eqn. (2.1)), and θ is the angle between the β-decay emission direction and the spin polarization axis. Thus the β-electrons are emitted preferentially in the opposite direction (negative a) to the nuclear spin polarization at the moment they decay. As described in Section 2.2, the 8Li+ ions are implanted with their polarization either parallel or antiparallel to their momentum, depending on the helicity of the laser light. The emitted β-electrons are detected by the forward (F-) or backward (B-) detector, and the counting rate NF/B is: NF/B = F/BW (θ = 0/pi) = F/B(1± aP ) (2.5) 332.4. β-nmr Data Collection where F (B) is the experimental factor depending on the detection efficiency of the forward (backward) detector and their geometry. Therefore the ratio of the two detectors’ counting rates is: NF NB = F (1 + aP ) B(1− aP ) (2.6) Assuming similar detection efficiencies and solid angles of both detectors (F ≈ B)), one can find: aP = NF −NB NF +NB ≡ A(t) (2.7) The final polarization (P ) of 8Li just before it decays is directly propor- tional to the asymmetry (A), defined by Eqn. (2.7) of the β counting rates between the two detectors, and its evolution can be deduced by measuring the asymmetry A(t) as a function of time. The measured asymmetry can be affected by many factors such as the scattering of the β-electrons in the sample, the background count rates, and the geometrical inequalities between the two detectors. To overcome the instrumental effects, the asymmetry is measured in positive (A+) and negative (A−) helicity of the laser light. The separate helicities are combined to calculate the difference in asymmetry A: A = A + −A− 2 (2.8) Multiple scans are accumulated alternately between the two helicities to improve the statistics. Each scan can be viewed individually and discarded if it’s of poor quality. Scans in a given helicity are averaged before combination into a single spectrum. 2.4.1 β-nmr Resonance Spectra β-nmr adopts a method similar to conventional Continuous-wave (CW) NMR to measure the spin resonance. Spin-polarized 8Li ions are contin- uously injected into the sample and interact with sample nuclear and elec- 342.4. β-nmr Data Collection s49s51s56s54s48 s49s51s56s55s53 s45s48s46s54s48 s45s48s46s53s54 s45s48s46s53s50 s110s101s118s101s114s32s109s101s101s116 s65 s115s121 s109 s109 s101 s116 s114 s121 s70s114s101s113s117s101s110s99s121s32s40s107s72s122s41 s105s110s99s111s109s112s108s101s116s101s32s115s97s116s117s114s97s116s105s111s110 s32 s32 Figure 2.10: An example of the incomplete saturation. The resonance in two helicites does not meet at midway. tronic spins, as well as electronic currents, before they decay and emit β- electrons. One can perturb the 8Li spins by applying a small oscillating radio frequency (rf) field B1, normal to the static field Bo, and record the asymmetry as a function of this rf frequency ν (Fig. 2.4 b). The Larmor frequency of 8Li+ is defined as: νL = γBtot (2.9) where γ = 630.15 Hz/G is the gyromagnetic ratio of 8Li+, and Btot is the total local magnetic field. When ν matches the Larmor frequency, the 8Li+ precess about Btot, resulting in depolarization of 8Li+ spin, and thus a reduction of the asymmetry. With enough rf power, all the 8Li+ could be excited at the resonance frequency. In this case, the 8Li+ polarization is completely suppressed, and the asymmetry in each helicity meets at midway. Sometimes the rf power is not high enough, the resonances in two helicities do not meet as shown in Fig. 2.10. An example of complete saturation is shown in Fig. 4.14 (open blue squares in the top panel). In conventional NMR, a large static magnetic field is applied to polarize the nuclear spins sample under study, and a pick-up coil is needed to detect the induced signal from the ensemble’s nuclear spin polarization. There- fore, a large number of particles (∼ 1018) are required. However in β-nmr 352.4. β-nmr Data Collection the signal is generated by the injected 8Li+ which is already highly spin- polarized (Section 2.1) and is detected by measuring the asymmetry of the electrons emitted by 8Li+ in the β-decay rather than a pick-up coil. There- fore only ∼ 107 particles are needed for a resolvable signal, β-nmr is in this sense more sensitive than conventional NMR and can be used to study, for example, materials only available in thin film form such as Mn doped GaAs (Chapter 4) and thin film interfaces (Chapter 5). The β-nmr resonance provides information about the magnetic and elec- tronic properties in the material. The Larmor frequency νL indicates the total magnetic field at the probe site Btot. Btot is determined by the applied external field Bo and the static and time-averaged internal magnetic field Bint from the atomic environment: Btot = Bo +Bint (2.10) A shift of the resonance frequency ∆ν is calculated by comparing the reso- nance frequency in the material of interest ν to that in the reference material νref : ∆ν = ν − νref (2.11) = γ(Btot −Bref ) Usually we use MgO as the standard reference material to calculate the res- onance shift. MgO is nonmagnetic insulator with a simple cubic lattice, and the nuclear moments from Mg and O are negligible and this 8Li+ resonance is very narrow. Therefore the total local magnetic field in MgO is the same as the applied external field (νMgO = γBo) and the resonance is very sharp (only ∼ 0.4 kHz in pulsed rf mode (see Section 2.4.1.2)). Therefore, Eqn. (2.12) can be further written as : ∆ν = ν − νMgO = γ(Btot −Bo) = γBint (2.12) 362.4. β-nmr Data Collection Sometimes we convert the resonance shift (∆ν) into the relative shift (δ) in the unit of parts per million (ppm): δ = ν − νref νref × 106 (2.13) The frequency shift ∆ν (or δ) reveals the homogeneous static field causing the enhancement or reduction of the external field by the electrons surround- ing the nucleus. The broadening and structure of the nuclear magnetic res- onance may reflect inhomogeneities in the static internal field. In a static approximation, the area under the resonance spectrum can be taken as a measure of the number of spins observed in the resonance. There are two modes of resonance data collection used in this thesis depending on the method used to apply the RF: (1) the continuous wave (CW) where a weak rf oscillating magnetic field is continuously applied; (2) the pulsed rf mode, where a short rf pulse is used. The pulsed rf mode is convenient for narrow resonances and has been used in Mn doped GaAs data (Chapter 4) and in the GaAs crystal (Chapter 3). While the CW mode is useful for measuring broader line and has been used to study the proximity effect of Fe in GaAs described in Chapter 5. 2.4.1.1 Continuous-Wave (CW) Mode In the CW mode, a small oscillating rf field B1 is continuously applied perpendicular to Bo in a sinusoidal form: B1(t) = B1 cos(ωt)xˆ (2.14) where B1 ∼ 0.1–1 G. To measure the asymmetry, the frequency ν = ω/2pi is scanned in steps of ∆f in a frequency range ∆R around the Larmor fre- quency νL. The frequency is stepped slowly (∼ 1 s per step) compared to the 8Li lifetime to avoid distortions due to 8Li+ memory effect–i.e. ions per- sisting in the sample from previous frequency steps[98]. At each frequency, the counts are measured in N bins of time at tp per bin. Therefore it takes tscan = Ntp∆R/∆f to record each scan. For example, if ∆R = 100 kHz, 372.4. β-nmr Data Collection ∆f = 200 Hz, N = 100, and tp = 10 ms, it is tscan = 500 s to finish one scan. After each scan, another scan is taken with the same helicity, but in the opposite direction of the frequency sweep. After two scans with one helicity, the helicity is flipped and new scans starts and so on. After several good scans for each helicity, the scans of each helicity are averaged and then the final asymmetry is calculated using Eqn. (2.8). The polarization of implanted 8Li+ ions depends on the 8Li+ lifetime τ and the relaxation time of the polarization T1 in the sample. For a contin- uous beam of ions implanted at a constant rate R and the initial nuclear spin polarization Po (Eqn. (2.1)), assuming a single relaxation mechanism (the spin-lattice relaxation rate is 1/T1), the dynamic equilibrium value of the polarization in the sample averaged over time is: ¯P = PoR ∫∞ 0 e −t/τe−t/T1dt R ∫∞ 0 e −t/τdt = Po 1 + (τ/T1) (2.15) The forward/backward counters’ counting rates NF/B are proportional to the polarization (Eqn. (2.5)). The observed asymmetry in each helicity A± is calculated by Eqn. (2.7) and then combined to yield the total asymmetry A by Eqn. (2.8). As discussed at the beginning of this section, when the rf field is tuned on the resonance Larmor frequency of the 8Li+ in the sample, the 8Li+ polarization precesses in a plane normal to B1, and β-electrons are emitted isotropically due to the result rapid precession in the rotating reference frame. Therefore the rapid precession during the integration time results in a loss of the average polarization and a decrease in the observed asymmetry. Fig. 2.11 shows an example of a CW resonance spectrum in MgO–the standard material in the β-nmr experiment. The resonance spectrum is taken at room temperature in a magnetic field of 2.2 T. The left panel shows spectra with positive and negative helicities. The combined asymmetry is shown in the right panel. The NMR line is not infinitely sharp. It could be broadened by inho- mogeneity of the internal field, power broadening due to the oscillating field 382.4. β-nmr Data Collection s49s51s56s54s48 s49s51s56s55s53 s45s48s46s55s48 s45s48s46s54s53 s45s48s46s54s48 s65 s115s121 s109 s109 s101 s116 s114 s121 s70s114s101s113s117s101s110s99s121s32s40s107s72s122s41 s77s103s79 s32 s32 s49s51s56s54s48 s49s51s56s55s53 s48s46s48s52 s48s46s48s56 s65 s115s121 s109 s109 s101 s116 s114 s121 s70s114s101s113s117s101s110s99s121s32s40s107s72s122s41 s77s103s79 s32 s32 Figure 2.11: Typical CW mode resonance spectrum of 8Li+ in MgO at room temperature in the external magnetic field of 2.2 T. The left panel is the spectra with positive and negative helicities, and the right panel is the combined asymmetry. The spectrum is fit to one Lorentzian (Eqn. (2.16)), and the linewidth is 3.7± 0.1 kHz. B1, and relaxation processes (e.g. relaxation rate 1/T1). For any line shape, we define its linewidth as the full-width at half maximum (FWHM). In CW mode, the large amplitude of B1 leads to power broadening of the resonance. The broadening due to B1 is temperature-independent and gives rise to a Lorentzian line[99]: A(ν) = Ao − Aampσ 2 4(ν − νo)2 + σ2 (2.16) where Ao is the baseline, νo, σ and Aamp are the resonance position, width (FWHM) and amplitude, respectively. When 8Li+ stop in a region with two distinct magnetic environments (e.g. the thin magnetic film and the substrate on which the film is grown epitaxially), one expects two resonances in the spectrum. In this case, we fit the spectrum to multiple peaks, two Lorentzians for example: A(ν) = Ao − ( Asubσ 2 sub 4(ν − νsub)2 + σ2sub + Aoverσ2over 4(ν − νover)2 + σ2over ) (2.17) where i = sub and over denotes the resonance in the substrate and in the 392.4. β-nmr Data Collection overlayer thin film respectively. An example of two component resonance spectrum will be shown in Chapter 4. Since Lorentzian widths add linearly, the measured width is approxi- mately: σ = σint + (γH1) + (1/τ + 1/T1) (2.18) where σint is the intrinsic static linewidth, γH1 is the power broadening, and (1/τ +1/T1) is the dynamic relaxation broadening. In the materials studied in this thesis, the dynamic contribution is at least 2 orders of magnitude smaller than σint at all temperatures, and thus negligible. 8Li+ are spin I = 2 ions with a small electric quadrupole moment Q = +31 mB[100]. In general, the quadrupole moment results in a quadruple splitting of the spectrum if 8Li+ ions stop at non-cubic sites where there is an electric field gradient (EFG). The data shown in this thesis were all collected in a high magnetic field (∼ 1 − −4 T) and in materials based on the GaAs crystal, a semiconductor of zinc-blende structure. When 8Li+ stop in the GaAs crystal, they prefer to take up the substitutional Ga sites or interstitial sites, both of which are of cubic symmetry. At cubic sites, the electric field gradient (EFG) is zero by symmetry, so that the quadrupole interaction also vanishes. However, any imperfections in the GaAs crystal, e.g. created by dislocations, strains, or vacancies, create non-vanishing EFGs at 8Li+ stopping sites, which vary both in orientation and in magnitude from site to site and have an influence on the lineshape of the spectrum. In a high magnetic field, the quadrupole interaction is much smaller than the Zeeman interaction, and can be treated as a perturbation. In this case, the quadrupole interaction contributes to the intrinsic β-nmr linewidth (σint), and the quadrupole broadening σQ is usually independent of temperature or the magnetic field (in the high field limit). From Eqn. (2.7) and Eqn. (2.15), we can see that the asymmetry is affected by the relaxation rate 1/T1, A ∝ Poτ/T1 for τ/T1  1. Therefore, a fast relaxation rate results in a lower baseline asymmetry Ao and smaller resonance amplitude. The average polarization Po is scaled down by the relaxation rate (1/T1). We divide the resonance amplitude Aamp by the 402.4. β-nmr Data Collection baseline Ao to account for the relaxation and calculate the normalized am- plitude Anorm. As already discussed, the area of the resonance in β-nmr is used as a measure of the number of 8Li+ contributing to the resonance. For a sharp peak, we use the multiple of the normalized amplitude Anorm and the width σ to approximate the peak area. This analysis will be applied to the data shown in Chapters 4 and 5. Using this mode, we can measure resonances as broad as ∼30 kHz. For narrow lines, the linewidth is comparable to the artificial power broadening γB1. In this case, we use the pulsed rf mode. The CW mode resonance is sensitive to instability of the beam. Such instability may result in a time-dependent change to the measured asymme- try A(t), which interferes with the measurement of the resonance lineshape. For example, a time-dependent change in the baseline asymmetry induced by the beam drifting can not be distinguished from a change in the polariza- tion induced by the rf field. Since these variations in A(t) occur on the time scale of 8Li+ lifetime τ or longer, we could avoid this problem by applying the rf field in the form of rf pulses instead of continuous waves. 2.4.1.2 Pulsed RF Mode If the β-nmr resonance is narrow, we use rf pulses to avoid the power broad- ening. The rf pulse is applied on a short time scale (10 – 160 ms), much shorter than the 8Li+ lifetime τ (∼ 1 s). Therefore the sensitivity of the β-nmr resonance to the instability of beam is reduced. In β-nmr short rf 90o pulses (ln-sech pulse) are applied periodically to suppress the polarization while the beam is continuously on. The shaped rf pulse is applied at the required frequency ω to excite a frequency band width ∆ω. A common shape in pulsed NMR is the frequency and amplitude modulated hyperbolic secant pulse[101]: B1(t) = B1sech(βt)(eiΦ(t))xˆ (2.19) where B1 is the rf field amplitude (∼ 0.1-1 G), β is a constant proportional to the bandwidth ∆ω, Φ(t) = µ(ln(sech(βt))) is the phase, and µ is a constant. 412.4. β-nmr Data Collection Figure 2.12: A typical rf pulse sequence used in β-nmr. The hyperbolic secant (ln-sech) pulse (black line) is on for tp = 80 ms corresponding to a bandwidth of ∆ω = 200 Hz. The pulse sequence (red line) regulates the rf delivery. The inset is the enlarged ln-sech pulse. Adapted from Ref. [96]. The rf is on periodically for a short time tp ∝ 1/∆ω and t is truncated between ±tp/2. Fig. 2.12 shows a typical rf pulse used in β-nmr. The rf pulse is on during tp = 80 ms corresponding to a bandwidth of ∆ω = 200 Hz. The rf pulse is shaped to destroy the polarization of 8Li+ whose Larmor frequency falls in the frequency interval ω ± ∆ω/2. The change in the polarization before and after the pulse is proportional to the number of spins with resonance frequency in that interval. Therefore the polarization change is non-zero only at the resonance frequency. To find the asymmetry, 422.4. β-nmr Data Collection the counts are measured in a time bin tp before and after the rf pulse. The asymmetry for each helicity (h = ±) is Ah(t) = Aha(t)−Ahb (t), where Aha/b(t) is the asymmetry after/before the pulse for helicity h. The final asymmetry is again the difference of the positive and negative helicity asymmetries A(t) = (A+(t)−A−(t))/2 (Eqn.(2.8)). In the pulsed rf mode, scanning a frequency range is much faster than in the CW mode. The time spent at each frequency (tp), determined by the bandwidth ∆ω, is typically 10 ms - 160 ms, i.e. at least 10 times smaller than the CW mode (usually ∼ 1 s per frequency). For example, for tp = 80 ms (the repetition rate = 1/80 ms = 12.5 Hz), and frequency steps ∆ω = 200 Hz, it would take tscan = 4 s to sweep a range ∆R = 10 kHz. The frequency sweep is repeated with changing helicities. Each run takes about an hour to accumulate enough statistics. Because the repetition rate is high, the time between rf pulses ∆t is short compared to the recovery time τ ′, therefore the polarization can be approximated to linearly scale with time before and after the rf pulse. However, the sweep time N∆t (N–number of pulses in the sweep) is long compared to τ ′, so that all spins in the given frequency interval have enough time to relax back to equilibrium before the next rf pulse is applied to the same interval. Within the frequency sweep, the frequencies of the rf pulse are generated randomly to minimize history effects. Because the rf pulse is short in time, the polarization is not very sensitive to beam instability. The instability in the beam will affect one frequency point and not the whole spectrum. There’s no power broadening because the rf pulse band width is not greater than the step size. The resulting lineshape is more clearly related to the intrinsic resonance lineshape. The asymmetry is calculated by measuring the difference before and after the short pulse. Therefore the baseline asymmetry is no longer important in this mode, and the scan range could be greatly reduced, which in turn allows for more scans and better averaging. Fig. 2.13 shows a typical pulsed rf mode resonance in MgO. The resonance is fit to one Lorentzian using Eqn. (2.16). Compared to the CW-mode resonance (Fig. 2.11), we scanned a much smaller frequency range and the resonance is much narrower (∼ 0.4 kHz). The pulsed rf mode resonance is particularly important in the high res- 432.4. β-nmr Data Collection s49s51s56s54s48 s49s51s56s54s51 s49s51s56s54s54 s45s48s46s48s50 s48s46s48s48 s48s46s48s50 s65 s115s121 s109 s109 s101 s116 s114 s121 s70s114s101s113s117s101s110s99s121s32s40s107s72s122s41 s77s103s79 s49s51s56s54s48 s49s51s56s54s51 s49s51s56s54s54 s45s48s46s48s51 s48s46s48s48 s65 s115s121 s109 s109 s101 s116 s114 s121 s70s114s101s113s117s101s110s99s121s32s40s107s72s122s41 s77s103s79 Figure 2.13: Typical pulsed rf mode resonance spectra of 8Li+ in MgO at room temperature in the external magnetic field of 2.2 T. The left panel is the resonance spectra in positive and negative helicities, and the right panel is the combined asymmetry. The spectrum is fit to one Lorentzian using Eqn. (2.16) and linewidth is 0.44 ± 0.04 kHz, much narrower than that in CW mode (Fig. 2.11). olution measurements when the resonance is narrow. Any resonance with a linewidth on the order of 400 Hz can be accurately measured in pulsed rf mode within a moderate scan time to build up enough signal-to-noise (S/N) ratio. If the resonance is much wider than ∼ 400 Hz, the S/N ratio accu- mulates very slowly so that it takes too long time to get enough data. We will present some high resolution measurement using the pulsed rf mode in Chapters 4 and 3. 2.4.2 β-nmr Spin Lattice Relaxation (SLR) Spectra β-nmr resonance data senses the static time-averaged possibly inhomoge- neous local field at the probe site. In contrast, in a spin lattice relaxation (SLR) measurement, we monitor the polarization of the probes as a func- tion of time in the absence of an rf field. The rate of decay (SLR rate λ) is determined by magnetic fluctuation at the resonance Larmor frequency. For such measurements, the ion beam is pulsed with an electrostatic kicker such that a pulse of beam of duration to is delivered to the sample. The time-dependent β-decay asymmetry is monitored both during and after 442.4. β-nmr Data Collection the pulse. In all SLR data shown in this thesis, the ion beam is on con- tinuously for 4 s, yielding the sharp change at this time, and then off for a counting period of 12 s. While the beam is on, the measured asymmetry ap- proaches a dynamic equilibrium value determined by the SLR rate λ and the 8Li+ lifetime τ (Eqn. (2.15)). This cycle is repeated many times (typically ∼ 30 mins) to accumulate reasonable statistics. The counts from two detec- tors are used to generate the experimental asymmetry directly proportional to the 8Li+ nuclear polarization P (t) (Eqn. (2.7)). The time-differential spectra are measured in both helicities, averaged over each helicity and then combined to generate the final asymmetry (Eqn. (2.8)). The spin-lattice relaxation rate λ ≡ 1/T1 is extracted from the SLR spectra as follows. Assume a general spin relaxation function f(t, t′;λ) for the ions implanted at t′. The average polarization follows[102]: P (t) =    ∫ t 0 e −(t−t′)/τf(t,t′;λ)dt′∫ t 0 e −t/τdt t ≤ to ∫ to 0 e −(to−t′)/τf(t,t′;λ)dt′∫ to 0 e −t/τdt t > to (2.20) For example, assuming a single mechanism of relaxation with the relaxation rate λ, f(t, t′;λ) = Ae−λ(t−t′), the asymmetry A(t) which is proportional to the polarization P (t) is A(t) =    Ao 1−e −t/τ ′ 1−e−t/τ t ≤ to A(to)e−λ(t−to) t > to (2.21) where Ao is the maximum β-decay asymmetry at t = 0, τ is 8Li lifetime, 1 τ ′ = 1 τ + λ and A(to) = Aoe−λto . During the beam on time, the dynamic equilibrium asymmetry is (Eqn. (2.15)): A = ∫∞ 0 e −(t−t′)/τf(t, t′;λ)dt′∫∞ 0 e −t/τdt 452.4. β-nmr Data Collection s48 s53 s49s48 s45s48s46s55s48 s45s48s46s54s53 s84s105s109s101s32s40s115s41 s116 s111 s65 s45 s40s116s41 s65 s43 s40s116s41 s65 s43 s47 s45 s40 s116 s41 s48 s53 s49s48 s48s46s48s48 s48s46s48s51 s48s46s48s54 s116 s111 s65 s40 s116 s41 s84s105s109s101s32s40s115s41 Figure 2.14: Representative SLR spectrum. Left panel: the averaged asym- metry in each helicity. Right: the combined asymmetry. The combined asymmetry is fit to Eqn. (2.21) with one relaxing component (Eqn. (2.23)). The blue dotted line indicates the beam off time. = Ao 1 + λτ (2.22) and A approaches A asymptotically. In some cases, there is more than one relaxation mechanism, e.g. two relaxing components due to an overlayer thin film and its substrate: P (t, t′;λsub, λover) = Asubo e−λsub(t−t′) +Aovero e−λover(t−t′) (2.23) where Aio and λi are the initial amplitude and relaxation rate with i = sub and over for the substrate and the overlayer, respectively. We could fit the SLR data to Eqn. (2.21) with the combination of two components (Eqn. (2.23)), and extract the respective relaxation rates. Fig. 2.14 shows a typical SLR spectrum which is taken in Mn doped GaAs in the field of 1.3 T at 50 K. The spectrum of each helicity is shown in the left panel and the combined spectrum is shown at the right. The combined asymmetry is fit to two exponential components using Eqn. (2.23) (the red curve in Fig. 2.14 right). The slow relaxation is assigned to the GaAs substrate and the fast one to the magnetic Mn doped GaAs overlayer (TC= 72 K). More discussion 462.4. β-nmr Data Collection on these results are found in Chapter 4. 47Chapter 3 The Local Magnetic Field in Crystalline GaAs GaAs is one of the most widely used semiconductors in both industry and scientific research. As a common impurity in semiconductors, studies of Li in GaAs have a long history[103], but little is known about the NMR of isolated Li in GaAs. Moreover, as one of the best studied semiconductors, GaAs is often used as a substrate, upon which other materials are grown, such as Mn doped GaAs (Chapter 4) and Fe (Chapter 5). GaAs is well lattice matched with Fe (only ∼ 1.4% mismatch) for epitaxial growth of a magnetic Fe overlayer. In order to study such magnetic heterostructures, it is important to understand the behavior of 8Li+ in GaAs bulk crystal as a control study, and this is the topic of this chapter. The pure GaAs crystal (“undoped” GaAs) does not display either n– or p– type conductivity. Electrons are thermally activated from the valence band to the conduction band, and holes are left in the valence band. Hence electrons and holes are of the same concentration (n = p ∼ 106 cm−3 at room temperature). The semi-insulating GaAs used in this thesis is undoped GaAs with a very low intrinsic carrier concentration (n = ∼ 107 cm−3) and very high room temperature resistivity (∼ 5.7× 107 Ωcm) . The electronic properties and conductivity of GaAs can be changed in a controlled manner by adding very small quantities of other elements – “dopants”. In crystalline GaAs, typically the doping process is achieved by adding impurities of Si or Zn to the melt at high temperatures and then allowing it to solidify into the crystal. The GaAs crystal can be changed from semi-insulating to metallic by varying the dopant concentration. For 483.1. The Susceptibility of GaAs this metal-insulator transition, we can use the Mott criterion[16] to estimate the critical dopant density Nc at which the metal-insulator transition occurs: a∗B ·N1/3c ≈ 0.24 (3.1) with a∗B = 103 ˚A the effective Bohr radius for GaAs[16]. The critical dopant density is estimated to be 1.26 × 1016 cm−3. We expect β-nmr of 8Li+ in GaAs to be quite different from metallic to the semi-insulating GaAs if 8Li+ is sensitive to the mobile carriers introduced by the doping. Moreover, the magnetic proximity effect and spin injection are likely very different for undoped and heavily doped GaAs (Chapter 5). In this chapter, we first discuss various contributions to the susceptibility of GaAs in Section 3.1, and review the previous β-nmr study on semi- insulating GaAs (published in Ref. [104]) in Section 3.2. In Section 3.3, we report an unexpected shift of the 8Li+ NMR, depending on both temperature and depth, that is revealed by the higher resolution pulsed rf measurements on a different semi-insulating GaAs crystal (sample: 09-B1) and a heavily doped n-type GaAs crystal (sample: 09-B2). 3.1 The Susceptibility of GaAs The uniform static magnetic susceptibility of a material gives rise to a mag- netic field within the material that differs from the applied field. This gen- erally causes a magnetic shift of the resonance, i.e. a frequency shift that scales with the applied field. However, if the susceptibility consists of several contributions, one may be much more strongly coupled to the nucleus than the others. This is the case, for example, in metals, where the Pauli sus- ceptibility yields the Knight shift, which is often the dominant shift. Other contributions to the susceptibility yield the temperature independent orbital (or chemical) shift. Assuming that the resonance shift is proportional to the susceptibility of GaAs, it is necessary to review the magnetic properties of GaAs first before we proceed to the β-nmr results. GaAs is a diamagnetic solid with a small and weakly temperature- 493.1. The Susceptibility of GaAs dependent magnetic susceptibility[105]. Its susceptibility can be decom- posed into several components: χ = χcore + χLangevindiamag + χ van V leck paramag + χionized dopants + χfree carriers (3.2) where χcore is the diamagnetic (negative) susceptibility due to the ion cores (Ga3+ and As5+). χLangevindiamag is the Langevin contribution to the suscepti- bility due to the valence band, sensitive to the spatial distribution of the valence electrons in the chemical bonds in this network covalent structure. χvan V leckparamag is the van Vleck type paramagnetic (positive) susceptibility, which originates from the second order perturbation of Zeeman energy, and in- versely proportional to the band gap. The band gap of GaAs is weakly temperature dependent, being 1.43 eV at room temperature while 1.52 eV at low temperatures[15]. χionized dopants, the contribution from ionized dopants, is diamagnetic and usually considered negligible at all tempera- tures. χfree carriers is the contribution from free electrons, e.g. electrons in the conduction bands in our case. χfree carriers can be further decomposed into 2 contributions: χfree carriers = χPauli + χLandau (3.3) where χPauli and χLandauare the Pauli and Landau susceptibilities of free carriers, respectively. Paramagnetic χPauli (spin susceptibility) is usually very small and temperature-independent in a metal because of the Pauli exclusion principle and an electronic density of states that is only weakly dependent on energy in the vicinity of the Fermi level. Only the carriers near the Fermi energy (within ∼ kBT ) contribute to the susceptibility with a constant density of states near EF . The net electronic moment leads to an effective field at the probe 8Li+ nucleus. The shift produced by this field in a metal is the famous Knight Shift[15]. As in Eqn. (4.9), the Knight shift δKnight can be written as: δKnight = ( A NAµB ) χPauli (3.4) 503.2. Previous β-nmr Study on Semi-Insulating GaAs Figure 3.1: Left: the temperature dependence of the amplitude of the β-nmr resonance at the 8Li+ Larmor frequency in GaAs. The inset shows example resonance data for two temperatures, offset for clarity. Right: temperature dependence of the linewidth of the β-nmr resonance in GaAs. Adapted from Ref. [104]. where NA, µB, A are Avogadro’s number, the Bohr magneton and the hyper- fine coupling constant between the 8Li+ probe and the conduction electrons, respectively. In contrast to a metal, the density of states of free carriers in heavily doped GaAs is no longer a constant as in metals. The electrons freeze out into bound states at the dopant ions at low temperature. Therefore the paramagnetic χPauli in n-GaAs changes with temperature. The hyperfine interaction between the 8Li+ probe and the conduction electrons in n-GaAs may lead to a resonance frequency shift like the Knight shift in a metal, but which depends on temperature. The diamagnetic χLandau is −13χPauli in a metal, but is significantly enhanced in semiconductors generally, par- ticularly in n-GaAs, which χLandauχPauli ∝ ( me m∗ )2 because of the small effective mass m∗ in n-GaAs[15]. χLandau, as an orbital contribution, is unlikely to strongly couple to 8Li+ nucleus, but it may contribute to an orbital shift. 513.2. Previous β-nmr Study on Semi-Insulating GaAs 3.2 Previous β-nmr Study on Semi-Insulating GaAs Here we summarize previous β-nmr measurements on GaAs[104]. β-nmr because of its sensitivity, has been proved an effective probe to study isolated impurities in semiconductors[106, 107]. Early resonance measurements on GaAs using CW mode were conducted in the presence of a static magnetic field Ho ∼ 3 T parallel to the 〈100〉 crystal direction. The 8Li+ with full energy was implanted into a ∼ 350 µm thick semi-insulating GaAs substrate, stopping at a penetration depth of ∼ 140 nm. As shown in the inset of Fig. 3.1 left panel, a single broad resonance with no quassdrupolar splitting is observed at all temperatures, indicating that Li is located at cubic sites (the discussion on the quadrupole splitting is in Section 2.4.1.1). In the Zincblende lattice, that is the interstitial tetrahedral or substitutional site. The resonance does not shift substantially below 300 K. The Left panel of Fig. 3.1 shows the amplitude of the resonance. At high temperatures, all of the Li stay in a high symmetry site, while at low temperatures, about 70% of the Li are in such locations with 30% unaccounted for, possibly in a broad unresolved resonance. The amplitude loss at low temperatures can be attributed to 8Li+ moving out of a high symmetry site as temperature decreases[108, 109]. 8Li+ stopping at sites of lower symmetry in the near vicinity of some lattice disorder experience an EFG (we don’t know how big), so the set of all such sites experiences a distribution of EFGs, likely resulting in a broad component in the resonance that is not resolved and a corresponding loss of amplitude in the narrow resonance as observed in the β-nmr in ZnSe[107]. The temperature dependence of the resonance linewidth is shown in the right panel of Fig. 3.1. The power broadening in CW mode γH1 ∼ 1.3 kHz (Section 2.4.1.1) contributes to the linewidth (∼ 3 kHz) below 200 K. Another contribution to the linewidth is the nuclear dipolar interactions between the static Li and the Ga and As nuclear moments. The linewidth slightly decreases from 5 K to 150 K, followed by a broadening above 150 K. It peaks at about 290 K and decreases again. This peak is likely due to 523.2. Previous β-nmr Study on Semi-Insulating GaAs a site change. Now let’s discuss the possible 8Li+ sites in the GaAs crystal lattice. Fig. 3.2 shows possible sites Li may take in a simple analogous 2D lattice. The substitutional sites and interstitial sites (top panels of Fig. 3.2) are well- defined cubic sites, at which the quadrupole splitting is zero. Some 8Li+ may also stop in the vicinity of implantation-created crystal defects, Frenkel (vacancy–interstitial) pairs (panel c of Fig. 3.2). These are not well-defined high symmetry sites, therefore the quadruple splitting does not vanish and unresolved quadrupole splitting contributes to the resonance linewidth. If the probe 8Li+ stops very close to such a defect (panel d of Fig. 3.2), the EFG may be so large that the corresponding resonance may be too broad to be detected. An alternate possible explanation for the temperature dependence is 8Li+ diffusion and trapping as has been observed in some materials for the positive muon[110, 111]. The 8Li+ is much more massive than µ+, so this is unlikely. If there were any fast long-range diffusion of 8Li+, we would expect a dramatic narrowing of the linewidth at high temperatures, as observed in 7Li NMR[112]. However, as shown in the right panel of Fig. 3.1, the linewidth at 300 K is not substantially narrower than at 5 K. There is no sign of a motional narrowing at high temperatures, therefore the linewidth change can not be attributed to 8Li+ diffusion. It is also possible that 8Li+ diffuses quickly to a trap (in a small fraction of its lifetime 1.2 s). The resonance would thus be characteristic of the trap site instead of pure GaAs. In this case, one would expect to freeze out such a transition at low temperatures. However, we did not observe a dramatic change in the resonance linewidth at low temperatures as shown in the right panel of Fig. 3.1. Moreover, α emission channeling studies of 8Li in GaAs[109] show that below 200 K, the tetrahedral interstitial sites (panel b of Fig. 3.2) are prefer- entially occupied by 8Li+; while substitutional sites (panel a of Fig. 3.2) are occupied above 200 K. In these experiments, a beam of 8Li+ was injected as the probe. 8Li+ decays into an excited state of 8Be (Eqn. 2.3) which imme- diately breaks into two α particles. Within a single crystal, these α parti- 533.3. High Resolution Measurements of β-nmr in GaAs Crystals cles experience channeling and blocking effect along major crystal axes and planes, resulting in an anisotropic emission yield from the surface, depending on the lattice site of 8Li+ at the same time of decay. The 8Li+ occupation sites were determined by measuring the distribution of α transmission flux parallel to the sample surface. The probes used in these experiments (8Li+) is the same used in our measurements, therefore their results measured di- rectly the 8Li+ occupation sites in the GaAs lattice. Theory[113] predicts that the equilibrium site for isolated interstitial 8Li+ is the tetrahedral site surrounded by four nearest As atoms, TAs. At low temperatures, a signifi- cant fraction of the Li ends up in a TAs sites with possible occupancy of a TGa or substitutional site. However, as the temperature is raised above ∼ 200 K, the environment around many of the Li ions is changing significantly. These Li approach nearby implantation-created vacancies (Panel c of Fig. 3.2), and the broadening of the resonance (the left panel of Fig. 3.1) may be due to small unresolved quadrupole splittings. At higher temperatures, Li preferentially occupies the Ga vacancy VGa where the quadrupole splitting is identically zero, and hence the linewidth is observed to decrease again. Similar behavior has been observed in β-nmr of 12B implanted in the II–VI zincblende semiconductor ZnSe[114]. 3.3 High Resolution Measurements of β-nmr in GaAs Crystals The previous studies were carried out in CW mode which is generally subject to power broadening (Section 2.4.1). Higher resolution measurements could be made in pulsed rf mode, which reproduces the intrinsic lineshape more faithfully (Section 2.4.1.2). The rf pulsed mode measurements reveals a small unexpected temperature-dependent shift of the β-nmr resonance in both the semi-insulating GaAs (09-B1) and the heavily Si doped n-GaAs (09-B2). In addition, depth dependence of the shift is observed in the semi- insulating GaAs (09-B1) but not in the n-GaAs (09-B2). 543.3. High Resolution Measurements of β-nmr in GaAs Crystals Figure 3.2: Possible sites 8Li+ may take in an analogous 2D lattice. The gray points represent the analogous GaAs 2D lattice, and the blue points represent 8Li+ stopping sites. Panel c and d show 8Li+ sites in the vicinity of a lattice defect, a vacancy-interstitial Frenkel pair. See text for more details. 553.3. High Resolution Measurements of β-nmr in GaAs Crystals 3.3.1 Experimental The semi-insulating GaAs is provided by Wafer Technology Ltd., UK in the form of a 3" diameter ∼ 350µm thick wafer grown at low pressure from high purity polycrystalline GaAs in a vertical temperature gradient (VGF – Vertical Gradient Freeze) with one side polished. For the semi-insulating GaAs crystal (09-B1), no compensation dopants are deliberately added to produce the semi-insulating property. The carrier concentration n is in the range of (2.00–6.30)×107 cm−3 measured by the provider. The surface is carefully cleaned before delivery and any surface contamination will be bound up in the surface oxide (a native oxide layer ∼3 nm thick ideally Ga2O3). The sample used in the experiment is 8 mm × 10 mm cut from the 3" diameter wafer without any further surface preparation. The heavily doped n-GaAs crystal (09-B2) is cut from a 3" diameter wafer (∼ 350µm thick) from AXT Inc., USA, also grown by VGF. It is heavily doped by Si to give n-type conductivity. The carrier concentration n is in the range of (1.5−1.7)×1018 cm−3, well into the metallic region. The Si dopant is nearly 100 % activated at room temperature, donating one free electron per Si, therefore the dopant concentration Nd is very similar to the carrier concentration n. So Nd in this n-GaAs crystal (09-B2) is much higher than the critical dopant concentration Nc for the metal-insulator transition, therefore 09-B2 is highly metallic. One side of the wafer is polished and the other side is rough but flat, and chemically etched. The 8Li+ implantation profile is simulated by SRIM-2006.02 (Section 2.3). The energy dependence of the average implantation depth and the width of the distribution are shown in the inset of Figure 3.3. The pulsed rf mode β-nmr spectra in the semi-insulating GaAs crystal (09-B1) were measured in the field of 2.2 T while the same measurements in the heavily doped n-GaAs (09-B2) were taken at 4.1 T. The resonance spectra are fit to a single Lorentzian using Eqn. (2.16) and the shift is calculated with respect to the frequency of 8Li+ in MgO at 300 K by Eqn. (2.13). As we discussed in Section 4.4.3, we need to correct for the demagneti- 563.3. High Resolution Measurements of β-nmr in GaAs Crystals s48 s49s48s48 s50s48s48 s51s48s48 s48s46s48 s48s46s50 s48 s49s48 s50s48 s48 s54s48 s49s50s48 s48 s54s48 s49s50s48 s56s32s107s101s86 s49s32s107s101s86 s49s56s32s107s101s86 s32 s32 s80 s114 s111 s98 s97 s98 s105 s108 s105 s116 s121 s73s109s112s108s97s110s116s97s116s105s111s110s32s68s101s112s116s104s32s40s110s109s41 s50s56s32s107s101s86 s71s97s65s115 s68 s101 s112 s116 s104 s32 s40 s110 s109 s41 s73s109s112s108s97s110s116s97s116s105s111s110s32s69s110s101s114s103s121s32s40s107s101s86s41 s87 s105 s100 s116 s104 s32 s40 s110 s109 s41 Figure 3.3: SRIM simulation of 8Li+ in the GaAs single crystal. The im- plantation profiles in GaAs simulated by SRIM-2006.02 with different im- plantation energies. The implantation energy varies from full beam energy 28 keV to 3 keV, corresponding to the average implantation depth from ∼ 140 nm to ∼ 20 nm. The inset shows the implantation depth and width with different beam energies. zation effect in the GaAs[115]. The total field can be decomposed in Eqn. (4.3) where all components are defined the same as in Section 4.4.3. Note that ν = γBtot, the relative shift is: δ = ν − γBo γBo (3.5) = Bdemag +BLor +Bloc Bo here ν = γB is the frequency in MgO. We need to account for Bdemag and BLor to obtain the shift of interest δc = BlocBo . As discussed in Section 4.4.3, BLor = 4pi/3 for a spherical Lorentz cavity, and the demagnetization field Bdemag = −NM where the dimensionless demagnetization factor N ranges from 0 to 4pi in the cgs system. For a finite size thin film sample, N can be written as: N ≈ 4pi(1− pi 2 ξ + 2ξ2) (3.6) where ξ is the aspect ratio of the sample (thickness to transverse dimension). 573.3. High Resolution Measurements of β-nmr in GaAs Crystals In the GaAs samples, the GaAs wafer is ∼ 350µm and cut into an 8 mm × 10 mm plate. Thus ξ ≈ 350µm8mm = 0.043. So the demagnetization factor N is estimated as 4pi × 0.94. Substituting these quantities in Eqn. (3.6) and noting that χv = M/B with χv the volume susceptibility of GaAs, we obtain that δc = δ − (−4pi × 0.94 + 4pi/3)χv × 106 (3.7) For example, at room temperature, χv = −1.32× 10−6 emu/cm−3, the res- onance shift we measured in SI-GaAs (09-B1) is -5 ppm. The shift after demagnetization correction is -15 ppm. The fit results after demagnetiza- tion correction are shown in Fig. 3.5 (depth dependence) and Fig. 3.7 (temperature dependence). 3.3.2 Results and Analysis 3.3.2.1 Depth Dependence of the Local Magnetic Field in GaAs The spectra of 8Li+ in the semi-insulating GaAs crystal (09-B1) at 5.5 K in the field of 2.2 T as a function of implantation depth is shown in the top panel of Figure 3.4. The shift at 3 keV (corresponding to the average implantation depth d ∼ 20 nm) amounts to about −50 ppm relative to the resonance position in crystalline MgO, our standard reference material. The magnitude of the shift is comparable with Knight shifts of 8Li+ in some noble metals[116]. At this temperature, the shift is clearly depth dependent being more negative deeper in the crystal (28 keV, corresponding to d ∼ 140 nm) than near the surface (3 keV, d ∼ 20 nm). Note that the linewidth, however, shows no significant energy dependence. In contrast, the bottom panel of Fig. 3.4 shows the β-nmr spectra in the heavily doped n-type GaAs crystal (09-B2) at 5 K with implantation energy of 28 keV (d ∼ 140 nm) and 9 keV (d ∼ 50 nm) in 4.1 T magnetic field. At the time of this experiment, we could not decelerate 8Li+ down to 3 keV, therefore we measured at 9 keV, the lowest beam energy we could achieve. Both resonances shift negatively compared to MgO (the blue dashed line), but neither the shift nor the linewidth changes significantly as a function of 583.3. High Resolution Measurements of β-nmr in GaAs Crystals s49s51s56s54s53 s49s51s56s55s48 s49s51s56s55s53 s45s48s46s48s53s48 s45s48s46s48s50s53 s48s46s48s48s48 s84s32s61s32s53s46s53s32s75 s65 s115 s121 s109 s109 s101 s116 s114 s121 s82s101s115s111s110s97s110s99s101s32s70s114s101s113s117s101s110s99s121s32s40s107s72s122s41 s50s56s32s107s101s86 s51s32s107s101s86 s32 s32 s115s101s109s105s45s105s110s115s117s108s97s116s105s110s103 s71s97s65s115s32s40s48s57s45s66s49s41 s50s53s56s51s48 s50s53s56s52s48 s45s48s46s48s53 s48s46s48s48 s48s46s48s53 s57s32s107s101s86 s84s32s61s32s53s32s75 s110s45s71s97s65s115s32s40s48s57s45s66s50s41 s32 s65 s115 s121 s109 s109 s101 s116 s114 s121 s82s101s115s111s110s97s110s99s101s32s70s114s101s113s117s101s110s99s121s32s40s107s72s122s41 s50s56s32s107s101s86 s32 s32 Figure 3.4: Top: β-nmr spectra in of the semi-insulating GaAs crystal (09- B1) in the field of 2.2 T at 5.5 K with implantation energies of 28 keV (black open squares) and 3 keV (blue solid circles). The resonance shifts negatively without broadening as the beam goes deeper into the GaAs crystal. Bottom: β-nmr spectra of heavily doped n-type GaAs (09-B2) with dif- ferent implantation energies at 5 K in the presence of an external field of 4.1 T. Although both spectra negatively shift compared to the reference, the frequency shift is not implantation energy dependent and no obvious broadening appears. Spectra are vertically offset for clarity. In both panels, the blue dashed line is the reference resonance frequency of 8Li+ in crystalline MgO. 593.3. High Resolution Measurements of β-nmr in GaAs Crystals s48 s49s48 s50s48 s51s48 s49s46s50 s49s46s56 s50s46s52 s87 s105 s100 s116 s104 s32 s40 s107 s72 s122 s41 s73s109s112s108s97s110s116s97s116s105s111s110s32s69s110s101s114s103s121s32s40s107s101s86s41 s45s56s48 s45s52s48 s48 s77s103s79 s32s71s97s65s115s32s53s75 s32s110s71s97s65s115s32s53s75 s83 s104 s105 s102 s116 s32 s40 s112 s112 s109 s41 Figure 3.5: Implantation energy dependence of the frequency shift (top) and width (bottom) measured in semi-insulating GaAs (open black squares) and heavily doped n-GaAs (solid blue dots) at 5 K. The black dashed line indicates the 8Li resonance position in MgO. implantation energy. Fig. 3.5 summarizes the fit results of the β-nmr spectra in both GaAs crystals as a function of implantation energy. In the semi-insulating GaAs (09-B1), the resonance shift close to the surface (d ∼ 20 nm) is comparable to the depth-independent resonance shift in the n-GaAs (09-B2), but is more negative when 8Li+ stops in the bulk (d ∼ 140 nm). The linewidths are ∼ 1.8 kHz, comparable in both GaAs crystals at 28 keV (d ∼ 140 nm). The resonance is slightly broadened at the beam energy of 9 keV (∼ 50 nm implantation depth) in n-GaAs (09-B2). 603.3. High Resolution Measurements of β-nmr in GaAs Crystals 3.3.2.2 Temperature Dependence of the 8Li+ Resonance in GaAs Now we present the temperature dependence of 8Li+ resonance in both GaAs crystals at 28 keV. Fig. 3.6 shows the resonance spectra at various temperatures in both semi-insulating GaAs (left panel) and heavily doped n-GaAs (right panel) crystals at 28 keV implantation energy – corresponding to an average depth of ∼ 140 nm. The fit results are summarized in Fig. 3.7, and the shift is also corrected for the demagnetization effect as discussed above. As evident in the spectra, the resonance does not move at high temperatures, but starts to shift to lower frequencies below 150 K in both samples. The resonance shifts further negative as temperature decreases, saturating at about 10 K (see the first two points in the red circle shown in the top panel of Fig. 3.7). The shift in the heavily doped n-GaAs crystal (09-B2) is smaller in magnitude than in the semi-insulating GaAs (09-B1). Above 150 K, there is still a temperature-independent negative shift in both crystals. The resonance linewidth (bottom panel of Fig. 3.7) is minimum at ∼ 150 K and peaks at ∼ 240 K. The linewidth is consistent with the value measured in CW mode subtracting the power broadening (Section 3.2). 3.3.3 Discussion In GaAs, we expected only a small chemical (orbital) shift independent of implantation depth and temperature. So it is really surprising to find depth dependence in the SI GaAs and significant temperature dependence in both SI- and n-GaAs. In this section, we will discuss what this could mean. The resonance only shifts with the implantation depth in the semi- insulating GaAs crystal (09-B1). This may indicate that the resonance shift is related to the carrier concentration. The periodic structure of chemical bonds in the GaAs crystals is terminated at the surface, resulting in unsat- urated (dangling) bonds. These dangling bonds can rearrange themselves and might bond to a (mono) layer of adatoms, e.g. oxygen, forming a native oxide layer. The native oxide of GaAs generates states localized at the sur- face and the energy of these surface states form an energy band in the band 613.3. High Resolution Measurements of β-nmr in GaAs Crystals s49s51s56s54s52 s49s51s56s54s56 s49s51s56s55s50 s50s53s52s32s75 s70s114s101s113s117s101s110s99s121s32s40s107s72s122s41 s69s32s61s32s50s56s32s107s101s86 s115s101s109s105s45s105s110s115s117s108s97s116s105s110s103s32s71s97s65s115 s32 s49s53s48s32s75 s32 s55s53s32s75 s32 s53s48s32s75 s32 s49s48s32s75 s32 s32 s50s53s56s50s53 s50s53s56s51s48 s50s53s56s51s53 s50s53s56s52s48 s50s53s56s52s53 s102 s48 s61s50s53s56s51s52s46s56s48s32s107s72s122 s32 s50s57s53s32s75 s82s101s115s111s110s97s110s99s101s32s70s114s101s113s117s101s110s99s121s32s40s107s72s122s41 s110s45s71s97s65s115 s69s32s61s32s50s56s32s107s101s86 s32 s49s53s48s32s75 s32 s53s32s75 Figure 3.6: β-nmr spectra as a function of temperature in the semi- insulating GaAs (left) and in the n-GaAs (right) crystal. The resonance frequency in both crystals shifts negatively when cooled without significant broadening. Spectra are vertically offset for clarity. gap with a high density of levels. The Fermi level is pinned about 0.5 eV above the valence band[117]. The electrons in the semiconductor flow into the surface region to match the chemical potential in the surface with the bulk, making the surface negatively charged. The immovable positive ions are left in the near surface region and a thin layer depleted of free electrons is created. The conduction and valence bands bend upwards (for n-GaAs) near the surface region forming a surface barrier[117], just like the Schottky barrier formed at the interface when the semiconductor is in contact with a metal layer. The upward bending of the conduction and valence bands could make the EL2 deep defect level (located ∼ 0.8 eV below the conduc- tion band) a possible donor, since for an EL2 level, the emission rate of an electron into the conduction band is sensitive to the electric field[118]. In bulk materials, its concentration is on the order of 1016/cm−3[119]. The sur- face barrier width can be roughly estimated by assuming a uniform charge distribution using Eqn. (1.6). In this case, eφB is the height of the surface barrier ∼ 0.52 eV[120]. According to Eqn. (1.6), the band bending results in a barrier width of ∼ 100 nm, which is the order of implantation depth. 623.3. High Resolution Measurements of β-nmr in GaAs Crystals s48 s49s48s48 s50s48s48 s51s48s48 s49s46s53 s49s46s56 s50s46s49 s70 s87 s72 s77 s32 s40 s107 s72 s122 s41 s84s101s109s112s101s114s97s116s117s114s101s32s40s75s41 s45s56s48 s45s52s48 s48 s84 s83s105 s73s111s110s32 s126s55s48s32s75 s116s101s116s114s97s104s101s100s114s97s108s32 s105s110s116s101s114s115s116s105s116s97s108s32 s32 s32s110s45s71s97s65s115s32s40s48s57s45s66s50s41 s32s71s97s65s115s32s40s48s57s45s66s49s41 s83 s104 s105 s102 s116 s32 s40 s112 s112 s109 s41 s69s61s32s50s56s32s107s101s86 s115s117s98s115s116s105s116s117s116s105s111s110s97s108 Figure 3.7: Temperature dependence of the frequency shift (top panel) and width (bottom) in semi-insulating GaAs (open black squares) and heavily doped n-GaAs (solid blue dots). The negative resonance shift is small and temperature-independent above 150 K, but increases as temperature de- creases below 150 K, saturating at ∼ 10 K. Resonance shift in the heavily doped n-type GaAs (09-B2) is prominently smaller than that in the SI- GaAs (09-B1) at low temperature. In contrast to the resonance shift, the resonance linewidth, consistent with the preliminary study, peaks at ∼ 290 K and narrows at ∼ 150 K. 633.3. High Resolution Measurements of β-nmr in GaAs Crystals This may explain the depth dependence of the resonance shift. Using the same assumption for n-GaAs (09-B2) with a larger carrier concentration n ∼ 1.6 × 1018 cm−3, we estimate that the surface barrier width is ∼ 20 nm, much narrower than that in the semi-insulating GaAs (09-B1). The detection range (50 nm – 140 nm) is far beyond the surface barrier. Therefore 8Li+ stopping either in the bulk (∼140 nm) or closer to the surface (∼50 nm) see the same magnetic field, and the resonance frequency is depth independent. Now we consider possible origins for this unexpected temperature de- pendence of the resonance shift found in both SI-GaAs (09-B1) and n-GaAs (09-B2). First we discuss a number of effects that can be ruled out. 1). The resonance shift can’t be due to the field inhomogeneity. The applied field generated by the superconducting solenoid is very uniform at the sample position. The magnetic field difference within 1 cm from the magnet center is less than 3 ppm. The movement of the sample position, e.g. the thermal contraction of the cryostat (∼ 4 mm from 300 K to 10 K), or the move- ment of the beam spot (less than the sample size ∼ 8 mm×mm), will result in shifts less than 3 ppm, much smaller than the observed shift. 2) One may consider whether this shift is due to some dilute paramagnetic mag- netic impurities, like the demagnetization effect in Ga1−xMnxAs(discussed in Chapter 4). In this case one would expect the shift to follow Curie’s law, i.e. inversely with temperature. This is evidently not the case as such a shift would double going from 10 K to 5 K, in contrast to the observed constant value below 10 K (the first two open black squares in the top panel of Fig. 3.7). 3). The shift might be related to the temperature dependent bulk susceptibility of GaAs, either by the demagnetization field or by a local hyperfine field. However, the susceptibility χ of GaAs is weakly tempera- ture dependent[105]. At T = 10 K, it only changes by ∼ 1% from the room temperature value (−1.32×10−6)[121]. The demagnetization correction due to the GaAs magnetization (similar to the analysis in Section 4.4.3) is es- timated to be ∼ 17 ppm, and very weakly temperature-dependent. So the observed shift is not the demagnetization effect of GaAs. Ruling these out, now we discuss what possibilities remain. There is a 643.3. High Resolution Measurements of β-nmr in GaAs Crystals temperature-independent negative shift above 150 K in both undoped and heavily doped GaAs. This is consistent with 71Ga NMR shift measure- ments [122, 123]. In Ref.[122], Fistul et al. find the 69Ga shift increases at low temperature in both undoped GaAs crystal (the carrier concentration n = 1.5 × 1016 /cm−3) and p-type GaAs doped (p ∼ 1012 /cm−3). They excluded the conduction electrons as the source of the shift because of the low carrier concentration. In our case, the carrier concentration in the semi- insulating GaAs is so low (n ∼ 107 /cm−3) that a Knight shift also seems unreasonable. However, band bending may change the carrier concentration near the surface, making the Knight shift possible. As already discussed in Section 3.1, χPauli from conduction electrons may depend on temperature in GaAs and lead to a temperature dependence of β-nmr resonance shift analogous to the Knight shift in metals. The temperature dependence of the shift in GaAs (Fig. 3.7) appears to be activated with an activation energy comparable to shallow donors like Si (Ei = 5.8 meV[124], corresponding to a temperature of ∼ 70 K). This suggests that, surprisingly, there is a contribution to the shift from free carriers. This is surprising because the carrier density is so low. Despite this, let’s consider the possibility that there is a contribution from the free carrier. In a simple picture, the shift may consist of two parts (as shown in Fig. 3.8): δ = δd + δp (3.8) where δp is a positive shift, analogous to a Knight shift in metal, associated with the free carriers. It exhibits an activated temperature dependence, but it may also contain a constant part in the metallic sample. δd, on the other hand, is a diamagnetic temperature independent shift likely connected with the overall diamagnetism of GaAs, i.e. an orbital shift. Now let’s consider this possibility further. In the semi-insulating GaAs (09-B1) with such low carrier density (107 cm−3), impurities such as Si form isolated energy levels below the conduction band. Some electrons in the impurity levels could be thermally excited to the conduction band. The thermally excited carriers contribute to χPauli which may be related to the 653.3. High Resolution Measurements of β-nmr in GaAs Crystals s48 s49s48s48 s50s48s48 s51s48s48 s45s56s48 s45s52s48 s48 s112 s32s40s84s41 s100 s84 s83s105 s73s111s110s32 s126s55s48s32s75 s32s84s101s109s112s101s114s97s116s117s114s101s32s40s75s41 s32s110s45s71s97s65s115 s32s71s97s65s115s32 s83 s104 s105 s102 s116 s32 s40 s112 s112 s109 s41 s69s61s32s50s56s32s107s101s86 Figure 3.8: The resonance shift may be decomposed into two part: a posi- tive shift δp(T ) related to the free carrier, and the temperature-independent negative shift δb. resonance frequency shift δp. At high temperatures, both χPauli and χd con- tributes to the resonance shift, generating a positive shift δp and a negative shift δd. At 150 K, the electrons start to localize in the impurity levels and χPauli starts to decreases as the carrier concentration decreases. Consider- ing the temperature independent δd contributed by χd, the total resonance shift is getting more negative with temperature decrease. Below 10 K, the electrons are fully localized in the impurity levels, no electrons can be ther- mally excited to the conduction band. δp completely disappears, and there is only the temperature-independent χd contribution to the resonance shift (δd ∼ −80 ppm). The total shift is saturated below 10 K. For the metallic n-GaAs (09-B2), the carrier concentration on the order of ∼ 1018 cm−3 is so high that the impurity band is formed due the heavily doped Si and merged with the conduction band, making the n-GaAs crystal metallic. At ∼ 70 K, the Si donors start to freeze and the conduction elec- tron concentration decreases as temperature decreases. However, there are still conduction electrons at low temperatures because of the impurity band formed by the high Si doping. Using the saturated shift at low tempera- tures in semi-insulating GaAs (09-B1) as δd in the heavily doped n-GaAs (09-B2), the positive shift δp observed in n-GaAs (09-B2) is ∼ 70 ppm at 663.3. High Resolution Measurements of β-nmr in GaAs Crystals room temperature, and ∼ 35 ppm at 5 K, on the same order of the Knight shift observed in the noble metal gold. One can roughly estimate Pauli susceptibility in the heavily Si doped n-GaAs (09-B2) using χPauli = µ2Bg(EF )[15] with g(EF ) the density of states at Fermi energy EF . In the free electron case, valid in the highly metallic n-GaAs, g(EF ) = 3n2EF at T = 0. Pauli susceptibility is roughly estimated to be 0.026 × 10−6 emu/cm3, which is much smaller than Pauli susceptibility in Au. Pauli susceptibility of Au is χPauli = 1.21 × 10−6 emu/cm3, and the Knight shift of 8Li+ in Au is measured to be +73(5) ppm for the substitutional site and +141(4) ppm for the octahedral interstitial sites[116]. However, considering the fact that χPauli in n-GaAs (09-B2) estimated above is two orders of magnitude smaller than χPauli in Au, the coupling constant AHF would also need to be two orders of magnitude larger (which seems unreasonable) unless the carrier content is quite drastically different near the surface. We have no clear explanations for the observed temperature dependent shift in GaAs, but the detailed shift is somewhat sample dependent, so it may be controlled by other factors which we may not control, such as the native oxide on the surface and the surface preparations done by the provider. A clearer picture could be obtained by testing more carefully prepared samples. This would be best done using a GaAs layer grown by MBE on commercial GaAs wafers with a better surface quality control. 3.3.4 Summary In summary, pulsed rf β-nmr provides higher frequency resolution for study- ing the magnetic properties of GaAs. A resonance frequency shift is observed in both SI-GaAs (09-B1) and n-GaAs (09-B2) as a function of temperature. It does not exhibit a Curie temperature dependence, but saturates below 10 K. The resonance shift is likely a combination of temperature-independent δd and temperature dependent Knight shift δKnight. It moves as a func- tion of implantation depth only in SI-GaAs (09-B1). The depth dependence suggests it may be related to surface barrier due to the band-bending. 673.3. High Resolution Measurements of β-nmr in GaAs Crystals Similar temperature dependence of the resonance shift was observed in two commercial GaAs crystals from independent sources. This may indicate that the resonance shift is intrinsic to GaAs. However, the resonance ob- served in the control experiment on n-GaAs (10-B1) (Section 5.2.2) provided by the same company as SI-GaAs (09-B1) shifts to a higher frequency as temperature decreases, in the opposite direction of what is observed in this chapter. Moreover, a careful examination of the resonance in the substrate of Ga1−xMnxAs which is MBE grown pure GaAs on commercial SI-GaAs wafer, does not show a similar temperature dependence (Section 4.4), re- maining a constant within error bars. The small temperature-independent negative shift of the resonance above 150 K seems an intrinsic property of GaAs crystals. However, below 150 K, the magnitude and the direction of the resonance shift are sample dependent. In contrast, the temperature dependence of the resonance width in all GaAs samples is consistent. It is intrinsic to the GaAs crystals that the resonance linewidth is minimum at ∼ 150 K and peaks at ∼ 250 K. Regardless of the source of this shift, these control measurements estab- lish the baseline behavior of the 8Li+ probe in GaAs from which we can assess the effects of proximity to a ferromagnetic layer of Fe and of an injected cur- rent from this layer in Chapter 5. This is primarily important for the results presented in Chapter 5. The resonance observed in Ga1−xMnxAs(Chapter 4) has a shift orders of magnitude larger and is much broader, so that we can neglect the tiny shift in the GaAs substrate and concentrate on the resonance in the magnetic Ga1−xMnxAs layer. 68Chapter 4 β-Detected NMR of Li in Ga1−xMnxAs 4.1 Introduction As discussed in Section 1.2.1, it is widely accepted that ferromagnetism in the dilute magnetic semiconductor Ga1−xMnxAs is driven by coupling be- tween local Mn2+ S = 52 moments mediated by delocalized holes [24, 28]. However, there is a controversy over the properties of delocalized holes for the highest TC compositions—the valence band model vs. the impurity band model. It is thus important to elucidate the magnetic properties of the itiner- ant holes. Some information can be gleaned from tunnelling spectroscopy in specially designed heterostructures[37, 125], while magneto-optical studies probe the polarization of the carriers and their hybridization with the local moments[126, 127]. However, a complementary, atomically resolved probe such as nuclear magnetic resonance (NMR) would provide a more complete picture of the magnetic properties at the atomic level. In this context, NMR senses the average hole contribution through a shift of the resonance, anal- ogous to the Knight shift in a paramagnetic metal[99]. As the material is intrinsically inhomogeneous, an atomically resolved probe also reveals the associated magnetic inhomogeneity, through broadening and structure of the resonance line, for example, in the controversial proposal of magnetic phase separation[50, 51, 52] (more discussions in Section 4.6). As discussed in Section 1.2.1, Ga1−xMnxAs is only available in the form of thin films. Because of signal limitations, conventional NMR cannot gen- erally be used for thin films, but when NMR is detected by the anisotropy of 694.1. Introduction radioactive beta decay (for a β-radioactive NMR nucleus), it is possible to overcome this limitation. In this chapter, we use an implanted spin-polarized beam of 8Li+ to study a 180 nm thick epitaxial film of Ga1−xMnxAs with x = 0.054 (TC = 72 K) using β-nmr. All measurements were carried out in a field of 1.33 T applied normal to the sample surface. Note that the easy magnetization axis of Ga1−xMnxAs is in the plane. A field of 1.33 T is strong enough to rotate the magnetization out of plane and to polarize it along the field. This value of the field was chosen as it allowed a good beam spot. Moreover, this field was found to represent a good compromise in that the magnetic shift of the signal in the Mn doped layer was measurable, while the magnetic broadening and relaxation were not excessive. One of the major advantages of β-nmr using a low–energy ion beam is the possibility to vary the implantation energy by electrostatic deceleration and thus probe the sample as a function of depth (Section 2.2 and 2.3). Such a depth dependent study in a thin film of Ga1−xMnxAs at 50 K (below TC) is discussed in Section 4.3. Section 4.4 presents both resonance (in pulsed rf mode) and spin lattice relaxation data as a function of temperature in the current Ga1−xMnxAs thin film. Only in a few cases has β-nmr been carried out in a ferromagnet[128, 129]. Since this is the first example in a disordered ferromagnet, it was not clear, prior to the experiment, whether the 8Li+ spin relaxation would be slow enough, or the resonance narrow enough, to be able to follow it through the magnetic transition; however, the signals are clearly observable, and the results afford a novel local–probe view of the magnetic state in this impor- tant dilute ferromagnet. The discovery of magnetism in Mn doped GaAs[20], has propelled the field of dilute magnetic semiconductors (DMS) into an extremely active branch of material science over the past decade. Despite extensive inves- tigations, the origin and control of ferromagnetism in Ga1−xMnxAs are still controversial. There is still a debate if Ga1−xMnxAs is magnetically phase separated at low temperature[50, 51, 52]. In Section 4.6, we use low–energy spin–polarized 8Li+ as a local magnetic probe to seek evidence for magnetic 704.2. Sample Preparation and Characterization phase separation in GaAs:Mn. 4.2 Sample Preparation and Characterization The 180 nm Ga1−xMnxAs film was grown by MBE on a 8.5 mm × 6.5 mm semi–insulating (100) GaAs single crystal substrate in a Riber 32 R&D molecular beam epitaxy system and subsequently annealed at 280 oC for 1 hour. More information on the epitaxial growth can be found elsewhere[27]. Low field SQUID magnetometry was used by the grower to determine TC= 72 K, and the Mn site occupancies were determined by c–PIXE and c–RBS to be 74.5% of Mn at Ga substitutional sites, 21.5% Arsenic interstitial sites, and 4% in nonspecific “random” sites[29]. Transport measurements indicate this film is metallic with low temperature resistivity ∼ 30 mΩ-cm. We independently measured the volume magnetization M at 1.33 T using SQUID at AMPEL. The resulting magnetic moment was then corrected for substrate and sample holder contributions and converted to the average volume magnetization using the nominal film thickness (180 nm), as shown in Fig. 4.1. M(T → 0) is on the order expected for full polarization of Mn local moments for the known Mn concentration and thickness. More discussions on the magnetization are in Appendix B. The magnetization M is the order parameter in the ferromagnet[130]. However, because of the high field, M is nonzero even above TC, erasing the symmetry distinction between the ferromagnetic and paramagnetic phases. So the sharp phase transition point TC disappears and the transition is “smoothed out”. Instead of the sharp discontinuity, M changes gradually through TC[130, 131]. Analysis of M(T ) and other thermodynamic quantities using magnetic equations of state[132] and other methods can still be used to determine TC in field (B). In simple ferromagnets, TC(B) is generally an increasing function of B, e.g. the case of Gd[133]. Implantation profiles of the 8Li+ as a function of beam energy (shown in Fig. 4.2) were performed using the SRIM-2006.02[134] Monte Carlo code based on 104 incident ions. Predicted profiles have been found to be reliable for light ions at low energies in a few detailed comparisons[135, 136]. At the 714.3. The Depth Dependence of the Local Magnetic Field in Epitaxial GaAs:Mn s48 s49s48s48 s50s48s48 s51s48s48 s48 s49s53 s77 s97 s103 s110 s101 s116 s105 s122 s97 s116 s105 s111 s110 s32 s40 s101 s109 s117 s47 s99 s109 s51 s41 s84s32s40s75s41 s49s46s51s51s32s84 s32 s32 Figure 4.1: The temperature dependence of volume magnetization M at 1.33 T field. The magnitude of M(T → 0) is of the order expected for full polarization of the Mn local moments for the known Mn concentration and thickness. highest energy (28 keV), near 30% 8Li+stops in the substrate, while at 8 keV (Fig. 4.2b), all the 8Li+should stop in the overlayer, and no substrate signal should be apparent. Because of the sensitivity of the β detection, relatively few ions are re- quired for the measurement. The total implanted fluence of 8Li+ (in ∼4 days of measurement) was on the order of 1012/cm2. Comparison with the effects of much higher energy ions indicates we can expect little or no net effect of the implantation on the macroscopic properties of the sample[137]. This is confirmed by the fact that we found no time dependence in the results over the course of the experiment and between runs on the same sample[138]. 4.3 The Depth Dependence of the Local Magnetic Field in Epitaxial GaAs:Mn In this section, we present β-NMR results of the 8Li+ implanted in a Mn doped GaAs heterostructure, including both resonance (in pulsed rf mode) and spin lattice relaxation results as a function of implantation energy at 50 K (below TC=72 K). Below TC, the Ga1−xMnxAs overlayer is in the 724.3. The Depth Dependence of the Local Magnetic Field in Epitaxial GaAs:Mn s48 s49s48s48 s50s48s48 s51s48s48 s52s48s48 s48s46s48s48 s48s46s48s50 s48s46s48s52 s97s41s32s51s107s101s86 s100s41s32s50s56s107s101s86 s32s71s97s65s115s32s71s97s65s115s58s77s110 s80 s114 s111 s98 s97 s98 s105 s108 s105 s116 s121 s73s109s112s108s97s110s116s97s116s105s111s110s32s100s101s112s116s104s32s40s110s109s41 s99s41s32s49s56s107s101s86 s98s41s32s56s107s101s86 Figure 4.2: The 8Li+ implantation profiles of 8Li+ in Ga1−xMnxAs for var- ious energies simulated by SRIM-2006.02. ferromagnetic state, in which both β-nmr resonance and spin dynamics are very different from the semi-insulating GaAs substrate. We expect a significant contrast between the two layers. 4.3.1 Results and Analysis Fig. 4.3 shows the β-nmr frequency spectrum in the pulsed rf mode observed in the GaAs:Mn/GaAs sample for various implantation energies between 3 keV and 28 keV at 50K (below TC). The observed spectrum consists of two lines, one narrow (width consistent with semi-insulating GaAs) and one much broader and centred at a lower frequency. By examining the system- atic dependence of this composite spectrum on implantation energy, we can assign the main resonance in the 28 keV spectrum (the cyan dots in Fig. 4.3) to the GaAs substrate, as its linewidth is close to that in undoped GaAs[104], and its amplitude decreases upon deceleration of the 8Li+. Remarkably, as the beam is decelerated, we find a broad, but clearly resolved, resonance 734.3. The Depth Dependence of the Local Magnetic Field in Epitaxial GaAs:Mn (e.g. the green triangles in Fig. 4.3) shifted to lower frequency, which we assign to the ferromagnetic Ga1−xMnxAs overlayer. The amplitude of the substrate signal diminishes sharply as the beam energy decreases from 28 keV, indicating that the fraction of 8Li+ stopping in the substrate is decreas- ing. However, both peaks can still be clearly observed when the beam energy is 8 keV (the green triangles in the small right panel of Fig. 4.3), while the broad peak becomes predominant at 3 keV implantation energy (the black squares in Fig. 4.3). We fit the pulsed rf resonances to the function con- sisting of two Lorentzian components (Eqn. (2.17)). In this case, i = mag and sub denotes the broad line in the magnetic Ga1−xMnxAs overlayer and the narrow substrate resonance, respectively. The product of amplitude and width can be approximated as a measure of the peak area. The fit results show that the negatively shifted resonance observed in the overlayer is centred at -770(20) ppm relative to the substrate signal, a shift comparable to Knight shifts of 8Li in ferromagnetically enhanced paramagnetic metals[139, 140]. Like the Knight shift, this shift represents a direct measure of the average spin polarization of the mobile holes, a quantity whose field and temperature dependence is of great interest. We will follow its temperature dependence in Section 4.4 below. Spin lattice relaxation (SLR) data at 50 K are shown in Fig. 4.4. The asymmetry relaxes from the same initial value at both energies. After 8 seconds, the asymmetry in Fig. 4.4a decreases to about 50% of its initial value, while in Fig. 4.4b the asymmetry drops to only 25% , indicating a faster relaxation rate of 8Li+ in the overlayer. The data are fit to a bi- exponential spin relaxation function (Eqn. (2.23)) convoluted with the 4 second beam pulse[141]. In this case, i = sub and mag represents the GaAs substrate and the Ga1−xMnxAs overlayer. Note that the SLR data start at the same initial point, showing no indication of a missing fraction at 50 K in the Mn doped layer. This is rather remarkable as some of the 8Li will stop in the near vicinity of Mn moments (5µB for Mn2+, 4µB for Mn3+[20]) and experience large fields. However, the SLR data show that even these 8Li+, though they may not contribute to the broad line, do not relax very quickly at 1.33 T. 744.3. The Depth Dependence of the Local Magnetic Field in Epitaxial GaAs:Mn s56s49s55s48 s56s49s56s48 s56s49s57s48 s56s50s48s48 s56s50s49s48 s56s50s50s48 s56s49s57s48 s56s50s50s48 s40s97s41s32s51s32s107s101s86 s40s98s41s32s56s32s107s101s86 s40s99s41s32s49s56s32s107s101s86 s70s114s101s113s117s101s110s99s121s32s40s107s72s122s41 s32 s40s100s41s32s50s56s32s107s101s86 Figure 4.3: Implantation energy dependence of the pulsed βNMR spectrum at 50K, below the Curie temperature (72K). The narrow resonance is char- acteristic of the semi-insulating GaAs substrate. The broad line associated with the overlayer is negatively shifted by ∼5kHz. The small panel on the right is the spectrum at low implantation energies shown in a smaller scale. All spectra offset for clarity. 0 2000 4000 6000 8000 0.00 0.05 0.10 b) 8 keV Asy m m et ry Time (ms) a) 28 keV Figure 4.4: Spin Lattice Relaxation (SLR) spectrum at 50K, below the Curie temperature (72K), during and after a 4 second pulse of beam. Li in the magnetic overlayer relaxes much faster than in the nonmagnetic GaAs substrate. 754.3. The Depth Dependence of the Local Magnetic Field in Epitaxial GaAs:Mn As we already discussed in Section 2.4.1, to understand the implanta- tion energy dependence of the resonance amplitudes, we must consider the spin-lattice relaxation as it determines the maximum resonance amplitude (Eqn. (2.15)). In a simple model of the heterostructure, we have two single exponential relaxation rates λsub and λmag for the substrate and the over- layer. Assume that the optical polarizer produces 8Li+ of polarization P0, according to Eqn. (2.15), the dynamic equilibrium value of the polarization is ¯P = Pofsub 1 + λsubτ + Po(1− fsub) 1 + λmagτ , (4.1) where fsub is the fraction of the 8Li+ stopping in the substrate and is energy dependent. The approach to ¯P during beam on period (during time 0-4s) is clearly evident in Fig. 4.4. The maximum resonance amplitude is de- termined by this “baseline” asymmetry under constant beam rate, meaning that if the substrate and overlayer have significantly different spin relaxation rates, one must scale by the ratio of the relaxation rates to get a comparable measure of the amplitude. Based on Eqn. (4.1), we multiply the broad resonance area associated to the magnetic overlayer by (1+λmagτ)/(1 + λsubτ) to account for the fast relaxation in the magnetic thin film layer. The sum of the two resonance peak areas are normalized to 1, and each peak area is accordingly normalized to obtain a measure of fsub and fmag = 1− fsub. The normalized peak area of each component is a measure of the fraction of 8Li+ stopping in the associated layer.These are plotted in Fig. 4.5 and compared to the SRIM prediction. 4.3.2 Discussion The broad line observed in the magnetic Ga1−xMnxAs overlayer is surpris- ing. Since the heterovalent Mn dopants must locally break cubic symmetry, 8Li that stop in sites immediately adjacent to Mn will experience such strong local magnetic fields, and fast spin relaxation, that they will not likely con- tribute to the observed resonance. Such 8Li+ will also experience the largest electric field gradients, and hence the largest quadrupolar splittings. Cubic 764.3. The Depth Dependence of the Local Magnetic Field in Epitaxial GaAs:Mn s53 s49s48 s49s53 s50s48 s50s53 s48s46s48 s48s46s53 s49s46s48 s32s102s95s115s117s98 s32s102s95s109s97s103 s78 s111 s114 s109 s97 s108 s105 s122 s101 s100 s32 s70 s114 s97 s99 s116 s105 s111 s110 s73s109s112s108s97s110s116s97s116s105s111s110s32s69s110s101s114s103s121s32s40s107s101s86s41 s32 s32 Figure 4.5: The portion of Li stopping in the GaAs substrate (circles) com- pared with that stopping in the magnetic overlayer (squares). Open and solid symbols are SRIM simulation and the experimental results at 50 K, respectively. 774.3. The Depth Dependence of the Local Magnetic Field in Epitaxial GaAs:Mn symmetry will be restored upon averaging over all sites, but a distribution of unresolved quadrupolar interactions may contribute to the width of the resonance (Section 2.4.1). Fig. 4.5 clearly shows that there is disagreement between the data and the SRIM simulation, with the substrate fraction always exceeding the predicted value. For example, according to the simulation, all the Li should stop in the overlayer at 8 keV (Fig. 4.2b, while there is a clear sharp peak in the experimental spectrum (Fig. 4.3b, showing that as much as ∼15% of the 8Li+ experiences a substrate-like environment at this energy. We now discuss possible origins of the discrepancy between the implan- tation energy dependence of the resonances and the SRIM prediction. First we note that the thickness of the overlayer is accurate to better than 10% from calibrations of the growth rate. Similarly, the film is expected to be uniformly thick even over the mm size of the beam spot, so neither an over- estimate of the film thickness, nor bare patches of substrate are likely origins for the inconsistency. One possible explanation is that the overlayer is not microscopically homogeneous, i.e. it may contain Mn deficient regions. Yu et al. have argued that MnI out-diffuses and forms a Mn-rich oxide layer on the surface, leaving Mn depleted regions behind[27]. Another possibility is that the overlayer, though ferromagnetic, is magnetically phase-separated into regions that remain paramagnetic (Mn moments fast fluctuating) and magnetically frozen regions[50]. However, both models have difficulty ex- plaining the occurrence of two distinct environments instead of a continuous range. The nonmagnetic (or Mn deficient) regions must be rather large (so that their boundaries account for at most a small fraction of the area), but rather sparse (since the fraction is small), which seems unlikely. The clearest source for two well-resolved environments is the engineered inhomogeneity in the growth direction which has a single sharp boundary. In this regard, we note that the SRIM prediction may significantly underestimate the stopping range since the 〈100〉 direction in GaAs is a channeling direction (Section 2.3). It is known that implanted ions can penetrate much further in specific crystal directions where there are long open channels in the structure[142] and SRIM does not account for this[94]. SRIM is expected to be accurate to 784.4. Temperature Dependence of in Ga1−xMnxAs the level of a few percent over a wide range of implantation conditions[143], but, this is not so well tested at the relatively low energies used here. We will come back to the magnetic phase separation problem later in Section 4.6. In summary, we find both spin lattice relaxation and resonance signals of 8Li+ in Ga1−xMnxAs in the ferromagnetic state at 50 K and in the GaAs sub- strate. Two resonances are clearly resolved in the pulsed rf mode resonance data. The narrow resonance is associated from the GaAs substrate, and the other one from the magnetic Ga1−xMnxAs overlayer is much broader and negatively shifted to a lower frequency. We also observe two relaxing compo- nents in SLR data. The fast relaxing component is assigned to the magnetic Ga1−xMnxAs layer, and the slower relaxation to the GaAs substrate. An unexpected implantation energy dependence is found in the pulsed rf mode resonance, with a substrate signal persisting down to low implantation en- ergies. We attribute this to implantation channeling of 8Li. This could be tested by rotating the sample by a small angle, so that the probe 8Li+ are not incident along the GaAs channeling direction 〈100〉. In this case, the amplitude of the narrow resonance should be greatly reduced if it is the signal from the substrate. However, this would require a new sample holder that would allow the sample to be rotated. We will follow the evolution of the signal in Ga1−xMnxAs in temperature in next section. 4.4 Temperature Dependence of in Ga1−xMnxAs Following the last section, we study the β-nmr spectra of 8Li+ in the Ga1−xMnxAs thin film at 8 keV implantation energy as a function of tem- perature across the ferromagnetic transition. Both pulsed rf resonance and spin lattice relaxation data are presented and the magnetic properties of the Ga1−xMnxAs film are discussed. Since this is the first study on the temper- ature dependence of β-nmr resonances through TC in a ferromagnet, it will be an important reference point to compare with other ferromagnets. 794.4. Temperature Dependence of in Ga1−xMnxAs 8175 8190 8205 8220 253K 100K 50K 30K ν (kHz) 177K Figure 4.6: Temperature dependence of the β-nmr spectra (vertically off- set for clarity) of 8Li+ in Ga1−xMnxAs with the implantation energy of 8 keV. 8Li in the substrate produces the narrow resonance while the broad resonance originates in the Ga1−xMnxAs overlayer (See Section 4.3). 4.4.1 Resonance Spectra The resonance spectra of 8Li+ at 8 keV implantation energy and 1.33 Tesla are shown for various temperatures in Fig. 4.6. At 50 K, the spectrum is the same as that reported in Section 4.3[144], with both broad (overlayer) and narrow (substrate) resonances. There is no evidence of quadrupolar splittings in any of the spectra[145], consistent with the cubic 8Li+ sites known in GaAs (See 3.2). At the highest temperature, the two resonances are unresolved, and there is no evidence of the broad peak. But as T is reduced, the broad line shifts out of the narrow resonance and broadens continuously, becoming too broad to observe with the limited radio frequency (rf) magnetic field of the broadband spectrometer (amplitude, H1 ≤ 100µT) below about 30 K. In dilute magnetic alloys, the lineshape is expected to be approximately Lorentzian, though for concentrations at the level of a few percent, there are some deviations[146]. We fit the data to the sum of two Lorentzians (curves in Fig. 4.6) using Eqn. (2.17), with i = mag and sub denoting the 804.4. Temperature Dependence of in Ga1−xMnxAs broad line in the overlayer and the narrow substrate resonance, respectively in this case. The position of the substrate resonance νsub was constrained to be independent of temperature, consistent with measurements in semi- insulating GaAs (Section 3.2). Above 250 K and below 30 K, the two lines are unresolved, so a single Lorentzian was used (Eqn. (2.16)). The results of this analysis are summarized in Fig. 4.7. As is evident in the raw data (Fig. 4.6), the broad line shifts towards lower frequency and broadens as temperature is reduced. The slight temperature dependence of the amplitude of the substrate line Asub, is consistent with previous mea- surements in semi-insulating GaAs[104]. It may be due to 8Li stopping in noncubic sites produced by implantation–related damage, e.g. arsenic vacan- cies, as has been observed for 12B implantation in ZnSe[114]. The amplitude of the broad resonance Amag decreases as the line broadens, as expected for a constant applied rf field. There is no evidence of a sharp change of ei- ther amplitude through TC, nor is there a sharp change of the total area of the spectrum at TC. Continuity of the amplitude through TC is in contrast to the conventional NMR “wipeout effect” that often accompanies such a transition[147]. Using the substrate frequency νsub as the reference, we measure the average internal field Bint sensed by the 8Li in the Mn doped layer, Bint by the raw shift of the resonance ∆ν using Eqn. (2.12) with Bint = Btot − Bo and Bo the applied external field. We discuss the various contributions to Btot in Section 4.4.3. We now turn to the width of the overlayer resonance. The independent Lorentzian broadening combines linearly (Section 2.4.1), so that we decom- pose the linewidth into different contributions σmag = σsub + σMn, where σMn represents the additional broadening due to Mn doping. As shown in the middle panel of Fig. 4.7, σsub is approximately constant below 200K, therefore the increase in σmag at low temperature is due to the Mn dop- ing. As the shift of the broad line represents the average total field in the Ga1−xMnxAs layer, the broadening represents a distribution of this field; however, there can be other nonmagnetic sources of broadening. In particu- lar, as 8Li is quadrupolar, the width is sensitive to a distribution of electric 814.4. Temperature Dependence of in Ga1−xMnxAs s48 s53s48 s49s48s48 s49s53s48 s50s48s48 s50s53s48 s56s49s57s48 s56s50s48s48 s97s41 s32 s40 s107 s72 s122 s41 s84s101s109s112s101s114s97s116s117s114s101s32s40s75s41 s48 s54 s49s50 s98s41 s84 s99 s32 s40 s107 s72 s122 s41 s48s46s48s48 s48s46s48s49 s32 s65 s99s41 Figure 4.7: The amplitude A (top panel), linewidth σ (middle panel) and position ν (bottom panel) as a function of temperature from Lorentzian fits to the resonance spectra of 8Li implanted at 8 keV in an applied field of 1.33 T. The open squares refer to the narrow substrate resonance, the closed circles to the broad line from the Mn doped layer, and the filled triangles to single Lorentzian fits. The width and position of the substrate line do not change substantially with temperature, in contrast to the resonance from the magnetic layer. The broken vertical line indicates TC. 824.4. Temperature Dependence of in Ga1−xMnxAs field gradients caused by the static charge disorder produced by ionized Mn acceptors. The linear combination of the quadrupolar (σq) and magnetic broadening (σM ): σMn = σq +σm achieves a good fit (see Section 4.4.3). σq is expected to be independent of T when 8Li+ is not mobile, as is the case below room temperature. 4.4.2 Spin Lattice Relaxation In order to better understand the resonance data and to probe the magnetic dynamics in Ga1−xMnxAs, we performed spin lattice relaxation experiments under the same conditions as the resonances presented above. As expected from the two line spectra, we find a two component relaxation of the 8Li+ nu- clear spin polarization. At 8 keV implantation energy, we find a small almost non-relaxing component, consistent with slow relaxation in the GaAs sub- strate, and a large, much faster relaxing component from the Ga1−xMnxAs. As in Section 4.3, the relaxation is fit to a simple bi-exponential form (Eqn. (2.23)) for the polarization P at time t after implantation. with Ai is the initial amplitude for each component, and λi = 1/T i1 the corresponding re- laxation rate, and i = mag and sub denoting the Ga1−xMnxAs layer and the GaAs substrate. We fit the experimental data to the convolution of P (t) with the beam pulse to extract the relaxation rate λmag(T ) at 1.33 Tesla[148]. Examples of the fits are shown in the top panel of Fig. 4.8. That the 250 K relaxation spectrum lies consistently below the 30 K data is direct evidence that the relaxation is faster at 250 K. The data shown do not appear to have the same total amplitude, likely because there is some very fast relaxation at 250 K which is not captured with the experimental time resolution. Though the fits are reasonably good, this behaviour may indicate that the relaxation is not a simple exponential as in Eq. (2.23). In fact, in an inhomogeneous system, one expects a distribution of relaxation rates corresponding to the distribution of static fields evidenced by the line broadening. Since the polarization of 8Li in the beam is constant, we fixed the amplitudes in the fits, accounting for the full variation in temperature with only the relaxation rates. Thus λmag extracted from the fits represents 834.4. Temperature Dependence of in Ga1−xMnxAs s48 s49s48s48 s50s48s48 s51s48s48 s48 s50s48 s52s48 s51s48 s54s48 s57s48 s54s46s48 s54s46s53 s55s46s48 s48 s52 s56 s48s46s48s48 s48s46s48s52 s48s46s48s56 s65 s115 s121 s109 s109 s101 s116 s114 s121 s84s105s109s101s32s40s115s41 s50s53s48s32s75 s51s48s32s75 s32 s32 s32 s84s99 s32 s109 s97 s103 s40 s115 s45 s49 s41 s32 s84s101s109s112s101s114s97s116s117s114s101s32s40s75s41 s32 s32 s84s99 Figure 4.8: Top: Time dependence of the average 8Li+ spin polarization during and after the beam pulse at 30K (below TC) and at 250 K (above TC) at 8 keV beam energy in the field of 1.33 T. The relaxation rate is faster at 250 K than at 30 K. Bottom: The spin-lattice relaxation rate λmag in the overlayer as a function of temperature. The increase in λmag above 150K is consistent with an increase in semi-insulating GaAs[149] and may be due to the onset of the 8Li+ site change. Inset: An enlarged plot showing a slight enhancement of λmag in the vicinity of TC, in contrast to the divergence expected from critical slowing down of spin fluctuations at the transition. an average relaxation rate for 8Li+ in the Ga1−xMnxAs layer. While λsub varies with T , it remains much smaller than λmag for all temperatures. The temperature dependence of λmag is shown in the bottom panel of Fig. 4.8. Its behavior is very different from that of a conventional ferro- magnet e.g. Fe or Ni[150]. For conventional ferromagnetic metals in the paramagnetic state above TC, the spin lattice relaxation rate λ decreases with increasing temperature since the spins fluctuate faster. Far below TC, the spins are frozen and the spectral density of the spin fluctuations de- creases to zero as temperature decreases to zero. Therefore λ decreases to zero with temperature. In the critical region (near TC), λ diverges[150], re- 844.4. Temperature Dependence of in Ga1−xMnxAs flecting the critical slowing down of spin fluctuations as TC is approached. Compared with the conventional ferromagnets, λ in Ga1−xMnxAs behaves very differently. The most obvious feature is the substantial increase in λmag above 200 K. Such an increase is unexpected for a simple paramag- net which naively, should exhibit a monotonic decrease of the spin relax- ation rate above TC as spin fluctuations become progressively faster with increasing temperature. The increase, however, may be related to a similar increase[149] found in semi-insulating GaAs that is thought to be due to a 8Li+ site change[104, 108], see also Section 3.2. Enhanced relaxation could result from a stronger hyperfine coupling in the high temperature site, or, if the site change is due to the onset of interstitial 8Li+ diffusion, to the for- mation of Mn–Li defect complexes[151]. In this case, the 8Li+ may diffuse to the substitutional Mn2+ ion (which is effectively negatively charged since it replaces Ga3+) and become trapped. In close proximity to the Mn trap, the 8Li+ would have a strong coupling to the Mn spin and relax quickly. This diffusion–trapping behavior is observed in µSR experiments, e.g. in aluminum[110] and iron[152, 153]. The high temperature increase of λmag accounts in part for the disappearance of the broad resonance at higher tem- perature. λmag also increases at the lowest temperature, in contrast to the behavior of a homogeneous ferromagnet. This may be due to some Mn spins remaining paramagnetic well below TC making a Curie–law contribution to λmag. Between these limits, λmag is relatively constant but exhibits a slight peak near TC inset of Fig. 4.8 bottom panel, where critical slowing down of the Mn moments should yield a divergence in the relaxation rate[150]. While the critical region is broadened by the applied field, as well as the mi- croscopic inhomogeneity of the alloy, e.g. as in La0.67Ca0.33MnO3[148], the relatively weak temperature dependence through TC is still surprising. The magnitude of λmag is large, not only much larger than in undoped GaAs, but also ∼ 10 times the rate in metallic Ag, consistent with it originating in the magnetism of Ga1−xMnxAs. In general, λ is a measure of the spectral density of (transverse) magnetic fluctuations at the NMR frequency. The absence of a peak suggests that the spin dynamics that dominates the 8Li+ relaxation does not change dramati- 854.4. Temperature Dependence of in Ga1−xMnxAs cally through the formation of a static moment, in contrast to homogeneous metallic[150] or semiconducting[154] ferromagnets. Neither does λ follow the linear (Korringa) temperature dependence characteristic of metals[139, 141] that might be anticipated if the relaxation was predominantly due to in- teraction with a degenerate fluid of delocalized holes in this metallic alloy. However, it is similar to what is found in doped nonmagnetic semiconductors when the Fermi level lies in a narrow impurity band[155, 156, 157]. 4.4.3 Analysis and Discussion We now extend the analysis presented above beginning with the resonance shift. The difference in the average magnetic field between the overlayer and the substrate Bint is due to the Mn doping, so we decompose the total field into various contributions from the surrounding Mn doped magnetized layer and the applied field Bo, Btot = Bo +Bint (4.2) = Bo + (Bdemag +BLor +Bdip +Bloc) assuming for simplicity that all contributions are parallel at high applied fields. Here Bdemag is the demagnetization field determined by the macro- scopic shape of the sample, and BLor is the field due to the empty Lorentz cavity that divides the sample into a local region which must be treated atomically from the rest of the sample which may be treated as a homoge- neous magnetic continuum. Bdip is the net field from the atomic magnetic dipoles inside the Lorentz sphere. Bloc is the hyperfine contact field from the atomic environment within the Lorentz cavity. Bdip summarizes the dipolar fields inside the Lorentz cavity: Bdip = ∑ i 3(µi · ri)ri − r2iµi r5i (4.3) where µi is the dipole moment at each lattice site ri and the sum is over the Lorentz cavity. In high field, all dipoles are aligned parallel to the field (e.g. 864.4. Temperature Dependence of in Ga1−xMnxAs along z axis), assuming that they are of the same magnitude µ. Therefore, Bdip at the center due to all the dipoles inside the Lorentz sphere is: Bdip = µ ∑ i 3z2i − r2i r5i = µ ∑ i 2z2i − x2i − y2i r5i (4.4) The x, y, z directions are equivalent due to the symmetry of the zincblende cubic lattice and the sphere, thus ∑ i z2i r5i = ∑ i x2i r5i = ∑ i y2i r5i (4.5) Substituting Eqn. (4.5) into Eqn. (4.4), we obtain Bdip = 0, i.e. the net dipole field is zero, so it can not contribute to a shift of the resonance. In this dilute magnetic material, the Mn concentration is 5.4%, corresponding to about one Mn ion in every 5 GaAs unit cells. The dipole field at any particular 8Li+ site (especially those close to the Mn moments) will not be zero, since the surrounding Mn moments are generally not cubic. However, the Mn moments are randomly distributed over the Ga1−xMnxAs thin film, so that the 8Li+ site is on average in a site of cubic symmetry with respect to the Mn moments, therefore Bdip is averaged out to be zero when summing over the whole film. Note that the dipole field will still contribute to the width of the resonance, see Eqn. (4.11) below. The sum of Bdemag and BLor is defined as the continuum contribution to the internal field: Bcont = Bdemag +BLor (4.6) Bint can be written as: Bint = Btot −Bo = γ(νmag − νsub) (4.7) = Bcont +Bloc Bloc the local field from the atomic environment within the Lorentz cavity, including the contact hyperfine interaction between mobile holes and the probe nucleus that gives rise, for example, to the Knight shift in metals[115]. 874.4. Temperature Dependence of in Ga1−xMnxAs It is Bloc that is of interest as a measure of the polarization of the delocalized holes. At the Mn concentration of this sample, there is about one Mn ion per 5 GaAs unit cells (cubic lattice constant ∼ 5.7 ˚A[20]), so there is no difficulty defining a Lorentz cavity much smaller than the film thickness outside of which the Ga1−xMnxAs can be treated as a continuum. To an excellent approximation, a thin film of uniform thickness in a perpendicular magnetic field has the maximal demagnetizing field, Bdemag = −4piM (cgs), where M is the continuum magnetization, while for a spherical Lorentz cavity[115], BLor = (4pi/3)M . We use the M(T ) measured in SQUID (Fig. 4.1) to account for these contributions. The continuum field Bcont is plotted in Fig. 4.9 together with the measured Bint = Btot−Bo for comparison. In using the substrate frequency νsub as a measure of Bo, we have neglected any chemical shift of the 8Li in GaAs. The assumption is valid because the shift of 8Li in bulk GaAs relative to 8Li in MgO at room temperature is less than 10 ppm (Section 3.3.2.2). We have also assumed that the experimentally determined M is not contaminated by contributions from nonuniformity of the sample, such as impurity phases, e.g. occurring at either the surface of the film or at the interface with the substrate. This is reasonable as the measured M is consistent with the literature for films of this composition[158]. From Eq. (4.8), Bloc = Bint −Bcont, (4.8) so that the small observed value of Bint (Fig. 4.9) implies Bloc must oppose and nearly cancel Bcont, i.e. at low temperature Bloc is on the order of +150 G. We use Eqn. (4.8) to calculate Bloc(T ) and plot it as a function of M(T ) in Fig. 4.10, together with the shift Bint and linewidth σMn. The clear correlation between Bloc and M is embodied in the linear fit Bloc = (7.78± 0.09)×M [G] − (3± 1) shown in the top panel of Fig. 4.10. This linearity is not surprising, since Bloc is predominantly determined by the large contribution of Bcont (proportional to M) which is ∼ 15 times the size of Bint. The 8Li site is cubic on average, so only isotropic contributions to the average Bloc will be nonzero[159]. Such fields arise from the contact 884.4. Temperature Dependence of in Ga1−xMnxAs s48 s53s48 s49s48s48 s49s53s48 s45s49s54s48 s45s56s48 s48 s45s49s54s48 s45s56s48 s48 s84 s99 s32s66 s105s110s116 s32s66 s99s111s110s116 s66 s105 s110 s116 s32 s40 s71 s41 s84s32s40s75s41 s66 s99 s111 s110 s116 s32 s40 s71 s41 s32 Figure 4.9: A comparison of Bint = Btot−Bo (solid black triangles) and the continuum internal field Bcont = −83 piM (open red circles). The difference of these indicates that the local field is substantial and nearly cancels Bcont. hyperfine interaction, here due to a mixing of the unoccupied 8Li 2s orbital with partly occupied electronic states of the surroundings, principally the delocalized holes. In this case, Bloc should scale with the hole magnetization, Mh, rather than the full magnetization M , i.e. Bloc = ( AHF NAµB ) Mh (4.9) where NA is the Avogadro’s number, µB is the Bohr magneton and AHF is the hyperfine coupling constant. In paramagnetic metals this is usually stated as Bloc ∝ χ, the spin susceptibility of the conduction band. Instead, we express Bloc in terms of the field–cooled M to avoid the nonlinearity (hysteresis) in M(H) below TC. The total macroscopic M = Mh + MMn, where the dominant term is MMn the magnetization due to the Mn2+ local moments, and Mh is predicted to be negative, and much smaller on the order of a few percent of M [160]. While we have no independent measure of Mh, the strong coupling between the holes and Mn moments suggests that Mh(T ) should follow the temperature dependence of M(T ). Assuming Mh is ∼ 1 % of M , as theory suggests[28], the coupling A = −160 ± 2 kG/µB is much stronger than in metals such as Ag (20.6 kG/µB)[161, 162]. 894.4. Temperature Dependence of in Ga1−xMnxAs While Bloc is evidently positive, Mh is predicted to be negative[160], so AHF is also negative. Negative AHF is unexpected from a simple picture where it is due to hybridization of the Li 2s orbital with the surrounding GaAs derived valence band. Li is also not likely to exhibit negative AHF from “core polarization”[163]. For 8Li+ negative AHF does, however, have precedent in some transition metals where the Fermi level falls in the d band (Pd [139], Pt[140] as well as ferromagnetic Ni[128]). Here a negative s–d coupling arises from the d band wavefunction’s behaviour at the interstitial position[164, 165]. In Ga1−xMnxAs negative AHF may similarly originate in the Mn derived impurity band picture, where the holes have Mn d orbital character. However, detailed calculations for interstitial Li+ in both pure and doped GaAs would be necessary to put such a conclusion on a firm footing. A more stringent test of whether Mh(T ) is simply proportional to M(T ) comes from considering the raw field shift Bint which represents the bal- ance between two nearly cancelling terms, the continuum field that cer- tainly scales with the average M(T ) and Bloc which may have a different T dependence. In the middle panel of Fig. 4.10, Bint is plotted vs. M , demonstrating a linear relationship (−0.31 ± 0.03) × M − (5.2 ± 0.3) that persists through TC but breaks down at the lowest temperature (30 K), in- dicating that, well into the ferromagnetic state, the role of the delocalized holes is changing, possibly as temperature falls into the range of the impu- rity bandwidth. Alternatively, this deviation could be related to the onset of superparamagnetic effects seen in field–effect heterostructures[51]. which may also lead to the observed increase in the spin relaxation at low T (Fig. 4.8). We now consider the temperature dependence of the linewidth. Assum- ing the broadening of the resonance in the Ga1−xMnxAs layer is a linear com- bination of a temperature independent quadrupolar broadening (σq) from charge disorder and a magnetic broadening that scales with magnetization (σm = αM): σMn = σq + (αM) (4.10) 904.4. Temperature Dependence of in Ga1−xMnxAs s45s50s48 s45s49s48 s48 s48 s49s48s48 s97s41 s32 s66 s108 s111 s99 s32 s40 s71 s41 s48 s53 s49s48 s49s53 s50s48 s48 s52 s56 s99s41 s77 s110 s32 s40 s107 s72 s122 s41 s77s97s103s110s101s116s105s122s97s116s105s111s110s32s40s101s109s117s47s99s109 s51 s41 s98s41 s66 s105 s110 s116 s32 s40 s71 s41 s32 s84 s67 s32 s32 Figure 4.10: Top: The local field Bloc after demagnetization correction as a function of the volume magnetization M . The vertical intercept appears slightly different from zero. This is likely due to a slight uncertainty in the background correction for the SQUID measurement of M . Middle: The raw field shift Bint as a function of volume magnetization M . The nonlinearity at low temperature indicates Bloc is not simply proportional to the mea- sured bulk magnetization. Bottom: The excess linewidth σMn as a linear function of M fit to Eq. (4.10). The temperature independent quadrupolar broadening σq is found to be 2.7±0.5 kHz. 914.4. Temperature Dependence of in Ga1−xMnxAs We fit σMn to Eq. (4.10) as shown in the bottom panel of Fig. 4.10, and find the quadrupolar broadening σq is 2.7 ± 0.5 kHz and α = 0.20 ± 0.06 kHz/(emu/cm3). Due to the randomly located Mn2+ local moments, we expect a distribution in the local magnetic field at the 8Li site that will thus give rise to an inhomogeneous broadening of the line that scales with MMn (or practically with M). Such a broadening is well established in the NMR of dilute magnetic alloys[166]. The observed width indicates the local magnetic field distribution is relatively broad in the sense that its width is comparable to its average (the shift), e.g. at the highest M (lowest T ), σm at the highest magnetization is ∼ 8.05 kHz (corresponding to ∼ 13 G), comparable to the shift Bint in the middle panel of Fig. 4.10. Using the dilute limit result of Ref. [146], we can quantitatively estimate the broadening due to the MnGa dipolar fields σdip, neglecting interstitial Mn and any inhomogeneous polarization of the mobile holes (RKKY oscillations): σdip = 8pi 9 √ 3 ρcγ〈m〉 (4.11) where ρ is the density of sites available to the impurity (Mn in this case), c is the occupation probability of any given site, γ is the gyromagnetic ratio of 8Li+ and 〈m〉 is the average impurity moment. In the case of Ga1−xMnxAs, ρc〈m〉 = M . Therefore Eqn. (4.11) becomes: σdip = 8pi 9 √ 3 γM (4.12) Assuming M ≈ MMn, we estimate the linewidth to be ∼ 22.3 kHz at 30 K. Alternatively, this yields an estimate for the parameter α = 1.02 for coupling to M of the substitutional Mn, substantially larger than the fit value in the bottom panel of Fig. 4.10. This discrepancy is likely a consequence of the relatively high concentration (∼ 5%), where the dilute limit expression overestimates the broadening, and the magnetic compensating effect of the interstitial Mn[28]. Note that neutron reflectometry has shown there may be a gradient in the interstitial Mn concentration through the film[167], which may thus cause a depth dependence of the 8Li+ resonance. 924.5. The Effect of Magnetic Field on the β-nmr Spectrum of 8Li+ in Ga1−xMnxAs 4.4.4 Summary We have studied the magnetic properties of an epitaxially grown Ga1−xMnxAs thin film, a dilute ferromagnetic semiconductor, with low energy implanted 8Li+, a β-nmr local magnetic probe. We clearly resolve resonances from both the nonmagnetic GaAs substrate and surprisingly from the magnetic film. The temperature dependence of the resonance position in the film indicates that the hole contribution to the magnetization scales with the macroscopic magnetization through TC but then deviates below ∼ 40 K. The hyperfine coupling constant of 8Li+ in Ga1−xMnxAs is unexpectedly found to be negative, which may indicate the Fermi level falls into a Mn derived impurity band. The spin relaxation rate shows a small enhancement at TC and does not follow the Korringa’s Law that might be expected for this metallic alloy. This may also indicate that delocalized holes are from a Mn derived impurity band in Ga1−xMnxAs. 4.5 The Effect of Magnetic Field on the β-nmr Spectrum of 8Li+ in Ga1−xMnxAs In the last section, we observed the 8Li+ resonance spectrum in Ga1−xMnxAs consisting of two distinct resonances at 50 K in the field of 1.3 T. The narrow resonance is from the GaAs substrate, while the broad resonance is associated with the magnetic Ga1−xMnxAs layer and shifts to a lower frequency. In this section, we present resonance data in pulsed rf mode to study the effect of the external field on the β-nmr spectrum of 8Li+ in Ga1−xMnxAs thin film. The resonance data were taken in 3 different fields at 50 K with the beam energy of 8 keV under the same conditions (Fig. 4.11). Two resonance components are clearly resolved. The broad resonance shifts negatively out of the narrow resonance and broadens as the magnetic field increases. We fit the data to the sum of two Lorentzians (Eqn. (2.17)). Because 8Li+ resonate at different frequency (Eqn. (2.9)), we convert the frequency into frequency shift with respect to the position of the narrow resonance ν − νsub, so that 934.5. The Effect of Magnetic Field on the β-nmr Spectrum of 8Li+ in Ga1−xMnxAs s45s52s48 s45s50s48 s48 s50s48 s50s46s50s32s84 s83s104s105s102s116s32s40s107s72s122s41 s49s46s51s32s84 s53s48s48s48s32s71 Figure 4.11: Field dependence of 8Li+ resonance spectra in Ga1−xMnxAs with implantation energy 8 keV at 50 K below TC (TC= 72 K). Spectra are offset for clarity. 944.5. The Effect of Magnetic Field on the β-nmr Spectrum of 8Li+ in Ga1−xMnxAs s48 s49 s50 s45s49s48 s45s53 s48 s48 s49s48 s50s48 s83 s104 s105 s102 s116 s32 s40 s107 s72 s122 s41 s77s97s103s110s101s116s105s99s32s70s105s101s108s100s32s40s84s41 s32 s115s117s98 s32 s77s110 s32 s77 s110 s32 s40 s107 s72 s122 s41 s32 s32 s32 Figure 4.12: The analysis results of β-nmr spectra of 8Li+ with 8 keV at 50 K for various fields. Bottom panel: The raw frequency shift linearly scales with the external field. Top panel: The linewidth in the magnetic Ga1−xMnxAs overlayer σmag and in the GaAs substrate σsub as a function of the external field B. we can plot the resonance spectra of three magnetic fields in Fig. 4.11. As shown in Fig. 4.12, the broad resonance in the spectrum measured at 0.5 T is almost merged into the narrow resonance. Its presence is only evident by the small asymmetry of the narrow resonance at lower frequency. For the spectrum at 2.2 T, the resonance in the Ga1−xMnxAs layer is broadened by the magnetic field and approaches our detection limit, so that the baseline of the spectrum is not defined very clearly. These effects result in large errorbars in the fit results shown in Fig. 4.12. The fit results are summarized in Fig. 4.12 and we follow the analysis in Section 4.4. The resonance frequency shift ∆ν is calculated using Eqn. (2.12) with the substrate frequency νsub as the reference. The magnetic 954.5. The Effect of Magnetic Field on the β-nmr Spectrum of 8Li+ in Ga1−xMnxAs origin of the resonance shift is confirmed by the linearity of the frequency shift on the external field Bo: (−0.09±1)+(−5.0±0.9)×Bo. The y-intercept ((−0.09± 1) kHz/T) is close to zero, indicating that there is no additional orbital coupling in the Ga1−xMnxAs overlayer. Recall that the internal magnetic field Bint = Btot−Bo linearly depends on the bulk magnetizationM : Bint = (−0.31±0.03)×M−(5.2±0.3) (Section 4.4.3). Using χ the volume susceptibility χ = ∂M/∂Bo, we assume that the bulk magnetization of the Ga1−xMnxAs overlayer is a linear function of the external magnetic field M = χBo + Mo and Mo is a constant. It is natural that in a ferromagnet, the bulk magnetization does not vanish when the external field is zero once the material is magnetized. We could extract from both linear relations that χ = 26 ± 5 and Mo = −16 ± 7 T. Using the resulting volume susceptibility χ, the bulk magnetization M at 50 K and 1.33 T can be estimated as 18 ± 9 emu/cm3, consistent within error bars with the experimental value measured by SQUID (Section 4.2). The linewidth of the GaAs substrate σsub shown in the top panel of Fig. 4.12 is approximately a constant within errorbars, independent of the magnetic field. The nonmagnetic broadening in the GaAs substrate could be quadrupolar broadening, which is due to the small quadrupole moment of 8Li+. The quadrupole splitting resulting from EFG may not be resolved in the spectrum, but goes into the resonance broadening (Section 2.4.1.1). As already discussed in Section 4.4, the linewidths of Lorentzian lineshape add up linearly. Similar to Eqn. (4.10), the linewidth of the broad resonance σmag shown in Fig. 4.12 is fit to a linear relation of the external magnetic field Bo σmag = σq+(α′Bo). The fit line is (1±4)+(5±3)×Bo. Considering the linear relation between the magnetization and the magnetic field M = χBo+Mo assumed above and using the susceptibility χ = 26±5 we extracted from the analysis of the shift, we calculate α defined in Eqn. (4.10) α = α′/χ = 0.2± 0.1 kHz/(emu/cm3). This value is consistent within errorbars with the value (α = 0.2±0.06 kHz/(emu/cm3) we got from the temperature dependence data (Section 4.4.3). 964.6. Magnetic Phase Separation Problem 4.6 Magnetic Phase Separation Problem We now return to the question of phase separation. Based on low energy µSR (LEµSR) experiments, it was proposed that the ferromagnetic state is nanoscopically separated into comparable volumes of ferromagnetic and paramagnetic phases[50]. In contrast, Dunsiger et al. also using LEµSR, found no evidence for phase separation in their samples[52]. To address this controversy directly, it is essential to use a local probe, such as 8Li+ to look for evidence of phase separation. In the pulsed rf data presented in Section 4.4.1, the single broad reso- nance in the overlayer shows no indication of this inhomogeneity below TC. But unlike LEµSR, we lack an absolute calibration of the resonance ampli- tude which depends on a combination of factors, including the spin lattice relaxation rate (1/T1), the resonance linewidth, and details of the radio fre- quency (rf) magnetic field used to observe it. Therefore, from the data of Fig. 4.6, we cannot put a quantitative limit on the existence of other phases. However, with high enough rf power, the resonance collected in the con- tinuous wave (CW) mode may be saturated, providing a means to calibrate the full amplitude. In this section, we analyze the amplitudes from both pulsed and continuous wave (CW) rf measurements, and we conclude that there is no evidence in our data to support phase separation. 4.6.1 Further Analysis on the Amplitude of the Pulsed RF Resonance We already discussed in Section 2.4.1.2 that, in the pulsed mode, the res- onance data is the step in the polarization caused by the rf pulse at that frequency, so there is no direct information in the baseline on the steady state polarization ( ¯P ) that still determines the overall resonance amplitude. Using the amplitudes from the Lorentzian fits in Section 4.4.1, we do fur- ther analysis on the amplitude. We separately integrate the narrow and broad components to yield the integrated amplitudes Aint shown in Fig. 4.13 top panel. Note the substrate and overlayer amplitudes are essentially equal below 150 K before the relaxation rate λT = 1/T1 is taken into con- 974.6. Magnetic Phase Separation Problem s48 s49s48s48 s50s48s48 s51s48s48 s48s46s48s48 s48s46s48s53 s48s46s49s48 s32s65 s105s110s116 s115s117s98 s32s65 s105s110s116 s109s97s103 s32s65 s105s110s116 s116s111s116 s65 s105 s110 s116 s84s101s109s112s101s114s97s116s117s114s101s32s40s75s41 s84 s67 s48 s49s48s48 s50s48s48 s51s48s48 s48s46s48 s48s46s50 s48s46s52 s84 s67 s32s65 s110s111s114s109 s115s117s98 s32s65 s110s111s114s109 s109s97s103 s32s65 s110s111s114s109 s116s111s116 s65 s110 s111 s114 s109 s84s101s109s112s101s114s97s116s117s114s101s32s40s75s41 Figure 4.13: Top: Integrated amplitudes Aint from the pulsed rf data as a function of temperature. The total integrated amplitude Ainttot is constant below 150 K except at 6 K where the resonance in the magnetic layer is too wide to be detected. All integrated amplitudes change smoothly through TC. Bottom: Temperature dependence of normalized amplitude Anorm weighed by relaxation λi rate in each layer. 8Li in the Ga1−xMnxAslayer relaxes much faster than than in the substrate (Session 4.4.2). Therefore Anormmag is scaled much larger than Anormsub and is dominant in the total normalized amplitude Anormtot as expected from the 8 keV implantation energy. 984.6. Magnetic Phase Separation Problem sideration (Fig. 4.13 top panel). However, fast relaxation in the magnetic overlayer leads to a significant reduction of the apparent amplitude of the pulsed mode rf resonance. As described in Section 4.3.1, we multiply the integrated amplitudes Ainti by the factor (1 + λTi τ)/(1 + λ300Ksub τ)[141] to account for the contrast in relaxation rate λT . Relaxation rates (for each component) are obtained in the spin-lattice relaxation experiments discussed in Section 4.4.2. The resulting Anormi is plotted in Fig. 4.13 bottom panel. This essentially normalizes the amplitudes to the substrate signal at 300 K. From this, we see that the substrate fraction is only about ∼10% at 100 K. Above 200 K (and at the lowest temperature, 6 K), the overlayer signal cannot be resolved, and the single Lorentzian fits are treated as originating in the substrate, so these points represent only a lower limit for the total amplitude there. The amplitude Anormi should be a measure of the relative fractions of 8Li+ stopping in each layer. Most importantly for phase separation, the integrated amplitudes evolve smoothly through TC. In the proposed phase separation scenario[50], one might consider whether the narrow substrate resonance contains a signal from 8Li in regions of the overlayer that remain paramagnetic. As we already discussed in Secion 4.3, this is not supported by the implantation depth dependence that shows the narrow signal disap- pears completely at lower implantation energies (Fig. 4.3). Moreover, 8Li in nanoscopic paramagnetic regions within the Mn doped would also expe- rience the same large continuum demagnetizing field and thus would shift with temperature, in contrast to the narrow resonance in Fig. 4.6. On the other hand, if either of the two phase separated regions was unobserved in our spectra, e.g. if the spin relaxation was very fast or the static internal field was so large that the resonance occurred outside our frequency range, we would expect to lose some resonance amplitude at the transition. How- ever, the continuous change of both amplitudes (the top panel of Fig. 4.7) and the integrated area of the resonance through TC does not support this. The continuity of Anormi through TC thus also shows no evidence of phase separation. This result is, however, consistent with the full volume fraction magnetism found in LEµSR in samples with a range of Mn concentrations 994.6. Magnetic Phase Separation Problem encompassing that of the current sample[52]. 4.6.2 CW Mode Resonance Using resonance data collected in the continuous wave (CW) mode, we have sufficient rf power to fully saturate the resonance at room temperature[136], while at lower temperature, the line is too broad to saturate. The integral of the room temperature spectrum can be used as a calibration of the full amplitude corresponding to all the 8Li. Fig. 4.14 top panel shows the resonance spectra of 8Li+ in CW mode at full beam energy (28 keV) and at two temperatures, 30 K and 300 K. Please note that these resonance data were only collected as part of the tuning up procedure, so one of the data sets shown in Fig. 4.14 does not completely cover the resonance frequency range. Nevertheless, it is included as it clearly demonstrates complete saturation of the resonance at zero bias and 300 K. The two sets of resonances (up and down) correspond to two 8Li polarizations, parallel and antiparallel to the beam. The first factor influ- encing the resonance amplitude, the temperature dependent off-resonance baseline, is apparent in the figure. The baseline (steady state polarization) is determined by the spin lattice relaxation (λ = 1/T1) and the lifetime of 8Li+ τ (Section 2.4.1), so any temperature dependence of 1/T1 will affect it[141]. Simply normalizing to the baseline, i.e. the difference between the two polarizations, at each temperature accounts for this systematic effect. As shown in Fig. 4.14, at 28 keV, the 8Li+ penetrate the Ga1−xMnxAs layer and stop in the GaAs substrate (see Fig. 4.2 and discussion in Section 4.3), resulting in a single resonance, whose width is close to that in GaAs (Section 3.2). At 300 K, the resonances from the two polarizations meet, indicating the resonance is saturated, i.e. the rf power is high enough to destroy all the 8Li polarization. At 30 K the same CW rf is not sufficient to achieve saturation even though the resonance is somewhat narrower. This behaviour was also observed in semi-insulating GaAs[104]. It may be due to a fraction of 8Li+ that stops in disordered sites, e.g. near implantation related vacancies. The resonance from such sites is broadened by quadrupo- 1004.6. Magnetic Phase Separation Problem s56s49s55s53 s56s49s57s48 s56s50s48s53 s56s50s50s48 s45s48s46s55s50 s45s48s46s54s57 s45s48s46s54s54 s32s48s66s105s97s115s32s51s48s48s75 s32s48s98s105s97s115s32s51s48s75 s65 s115s121 s109 s109 s101 s116 s114 s121 s70s114s101s113s117s101s110s99s121s32s40s107s72s122s41 s56s49s56s48 s56s50s48s48 s56s50s50s48 s45s49s46s48 s45s48s46s53 s48s46s48 s48s46s53 s49s46s48 s32s51s48s48s32s75 s32s49s48s48s32s75 s32s32s54s48s32s75 s78 s111 s114 s109 s97 s108 s105 s122 s101 s100 s32 s65 s115 s121 s109 s109 s116 s114 s121 s70s114s101s113s117s101s110s99s121s32s40s107s72s122s41 Figure 4.14: Top: The CW β-nmr spectra in the Ga1−xMnxAs(28 keV implantation) at 300 K (black squares) and 30 K (blue circles). Only a single resonance is resolved. At 300 K, the resonances from the two helicities meet, indicating that the signal is fully saturated. Bottom: Normalized CW β-nmr resonance spectra at 8 keV implantation energy at different temperatures. 8Li+ in the substrate produces the narrow resonance, while the broad resonance (shoulder on the low frequency side) originates in the Ga1−xMnxAs thin film. 1014.6. Magnetic Phase Separation Problem lar effects and may be too broad to observe, as has been found in β-nmr of 12B implanted in ZnSe[114]. At a lower implantation energy (8 keV), the analogous behaviour of the CW amplitude in the Mn doped layer is shown in the bottom panel of Fig. 4.14. As discussed in previous sections, the two resonances in the spectra below room temperature are due to 8Li+ stopping in the Mn doped layer (broad, negatively shifted) and in the nonmagnetic GaAs substrate (narrow).Because of power broadening, they are not well-resolved here, with the broad line appearing as a low frequency shoulder. At 300 K, the spec- trum is not saturated, even though the width is comparable to that in the substrate. Similarly the lack of saturation here may be due to 8Li+ stopping in disordered sites. In this case such sites may include those neighboring the magnetic Mn2+ dopants which cause both quadrupolar and magnetic effects in the 8Li resonance. Again we fit the data to the sum of two Lorentzians (curves in Fig. 4.14) using Eqn. (2.17). At room temperature, a single Lorentzian was used. To account for the effect of 1/T1, we first normalize each spectrum by dividing it by its baseline Ao. Temperature dependent line broadening also affects the amplitude, so we integrate the normalized spectrum over the frequency range of the data to obtain Aintnorm, the integrated amplitude, that provides a measure of the corresponding 8Li+ fraction. The Aintnorm is then expressed as a fraction of its value at room temperature (and 8 keV), where we have full saturation at least for the fraction of the signal in the substrate. Using this procedure, Aintnorm at 100 K corresponds to 73% of the room temperature (8 keV) value, and at 60 K to about 62%. Thus, through the transition, the loss of signal corresponds to only about 11 % of the 8Li+ at room temperature, much smaller than found by LEµSR[50]. Recall that the amplitude in semi-insulating GaAs also depends on temperature, see the top panel of Fig. 4.7. This intrinsic change in the amplitude of the 8Li resonance may account for much or all of the amplitude change here. 1024.6. Magnetic Phase Separation Problem 4.6.3 Summary Although β-nmr does not provide a direct measure of the magnetic volume fraction, we can use the CW rf spectra to make a reasonable estimate. We can also use the pulsed rf spectra weighted by the spin lattice relaxation rate to show these fractions do not change abruptly at TC. The results both show no evidence for magnetic phase separation in this sample. The lack of evidence for phase separation may be a consequence of differences in the samples used in Ref. [50] which differed both in Mn concentration and in TC. In contrast, our results are consistent with the full volume fraction magnetism found by a “wipeout effect” of the weak transverse field LEµSR in samples with a range of Mn concentrations encompassing that of the current sample[52]. 103Chapter 5 Ferromagnetic Proximity Effect in Fe/GaAs Heterostructures The results of β-nmr measurements in GaAs were presented in Ch. 3. The high resolution pulsed rf spectra show a small intrinsic temperature- dependent shift of the 8Li+ resonance below 150 K in both semi-insulating and heavily doped n-type GaAs. The depth-dependent resonance shift, only observed in the semi-insulating GaAs, may be due to the band-bending at the free surface. The linewidth is narrow, not depth-dependent and weakly depends on temperature. Having carefully characterized the temperature- depth- and doping- dependence of the 8Li+ β-nmr signal in the GaAs crys- tals, we are ready to study the local magnetic properties of the Fe/GaAs heterostructures. In this chapter, we will first review the preparation and properties of the Fe/GaAs heterostructures in Section 5.1, and present the data on Fe/semi- insulating (SI) GaAs (09-A1) (Section 5.2.1) and Fe/n-GaAs (10-A1) (Sec- tion 5.2.2) with no injected current. Section 5.3 will discuss the current injection from the magnetic Fe layer into the heavily doped n-type GaAs (11-A1) detected by β-nmr. 1045.1. The MBE Growth and Properties of Fe/GaAs Heterostructures 5.1 The MBE Growth and Properties of Fe/GaAs Heterostructures 5.1.1 The MBE Growth of Fe/GaAs Heterostructures First let’s review the MBE growth of Fe/GaAs heterostructures and their properties. As we already discussed in Section 1.3, in addition to ferromag- netic semiconductors, another way of introducing polarized spins in semi- conductors is to “transfer” the ferromagnetism from a ferromagnet (FM) into a conventional semiconductor (SC). A direct solution is to fabricate an ultrathin ferromagnetic layer on a carefully-prepared semiconductor surface. Fe/GaAs is an obvious choice for such a hybrid FM/SC system. Fe (reviewed in Section 1.2.2) is a strong ferromagnet with a high Curie temperature (TC) and high spin polarization. GaAs, on the other hand, is the most widely used III-V semiconductor. The low lattice mismatch between Fe and GaAs provides the basis for good epitaxial growth[168]. Molecular Beam Epitaxy (MBE) is an evaporation technique to grow single crystal at a very low rate (e.g. 2–10 atomic layers per minute in the growth of 3d transition metals) under ultrahigh vacuum (UHV) conditions (with pressures ∼ 10−10 Torr). The UHV guarantees that the evaporated atoms or molecules form a beam directed towards the crystalline substrate and are not scattered by the residual gas molecules. The very low rate of impinging atoms or molecules ensures the controllable growth of a highly ordered crystalline layer of a new material with high purity. The individual layer thickness can range from a few atomic layers to hundreds of nanometers which makes MBE particularly suitable for growing ultrathin film structures. All the samples studied in this chapter were grown using MBE by B. Kardasz in the group of B. Heinrich at Simon Fraser University (SFU) in the same way, and they have the same interface features. We used both semi-insulating (SI) GaAs and heavily Si doped n-GaAs crystals as substrates. The SI-GaAs substrate is cut from the same wafer as Sample 09-B1 (Wafer Technology Ltd.). The characterization of the semi- insulating GaAs substrate was presented in Section 3.3. The n-GaAs sub- 1055.1. The MBE Growth and Properties of Fe/GaAs Heterostructures Figure 5.1: Left: diagrams of ideal interface–perfectly flat. Right: real interface. strate is similar to the one (09-B2) we reported in Section 3.3, but from Wafer Technology Ltd. with one side etched and polished. Its carrier con- centration is (1.1−1.8)×1018 cm−3. Each substrate was cleaned by hydrogen cleaning, sputtered with Ar+ and annealed at ∼ 600◦C before MBE growth to remove any surface native oxide. A 14 monolayer (ML) Fe thin film was epitaxially grown by MBE on the GaAs substrates (semi-insulating or heav- ily doped n-type GaAs). A 20 ML Au layer was deposited on top of Fe layer to protect it from oxidation. The Fe and Au films were deposited at a relatively low temperature for MBE under UHV (∼ 10−10 Torr). During the deposition, the temperature of GaAs substrate was measured to be ∼ 65 ◦C. The growth process was monitored by Reflection High-Energy Electron Diffraction (RHEED) intensity oscillations[169]. The MBE growth at SFU is highly standardized. Their growth studies show that after deposition of the equivalent of three atomic layers, a continuous Fe film was formed, having atomic terraces approximately 3–4 nm wide on average[169]. The interface is not perfectly flat as shown in Fig. 5.1. At the Fe/GaAs interface, the average roughness is 2 ML, and maximum deviation in height is 3.5 ML as measured by STM from characterization done on similar samples grown under the same conditions. 1065.1. The MBE Growth and Properties of Fe/GaAs Heterostructures Mo¨ssbauer studies were carried out by B. Kardasz [170] on a series of Fe/GaAs samples prepared in the same way but with different Fe layer thick- nesses. They indicate the interface is close to ideal, but some Fe atoms may penetrate into the GaAs substrate during deposition, which is in agreement with STM images[171]. These Fe atoms substitute for Ga atoms in the sec- ond layer and displace them into an interstitial position. It was suggested that the Fe atoms inside the top As layer together with the top Fe layer could form Fe2As compound. They did not comment on the thickness of the intermixing layer, but considering that a continuous film of Fe is formed after equivalent 3 atomic layers, the intermixing layer may be no thicker than 3 atomic layers, ∼ 0.7 nm. 5.1.2 Stopping Distribution of 8Li+ in Fe/GaAs Heterostructures The 8Li+ implantation profile (bottom panel of Figure 5.2) is simulated by SRIM-2006.02 [93]. The energy dependence of the implantation depth and width are shown in the inset of Figure 5.2 top panel. The 8Li+ beam was injected into the sample in the external field of 2.2 T. Implantation energy was varied from 28 keV to 2 keV, making the average 8Li+ depth vary from ∼ 140 nm down to ∼ 20 nm from the sample surface. The implantation depth in Fe/GaAs heterostructures is not substantially different from that in bare GaAs (Fig. 3.3), since the total thickness of the Au and Fe layers is only several nanometers. As shown in the top panel of Fig. 5.2, the higher carrier density in the heavily doped n-type GaAs greatly narrows the Schottky barrier at the Fe and GaAs interface compared with that in the semi-insulating GaAs (see discussions in Section 1.3.1). 5.1.3 Current-Voltage (IV) Characteristics of Fe/n-GaAs Samples Here I present the I-V characteristics of the Fe/n-GaAs (11-A1), which is directly related to the current injection measurements presented in Section 1075.1. The MBE Growth and Properties of Fe/GaAs Heterostructures s48 s49s48s48 s50s48s48 s51s48s48 s49s69s45s51 s48s46s48s49 s48s46s49 s49 s48s46s48 s48s46s51 s48s46s54 s48 s49s48 s50s48 s51s48 s48 s53s48 s49s48s48 s49s53s48 s48 s53s48 s49s48s48 s49s53s48 s65s117s47s70s101s47s71s97s65s115 s50s56s32s107s101s86 s50s48s32s107s101s86 s49s48s32s107s101s86 s49s32s107s101s86 s32 s32 s80 s114 s111 s98 s97 s98 s105 s108 s105 s116 s121 s73s109s112s108s97s110s116s97s116s105s111s110s32s68s101s112s116s104s32s40s110s109s41 s51s32s107s101s86 s70s101s47s110s45s71s97s65s115 s70s101s47s71s97s65s115 s32 s32 s32s73s109s112s108s97s110s116s97s116s105s111s110s32s69s110s101s114s103s121s32s40s107s101s86s41 s32 s68 s101 s112 s116 s104 s32 s40 s110 s109 s41 s32 s87 s105 s100 s116 s104 s40 s110 s109 s41 Figure 5.2: Top panel: The orange dashed line and the pale yellow dash-dot line are the Schottky barrier profiles in semi-insulating GaAs substrate and heavily doped n-type GaAs respectively[172]. The barrier width shrinks as the carrier density increases in the semiconductor. The inset is the energy dependent implantation depth and implantation distribution’s width. Bottom panel: Solid lines are the implantation profiles in Au/Fe/GaAs sim- ulated by SRIM-2006.02 with different implantation energy (shown on a log scale). The red solid squares are the SRIM simulation in n-type GaAs with implantation energy at 28 keV, which is similar to that in the Au/Fe/GaAs sample at the same energy. 1085.1. The MBE Growth and Properties of Fe/GaAs Heterostructures Figure 5.3: Field emission (FE) and thermoionic emission (TFE) tunneling through a Schottky barrier for forward (left) and reverse (right) bias on Fe/n-GaAs. Adapted from Ref. [172]. 5.3. As we discussed in Chapter 3, the Fermi level of the n-GaAs is above the bottom of the conduction band because of the high hoping level. In such heavily doped GaAs, the depletion region is very thin, therefore the current due to the tunneling of carriers through the barrier becomes the dominant transport process[172, 173]. Tunneling can occur in a Schottky barrier junction in two ways: field emission (FE) and thermionic field emission (TFE), which are shown in Fig. 5.3 for forward (left panel) and reverse (right panel) bias. Under forward bias, the I-V characteristic in the presence of tunneling in Fe/n-GaAs is[172]: I = Isexp ( eV Eo ) (5.1) where e is the electron charge, the saturation current Is depends only weakly on voltage, and Eo is a tunneling constant and is given by: Eo = Eoocoth ( Eoo kBT ) (5.2) with kB the Boltzmann constant, and Eoo is an important parameter in tunneling, inherently related to material properties of the semiconductor, and can be expressed as: Eoo = eh 4pi ( Nd m∗o )1/2 (5.3) 1095.1. The MBE Growth and Properties of Fe/GaAs Heterostructures where h is the Planck’s constant, Nd is the doping concentration, close to the carrier concentration in our case, m∗ = 0.067me is the conduction band effective mass of GaAs (me is the electron mass), e is the electron charge and  = 13.18 is the relative dielectric permeability for GaAs (Section 1.3.1). When Eoo is large or at low temperatures, Eoo  kBT . Under forward bias, electrons with energy close to EF can tunnel from the semiconductor into the metal, in a process known as Field Emission (FE). Eo ≈ Eoo, there- fore the slope of the ln(I)vs.V plot is constant, independent of temperature T . On the other hand, when Eoo is small or at higher temperatures, Eoo  kBT . A significant number of electrons can be thermally excited above Fermi level where the Schottky barrier is lower and thinner. These electrons thus can tunnel into the metal before reaching the top of the barrier. This tun- neling of thermally excited electrons is known as Thermionic Field Emission (TFE). The slope of the ln(I)vs.V plot is e/kBT , inversely proportional to temperature T . When a reverse bias is applied, the current is very small at low bias voltage. As the bias voltage increases, the current also has an exponential dependence on the applied bias. If field emission and/or thermionic field emission are the dominant conduction mechanisms under forward bias, they will also be the dominant mechanism for the reverse characteristics. The I-V characteristic curve of the Fe/n-GaAs is shown in Fig. 5.4. The I-V curve was measured on a test sample made exactly in the same way as Sample 11-A1. The 77 K measurement was taken in 4-wire configuration. The other 2 data sets were obtained by 2-wire measurement in situ in the β- nmr experiment on Sample 11-A1, so they may have some contribution from the lead resistance’s temperature dependence. Under positive voltage, the sample is forward biased with electrons flowing from the n-GaAs substrate to the Fe layer. The current grows exponentially with the bias voltage. In the right panel of Fig. 5.4, the slope of the ln(I)vs.V plot does not drastically vary with temperature, therefore the current transport through the Schottky barrier is mostly due to Field-Emission (FE). Under negative voltage, the structure was reverse biased. The current was initially small 1105.1. The MBE Growth and Properties of Fe/GaAs Heterostructures s45s50 s45s49 s48 s49 s50 s45s52s48s48 s45s50s48s48 s48 s50s48s48 s52s48s48 s67 s117 s114 s114 s101 s110 s116 s32 s40 s109 s65 s41 s86s111s108s116s97s103s101s32s40s86s41 s55s55s32s75s32s45s32s52s32s119s105s114s101 s32s49s53s48s75 s32s49s48s32s75 s32 s32 s45s50 s45s49 s48 s49 s50 s48s46s49 s49 s49s48 s49s48s48 s32s55s55s32s75s32s45s32s52s32s119s105s114s101 s32s49s53s48s32s75 s32s49s48s32s75 s124 s99 s117 s114 s114 s101 s110 s116 s124 s32 s40 s109 s65 s41 s86s111s108s116s97s103s101s32s40s86s41 s32 s32 Figure 5.4: I-V characteristic curve of Fe/n-GaAs plotted in original (Left) and log (Right) scale. The I-V curve was measured using 4-wire measure- ment on a testing sample of Fe/n-GaAs which is made exactly the same as Fe/n-GaAs (11-A1). The Fe/n-GaAs structure is forward biased under pos- itive voltage, and reversely biased under negative voltage. The right panel is plot in log scale. In the right panel, the absolute vale of current is plotted in log scale. for small reverse biases, and increases exponentially when the reverse bias exceeds ∼ 0.7 V. Under moderate reverse bias voltage, FE may occur in the heavily doped GaAs, resulting in the exponentially increasing current observed in Fig. 5.4. The Au/FeGaAs structure behaves as a Schottky barrier with highly non-linearly I-V characteristics. 5.1.4 Spin Current through Fe/GaAs Heterostructure Interface At zero bias, the Schottky barrier at the interface between the Fe metal and the semiconductor results in a charged depletion region which has a large spatially varying electric field. This has important consequences on charge current flow at metal/semiconductor interfaces. Thus, it is expected that this energy barrier and depletion region also have important consequences on spin transport at these interfaces. Theoretical calculations show that the Schottky barrier with a signifi- cant depletion region is highly undesirable for spin injection[174]. Spins are 1115.1. The MBE Growth and Properties of Fe/GaAs Heterostructures injected into a high-resistive region of the semiconductor that is depleted of carriers. The presence of an energy barrier degrades the performance of the spin-injecting structure, and the current spin polarization strongly depends on the barrier height. The tunneling probability T t of electrons from the magnetic Fe layer to the n-GaAs is proportional to the factor exp(−2 √ 2me(φB−E) h¯ ω) with me the electron mass, E the electron energy, φB and ω the Schottky barrier height and width, respectively. T t strongly de- pends on the Schottky barrier width and height. The high barrier and wide depletion region make electrons tunneling nearly impossible. We expect tunneling in the Fe/SI-GaAs (09-A1) to be negligible at zero bias. In contrast to the Fe/semi-insulating GaAs (09-A1), the Schottky bar- rier in Fe/n-GaAs (10-A1) is greatly narrowed to ∼ 20 nm because of the heavy doping. The narrow barrier makes tunneling possible, although the tunneling rate with zero bias is small. Due to the spliting of the Fe conduc- tion band, the current density j flowing from the magnetic Fe layer is split into j↑ and j↓ with j = j↑ + j↓. The tunneling current density j↑,↓ depends on the density of states on either side of the barrier[175, 176]: j↑,↓ = 4pieh¯ ∑∫ ∞ −∞ dE[gi↑,↓(E)f(E)]T t↑,↓(E)[gj↑,↓(1− f(E − eV ))] (5.4) where carriers are tunneling from i to j, g(E) is the density of states, f(E) is the Fermi-Dirac distribution, and T t(E) is the barrier dependent tunneling probability. The sum is taken over all the transverse momentum kx, ky states. The polarization of the injected current density αo is defined as αo = j↑ − j↓ j↑ + j↓ (5.5) αo is explicitly dependent on gi,j↑,↓ available to tunneling, which can change with the applied voltage. The spin diffusion length is defined as l = √ Dτs where D and τs are the electron diffusion coefficient and spin relaxation time, respectively. D can be evaluated by Einstein equation D = µekBT e with µe the mobility of the conduction electron. In n-GaAs (09-B2), µe at room temperature is ∼ 2300 1125.1. The MBE Growth and Properties of Fe/GaAs Heterostructures s48 s49s48s48 s50s48s48 s51s48s48 s49s69s45s51 s48s46s49 s48s46s48 s48s46s53 s49s46s48 s49s32s107s101s86 s53s32s107s101s86 s49s48s32s107s101s86 s50s48s32s107s101s86 s80 s114 s111 s98 s97 s98 s105 s108 s105 s116 s121 s73s109s112s108s97s110s116s97s116s105s111s110s32s68s101s112s116s104s32s40s110s109s41 s50s56s107s101s86 s32 s80 s101 s40 s120 s41 s47 s80 s111s101 Figure 5.5: The spin polarization decay as a function of z¯ (the dashed wine line), in comparison with the 8Li+ stopping distribution simulated by SRIM. cm2V−1s−1. The spin lifetime of electrons in the conduction band of n-GaAs is known to be as long as ∼ 100 ns in a small doping window around 1016 cm−3 at low temperature, falling off precipitously for higher dopings[177]. It is suggested that 15 ps < τs < 35 ps at room temperature for a heavily doped n-GaAs with the doping concentration of 2×1018 cm−3[178]. The spin diffusion length l is thus estimated to be ∼ 400 nm at 300 K. As temperature decreases, D decreases but τs, weakly dependent on T , slightly increases[14]. The spin diffusion length l depends on the competition between these two factors at low temperature. The electron spin polarization density Pe = n↑−n↓ n↑+n↓ decays exponentially with z¯ the distance from the interface at a length scale of l[14]: Pe(z¯)/P oe = exp(−z¯/l) (5.6) where P oe is the spin polarization at the interface. Fig. 5.5 shows the decay of the spin polarization density Pe(z¯) = n↑−n↓n↑+n↓ together with the 8Li+ implan- tation distribution by SRIM simulation. The spin polarization is maximum P oe at the interface where the tunneling happens, and 8Li+ would detect the strongest effect (via resonance shift and broadening). With full implanta- tion energy, z¯ is ∼ 130 nm from the interface, and Pe(z¯) decreases to ∼ 50% of P oe . The resonance spectrum may be less shifted but more broadened compared with the resonance spectrum at low implantation energy. 1135.2. β-nmr Study on Zero-Biased Fe/GaAs Heterostructures Now we consider the case with nonzero injection current. When a bias voltage is applied, non-equilibrium spin polarization accumulates near the interface. The accumulation layer is either expanded or shrunk, depending on the direction of the bias voltage. Under reverse bias, electrons tunnel into GaAs from the Fe contact, and the accumulation layer is extended as drift and diffusion transport electrons into the bulk of the GaAs. As the bias volt- age increases, the spin polarization density Pe increases as more polarized electrons are injected. However, the accumulation layer is also expanded to balance the increase in the total number of injected spins. Therefore the actual density of spin-polarized electrons Pe saturates for large reverse bias voltage. The time-averaged inhomogeneous magnetic field generated by the spin polarized injected electrons may be picked up by the resonance of 8Li+ in the n-GaAs substrate, as shown in Fig. 5.5. The interaction between the 8Li+ probe and the injected electrons should be affected by the den- sity of spin-polarized electrons as was the case in Ga1−xMnxAs (Chapter 4). Therefore we can expect the resonance taken at a certain penetration depth to shift as a function of the bias voltage and this shift should saturate at high reverse bias voltage. Under forward bias, on the other hand, electrons are pushed towards the Fe layer, counter to the direction of spin diffusion, therefore the accumulation layer of polarized electrons shrinks. The resonance shift of 8Li+ in GaAs may not be able to be detected at the same penetration depth. 5.2 β-nmr Study on Zero-Biased Fe/GaAs Heterostructures As discussed in last section, a high Schottky barrier and the wide depletion region at the Fe/GaAs interface is detrimental to spin injection[174]. In Fe/SI-GaAs (09-A1), the wide Schottky barrier due to the low carrier density makes electron tunneling almost impossible at zero bias. Therefore, there is little chance to observe any thermal equilibrium injection from the iron layer into the SI-GaAs substrate. In Fe/n-GaAs (10-A1), the Schottky barrier is 1145.2. β-nmr Study on Zero-Biased Fe/GaAs Heterostructures greatly reduced to ∼ 23 nm due to the high doping density, making the electron tunneling easier even at zero bias, but the tunneling probability may still be small. The spin diffusion length is estimated to be ∼ 400 nm at room temperature. As long as the spin polarization is big enough at the interface, 8Li+ should be able to detect it even with full implantation energy. All β-nmr resonance measurements were taken in CW mode in 2.2 T. The 8Li+ resonance spectra are fit to a single Lorentzian using Eqn. (2.16). The resonance shift is calculated with respect to the resonance frequency of 8Li+ in MgO at 300 K by Eqn. (2.13), and corrected for demagnetization effect. 5.2.1 β-nmr on Fe/Semi-Insulating GaAs In these preliminary experiments, measurements are all done with zero cur- rent. We use the narrow SI-GaAs resonance to detect changes in the local magnetic environment to map the depletion region. Following this line, we took implantation energy scans in 2.2 T at 240 K, 150 K, 60 K and 10 K, which are all far below the Curie temperature of Iron (TC= 1043 K), and a temperature scan at the full implantation energy of 28 keV. As discussed in Chapter 2, any changes of the static local magnetic field would be detected by the 8Li resonance for the Li stopping in the GaAs substrate. Figure 5.6 shows the depth-dependent scans at 240 K, 150 K and 10 K, respectively. At 240 K and 150 K, the resonance does not shift, but it broadens as the implantation energy decreases, i.e. 8Li stops closer to the interface. The energy dependence of the resonance changes below 150 K, e.g. at 10 K there is a significant resonance shift as a function of implanta- tion energy, as shown in the bottom panel of Figure 5.6. The resonance is negatively shifted as the beam stops deeper in the GaAs substrate. With the full implantation energy (28 keV), the resonance is shifted by 1 kHz, corre- sponding to a field ∼ 1.6 G lower than the external field. Comparing to the β-nmr resonance in the bare SI GaAs substrate (09-B1) (Section 3.3), the resonance position in Fe/SI-GaAs with the full implantation energy at 10 K shifts ∼ −22 ppm to a lower frequency. At all temperatures, the baseline 1155.2. β-nmr Study on Zero-Biased Fe/GaAs Heterostructures s49s51s56s54s48 s49s51s56s56s48 s48s46s48s53 s48s46s49s48 s48s46s49s53 s50s56s32s107s101s86 s49s48s32s107s101s86 s65 s115 s121 s109 s109 s101 s116 s114 s121 s70s114s101s113s117s101s110s99s121s32s40s107s72s122s41 s53s32s107s101s86 s84s32s61s32s50s52s48s32s75 s32 s32 s49s51s56s54s48 s49s51s56s56s48 s48s46s49s50 s48s46s49s54 s32s50s56s32s107s101s86 s32s53s32s107s101s86 s32s50s32s107s101s86 s50s56s32s107s101s86 s50s32s107s101s86 s65 s115 s121 s109 s109 s101 s116 s114 s121 s70s114s101s113s117s101s110s99s121s32s40s107s72s122s41 s53s32s107s101s86 s84s32s61s32s49s53s48s32s75 s32 s32 s49s51s56s54s48 s49s51s56s56s48 s48s46s49s50 s48s46s49s53 s32s50s56s32s107s101s86 s32s53s32s107s101s86 s32s51s46s53s107s101s86 s50s56s32s107s101s86 s51s46s53s32s107s101s86 s65 s115 s121 s109 s109 s101 s116 s114 s121 s70s114s101s113s117s101s110s99s121s32s40s107s72s122s41 s53s32s107s101s86 s84s32s61s32s49s48s32s75 s32 s32 Figure 5.6: Implantation energy dependence of βNMR spectra in the sample Au/Fe/GaAs at 240 K (top), 150 K (middle) and 10 K (bottom) at zero injected current. At 240 K and 150 K, the resonance does not shift as a function of energy, but it broadens as the implantation energy decreases, i.e as the 8Li+ moves closer to the Fe interface. At 10 K, the resonance is negatively shifted as the beam stops deeper into the GaAs substrate. The blue dashed line indicates the position of the resonance in MgO. 1165.2. β-nmr Study on Zero-Biased Fe/GaAs Heterostructures 13860 13880  Frequency (kHz) As ym m et ry 150 K  40 K   60 K   100 K  10 K  f o =13870.377 kHz   Figure 5.7: Temperature dependence of β-nmr spectra in the sample Au/Fe/GaAs at the full implantation energy. The resonance shifts nega- tively as the temperature decreases and broadens slightly at low tempera- ture. Spectra are offset for clarity. asymmetry of the resonance systematically decreases as the implantation energy decreases. The temperature-dependent spectra are shown in Figure 5.7. The reso- nance starts to shift to a lower frequency below 150 K and broadens as the temperature decreases. Similar temperature dependence was also observed in bare SI GaAs (09-B1) (Section 3.3), but the resonance shift in Fe/SI-GaAs (09-A1) is more negative than in the bare SI-GaAs substrate (09-B1). The analysis of the spectra in Au/Fe/SI-GaAs (09-A1) is shown in Fig. 5.8, together with β-nmr results in the SI-GaAs (09-B1) and heavily doped n-type GaAs crystals (09-B2) (discussed in Section 3.3) for a direct compar- ison. All shifts have been corrected for the demagnetization effect[115]. In the left panel, the resonance shifts significantly below 150 K and increases as the beam stops deeper in the GaAs not only in the Fe/GaAs (09-A1) but also in the SI-GaAs (09-B1). The temperature dependence of the shift and width is shown in the right panel of Figure 5.8. The Fe/SI-GaAs (09-A1) shows a temperature dependence similar to that in the bare SI-GaAs (09-B1), while the shift is slightly more negative, indicating that the temperature dependent shift is 1175.2. β-nmr Study on Zero-Biased Fe/GaAs Heterostructures s48 s53s48 s49s48s48 s49s53s48 s48 s52 s56 s87 s105 s100 s116 s104 s32 s40 s107 s72 s122 s41 s73s109s112s108s97s110s116s97s116s105s111s110s32s68s101s112s116s104s32s40s110s109s41 s45s49s50s48 s45s56s48 s45s52s48 s48 s77s103s79 s32s70s101s47s71s97s65s115s32s49s48s75 s32s71s97s65s115s32s53s75 s32s110s71s97s65s115s32s53s75 s83 s104 s105 s102 s116 s32 s40 s112 s112 s109 s41 s48 s49s48s48 s50s48s48 s51s48s48 s49s46s54 s50s46s52 s70 s87 s72 s77 s32 s40 s107 s72 s122 s41 s84s101s109s112s101s114s97s116s117s114s101s32s40s75s41 s45s49s48s48 s45s53s48 s48 s32 s32s99s111s114s114s83s104s105s102s116 s32s110s45s71s97s65s115 s32s71s97s65s115 s83 s104 s105 s102 s116 s32 s40 s112 s112 s109 s41 s69s61s32s50s56s32s107s101s86 Figure 5.8: Implantation depth- (left panel) and temperature- (right panel) dependence of the frequency shift (top) and width (bottom) in Fe/GaAs (09-A1) (open black squares), SI-GaAs crystal (09-B1) (open blue circles) and n-type GaAs (09-B2) (solid red triangles). Left: For both the Fe/GaAs and SI-GaAs, the resonance shift only ap- pears below 150 K and increases as the beam stops further from the in- terface/surface. In contrast, the resonance shift is depth independent in the heavily doped n-GaAs. The resonance broadening observed in Fe/GaAs is slightly temperature dependent, while the resonance line shape in both SI-GaAs and n-type GaAs does not vary with the implantation energy. Right: The spectra are measured with full implantation energy (28 keV). The shift appears to be characteristic to the GaAs, but the broadening does not. intrinsic to GaAs. More discussion on the 8Li+ resonance in GaAs substrates was presented in Section 3.3.3. 5.2.1.1 β-nmr Resonance Shift of 8Li+ in Fe/SI-GaAs (09-A1) As a function of temperature, at the full implantation energy of 28 keV, the resonance shift is qualitatively similar to the bare SI-GaAs (09-B1). Possible origins of this shift was discussed in Section 3.3.3. There is a significant difference in the shift only below 50 K, with the shift in the Fe capped sample being ∼ 20 ppm more negative. At low temperature (5 – 10) K, the 1185.2. β-nmr Study on Zero-Biased Fe/GaAs Heterostructures implantation depth dependence of the shift is also qualitatively similar to the bare substrate, though the data are sparse. It is unlikely that the difference in the shifts is related to the magnetism of Fe, since the temperature and energy dependence are so similar to the bare SI-GaAs (09-B1). Let’s consider the possibility that the shift is due to a depletion region in the SI-GaAs. This requires that the bare substrate (SI-GaAs with its native oxide) have a similar interfacial behavior to the Fe/SI-GaAs heterostructure. As already discussed in Section 3.3.3, the surface states in the GaAs makes the energy band bend up near the GaAs surface, forming a surface barrier of the width similar to that in the Schottky barrier in Fe/SI-GaAs (09-A1) interface[117], so this is at least a reasonable possibility. Such an interpretation would be consistent with the absence of a depth dependence in the heavily doped n-GaAs (see the solid blue circles in the left panel of Fig. 5.8) where screening limits electrostatic band bending effects to very near the interface. Now let’s consider whether the magnetic field due to the Fe layer could account for the shift. Inside the Fe layer, the net dipole field due to a thin Fe layer is just the demagnetization field Bdemag discussed in Section 4.4.3. Outside of the Fe, at a distance much smaller than the transverse film dimension, this proximal field Bp is uniform and can be estimated as[115]: Bp = ξ4piM (5.7) where ξ is the aspect ratio of the film (thickness to transverse dimension), which is on the order of 3nm/4mm ∼ 10−6, and M is the magnetization of Fe. Considering that the 2.2 T is high enough to saturate its magnetization, we use Ms = 1630 emu/cm3 the saturated magnetization value of Fe[179] to estimate Bp. The proximal field Bp inside the GaAs is: Bp = 10−6 × 4pi × 1630 ≈ 0.02 G, corresponding to a shift of ∼ 1 ppm, which is too small for the observed extra shift. Bp is also independent of temperature since TC of Fe is far above room temperature, so it can not explain the extra shift that is only observed below 150 K. 1195.2. β-nmr Study on Zero-Biased Fe/GaAs Heterostructures 5.2.1.2 Resonance Broadening of 8Li+ Resonance in Fe/SI-GaAs (09-A1) The resonance spectra of 8Li+ in both SI-GaAs (09-B1) and heavily n-type doped GaAs (09-B2) were taken in pulsed mode (Section 3.3) which is good to measure narrow resonance of only a few kHz wide, while the spectra in Fe/GaAs is CW mode suitable for wide resonance, which is power broadened by the rf field. Therefore the linewidths are substantially different as shown in Fig. 5.8. In contrast to the shift, the energy-dependent broadening appears related to the Fe overlayer: it increases with decreasing energy and is absent in both the bare semi-insulating GaAs and the n-type GaAs. Such a broadening is likely the result of an inhomogeneous local magnetic field in the region sampled by 8Li+. As discussed in the last section, Bp is uniform outside the Fe layer if the film is perfectly flat. However, for a non-ideal film with interface roughness (right panel of Fig. 5.1), the dipole field can give rise to an inhomogeneous field outside the film. We can estimate the linewidth in the GaAs due to the Fe/GaAs interface roughness, assuming that the atomic terrace on the Fe/GaAs interface is approximately 3-4 nm wide on average[169]. In the high field of 2.2 T, the magnetization Fe layer is aligned parallel to the applied field. For a thin magnetic layer with a periodically corrugated magnetization, the broadening due to the interface roughness (σroughness) falls exponentially with z¯ the distance away from the interface, depending on the transverse corrugation wavelength λc[115]: σroughness ∝ exp(−2piz¯λc ) (5.8) The rough interface can be related to the idealized periodic corrugation in the following way. Consider traversing the rough interface in a transverse direction, the magnetization will vary between the extremes of the saturation magnetization of the Fe (MS = 1630 emu/cm3[179]) and ∼ zero in the GaAs. While we do not expect a single wavelength for the interface roughness, there may be some characteristic length scale. In fact, the GaAs surface upon which the Fe is grown is a vicinal surface, meaning that it is constituted 1205.2. β-nmr Study on Zero-Biased Fe/GaAs Heterostructures of a set of unit cell high terraces that make the surface a shallow staircase with a direction slightly off the 〈100〉 crystal direction. Characterization during growth on similar samples reveals such terraces are λc ∼ 3 − 4 nm wide. While this does not constitute a periodic transverse structure, it would perhaps correspond to a prominent Fourier component in the real interface roughness. We can thus coarsely estimate the interface as a sinusoid: M(x) = Mscos(2pixλc ) (5.9) with x a direction in the plane of the film. In reality, the roughness will contain a broad range of Fourier components. With this approximation, the broadening σroughness can be estimated as: σroughness ≈ γMsexp(−2piz¯λc ) (5.10) and shown in the bottom left panel of Fig. 5.8 (the black curve). It is large close to the interface, but falls very quickly to zero away from the interface. From this estimate, even at the lowest penetration depth of 8Li+ in this experiment (∼ 27 nm), σroughness is negligible and much smaller than the observed broadening. There might be significant magnetic inhomogeneity in the Fe/GaAs interface on a length scale much longer than the terrace size, however, and we cannot rule this out as the origin of the broadening. However, such a broadening would be independent of temperature, since MS is approximately constant below 300 K, in contrast to the observed width in Fig. 5.8. The temperature dependence of the linewidth in Fe/SI-GaAs (09-A1) is typical for 8Li+ in GaAs crystals (Section 3.2). The resonance narrows from 250 K to 150 K and broadens as temperature further decreases. With the implantation energy of 28 keV, 8Li+ stop deep in the GaAs substrate, and feels less effect of the Fe layer. Therefore the temperature dependence of the line width (bottom right panel of Fig. 5.8) resembles pure GaAs[104]. The broadening is not likely due to the inhomogeneous hyperfine field as observed in Ref. [180]. The Schottky barrier in Fe/SI-GaAs (09-B1) is as wide as 100 1215.2. β-nmr Study on Zero-Biased Fe/GaAs Heterostructures nm because of the low carrier concentration. 8Li+ even with 28 keV (d ∼ 140 nm) stops in the barrier region where the conduction electrons are depleted. The lack of conduction electrons makes the hyperfine coupling impossible inside the Schottky barrier. There is no evidence of spin proximity effect observed in the Fe/SI-GaAs. 5.2.2 β-nmr on Fe/n-GaAs As discussed in Section 5.2.1, the negative shift of the β-nmr spectra in Fe/GaAs is unrelated to the magnetic iron layer, but seems to be an intrin- sic property of semi-insulating GaAs. To get rid of the wide Schottky barrier in the interface of Fe/SI-GaAs (09-A1), we could use the heavily doped n- type GaAs as a substrate, since the β-nmr resonance in the heavily doped n-type GaAs (09-B2) has been shown independent of depth in Section 3.3. Therefore, we tested a new sample with the same structure as the one dis- cussed in Section 5.2.1, but using a heavily doped n-type substrate. The β-nmr resonance in Au/Fe/n-GaAs (10-A1) was measured as a function of implantation depth and temperature in CW mode. The corresponding bare substrate (10-B1) was also measured in CW mode as a control experiment. The implantation profile of the beam is shown in the bottom panel of Fig. 5.2, and the Schottky barrier is much narrower than the 8Li+ implantation depth (the dark yellow dash-dot line in Fig. 5.2). 5.2.2.1 Results and Analysis The implantation depth-dependence of the 8Li+ resonance in Au/Fe/n-GaAs (10-A1) was measured at different temperatures in CW mode. Fig. 5.9 shows the resonance spectra in Fe/n-GaAs (left panel) and n-GaAs (right panel) at 300 K with various beam energies. Compared to the frequency in MgO, the resonance frequency in Fe/n-GaAs shifts to a lower frequency with full implantation energy. As the implantation energy decreases, 8Li+ stop closer to the Fe/n-GaAs interface, and the resonance shifts more neg- atively and broadens. For comparison, the β-nmr resonance in the n-GaAs substrate (10-B1) at 300 K is shown in the right panel of Fig. 5.9. It nei- 1225.2. β-nmr Study on Zero-Biased Fe/GaAs Heterostructures s49s51s56s52s53 s49s51s56s54s48 s49s51s56s55s53 s48s46s48s54 s48s46s48s57 s102 s111 s61s49s51s56s54s53s46s57s49s53s32s107s72s122 s50s32s107s101s86 s56s32s107s101s86 s50s56s32s107s101s86 s65 s109 s112 s70s114s101s113s117s101s110s99s121s32s40s107s72s122s41 s65s117s47s70s101s47s110s71s97s65s115 s84s61s32s51s48s48s32s75 s32 s32 s49s51s56s54s48 s49s51s56s55s48 s48s46s48s51 s48s46s48s54 s84s61s32s51s48s48s32s75 s32s50s56s32s107s101s86 s32s50s32s107s101s86 s110s71s97s65s115 s65 s109 s112 s70s114s101s113s117s101s110s99s121s32s40s107s72s122s41 s32 s32 Figure 5.9: Energy dependence of the β-nmr spectra (in CW mode) in Au/Fe/n-GaAs (left panel) and n-GaAs (right panel) at 300 K in the exter- nal field of 2.2 T with no current injection. Left panel: The resonance in Fe/n-GaAs shifts more negatively and gets broadened as 8Li+ stops closer to the interface. Right panel: the β-nmr spectra in n-GaAs neither shifts nor broadens as the implantation energy decreases from 28 keV to 2 keV. The dotted lines in each panel indicates the resonance frequency in MgO. ther shifts nor broadens as the implantation energy changes. This difference indicates that the resonance changes may be the results of the proximity effect of the Fe layer, NOT intrinsic to GaAs. The analysis of the depth-dependent β-nmr is summarized in Fig. 5.10. As discussed in Sections 2.4.1.1 and 4.6.2, the amplitude of CW mode res- onance is not a measure of the 8Li+ fraction, but is affected by both the linewidth and the baseline. We divide the amplitude by its baseline to ac- count for the relaxation effect and multiply it by its linewidth to approximate the area under the resonance Aintnorm which is plotted in the bottom panel of Fig. 5.10. In Fig. 5.10, the open blue circles represent the resonance in the n- GaAs substrate (10-B1) which is measured as a control experiment at 300 K with implantation energy of 28 keV and 2 keV. The resonance in the n-GaAs substrate (10-B1) does not vary with implantation energy. At 2 keV, there’s no obvious resonance shift or broadening compared to 28 keV at room temperature, and the Aintnorm is ∼90% of its value at 28 keV. This 1235.2. β-nmr Study on Zero-Biased Fe/GaAs Heterostructures s45s51s48 s48 s52 s56 s48 s49s48 s50s48 s51s48 s48s46s53 s49s46s48 s49s46s53 s77s103s79 s97s41 s83 s104 s105 s102 s116 s32 s40 s112 s112 s109 s41 s32 s32 s32 s98s41 s32s70s101s47s110s71s97s65s115s32s51s48s48s32s75 s32s70s101s47s110s71s97s65s115s32s49s53s48s32s75 s32s70s101s47s110s71s97s65s115s32s49s48s32s75 s32s110s71s97s65s115s32s51s48s48s32s75 s87 s105 s100 s116 s104 s32 s40 s107 s72 s122 s41 s32 s99s41s78 s111 s114 s109 s97 s108 s105 s122 s101 s100 s32 s65 s109 s112 s73s109s112s108s97s110s116s97s116s105s111s110s32s69s110s101s114s103s121s32s40s107s101s86s41 Figure 5.10: The analysis of β-nmr resonance in Fe/n-GaAs (10-A1) as a function implantation energy at different temperatures from single Lorentzian fits. The open blue circles represent β-nmr resonance in the bare n-GaAs substrate (10-B1) at 300 K. The solid symbols refer to the Fe/n-GaAs heterostructure. Curves are guides to the eye. small reduction may be due to backscattering at lower energy (Section 2.3). Therefore, any resonance changes (shift or broadening) in the Fe/n-GaAs heterostructure (10-A1) can be attributed to the effect of the magnetic Fe layer. As shown in the top panel of Fig. 5.10, the resonance shifts negatively as 8Li+ stop closer to the Fe/n-GaAs interface. When the temperature is reduced, the resonance moves to higher frequencies, and becomes less depth- dependent. The resonance width as a function of implantation energy is shown in the middle panel of Fig. 5.10. Compared to the resonance width in the n-GaAs substrate (10-B1) (open blue circles), the 8Li+ resonance in Fe/n-GaAs remains narrow when the implantation energy is above 13 keV (the average implantation depth d ∼ 70 nm), and is substantially broadened at lower energies. The resonance broadening is also slightly temperature dependent. For example, at 5 keV, the resonance is slightly more broadened at 10 K (solid purple triangle) than that at 150 K (solid cyan star). 1245.2. β-nmr Study on Zero-Biased Fe/GaAs Heterostructures s49s51s56s52s53 s49s51s56s54s48 s49s51s56s55s53 s48s46s48s52 s48s46s48s56 s48s46s49s50 s48s46s49s54 s49s48s32s75 s49s53s48s32s75 s102 s111 s61s49s51s56s54s53s46s57s49s53s32s107s72s122 s51s48s48s32s75 s65 s109 s112 s70s114s101s113s117s101s110s99s121s32s40s107s72s122s41 s65s117s47s70s101s47s110s71s97s65s115 s50s56s32s107s101s86 s32 s32 s49s51s56s54s48 s49s51s56s55s48 s48s46s48s52 s48s46s48s56 s48s46s49s50 s110s71s97s65s115 s49s48s32s75 s49s53s48s32s75 s65 s109 s112 s70s114s101s113s117s101s110s99s121s32s40s107s72s122s41 s51s48s48s32s75 s32 s50s56s32s107s101s86 Figure 5.11: Temperature dependence of the β-nmr spectra (CW mode) in Au/Fe/n-GaAs (left panel) and n-GaAs (right panel) with full implantation energy (28 keV) in 2.2 T magnetic field. The dotted blue lines indicate the resonance frequency in MgO. In both panels, the resonance positively shifts and broadens as temperature decreases. The increasing baseline suggests a slower relaxation at lower temperatures, which is consistent with results of independent spin lattice relaxation (SLR) measurements[104]. Aintnorm is shown in the bottom panel of Fig. 5.10. At room temperature, it remains approximately constant when the implantation energy is above 13 keV (d ∼ 70 nm). Then it starts to decrease with reduced implantation energy. At 2 keV (d ∼ 20 nm), Aintnorm is only ∼ 50 % of its value measured with full implantation energy. At low temperatures (for example 10 K, the purple triangles in the bottom panel of Fig. 5.10), the amplitude decreases with implantation energy, but the amplitude loss is much less than at room temperature. Now we present the temperature dependence of the resonance. The T-dependent β-nmr spectra in Fe/n-GaAs (10-A1) (left panel) and in the n-GaAs substrate (10-B1) (right panel) are shown in Fig. 5.11 as a function of temperature with the implantation energy 28 keV. In both panels, the resonance shifts positively and broadens as temperature decreases. The increasing baseline indicates a decreasing relaxation rate of 8Li+ at lower temperatures. The results of the analysis of T-dependent β-nmr resonance in both 1255.2. β-nmr Study on Zero-Biased Fe/GaAs Heterostructures s45s53s48 s48 s48 s49s48s48 s50s48s48 s51s48s48 s48 s49 s50 s97s41 s83 s104 s105 s102 s116 s32 s40 s112 s112 s109 s41 s77s103s79 s32 s32 s32s110s71s97s65s115s32s40s49s48s45s66s49s41s32s50s32s107s101s86 s32s110s71s97s65s115s32s40s49s48s45s66s49s41s32s50s56s32s107s101s86 s32s70s101s47s110s71s97s65s115s32s40s49s48s45s65s49s41s32s50s32s32s107s101s86 s32s70s101s47s110s71s97s65s115s32s40s49s48s45s65s49s41s32s50s56s32s107s101s86 s99s41 s78 s111 s114 s109 s97 s108 s105 s122 s101 s100 s32 s65 s109 s112 s84s101s109s112s101s114s97s116s117s114s101s32s40s75s41 s48 s49s48s48 s50s48s48 s51s48s48 s48 s49s48 s50s48 s48 s49s48s48 s50s48s48 s51s48s48 s50s46s48 s50s46s53 s98s41 s87 s105 s100 s116 s104 s32 s40 s107 s72 s122 s41 s84s101s109s112s101s114s97s116s117s114s101s32s40s75s41 s32 s32 s87 s105 s100 s116 s104 s32 s40 s107 s72 s122 s41 s84s101s109s112s101s114s97s116s117s114s101s32s40s75s41 Figure 5.12: The temperature-dependence of the resonance shift (left panel) and width (right panel) of β-nmr spectra in Au/Fe/n-GaAs (blue squares) and n-GaAs (red stars). The lines are guides to the eye. Fe/n-GaAs (10-A1) and the bare n-GaAs substrate (10-B1) are summarized in Fig. 5.12. The amplitude is again converted into Aintnorm by multiplying by the resonance width and diving by the baseline to account for different relaxation rates and linewidths(Section 2.4.1.1). The shift in the n-GaAs substrate (10-B1) differs from the results presented in Section 3.3.2.2. It moves positively as temperature decreases, which is in contrast to the shift in the other n-GaAs (09-B2) (Section 3.3.2.2), but the temperature depen- dence of the width resembles: slightly decreasing from 5 K to 100 K and broadening above 150 K. Note that unlike n-GaAs (09-B2) (from AXT Inc, USA), the substrate used in Fe/n-GaAs (10-A1) is from another provider (Wafer Technology Ltd., UK). The positive resonance shift may be sample- dependent. Comparing with the bare n-GaAs substrate (10-B1), the reso- nance in Fe/n-GaAs (10-A1) with full implantation energy shifts a little less positively and is slightly broader (inset of Fig. 5.12 right panel). At 28 keV, 8Li+ stop deep in the n-GaAs substrate. The influence of the Fe capping layer is observable, but small. The Aintnorm in Fe/n-GaAs (10-A1) is approximately the same as that in n-GaAs (10-B1) through all temperatures. When the implantation energy is 2 keV, 8Li+ stop much closer to the interface (d ∼ 20 nm). The effect of the magnetic Fe capping layer is more obvious with a more broadened resonance and the loss of the Aintnorm 1265.2. β-nmr Study on Zero-Biased Fe/GaAs Heterostructures (open cyan squares in Fig. 5.12). The resonance shifts slightly upwards as temperature decreases. The resonance width is approximately a constant from room temperature to 30 K and significantly broadened below 30 K. The Aintnorm is approximately a constant through all temperatures. 5.2.2.2 Discussion Here we discuss the results in the Fe/n-GaAs heterostructures without any injected current that are presented above. The change in the resonance shift could be possibly caused by a) the dipolar field of the Fe layer, b) the demagnetization field of Fe atoms diffused into the n-GaAs substrate, or c) the spin-polarized electrons tunneling from Fe into the n-GaAs substrate. Now we consider them separately. As already estimated in last section (Section 5.2.1.1), the dipolar field generated by the magnetic Fe layer Bp is only ∼ 0.02 G, negligible compared to the observed shift in the top panel of Fig. 5.10, so it cannot account for the observed shift. We discussed in Section 5.1.1 that Fe may diffuse into GaAs forming a intermix layer. Any iron that diffuses into the n-GaAs substrates behaves as a paramagnetic impurity, like the Mn ions in GaAs (Chapter 4). Any 8Li+ stopping close to it will feel its dipolar field likely resulting in a loss in Aintnorm. The primary effect of the dipolar fields of dilute random magnetic impurities is a broadening of the resonance (see Chapter 4). They can cause a shift, but only via their net demagnetization field, which is estimated above to be really small. Moreover, a broadening or shift from this source would follow a Curie Law with temperature unlike the data. Therefore, we can rule out this possibility as the main contribution of the observed shift. Another possibility is that electrons are traversing the barrier sponta- neously. With zero current, this means that the rate of electrons tunneling to the GaAs must equal the rate returning to the Fe. Such a process in a superconductor/normal metal system gives rise to the superconducting proximity effect, where the superconducting order is transferred to the nor- mal metal by the exchange of electrons. In a similar way, we may find spin 1275.2. β-nmr Study on Zero-Biased Fe/GaAs Heterostructures polarization is transferred to the semiconductor. As shown in Fig. 5.5, if there are electrons tunneling from the Fe layer, the spin polarized electrons could drift into the n-GaAs substrate and inter- act with 8Li+ stopping at different depths. It is possible that such electrons result in the depth dependence of 8Li+ resonance. The spin diffusion length l is estimated to be ∼ 400 nm in n-GaAs at room temperature. The spin polarization density Pe(z¯) decreases exponentially with z¯ the distance from the interface (Eqn. (5.6)). The inhomogeneous magnetic field generated by the spin-polarized injection electrons scales with Pe(z¯), leading to the shift changes exponentially with z¯. We fit the depth-dependent resonance shift at room temperature (the solid black squares in the top panel of Fig. 5.10) to Eqn. (5.6), resulting a length scale l = 57 nm, which is much shorter than the spin diffusion length estimated above. The temperature dependence of the resonance shift in Fe/n-GaAs (10- A1) is shown in Panel a) of Fig. 5.12. At 28 keV, the slight positive shift and the temperature dependence of the width appear to be the intrinsic properties of the n-GaAs substrate, rather than a result of the Fe layer. The decrease of Aintnorm in Fe/n-GaAs with temperature is also due to the n-GaAs substrate. The resonance shift in Fe/n-GaAs (10-A1) is approxi- mately the same as in n-GaAs (10-B1). There is no sign of spin-polarized electrons tunneling from the Fe layer in the n-GaAs. At 2 keV, 8Li+ stop very close to the interface (z¯ ∼ 11 nm). Pe is ∼ 0.96P oe using Eqn. (5.6), sig- nificantly increasing the possibility that 8Li+ can detect the inhomogeneous field generated by the spin-polarized electrons, assuming that spin-polarized electrons could tunnel from the magnetic Fe layer into the n-GaAs substrate and be detected by the 8Li+. Since both the electron injection rate and dif- fusion length increases at low temperatures[12], the resulting inhomogeneous field should be larger and the resonance may shift more at low temperature. However, this is not the case in Fe/n-GaAs (10-A1). The resonance shift is approximately constant through all temperatures, and we have no evidence for spin polarized electrons from the Fe layer at the penetration depth of ∼ 20 nm. Now we turn to the resonance broadening observed in Fe/n-GaAs (10- 1285.2. β-nmr Study on Zero-Biased Fe/GaAs Heterostructures A1). Compared with the resonance in n-GaAs (10-B1), the additional broad- ening in Fe/n-GaAs (10-A1) (middle panel of Fig. 5.10 and left panel of Fig. 5.12) is due to the magnetic Fe layer. There are several possible broadening mechanisms. One possibility is the Fe/GaAs interface roughness. As discussed in the last section, the broaden- ing caused by the imperfect interface falls exponentially (Eqn. (5.10)) with a lengthscale determined by the transverse wavelengths of the roughness. The Fe/n-GaAs sample (10-A1) is fabricated in the same way as Fe/SI- GaAs (09-A1), and is likely similar in the interface roughness. We already showed that the roughness caused a broadening that falls too quickly to ex- plain the observation if the length scale of the terrace size is relevant (Fig. 5.8). Another possibility is the diffusion of Fe atoms into the n-GaAs sub- strate. Any Fe atom diffuses into GaAs substrate and takes the Ga site or interstitial site as a paramagnetic impurity much like the Mn2+ in Chap- ter 4, causing a distribution of local fields due to the varying distances of random 8Li+ sites. In this case, the broadening scales with temperature as 1/T , which is consistent with the data shown in Panel b) of Fig. 5.12 though the data are sparse. One could estimate the dipolar broadening due to dissolved dilute Fe atoms in GaAs as we did in Chapter 4, but one would need an estimate of its concentration and depth distribution that is beyond our abilities to establish at present. Spin-polarized electrons tunneling from the Fe layer into the GaAs could also contribute to the resonance linewidth, e.g. an unresolved oscillatory response in metallic n-GaAs like in the Ag[180]. However, although the Fermi surface in the metallic n-GaAs is much smaller than that of Ag, which makes the oscillatory wavelength long, the carrier density is so low that the amplitude of the oscillation may be too small to detect compared with that of Ag[180]. In summary, no spin injection is observed in either Fe/SI-GaAs (09- A1) or Fe/n-GaAs (10-A1) at thermal equilibrium under zero bias. The Schottky barrier in the Fe/SI-GaAs interface makes the tunneling almost impossible. Although the high doping of n-GaAs substrate greatly reduces 1295.3. Spin-Polarized Current Injection Measurement s65s117s58s32s49s57s48s32s110s109 s65s117s58s32s49s57s48s32s110s109 s84s105s58s32s51s32s110s109 Figure 5.13: “Edge-on” view on the sample with current contacts. Left: the geometry of the sample contacts labeled with the thickness of each layer. Right: the circuit setup. For positive current as shown, the current is flowing from the n-GaAs substrate to the Fe layer. the Schottky barrier width, no strong evidence of spin polarization is found in the GaAs. The temperature- and depth- dependence of the resonance shift in both Fe/SI-GaAs (09-A1) and Fe/n-GaAs (10-A1) appear to be intrinsic properties of the GaAs substrates. 5.3 Spin-Polarized Current Injection Measurement After carefully measuring β-nmr of 8Li+ in Fe/GaAs heterostructure with semi-insulating and heavily doped n-type GaAs substrate without any cur- rent, we are ready to inject current from the magnetic Fe layer into the semiconductor GaAs substrate to see if we can affect the resonance. As reviewed in Section 5.1.4, the Schottky barrier is crucial for efficient spin injection. So we used the sample Fe/n-GaAs, grown in the same way as the one used in Section 5.2. 5.3.1 Experimental First I summarize the extra sample preparation required for the current injection experiments. Two thick gold (Au) contacts were deposited onto the top and back side of the sample by thermal evaporation at UBC. The sample geometry and experiment setup are shown in detail in Appendix D. To help the 200 nm 1305.3. Spin-Polarized Current Injection Measurement Figure 5.14: The beam view of the sample glued to the sapphire plate (8×15 mm × mm) using Ag paint. There are 2 Au pads on the surface of the sapphire plate to make electric connection of the sample. Au contact at the back side of the substrate (see the left panel of Fig. 5.13) better bond to the n-GaAs substrate, a thin titanium (Ti) layer ∼ 2 nm thick was thermally evaporated onto the n-GaAs substrate backside before the Au layer. The geometry of the sample contacts is shown in the left panel of Fig. 5.13. The sample is attached to a sapphire plate with two Au pads on top to complete the electric circuit. The Au pads on the sapphire plate are ∼ 200 nm thick and also thermally evaporated. More details of sample preparation and experiment setup are given in Appendix D and Appendix C. A picture of the sample is also shown in Fig. 5.14. The Au contacts are connected to a current source as shown in the right panel of Fig. 5.13. The positive current is defined as injected from the backside of the sample (the n-GaAs substrate) to the top surface (the Fe thin film) and accordingly the electrons move from the Fe layer to the n- GaAs substrate. In this case, the Au/Fe/n-GaAs junction is reverse biased, so that the Schottky barrier is highly resistive, like a diode under reverse bias. On the other hand, the current is defined negative when the structure is forward biased with electrons moving from the n-GaAs substrate to the Fe layer. In this case, the current increases quickly with the forward bias voltage. The I-V characteristic curve is shown in Fig. 5.4 and discussed in Section 5.1.3. The equivalent resistor network of the Fe/n-GaAs (11-A1) with contacts is shown in Fig. 5.15. The solid arrow represents the direction of positive current under positive voltage and the big open arrow is the direction of the 1315.3. Spin-Polarized Current Injection Measurement Figure 5.15: A diagram of the equivalent resistor network of the sample including contacts. 1325.3. Spin-Polarized Current Injection Measurement incident 8Li+ beam. Note that the sample with a positive current is actually reversely biased. RtAu and RbAu are the resistance of top and bottom gold contacts respectively, and are estimated to be on the order of 10−8 Ω using their dimensions and a standard value for the resistivity of Au. Rtm is the resistance of the transverse gold and iron thin films, which is estimated to be ∼ 3 Ω. Rsub and Rtsub are the vertical and transverse resistance of the n- GaAs substrate, respectively. The n-GaAs substrate is highly Si doped with a low resistivity of ∼ 2.8 × 10−3 Ωcm. Therefore RGaAs is estimated to be on the order of 10−4 Ω and RtGaAs is about 0.08 Ω. All estimations are based on the resistivity of each material at room temperature. Rsch represents the resistance of the Schottky barrier, and is estimated to be ∼ 9Ω at 77 K from 4-wire measurement data shown in Section 5.1.3. Other sample resistance was measured with a multimeter at room temperature. The gold contact resistance is negligibly small, so there’s no voltage drop on the gold contact. The resistance transverse through the film RAB is ∼ 1.2 Ω, and the total resistance between Point A and Point C RAC is ∼ 8.7 Ω, much higher than RAB. So the current will be uniform over the whole sample area at the Schottky barrier. The spin polarized electrons could tunnel through the reverse biased Schottky barrier or pass over it if the bias voltage is high enough. The applied current could be remotely controlled between ± 500 mA with a resolution of 1 mA supplied by the “0937 current source” built at TRIUMF. With the sample geometry shown, the current density j ≈ 2 × 104 A/m2 at +500 mA. We expect that the injected electron spin polarization in the GaAs could be detected by the local probe 8Li+ via their effect on the time- averaged local magnetic field in the GaAs. We carefully measured the 8Li+ spectra in Fe/n-GaAs (11-A1) as a func- tion of injected current with the implantation energy of 20 keV and 10 keV, and also its temperature dependence with the implantation energy of 20 keV in CW mode at 2.2 T. 1335.3. Spin-Polarized Current Injection Measurement s49s51s56s54s48 s49s51s56s55s53 s48s46s48s52 s48s46s48s56 s48s46s49s50 s50s48s32s107s101s86s44s32s45s52s48s48s32s109s65 s32s49s53s48s32s75 s32s49s48s32s75 s65 s115s121 s109 s109 s101 s116 s114 s121 s82s101s115s111s110s97s110s99s101s32s70s114s101s113s117s101s110s99s121s32s40s107s72s122s41 s32 s32 s49s51s56s54s48 s49s51s56s55s53 s48s46s48s52 s48s46s48s56 s48s46s49s50 s49s48s32s107s101s86s44s32s45s52s48s48s32s109s65 s32s49s53s48s32s75 s32s49s48s32s75 s65 s115s121 s109 s109 s101 s116 s114 s121 s82s101s115s111s110s97s110s99s101s32s70s114s101s113s117s101s110s99s121s32s40s107s72s122s41 s32 s32 Figure 5.16: The temperature dependent 8Li+ spectra in the Au/Fe/n-GaAs heterostructure with the current of -400 mA and implantation energy of 20 keV (left) and 10 keV (right) in 2.2 T field. In both panels, the resonance at 150 K slightly shifts to a lower frequency and is broadened. The red dotted line indicates the resonance frequency of 8Li+ in MgO. 5.3.2 Temperature Dependence of 8Li+ Resonance in Fe/n-GaAs with Current Injection For comparison, the 8Li+ spectra as a function of temperature are plotted in Fig. 5.16 with an applied current of -400 mA and the implantation energy of 20 keV (left panel) and 10 keV (right panel). In both panels, the spectrum at 10 K shifts negatively and slightly broadens compared to that at 150 K. We fit each scan in the spectrum to a single Lorentz function, and use the averaged νo as the resonance frequency. Its error is calculated as the standard deviation of the resonance frequency divided by the square root of the number of complete frequency scans in the run. The analysis of the spectra in CW mode is summarized in Fig. 5.17. The resonance frequency stays approximately constant above 150 K, and negatively shifts as temperature decreases below 150 K. Compared to zero current (solid black squares in the left panel of Fig. 5.17), the resonance shifts negatively with positive current (reverse biased), and positively with negative current (forward biased). With zero current, the resonance width decreases from 10 K to 150 K and then increases up to room temperature, which is consistent with the results in GaAs[104]. But with the injected current (open red circles and blue triangles in the right panel of Fig. 5.17), 1345.3. Spin-Polarized Current Injection Measurement s48 s49s48s48 s50s48s48 s51s48s48 s45s52s48 s45s50s48 s48 s32s53s48s48s32s109s65 s32s48s32s109s65 s32s45s53s48s48s32s109s65 s83 s104 s105 s102 s116 s32 s40 s112 s112 s109 s41 s84s101s109s112s101s114s97s116s117s114s101s32s40s75s41 s32 s32 s48 s49s48s48 s50s48s48 s51s48s48 s51s46s48 s51s46s53 s52s46s48 s52s46s53 s32s53s48s48s32s109s65 s32s48s32s109s65 s32s45s53s48s48s32s109s65 s87 s105 s100 s116 s104 s32 s40 s107 s72 s122 s41 s84s101s109s112s101s114s97s116s117s114s101s32s40s75s41 s32 s32 Figure 5.17: The temperature dependent resonance shift (left) and width (right) in Au/Fe/n-GaAs with 20 keV implantation energy with the current of -500 mA (open blue triangles), zero (solid black squares) and +500 mA (open red circles) in the field of 2.2 T. Curves are the guide to the eye. the resonance linewidth is narrow below 150 K, and broadens above 150 K until 290 K above which it narrows again. The distinct current dependence of the resonance linewidth below and above 150 K can be attributed to the resistive heating effect of the current. Without current, the width is minimal at about 150 K. Any heating results in a local temperature in the sample that exceeds the thermometer reading. Such a temperature increase will cause line broadening above 150 K. Below 150 K, for example 10 K, the 8Li+ resonance narrows if the sample is locally heated by the injected current. With I = −500 mA current, U the voltage across the sample (between Point A and C in Fig. 5.15) is ∼ -1.832 V at 150 K measured in situ. The power generated by the current is estimated as P = UI ∼ 1.832V× 0.5A = 0.916 W. ∼ 1 W of power is delivered to the sample by the current. The sample is glued to a sapphire plate with some silver paint at the backside. Although the sapphire plate is tightly bolted to the copper sample holder, and sapphire itself is a good thermal conductor, the power delivered by the current is still higher than the power dissipated through heat conduction to the cryostat. The electric power is dissipated along the sample according to the resistance distribution along the sample, mainly in the resistive Schottky 1355.3. Spin-Polarized Current Injection Measurement barrier region, and this heats the sample locally. The local heating results in a sample temperature higher than the temperature read by the thermometer. Note that the thermometers indicating the sample temperature are mounted on the copper enclosure and located on the coldest point of the cryostat which is an ultra-high vacuum (UHV) coldfinger, several centimeters away from the sample. Usually the thermometer reading is accurate within ∼ 0.1 K when there is no current. The local resistive heating sets up a dynamic temperature gradient in the sample. At 10 K, by the observed width, the temperature at the 8Li+ appears to be above 50 K with ±500 mA current. As discussed in Section 3.3.2.2, the width in GaAs is minimal at 150 K and then increases from 150 K to 10 K. In combination with local heating, this characteristic dependence of the width explains the observed width with an applied current. A slightly enhanced width may also be the result of an inhomogeneous stray field due to the geometry of the lead wires (see Section 5.3.3). 5.3.3 Current Dependence of 8Li+ Resonance in Fe/n-GaAs with Current Injection The resonance spectra as a function of current are shown in Fig. 5.18 with implantation energy of 20 keV (left panels) and 10 keV (right panels) at 10 K (top panels) and 150 K (bottom panels) in 2.2 T. Contrary to expecta- tions, there’s only a very small frequency shift and the resonance linewidth changes only slightly as a function of current. The overlapping baselines with different current indicates that the spin relaxation rate does not change sig- nificantly with the current. At 10 K, the resonance is slightly narrowed with high injected current, while at 150 K the injected current broadens the res- onance linewidth. This is consistent with sample heating effect as discussed above. Fig. 5.19 shows the spectra as a function of the implantation energy at 10K (left panel) and 150 K (right panel) with -400 mA current. As men- tioned in last section, lower implantation energy means 8Li+ stops closer to the interface. The spectra taken with 10 keV (open symbols) are negatively 1365.3. Spin-Polarized Current Injection Measurement s49s51s56s52s48 s49s51s56s54s48 s49s51s56s56s48 s48s46s48s54 s48s46s48s57 s48s46s49s50 s49s48s32s75s44s32s50s48s32s107s101s86 s32s48s32s109s65 s32s45s52s48s48s32s109s65 s32s43s52s48s48s32s109s65 s65 s115s121 s109 s109 s101 s116 s114 s121 s82s101s115s111s110s97s110s99s101s32s70s114s101s113s117s101s110s99s121s32s40s107s72s122s41 s32 s32 s49s51s56s52s48 s49s51s56s54s48 s49s51s56s56s48 s48s46s48s57 s48s46s49s50 s49s48s32s75s44s32s49s48s32s107s101s86 s32s48s32s109s65 s32s52s48s48s32s109s65 s32s45s52s48s53s32s109s65 s65 s115s121 s109 s109 s101 s116 s114 s121 s82s101s115s111s110s97s110s99s101s32s70s114s101s113s117s101s110s99s121s32s40s107s72s122s41 s32 s32 s49s51s56s54s48 s49s51s56s56s48 s48s46s48s52 s48s46s48s56 s48s46s49s50 s49s53s48s32s75s44s32s50s48s32s107s101s86 s32s45s52s48s48s32s109s65 s32s48s32s109s65 s32s43s52s48s48s32s109s65 s65 s115s121 s109 s109 s101 s116 s114 s121 s82s101s115s111s110s97s110s99s101s32s70s114s101s113s117s101s110s99s121s32s40s107s72s122s41 s32 s32 s49s51s56s54s48 s49s51s56s56s48 s48s46s48s52 s48s46s48s56 s49s53s48s32s75s44s32s49s48s32s107s101s86 s32s45s52s48s48s32s109s65 s32s48s32s109s65 s32s43s52s48s48s32s109s65 s65 s115s121 s109 s109 s101 s116 s114 s121 s82s101s115s111s110s97s110s99s101s32s70s114s101s113s117s101s110s99s121s32s40s107s72s122s41 s32 s32 Figure 5.18: The resonance spectra as a function of the current with the implantation energy of 20 keV (left panels) and 10 keV (right panels) at 10 K (top panels) and 150 K (bottom panels) in 2.2 T. The dotted red line indicates the resonance frequency in MgO. 1375.3. Spin-Polarized Current Injection Measurement s49s51s56s52s48 s49s51s56s54s48 s49s51s56s56s48 s48s46s48s57 s48s46s49s50 s49s48s32s75s44s32s45s52s48s48s32s109s65 s32s50s48s32s107s101s86 s32s49s48s32s107s101s86 s65 s115s121 s109 s109 s101 s116 s114 s121 s82s101s115s111s110s97s110s99s101s32s70s114s101s113s117s101s110s99s121s32s40s107s72s122s41 s32 s32 s49s51s56s54s48 s49s51s56s56s48 s48s46s48s52 s48s46s48s56 s48s46s49s50 s49s53s48s32s75s44s32s45s52s48s48s32s109s65 s32s50s48s32s107s101s86 s32s49s48s32s107s101s86 s65 s115s121 s109 s109 s101 s116 s114 s121 s82s101s115s111s110s97s110s99s101s32s70s114s101s113s117s101s110s99s121s32s40s107s72s122s41 s32 s32 Figure 5.19: The β-nmr spectra in Au/Fe/n-GaAs with 2 implantation energies at 10 K (left) and 150 K (right) with the current of -400 mA in the field of 2.2 T. shifted and broader than with 20 keV. The analysis of the spectra in CW mode is the same as discussed in Section 5.3.2, and is summarized in Fig. 5.20. At either 150 K or 10 K, the resonance with 10 keV implantation energy (open squares in Fig. 5.20 left panel) shifts negatively compared to that taken with 20 keV implantation energy. There’s only a very small frequency shift as a function of the current at either 150 K or 10 K. At 150 K, the small resonance shifts seems linearly proportional to the current. While at 10 K, the shift only linearly scales with negative current and remains constant with positive current though the error bars are large. Remember that the sample is reverse biased for positive current. That means that the resonance only shifts with current when the sample is forward biased and remains constant when reverse biased. This is different from our expectation. Based on the analysis in Section 5.1.4, we expected that the resonance shifts when reverse biased, and may remain constant when forward biased with full implantation energy. The resonance shift at 150 K (squares and stars) was fit to a linear function of current with a shared slope, and the fit result is shown in Ta- ble 5.1. The shared slope is −0.0162 ± 0.0002 ppm/mA, corresponding to −0.35±0.04 G/A. The y-intercepts, the shifts without any injected current, are −3.4± 0.1 ppm for 20 keV and −8.8± 0.1 ppm for 10 keV. The relative 1385.3. Spin-Polarized Current Injection Measurement s45s54s48s48 s45s51s48s48 s48 s51s48s48 s54s48s48 s45s54s48 s45s52s48 s45s50s48 s48 s32s49s48s75s32s50s48s32s107s101s86 s32s49s48s75s32s49s48s32s107s101s86 s32s49s53s48s75s32s50s48s32s107s101s86 s32s49s53s48s75s32s49s48s32s107s101s86 s32s49s53s48s75s32s50s48s32s107s101s86s32s40s112s117s108s115s101s100s32s109s111s100s101s41 s83 s104 s105 s102 s116 s32 s40 s112 s112 s109 s41 s99s117s114s114s101s110s116s32s40s109s65s41 s32 s32 s45s54s48s48 s45s51s48s48 s48 s51s48s48 s54s48s48 s51 s52 s53 s32s49s48s75s32s50s48s32s107s101s86 s32s49s48s75s32s49s48s32s107s101s86 s32s99s117s114s114s101s110s116s32s40s109s65s41 s49s53s48s75s32s50s48s32s107s101s86 s49s53s48s75s32s49s48s32s107s101s86 s76 s105 s110 s101 s119 s105 s100 s116 s104 s32 s40 s107 s72 s122 s41 s32 s32 Figure 5.20: The resonance shift (left) and width (right) of 8Li+ resonance as a function of current at 150 K (squares) and 10 K (diamonds) with the implantation energy of 20 kV (solid symbols) and 10 keV (open symbols) in the field of 2.2 T. The peak in the linewidth is attributed to the local heating effect of the current in the GaAs. The linear shift with current appears to be mostly the result of a small stray field. T (K) E (keV) slope (ppm/mA) constant (ppm) 150 10 −0.0162± 0.0002 −8.8± 0.1 150 20 −0.0162± 0.0002 −3.4± 0.1 10 10 −0.0352± 0.0006 −40.9± 0.1 10 20 −0.0246± 0.0009 −28.0± 0.2 Table 5.1: Fit results of the resonance shift as a linear relation to the current at 150 K and 10K. shift between the two implantation energies is consistent with that extrap- olated from the top panel of Fig.5.10 shown in Section 5.2.2. Shifts at 10 K (diamonds in Fig. 5.20) are fit to a linear function for negative current and a constant for positive current. The fit results are also shown in Table 5.1. A simple and quick estimate shows that the current loop, formed due to the arrangement of the lead wires on the sample (Fig. 5.14), should generate a stray field on the order of 0.2 G with 500 mA current, corresponding to a shift of ∼ 10 ppm, which linearly scales by the current. This likely explains the linear relation between the small shift and the current. Fig. 5.21 shows the shift corrected by removing the stray-field effect of the current. After correction, the shifts at 150 K (squares and stars in Fig. 1395.3. Spin-Polarized Current Injection Measurement s45s54s48s48 s45s51s48s48 s48 s51s48s48 s54s48s48 s45s54s48 s45s52s48 s45s50s48 s48 s32s49s48s75s32s50s48s32s107s101s86 s32s49s48s75s32s49s48s32s107s101s86 s32s49s53s48s75s32s50s48s32s107s101s86 s32s49s53s48s75s32s49s48s32s107s101s86 s32s49s53s48s75s32s50s48s32s107s101s86s32s40s112s117s108s115s101s100s32s109s111s100s101s41 s83 s104 s105 s102 s116 s32 s40 s112 s112 s109 s41 s99s117s114s114s101s110s116s32s40s109s65s41 s32 s32 Figure 5.21: The current-dependent shift of 8Li+ resonance (CW mode) corrected for the stray-field effect of the current at 150 K (squares) and 10 K (diamonds) at the implantation energy of 20 keV (solid symbols) and 10 keV (open symbols) at 2.2 T. The stars are measured in pulsed mode at 150 K with 20 keV in 2.2 T. 5.21) are approximately constant at all currents, while at 10 K, the shift (diamonds in Fig. 5.21) increases with current both positively and nega- tively at approximately the same slope. This indicate contributions from mechanisms other than the stray field of the current. However, the sym- metric shift with current is likely another consequence of the local heating effect. Note that the resonance is approximately constant above 150 K, and negatively shifts with temperature below 150 K (the left panel of Fig. 5.17). The injected current locally heats up the sample, resulting in different final local temperatures with the magnitude of the current. At 150 K, the res- onance does not shift with current even though the final temperature may be different. At 10 K, the resonance shift is sensitive to the actually local temperature. Heating in combination with the intrinsically increasing shift at 10 K is consistent with the sign of the symmetric current effect. The resonance width also shows different current dependence at 150 K and 10 K (Fig. 5.20, right panel). The resonance is symmetrically broadened with current injection (both positive and negative) at 150 K, while at 10 K, the injected current narrows the resonance linewidth. If there’s any broadening due to the current-induced spin polarization, it may be on the same order as the shift, which is tiny in this case. The different current 1405.3. Spin-Polarized Current Injection Measurement dependence of the linewidth could also be attributed to the heating effect of the current. The resonance width in GaAs changes monotonically with temperature below 150K (Section 3.3.2). Therefore the width itself could be used as an indication of local temperature to measure the heating effect of current at low temperature (below ∼ 100 K). Alternatively it might be possible to install another thermometer close to the sample surface where the measure- ment is actually taken. This would require significant modification of the current sample holder. 5.3.4 Summary We measured the 8Li+ resonance spectra (CW mode) in Fe/GaAs het- erostructures with semi-insulating and heavily n-type GaAs, and with/without injection current. The Schottky barrier formed due to the contact of the fer- romagnetic metal with a semiconductor turns out to be an important factor determining the electron tunneling over the barrier and transport in the semiconductor. Any effect of spin injection on the 8Li+ resonance is smaller than that of the stray field effect of the contacts, which is already small. The upper limit of the resonance shift due to spin injection is only ∼ 10 ppm at 10 K with 500 mA current compared with zero current. This negative result is surprising in light of other measurements that have found spin injection in similar Fe/GaAs heterostructures using other methods of detection[76, 77, 78, 80, 83]. One reason the effect may appear so small in our data is that the hyperfine coupling to the conduction electrons in GaAs for interstitial 8Li+ is very small, but this is not likely based on the results in Mn doped GaAs (Chapter 4). Although the result is negative, we have made significant progress in establishing how to do such measurements and in measuring an upper limit on the effect. 141Chapter 6 Summary and Future Work 6.1 Summary In this work, we have applied β-nmr to study the local magnetic field in three spintronic materials: GaAs crystals, Mn doped GaAs and Fe/GaAs heterostructures. The behavior of 8Li+ probe in GaAs crystals is studied as control experiments, from which we can access the effects of ferromagnetic thin film heterostructures. Both Ga1−xMnxAs and Fe/GaAs heterostruc- tures are in the form of thin films epitaxially grown on GaAs substrates. It’s generally hard to detect such thin film samples by conventional NMR due to signal limitations. As a local probe, depth-controlled β-nmr pro- vides a depth profile of the magnetic properties at the atomic level in both Ga1−xMnxAs and Fe/GaAs heterostructure and broadens our knowledge of the hyperfine interaction of the implanted probe (8Li+) in each host mate- rial. 6.1.1 β-nmr Study of GaAs Crystals The high resolution measurements in the GaAs crystals by pulsed β-nmr provides more information on the magnetic properties of GaAs. We observed a small temperature-, depth- and doping- dependent shift of the resonance. The depth dependence is only observed in the semi-insulating GaAs crystal, which seems related to doping. In the heavily doped n-GaAs with much higher carrier density, the resonance does not shift with implantation energy. The resonance shift below 150 K in both semi-insulating and n-type GaAs, at ∼ 100 ppm or less, is on the order of some smaller Knight shifts of 8Li+ in metallic hosts. Moreover, the shift in n-GaAs appears to be somewhat 1426.1. Summary sample dependent (Section 3.3.2.2 vs. 5.2.2). However, it neither behaves like a chemical shift or Knight shift, nor follows Curie’s Law. The activated temperature dependence suggests the role of shallow impurities in giving rise to the temperature dependent shift, but there is no obvious mechanism for it, since the carrier density of so low particularly in the semi-insulating GaAs. The shift is of interest in understanding the behavior of 8Li+ in semicon- ductors and forms the “baseline” behavior of the substrate for the current injection experiment, from which we can assess additional effects of spin injection. 6.1.2 β-nmr Study of Ga1−xMnxAs Ga1−xMnxAs is the β-nmr study on a ferromagnetic material that follows its temperature dependence through ferromagnetic transition, therefore it is an important reference point to compare with other ferromagnets. We find both spin lattice relaxation and resonance signals of 8Li+ in Ga1−xMnxAs in the ferromagnetic state. Two resonances are clearly resolved from the nonmagnetic GaAs substrate and the magnetic Ga1−xMnxAs film. The latter is negatively shifted compared to the resonance in GaAs and this shift is linearly proportional to the external magnetic field. The substrate signal persists down to implantation energy as low as 5 keV – at this energy most 8Li+ stop in the magnetic Ga1−xMnxAs layer. The temperature dependence of the resonance position and the spin relaxation rate in the film is followed through TC. It has long been debated whether the delocalized holes in Ga1−xMnxAs originate from valence band or impurity band carriers (Section 4.1). β-nmr data may help to elucidate the properties of the itinerant carriers. Based on the temperature dependence of the resonance position in Ga1−xMnxAs the hole contribution to the magnetization scales with the macroscopic mag- netization through TC and only deviates below ∼40 K. Unexpectedly, the hyperfine coupling constant of 8Li+ in Ga1−xMnxAs is found to be negative, which may indicate the Femi level falls into a Mn derived impurity band. 1436.1. Summary To make this conclusion more firm, one would need to verify that the 8Li+ hyperfine coupling constant AHF to the valence band holes is of positive sign. One might be able to probe this experimentally by creating optically polarized holes in the valence band of pure GaAs by pumping with circularly polarized light[68, 181, 182]. Alternatively, electronic structure calculation may be able to predict the sigh of AHF reliably (e.g. for 8Li+ in ZnO[183]). However, calculation of such a low energy property is difficult to carry out convincingly even with the best modern electronic structure codes. The spin relaxation rate λ is also studied to elucidate the origin of the delocalized holes. As a measure of the spectral density of transverse mag- netic fluctuations at the NMR frequency, λ in homogeneous metallic[150] or semiconducting[154] ferromagnets usually peaks at TC when the spin dy- namics change dramatically through the formation of a static moment. The amplitude of λ in the magnetic Ga1−xMnxAs layer is ∼ 10 times larger than the rate in metallic Ag[141], but surprisingly shows a relatively weak temperature dependence through TC with only a small enhancement at TC. λ neither peaks at TC, nor follows Korringa’s Law, which is anticipated in such metallic alloy. It is, however, similar to what is found in doped non- magnetic semiconductors when the Fermi level lies in a narrow impurity band[155, 156, 157]. Another important problem is the possibility of magnetic phase separa- tion in Ga1−xMnxAs observed in some µSR measurements[50]. A careful analysis of the resonance spectra in Ga1−xMnxAs shows a continuous change of amplitude through TC. If the Ga1−xMnxAs layer were magnetically phase separated, much 8Li+ would be undetectable once the Ga1−xMnxAs layer is in the ferromagnetic phase below TC and we would expect to see a sharp and dramatic loss in amplitude in contrast to the results of the measurement. No evidence is found, in this sample, for the magnetic phase separation. 6.1.3 β-nmr Study of Fe/GaAs Heterostructures Spin injection from the magnetic layer into semiconductor GaAs has been successfully demonstrated by other techniques[76, 83, 184]. The injected 1446.2. Future Work spin polarization is generated and detected either optically[184] or electrically[83]. In such heterostructures, spin dynamics is influenced by the contact hyper- fine interaction[185]. β-nmr provides a local depth-resolved probe to detect the injected spin polarization. We have measured the 8Li+ resonance in Fe/GaAs heterostructure with semi-insulating and heavily doped n-type GaAs substrates, with and with- out injected current. The maximum penetration depth of 8Li+ in GaAs is ∼ 140 nm. The heterostructure on the semi-insulating GaAs substrate is un- likely to show spin injection due to the wide Schottky barrier formed at the interface (Section 5.1). With zero current, no effect of thermal equilibrium tunneling in the Fe/nGaAs is found. In order to conduct current injection from the magnetic Fe layer into the n-GaAs substrate, we designed and setup a new current injection system in the existing β-nmr spectrometer. The system reliably gives electrical con- tact to the sample in the ultra-high vacuum (UHV) spectrometer without venting. We found effects of local Joule heating and a very small stray mag- netic field caused by the injected current. However, we found no convincing evidence of injected spin polarization in either heterostructure for current densities up to j ≈ 2× 104 A/m2. 6.2 Future Work We have successfully injected current into the sample in the UHV spectrom- eter. The current injection system has been tested and proven capable of biasing the Fe overlayer with respect to the GaAs. However, to minimize the (already small) stray magnetic field generated by the injection current, it is necessary to redesign the arrangement of the Au contacts and the wiring on the sample. A new design needs to consider the way the sample is con- nected to the current source and how to cancel the field generated by the leads. The center of the sample is reserved for accepting 8Li+ so that this area should be clear of wires or contacts. A more symmetric geometry is better to minimize the stray field. Since the sample used in β-nmr can not be very small, a large current is required to reach a current density com- 1456.2. Future Work parable to that in reported experiments[76, 83, 184]. The resistive heating is inevitable. How to minimize the resistive heating and the temperature gradient is also a problem requiring serious consideration, e.g. to make a better thermal contact to the sample to reduce heating effect. Alternatively a sequence of carefully programmed current pulses could be used instead of the continuous current in order to lower the overall heating effect. To mea- sure the heating effect requires a thermometer on the sample. This could be an actual thermometer very close to the sample surface, but not so close as to be in the beam, or we could use the resonance width in GaAs as a built-in thermometer after careful calibration. We could also make a thicker Au layer (e.g. 50 monolayer) to make the current distribution more uniform along the sample. With a next generation design, the spin injection in FM/SC heterostruc- tures could be further explored. We would then study the temperature, current, and depth dependence of the injected spin polarization. A bet- ter understanding of the hyperfine interaction in the heterostructure could be achieved by the local probe 8Li+. The ferromagnetic semiconductor Ga1−xMnxAs could be also used in the spin injection as a polarized spin source with the advantage that there’s no Schottky-like barrier at the in- terface. EuO is another candidate spin polarization source with the ad- vantage/disadvantage of TC= 69 K. This may provide a new point of view on the spin injection from a ferromagnetic source to conventional semicon- ductors. Spin accumulation was successfully demonstrated in the interface of forwarded biased MnAs/GaAs structure[184]. MnAs, as a ferromagnetic metal with TC ≈ 320 K[186], could also be used as a spin source. The Schot- tky barrier in this case is similar to Fe/GaAs (∼ 0.8 V)[184]. For all such structures, one should consider growing a layer of n-GaAs by MBE before depositing the magnetic thin films on commercial GaAs substrates to avoid variability in commercial GaAs wafers. Another possibility is to produce spin polarization directly in a GaAs crystal by optical pumping with circularly polarized light and use the 8Li+ probe to study the behavior of optically generated spins in GaAs. This would allow an independent measure of the hyperfine coupling of 8Li+ to 1466.2. Future Work the conduction band of GaAs. There are many unresolved puzzles in Ga1−xMnxAs itself. The channel- ing effect in the Ga1−xMnxAs/GaAs structure needs detailed exploration. Combined with the β-nmr results, reliable ab initio calculations of the hy- perfine coupling of 8Li+ to the valence band of GaAs and the Mn derived impurity band may distinguish the appropriate microscopic model for the delocalized carriers. A more complete picture will be obtained from a sys- tematic study of Ga1−xMnxAs as a function Mn concentration and film thickness and also from the study on the effects of field and of the optical carrier excitation. 147Bibliography [1] M.A. Ruderman and C. Kittel. Phys. Rev., 96:99, 1954. [2] T. Kasuya. Prog. Theor. Phys., 16:45, 1956. [3] K. Yosida. Phys. Rev., 106:893, 1957. [4] J. Bardeen and W. H. Brattain. Phys. Rev., 74:230, 1948. [5] M.N. Baibich, J.M. Broto, A. Fert, F.Nguyen Van Dau, F. Petroff, P. Etienne, G. Creuzet, A. Friederich, and J. Chazelas. Phys. Rev. Lett., 61:2472, 1988. [6] G. Binasch, P. Gru¨nberg, F. Saurenbach, and W. Zinn. Phys. Rev. B, 39:4828, 1989. [7] S. Datta and B. Das. Appl. Phys. Lett., 56:665, 1990. [8] M.E. Flatte´, Z.G. Yu, E. Johnston-Halperin, and D.D. Awschalom. Appl. Phys. Lett., 82:4740, 2003. [9] S. Sugahara and M. Tanaka. Appl. Phys. Lett., 84:2307, 2004. [10] J. Fabian, I. ˘Zutic´, and S.D. Sarma. Appl. Phys. Lett., 84:85, 2004. [11] K.C. Hall and M.E. Flatte´. Appl. Phys. Lett., 88:162503, 2006. [12] D.D. Awschalom, D. Loss, and N. Samarth. Semiconductor Spintron- ics and Quantum Computation. Springer, 2002. [13] R. Hanson, F.M. Mendoza, R.J. Epstein, and D.D. Awschalom. Phys. Rev. Lett., 97:087601, 2006. 148Bibliography [14] I. ˘Zutic´. Rev. Mod. Phys., 76:323, 2004. [15] Neil W. Ashcroft and N. David Mermin. Solid State Physics. Thomson Learning Asia Pte Ltd, 1976. [16] C. Kittel. Introduction to Solid State Physics. John Wiley & Sons, 2005. [17] Robert M. White. Magnetic Properties of materials, volume 32 of Springer Series in Solid-State Sciences. Spinger, 2007. [18] B.T. Matthias, R.M. Bozorth, and J.H. Van Vleck. Phys. Rev. Lett., 7:160, 1961. [19] T.R. McGuire and M.W. Shafer. J. Appl. Phys., 35:984, 1964. [20] H. Ohno, A. Shen, F. Matsukura, A. Oiwa, A. Endo, S. Katsumoto, and Y. Iye. Appl. Phys. Lett., 69:363, 1996. [21] L. Chen, X. Yang, F.H. Yang, J.H. Zhao, J. Misuraca, P. Xiong, and S. von Molnar. Nano Lett., 11:2584, 2011. [22] A.M. Nazmul, T. Amemiya, Y. Shuto, S. Sugahara, and M. Tanaka. Phys. Rev. Lett., 95:017201, 2005. [23] A.H. MacDonald, P. Schiffer, and N. Samarth. Nature Materials, 4:195, 2005. [24] T. Dietl, H. Ohno, F. Matsukura, J. Cibert, and D. Ferrand. Science, 289:1019, 2000. [25] T. Dietl, H. Ohno, and F. Matsukura. Phys. Rev. B, 63:195205, 2001. [26] J. Blinowski and P. Kacman. Phys. Rev. B, 67:121204, 2003. [27] K.M. Yu, W. Walukiewicz, T. Wojtowicz, J. Denlinger, M.A. Scarpulla, X. Liu, and J.K. Furdyna. App. Phys. Lett., 86:R042102, 2005. 149Bibliography [28] T. Jungwirth, J. Sinova, J. Mas˘ek, J. Kuc˘era, and A.H. MacDonald. Rev. Mod. Phys., 78:809, 2006. [29] K.M. Yu, W. Walukiewicz, T. Wojtowicz, I. Kuryliszyn, X. Liu, Y. Sasaki, and J.K. Furdyna. Phys. Rev. B, 65:201303, 2002. [30] V. Holy´, Z. Mateˇj, O. Pacherova´, V. Nova´k, M. Cukr, K. Olejn´ık, and T. Jungwirth. Phys. Rev. B, 74:245205, 2006. [31] T. Dietl. Nature Materials, 9:965, 2010. [32] J.M. Tang and M.E. Flatte. Phys. Rev. Lett., 92:047201, 2004. [33] P. Mahadevan and A. Zunger. Appl. Phys. Lett., 85:2860, 2004. [34] T. Dietl, A. Haury, and Y.M. d’Aubigne. Phys. Rev. B, 55:R3347, 1997. [35] C. Zener. Phys. Rev., 81:440, 1951. [36] E.O. Kane and T.S. Moss, editors. Handbook on Semiconductors, vol- ume 1. Springer, 1982. [37] S. Ohya, I. Muneta, P.N. Hai, and M. Tanaka. Phys. Rev. Lett., 104:167204, 2010. [38] F. Popescu, C. Sen, E. Dagotto, and A. Moreo. Phys. Rev. B, 76:085206, 2007. [39] K. Hirakawa, S. Katsumoto, T. Hayashi, Y. Hashimoto, and Y. Iye. Phys. Rev. B, 65:193312, 2002. [40] V.F. Sapega, M.Moreno, M. Ramsteiner, L. Da¨weritz, and K.H. Ploog. Phys. Rev. Lett., 95:137401, 2005. [41] K.S. Burch, D.B. Shrekenhamer, E.J. Singley, J. Stephens, B.L. Sheu, R.K. Kawakami, P. Schiffer, N. Samarth, D.D. Awschalom, , and D.N. Basov. Phys. Rev. Lett., 97:087208, 2006. 150Bibliography [42] K. Ando, H. Saito, K.C. Agarwal, M.C. Debnath, and V. Zayets. Phys. Rev. Lett., 100:067204, 2008. [43] L.P. Rokhinson, Y. Lyanda-Geller, Z.Ge, S. Shen, X. Liu, M. Do- browolska, and J.K. Furdyna. Phys. Rev. B, 76:161201, 2007. [44] K. Alber, K.M. Yi, P.R. Stone, O.D. Dubon, W. Walukiewicz, T. Wo- jtowicz, X. Liu, and J.K. Furdyna. Phys. Rev. B, 78:075201, 2008. [45] A. Richardella, P. Roushan, S. Mack, B. Zhou, D.A. Huse, D.D. Awschalom, and A. Yazdani. Science, 327:665, 2010. [46] M. Dobrowolska, K. Tivakornsasithorn, X.Liu, J.K. Furdyna, M. Berciu, K.M. Yu, and W. Walukiewicz. Nature Materials, 11:444, 2012. [47] D. Neumaier, M. Turek, U. Wurstbauer, A. Vogl, M. Utz, W. Wegscheider, and D. Weiss. Phys. Rev. Lett., 103:087203, 2009. [48] Y. Nishitani, D. Chiba, M. Endo, M. Sawicki, F. Matsukura, T. Dietl, and H. Ohno. Phys. Rev. B, 81:045208, 2010. [49] S. Ohya, K. Takata, and M. Tanaka. Nature Physics, 7:342, 2011. [50] V.G. Storchak, D.G. Eshchenko, E. Morenzoni, T. Prokscha, A. Suter, X. Liu, and J.K. Furdyna. Phy. Rev. Lett., 101:027202, 2008. [51] M. Sawicki, D. Chiba, A. Korbecka, Y. Nishitani, J.A. Majewski, F. Matsukura, T. Dietl, and H. Ohno. Nature Physics, 6:22, 2010. [52] S.R. Dunsiger, J.P. Carlo, T. Goko, G. Nieuwenhuys, T. Prokscha, A. Suter, E. Morenzoni, D. Chiba, Y. Nishitani, T. Tanikawa, F. Mat- sukura, H. Ohno, F. Ohe, S. Maekawa, and Y.J. Uemura. Nature Materials, 9:299, 2010. [53] M.D. Kapetanakis and I.E. Perakis. Phys. Rev. Lett., 101:097201, 2008. [54] P. Moriya and H. Munekata. J. Appl. Phys., 93:4603, 2003. 151Bibliography [55] Y. Ohno, D.K. Young, B. Beschoten, F. Matsukura, H. Ohno, and D.D. Awschalom. Nature, 402:790, 1999. [56] O. Gunnarsson. J. Phys. F: Metal Phys., 6 (4):587, 1976. [57] M. Shimizu. Rep. Prog. Phys., 44:1981, 329. [58] Ju¨rgen Ku¨bler. Theory of itinerant Electron Magnetism. Oxford Uni- versity Press Inc., 2000. [59] J.R. Waldrop. J. Vac. Sci. Technol. B, 2:445, 1984. [60] R. Fiederling, M. Keim, G. Reuscher, W. Ossau, G. Schmidt, A. Waag, and L. W. Molenkamp. Nature, 402:787, 1999. [61] P.R. Hammar, B.R. Bennett, M.J. Yang, and M. Johnson. Phys. Rev. Lett., 83:203, 1999. [62] G. Schmidt, D. Ferrand, and L.W. Molenkamp. Phys. Rev. B, 62:4790, 2000. [63] Y.Y. Wang and M.W. Wu. Phys. Rev. B, 72:153301, 2005. [64] J. C. Bruye`re, G. Clerc, O. Massenet, R. Montmory, L. Ne´el, D. Pac- card, and A. Yelon. J. Appl. Phys., 36:944, 1965. [65] J.J. Hauser. Phys. Rev., 187:580, 1969. [66] P. Gru¨nberg, R. Schreiber, Y. Pang, M.B. Brodsky, and H. Sowers. Phys. Rev. Lett., 57:2442, 1986. [67] R.K. Kawakami, Y. Kato, M. Hanson, I. Malajovich, J.M. Stephens, E. Johnson-Halperin, G. Salis, A.C. Gossard, and D.D. Awschalom. Science, 294:2001, 2001. [68] F. Meier and B. P. Zakharchenya. Optical Orientation. Elsevier Sci- ence Ltd., 1984. [69] J.M. Kikkawa and D.D. Awschalom. Science, 287:473, 2000. 152Bibliography [70] G. Salis, D.T. Fuchs, J.M. Kikkawa, D.D. Awschalom, Y. Ohno, and H. Ohno. Phys. Rev. Lett., 86:2677, 2001. [71] J. Kikkawa and D.D. Awschalom. Phys. Rev. Lett., 80:4313, 1998. [72] J. Kikkawa and D.D. Awschalom. Nature, 397:139, 1999. [73] R.J. Epstein, I. Malajovich, R.K. Kawakami, Y. Chye, M. Hanson, P.M. Petroff, A.C. Gossard, and D.D. Awschalom. Phys. Rev. B, 65:121202, 2002. [74] S.F. Alvarado and P. Renaud. Phys. Rev. Lett., 68:1387, 1992. [75] B.T. Jonker, G. Kioseoglou, A.T. Hanbicki, C.H. Li, and P.E. Thomp- son. Nature Physics, 3:542, 2007. [76] H.J. Zhu, M. Ramsteiner, H. Kostial, M. Wassermeier, H.P. Scho¨nherr, and K.H. Ploog. Phys. Rev. Lett., 87:016601, 2001. [77] A.T. Hanbicki, B.T. Jonker, G. Itskos, G. Kioseoglou, and A. Petrou. Appl. Phys. Lett., 80:1240, 2002. [78] V.F. Motsnyi, P. van Dorpe, W. van Roy, E. Goovaerts, V.T. Safarov, G.Borghs, and J. de Boeck. Phys. Rev. B, 68:245319, 2003. [79] S.A. Crooker, M. Furis, X. Lou, C. Adelmann, D.L. Smith, C.J. Palm- strøm, and P.A. Crowell. Science, 309:2191, 2005. [80] X. Lou, C. Adelmann, M. Furis, S.A. Crooker, C.J. Palmstrøm, and P.A. Crowell. Phys. Rev. Lett., 96:176603, 2006. [81] O.M. van ’t Erve, A.T. Hanbicki, M. Holub, C.H. Li, C. Awo-Affouda, P.E. Thompson, and B.T. Jonker. Appl. Phys. Lett., 91:212109, 2007. [82] M. Ciorga, A. Einwanger, U. Wurstbauer, D. Schuh, W. Wegscheider, and D. Weiss. Phys. Rev. B, 79:165321, 2009. [83] G. Salis, A. Furhrer, and S.F. Alvarado. Phys. Rev. B, 80:115332, 2009. 153Bibliography [84] A. Schmehl, V. Vaithyanathan, A. Herrnberger, S. Thiel, C. Richter, M. Liberati, T. Heeg, M. Rockerath, L.F. Kourkoutis, S. Muhlbauer, P. Boni, D.A. Muller, Y. Barash, J. Schubert, Y. Idzerda, J. Mannhart, and D.G. Schlom. Nature Mater., 6:882, 2007. [85] G. Srajera, L.H. Lewis, S.D. Bader, A.J. Epstein, C.S. Fadley, E.E. Fullerton, A. Hoffmann, J.B. Kortright, Kannan M. Krishnan, S.A. Majetich, T.S. Rahman, C.A. Ross, M.B. Salamon, I.K. Schulle, T.C. Schulthess, and J.Z. Sun. J. Magn. Magn. Mat., 307:1, 2006. [86] C.D.P. Levy, M.R. Pearson, G.D. Morris, J. Lassen, K.H. Chow, M.D. Hossain, R.F. Kiefl, R. Labbe´, W.A. MacFarlane, T.J. Parolin, L. Root, H. Saadaoui, M. Smadella, and D. Wang. Physica B, 404:1010, 2009. [87] J. Govaerts, M. Kokkoris, and J. Deutsch. J. Phys. G: Nul. Part. Phys., 21:1675, 1995. [88] The ISAC β NMR HomePage. Optical polarization for β-nmr at isac. [89] The ISAC β NMR HomePage. The high and low field spectrometers. [90] The ISAC β NMR HomePage. Beamline optics and deceleration. [91] J.F. Ziegler. http://www.srim.org/SRIM/SRIM 08.pdf. [92] W. Eckstein. Computer Simulation of Ion-Solid Interactions. Springer, 1991. [93] T.J. Jackson, T.M. Riseman, E.M. Forgan, H. Glu¨ckler, T. Prokscha, E. Morenzoni, M. Pleines, Ch. Niedermayer, G. Schatz, H. Luetkens, and J. Litterst. Phys. Rev. Lett., 84:4958, 2000. [94] M. Kokkoris, G. Perdikakis, R. Vlastou, C.T. Papadopoulos, X.A. Aslanoglou, M. Posselt, R. Gro¨tzschel, S. Harissopulos, and S. Kos- sionides. Nucl. Instrum. Methods in Phys. Research B, 201:623, 2003. [95] C.J. Andreen and R.L. Hines. Phys. Rev., 159:285, 1967. 154Bibliography [96] H. Saadaoui. Magnetic Properties Near the Surface of Cuparate Super- conductors Studied Using Beta-Detected NMR. PhD thesis, University of British Columbia, 2009. [97] C.D.P. Levy, A. Hatakeyama, Y. Hirayama, R.F. Kiefl, R. Baartman, J.A. Behr, H. Izumi, D. Melconian, G.D. Morris, R. Nussbaumer, M. Olivo, M. Pearson, R. Poutissou, and G.W. Wight. Nucl. Instrum. Methods in Phys. Research B, 204:689, 2003. [98] W.A. MacFarlane, G.D. Morris, K.H. Chow, R.A. Baartman, S. Daviel, S.R. Dunsiger, A. Hatakeyama, S.R. Krietzman, C.D.P. Levy, R.I. Miller, K.M. Nichol, R. Poutissou, E. Dumont, L.H. Greene, and R.F. Kiefl. Physica B, 326:209, 2003. [99] C.P. Slichter. Principles of Magnetic Resonance. Springer, 1990. [100] D. Borremans, D.L. Balabanski, K. Blaum, W. Geithner, S. Gheysen, P. Himpe, M. Kowalska, J. Lassen, P. Lievens, S. Mallion, R. Neugart, G. Neyens, N. Vermeulen, and D. Yordanov. Phys. Rev. C, 72:044309, 2005. [101] M. Garwood and L. DelaBarre. J. of Mag. Res., 153:1577, 2001. [102] Z. Salman, R.F. Kiefl, K.H. Chow, M.D. Hossain, T.A. Keeler, S.R. Kreitzman, C.D.P. Levy, R.I. Miller, T.J. Parolin, M.R. Pearson, H. Saadaoui, J.D. Schultz, M. Smadella, D. Wang, and W.A. Mac- Farlane. Phys. Rev. Lett., 96:147601, 2006. [103] C.S. Fuller and K.B. Wolestirn. J. Appl. Phys., 33:2057, 1962. [104] K.H. Chow, Z. Salman, W.A. MacFarlane, B. Campbell, T.A. Keeler, R.F. Kiefl, S.R. Kreitzman, C.D.P. Levy, G.D. Morris, T.J. Parolin, S. Daviel, and Z. Yamani. Physica B, 374. [105] A. Ney, G. Jan, and S. S. P. Parkin. J. Appl. Phys., 99:043902, 2006. [106] K. H. Chow, Z. Salman, R.F. Kiefl, W.A. MacFarlane, C.D.P. Levy, P. Amaudruz, R. Baartman, J. Chakhalian, S. Daviel, Y. Hirayama, 155Bibliography A. Hatakeyama, D.J. Arseneau, B. Hitti, S.R. Kreitzman, G.D. Morris, R. Poutissou, and E. Reynard. Physica B, 340-341:1151, 2003. [107] B. Ittermann, M. Fullgrabe, M. Heemeier, F. Kroll, F. Mai, K. Mar- bach, P. Meier, D. Peters, G. Welker, W. Geithner, S. Kappertz, S. Wilbert, R. Neugart, P. Lievens, U. Georg, M. Keim, and the ISOLDE Collaboration. Hyp. Int., 129:423, 2000. [108] G. Lindner, S. Winter, H. Hofsa¨ss, S. Jahn, S. Bla¨sser, E. Recknagel, and G. Weyer. Phys. Rev. Lett., 63:179, 1989. [109] U. Wahl. Phys. Rep., 280:145, 1997. [110] K.W. Kehr, D. Richter, and J.-M. Welter. Phys. Rev. B, 26:567, 1982. [111] R.C. Vil ao, J.M. Gil, H.V. Alberto, J. Piroto Duarte, N. Ayres de Campos, A. Weidinger, M.V. Yakushev, and S.F.J. Cox. Phys- ica B, 326:181, 2003. [112] M. Wilkening, D. Bork, S. Indris, and P. Heitjans. Phys. Chem. Chem. Phys., 4:3246, 2002. [113] C. Wang and Q.M. Zhang. Phys. Rev. B, 70:35201, 2004. [114] B. Ittermann, G. Welker, F. Kroll, F. Mai, K. Marbach, and D. Peters. Phys. Rev. B, 59:2700, 1999. [115] M. Xu, M.D. Hossain, H. Saadaoui, T.J. Parolin, K.H. Chow, T.A. Keeler, R.F. Kiefl, G.D. Morris, Z. Salman, Q. Song, D. Wang, and W.A. MacFarlane. J. Magn. Res., 191:47, 2008. [116] T.J. Parolin, Z.Salman, K.H. Chow, Q. Song, J. Valiani, H. Saadaoui, A. OHalloran, M.D. Hossain, T.A. Keeler, R.F. Kiefl, S.R. Kreitzman, C.D.P. Levy, R.I. Miller, G.D. Morris, M.R. Pearson, M. Smadella, D. Wang, M. Xu, , and W.A. MacFarlane. Phys. Rev. B, 77:214107, 2008. [117] W. Mo¨nch. Semiconductor Surfaces and Interfaces. Springer, 2001. 156Bibliography [118] S. Makram-Ebeid and M. Lannoo. Phys. Rev. B, 25:6406, 1982. [119] H.J. von Bardeleben, D. Stie´venard, D. Deresmes, A. Huber, and J.C. Bourgoin. Phys. Rev. B, 34:7192, 1986. [120] T.S. Wang, K.I. Lin, H.C. Lin, M.H. Lee, Y.T. Lu, and J.S. Hwang. Physica E, 40:1975, 2008. [121] A. Hudgens, M. Kastner, and H. Fritzsch. Phys. Rev. Lett. [122] D.G. Andriano, Y.B. Muravlev, N.N. Solovev, and V.I. Fistul. Sov. Phys. Semicond., 8:386, 1974. [123] W.D. Hoffmann, D. Michel, I.G. Sorina, and E.V. Charnaya. Phys. Solid State, 40:1288, 1998. [124] A.G. Milnes. Deep Impurities in Semiconductors. John Wiley and Sons, N.Y., 1973. [125] J.G. Braden, J.S. Parker, P. Xiong, S.H. Chun, and N. Samarth. Phys. Rev. Lett., 91:056602, 2003. [126] K.S. Burch, D.D. Awschalom, and D.N. Basov. J. Mag. Mag. Mater., 320:3207, 2008. [127] G. Acbas, M.-H. Kim, M. Cukr, V. Novak, M.A. Scarpulla, O.D. Dubon, T. Jungwirth, J. Sinova, and J. Cerne. Phys. Rev. Lett., 103:137201, 2009. [128] Y. Nojiri, K. Ishiga, T. Onishi, M. Sasaki, F. Ohsumi, T. Kawa, M. Mi- hara, M. Fukuda, K. Matsuta, , and T. Minamisono. Hyp. Interact., 121:415, 1999. [129] K. Matsuta, M. Sasaki, T. Tsubota, S. Kaminaka, K. Hashimoto, S. Kudo, M. Ogura, K. Arimura, M. Mihara, M. Fukuda, H. Akai, and T. Minamisono. Hyperfine Interact., 136:379, 2001. [130] L.D. Landau and E.M. Lifshitz. Statistical Physics Part 1. Reed Education and Professional Publishing Ltd, 3 edition, 1980. 157Bibliography [131] R.M. Bozorth. Ferromagnetism. D. van Nostrand Company, Inc., 1951. [132] A.S. Arrott. J. Magn. Magn. Mat., 322:1047, 2010. [133] S. Yu Dan’kov and A.M. Tishin. Phys. Rev. B, 57:3478, 1998. [134] J. F. Ziegler, J. P. Biersack, and U. Littmark. The stopping and Range of Ions in Matter. Pergamon Press: New York, first edition, 1985. [135] E. Morenzoni, H. Glucker, T. Prokscha, R. Khasanov, H. Luetkens, M. Birke, E.M. Forgan, C. Niedermayer, and M. Pleines. Nucl. In- strum. Methods in Phys. Research B, 192:254, 2002. [136] T.R. Beals, R.F. Kiefl, W.A. MacFarlane, K.M. Nichol, G.D. Morris, C.D.P. Levy, S.R. Kreitzman, R. Poutissou, S. Daviel, R.A. Baartman, and K.H. Chow. Physica B, 326:205, 2003. [137] E.H.C.P. Sinnecker, G.M. Penello, T.G. Rappoport, M.M. SantAnna, D.E. R. Souza, M.P. Pires, J.K. Furdyna, and X. Liu. Phys. Rev. B, 81:245203, 2010. [138] Q. Song, K.H. Chow, R.I. Miller, I. Fan, M.D. Hossain, R.F. Kiefl, S.R. Kreitzman, C.D.P. Levy, T.J. Parolin, M.R. Pearson, Z. Salman, H. Saadaoui, M. Smadella, D. Wang, K.M. Yu, J.K. Furdyna, and W.A. MacFarlane. Phys. Proc., 30:174, 2012. [139] T.J. Parolin, Z. Salman, J. Chakhalian, Q. Song, K. H. Chow, M.D. Hossain, T.A. Keeler, R.F. Kiefl, S.R. Kreitzman, C.D.P. Levy, R.I. Miller, G.D. Morris, M.R. Pearson, H. Saadaoui, D. Wang, and W.A. MacFarlane. Phys. Rev. Lett., 98:R047601, 2007. [140] I. Fan, K.H. Chow, T.J. Parolin, M. Egilmez, M.D. Hossain, J. Jung, T.A. Keeler, R.F. Kiefl, S.R. Kreitzman, C.D.P. Levy, R. Ma, G.D. Morris, M.R. Pearson, H. Saadaoui, Z. Salman, M. Smadella, Q. Song, D. Wang, M. Xu, and W.A. MacFarlane. Physica B, 404:906, 2009. 158Bibliography [141] M.D. Hossain, H. Saadaoui, T.J. Parolin, Q. Song, D. Wang, M. Smadella, K.H. Chow, M. Egilmez, I. Fan, R.F. Kiefl, S.R. Kreitz- man, C.D.P. Levy, G.D. Morris, M.R. Pearson, Z. Salman, and W.A. MacFarlane. Physica B, 404:914, 2009. [142] J.A. Davies and P. Jespersgard. Can. J. Phys., 44:1631, 1966. [143] J.F. Ziegler, M.D. Ziegler, and J.P. Biersack. Nucl. Instrum. Methods in Phys. Research B. [144] Q. Song, K.H. Chow, R.I. Miller, I. Fan, M.D. Hossain, R.F. Kiefl, S.R. Kreitzman, C.D.P. Levy, T.J. Parolin, M.R. Pearson, Z. Salman, H. Saadaoui, M. Smadella, D. Wang, K.M. Yu, J.K. Furdyna, and W.A. MacFarlane. Physica B, 404:892, 2009. [145] T.J. Parolin, J. Shi, Z. Salman, K.H. Chow, P. Dosanjh, H. Saadaoui, Q. Song, M.D. Hossain, R.F. Kiefl, C.D.P. Levy, M.R.Pearson, and W.A. MacFarlane. Phys. Rev. B, 80:R174109, 2009. [146] R.E. Walstedt and L.R. Walker. Phys. Rev. B, 9:4857, 1974. [147] M.H. Julien, A. Campana, A. Rigamonti, P. Carretta, F. Borsa, P. Kuhns, A.P. Reyes, W.G. Moulton, M. Horvatic´, C. Berthier, A. Vi- etkin, and A. Revcolevschi. Phys. Rev. B, 63:R144508, 2001. [148] R.I. Miller, D. Arseneau, K.H. Chow, S. Daviel, A. Engelbertz, M.D. Hossain, T. Keeler, R.F. Kiefl, S. Kreitzman, C.D.P. Levy, P. Morales, G.D. Morris, W.A. MacFarlane, T.J. Parolin, R. Poutis- sou, H. Saadaoui, Z. Salman, D. Wang, and J.Y.T. Wei. Physica B, 374:30, 2006. [149] K.H. Chow et al. . the 150 G T1(T ) measurement in pure GaAs, page unpublished. [150] M. Shaham, J. Barak, U. El-Hanany, and W.W. Warren Jr. Phys. Rev. B, 22:R5400, 1980. [151] R.S. Title. J. Appl. Phys., 40:4902, 1969. 159Bibliography [152] A. Yaouanc and J. Chappert. Hyperfine Interact., 8:667, 1981. [153] M. Hampele, D. Herlach, A. Kratzer, G. Majer, J. Major, H.-P. Paich, R. Roth, C.A. Scott, A. Seeger, W. Templ, M. Blanz, S.F.J. Cox, and K. F`‘urderer. Hyperfine Interact., 65:1081, 1990. [154] A. Comment, J.P. Ansermet, C.P. Slichter, H. Rho, C.S. Snow, and S.L. Cooper. Phys. Rev. B, 72:R014428, 2005. [155] S.E. Fuller, E.M. Meintjes, and W.W. Warren Jr. Phys. Rev. Lett., 76:R2806, 1996. [156] E.M. Meintjes, J. Danielson, and W.W. Warren Jr. Phys. Rev. B, 71:R035114, 2005. [157] M.J.R. Hoch and D.F. Holcomb. Phys. Rev. B, 71:035115, 2005. [158] I. Kuryliszyn, T. Wojtowicz, X. Lin, J.K. Furdyna, W. Dobrowolsky, J.M. Broto, O. Portugall, H. Rakota, and B. Raquet. Acta Phys. Polon., 102:649, 2002. [159] A. Abragam. Principles of Nuclear Magnetism. Clarendon Press, Oxford, 1961. [160] T. Jungwirth, J. Ma˘sek, K.Y. Wang, K.W. Edmonds, M. Sawicki, M. Polini, J. Sinova, A.H. MacDonald, R.P. Campion, L.X. Zhao, N.R.S. Farley, T.K. Johal, G.van der Laan, C.T. Foxon, and B.L. Gallagher. Phys. Rev. B, 73:R165205, 2006. [161] G.D. Morris, W.A. MacFarlane, K.H. Chow, Z. Salman, D.J. Ar- seneau, S. Daviel, A. Hatakeyama, S.R. Kreitzman, C.D.P. Levy, R. Poutissou, R.H. Heffner, J.E. Elenewski, L.H. Greene, and R.F. Kiefl. Phys. Rev. Lett., 93:R157601, 2004. [162] T.J. Parolin, Z. Salman, K.H. Chow, Q. Song, J. Valiani, H. Saadaoui, A. O’Halloran, M.D. Hossain, T.A. Keeler, R.F. Kiefl, S.R. Kreitzman, C.D.P. Levy, R.I. Miller, G.D. Morris, M.R. Pearson, M. Smadella, 160Bibliography D. Wang, M. Xu, and W.A. MacFarlane. Phys. Rev. B, 77:R214107, 2008. [163] S.D. Mahanti and T.P. Das. Phys. Rev. B, 3:R1599, 1971. [164] K.Terakura and J. Kanamori. J. Phys. Soc. Jpn., 34:1520, 1973. [165] H. Akai, M. Akai, S. Blugel, B. Drittler, H. Ebert, K. Terakura, R. Zeller, and P.H. Dederichs. Prog. Theor. Phys. Suppl., 101:11, 1990. [166] H. Alloul and P. Bernier. Ann. Phys. (Paris), 8:169, 1974. [167] B.J. Kirby, J.A. Borchers, J.J. Rhyne, K.V. O’Donovan, S.G.E. te Velthuis, S. Roy, Cecilia Sanchez-Hanke, T. Wojtowicz, X. Liu, W.L. Lim, M. Dobrowolska, and J.K. Furdyna. Phys. Rev. B, 74:245304, 2006. [168] G. Wastlbauer and J.A.C. Bland. Adv. in Phys., 54:137, 2005. [169] B. Kardasz and B. Heinrich. Phys. Rev. B, 81:094409, 2010. [170] B. Kardasz, J. Zukrowski, O. Mosendz, M. Przybylski, B. Heinrich, and J. Kirschner. J. of Appl. Phys., 101:09. [171] A. Ionescu, M. Tselepi, D.M. Gillingham, G. Wastlbauer, S.J. Stein- mueller, H.E. Beere, D.A. Ritchie, and J.A.C. Bland. Phys. Rev. B, 72:125404, 2005. [172] B.L. Sharma. Metal-Semiconductor Schottky Barrier Junctions and Their Applications. Plenum Press, 1984. [173] F.A. Padovani and R. Stratton. Solid State Electronics, 9:695, 1966. [174] J.D. Albrecht and D.L. Smiths. Phys. Rev. B., 66:113303, 2003. [175] W.F. Brinkman, R.C. Dynes, and J.M. Rowell. J. Appl. Phys., 41:1915, 1970. [176] W.A. Harrison. Phys. Rev., 123:85, 1961. 161Bibliography [177] R.I. Dzhioev, K.V. Korenev, M.V. Lazarev, B.Ya. Meltser, M.N. Stepanova, B.P. Zakharchenya, D. Gammon, and D.S. Karzer. Phys. Rev. B, 66:245204, 2002. [178] A.V. Kimel, F. Bentivegna, V.N. Gridnev, V.V. Pavlov, R.V. Pisarev, and T. Rasing. Phys. Rev. B, 63:235201, 2001. [179] B. Kardasz, O. Mosendz, B. Heinrich, M. Przybylski, and J. Kirschner. J. of Phys.:Conference Series, 200:072046, 2010. [180] T.A. Keeler, Z. Salman, K.H. Chow, B.Heinrich, M.D. Hossian, B. Kardasz, R.F. Kiefl, S.R. Kreitzman, C.D. P. Levy, W.A. MacFar- lane, O. Mosendz, T.J. Parolin, M.R. Pearson, and D. Wang. Phys. Rev. B, 77:144429, 2008. [181] Marcus Eickhoff, Stefanie Fustmann, and Dieter Suter. Phys. Rev. B. [182] Kannan Ramaswamy, Stacy Mui, and Sophia E. Hayes. Phys. Rev. B. [183] H. Kwak, M.L. Tiago, T.L. Chan, and J.R. Chelikowsky. Chem. Phys. Lett. [184] J. Stephens, J. Berezovsky, J.P. McGuire, L.J. Sham, A.C. Gossard, and D.D. Awschalom. Phys. Rev. Lett., 93:097602, 2004. [185] G. Salis, A. Furhrer, and S.F. Alvarado. Phys. Rev. B, 81:205323, 2010. [186] C.P. Bean and D.S. Rodbell. Phys. Rev. [187] MPMS Application Note 1014-822. Verifying the absolute sensitivity in the mpms. [188] MPMS Application Note 1014-202. Transverse detection system. [189] MPMS Application Note 1014-213. Subtracting the sample holder background from dilute samples. 162[190] MPMS Application Note 1014-819. Connecting a straw adapter to the standard transport rod. [191] Quantum Design. MPMS HP-150 OPERATING SYSTEM SOFT- WARE MANUAL. [192] Quantum Design. MPMS Application Notes/Technical Advisories. [193] Ralph E. Williams. Gallium Arsenide Processing Techniques. Artech House, Inc. 163Appendix A List of Samples A.1 Ga1−xMnxAs The Ga1−xMnxAs sample used in β-nmr experiment presented in Chapter 4 is shown in Fig. A.1. The sample is epitaxially grown by X. Liu and J.K. Furdyna in University of Norte Dame. The equilibrium solubility of Mn in GaAs is low (∼ 1019 cm−3 at most). Therefore low temperature MBE growth was used to realize non-equilibrium growth, so that a larger amount of Mn atoms can be incorporated into the GaAs host. They used a semi-insulating (SI) GaAs as the substrate. First a GaAs buffer layer of ∼ 400 nm was grown on the SI GaAs substrate at Tsubstrate = 590◦C. Then a thin layer of GaAs (∼ 2 nm) deposited at low temperature (Tsubstrate = 275◦C). The 180 nm Ga1−xMnxAs film was epitaxially grown on top of the GaAs layers at low temperature (Tsubstrate = 275◦C) with a slow rate ∼ 0.76 MonoLayer (ML) per second. The sample was annealed after growth at 280◦C for ∼ one hour. The transition temperature TC after annealing is 72 K. The concentration of Mn is estimated from lattice constant of Ga1−xMnxAs measured by x-ray diffraction (XRD). The Ga1−xMnxAs sample was mounted on a sapphire plate when measured in the β-nmr spectrometer. A.2 GaAs Crystals and Fe/n-GaAs Heterostructures There samples were provided by B. Kardasz in the group of B. Heinrich at Simon Fraser University (SFU). The GaAs crystals presented in Chapter 3 are shown in Fig. A.2. The 164A.2. GaAs Crystals and Fe/n-GaAs Heterostructures Figure A.1: 180 nm Ga1−xMnxAs on semi-insulating GaAs mounted on an 8 mm by 10 mm sapphire plate. semi-insulating(SI) GaAs crystal (09-B1) and the substrate of the sample Fe/SI-GaAs (09-A1) were cut from the same SI-GaAs wafer. The heavily doped n-type GaAs (09-B2) is provided by AXT, and was measured in β- nmr spectrometer to compare with SI-GaAs (09-A1). Fig. A.3 shows the sample of Fe/semi-insulating GaAs (09-A1) Fe/n- GaAs (10-A1). The MBE growth of Fe on GaAs is reviewed in Section 5.1.1. β-nmr studies under zero bias is discussed in Section 5.2. The Fe/n- GaAs substrate (10-B1) (Fig. A.4) was measured as control experiment (See Section 5.2.2). The sample Fe/n-GaAs (11-A1) used in the current-injection experiment is shown in Fig. A.5 left panel, and its substrate (11-B1) is shown in the right panel of Fig. A.5. Fe/n-GaAs (11-A1) was epitaxially grown in the same way as the sample Fe/n-GaAs (10-A1). Further sample preparation for the current injection experiment is detailed in Appendix C. We also measured its I-V characteristic, see discussions in Section 5.1.3. 165A.2. GaAs Crystals and Fe/n-GaAs Heterostructures Figure A.2: Top: 09-B1: Semi-insulating GaAs used as the substrate of Fe/SI-GaAs 09-A1. Bottom: 09-B2: heavily n-type GaAs. Figure A.3: Fe/GaAs samples used in β-nmr with zero bias. Left: Sample 09-A1: 20 Ml Au/14ML Fe/semi-insulating GaAs. Right: 10-A1: 20 ML Au/14ML Fe/heavily n-type GaAs. 166A.2. GaAs Crystals and Fe/n-GaAs Heterostructures Figure A.4: 10-B1: heavily Si doped n-type GaAs from Wafer Tech used as the substrate of 10-A1. Figure A.5: Left: 11-A1: 20 Ml Au/14ML Fe/heavily n-type GaAs made in exactly the same way as 10-A1. It was used in the β-nmr current-injection experiment. Right: 11-B1: heavily Si doped n-type GaAs from Wafer Tech, from the same batch as 10-B1, and used as the substrate of 11-A1. 167Appendix B SQUID Measurements on Ga1−xMnxAs B.1 SQUID at AMPEL and Sample Descriptions β-nmr probes a material’s magnetic properties which are closely related to the magnetic susceptibility (as a function of temperature and magnetic field). Therefore the temperature dependence of the overall “bulk” suscep- tibility measured independently is of great importance in the analysis and understanding of β-nmr experimental results. In such a measurement, the entire sample with all its various components (such as the sample holder and the substrate of a thin film) contributes to the signal. In contrast, for a local probe like β-nmr the signal is usually strongly coupled only to a subset of these components. The Superconducting Quantum Interference Device (SQUID) is a very sensitive magnetometer, providing a good measure of the sample magnetic moment, down to quite small values. It does, however, have a sensitivity limit. At low field, the magnetic moments can be routinely measured down to the range of 10−7 emu, while the resolution is 10−6 emu at high field[187]. Using special care and procedures, it is possible to extend this minimum down to the range of 10−8 emu. The device we used in AMPEL is the Magnetic Property Measurement System (MPMS) from Quantum Design. The temperature can be set to the resolution of 0.01 K, and the field of the instrument’s vertical solenoid varies by only 0.19% within a 4 cm scan length. The device is an “extraction SQUID”, meaning that the sample is physically scanned with a stepper mo- 168B.1. SQUID at AMPEL and Sample Descriptions Figure B.1: Left: the diagram of the pick up coil to measure the longitudinal moment. Right: SQUID response. tor in the vertical direction through a pickup coil (Fig. B.1 left panel)[188]) (centered in the high field solenoid) that is coupled to the SQUID itself. The SQUID response is then proportional to the magnetic moment within the pickup coil. Let the (vertical) scan direction be z. An ideal sample will have zero extent in z, and the scan will move the sample from well out of the pickup coil (below) to well out on the upper side. The resulting SQUID voltage (as a function of scan position) has a maximum when the sample is exactly in the coil surrounded by two symmetric (negative) minima (Fig. B.1 right panel)[188]). This characteristic signal may be inverted if the ma- terial is diamagnetic and represents the response for an ideal measurement where only the sample is moved. In reality the sample has some finite extent in the z direction, but more importantly for the samples under considera- tion here, the sample is held in a sample holder which itself may produce a response comparable to the sample itself. Subtracting a sample holder signal is possible during[189] or after the measurement. For a thin film sample, the overall signal is proportional to the net mag- netic moment mmag, mmag = m mag film +m mag substrate +m mag holder (B.1) At high fields, any material will have some magnetic response (even quartz or plastic, for example), i.e. the susceptibility χ is never exactly zero, and material surfaces may have additional magnetic response from either dirt or different surface structure and chemistry. The magnetic moments of the 169B.1. SQUID at AMPEL and Sample Descriptions various components all scale with mass and magnetic field, and because of mass differences, the last two terms in Eqn. B.1 may even dominate in the case of a thin film. The ideal sample holder for an extraction SQUID is completely uniform along the z direction, light weight and made of a material that is mini- mally magnetic. Often a colourless plastic drinking straw is used for these reasons[190]. Such a holder would at most contribute a small (due to low mass and small χ) constant (independent of scan position z, due to uni- formity) offset signal that would not interfere with the W-shaped signal from the sample. In this case, one could have mmagholder making a negligible contribution to mmag. In the experiments described here, we used 3 sample holders. The sample holder consists of one quartz tube and 2 quartz rods which can just slide inside the tube (Fig. B.2 left panel). It was found that the holder without the sample yielded a signal comparable to that with the sample above TC in the paramagnetic state at 1.3 T. The holder signal is probably due to the ends of the two solid quartz rods (pistons) which are just adjacent to the sample. If this is the case, one can, to a first approximation, simply subtract an independently measured mmagholder to remove it. This assumes that the holder signal has the same shape in the squid response, i.e. that of an ideal zero-z-extent W-shaped signal, as would be the case if the holder signal is from the rod ends. Another concern about the reproducibility and sensitivity of the mea- surement is magnet drift. Usually the MPMS magnet is operated in “no- overshoot mode” where the desired magnet current is approached monoton- ically from the initial magnet current without overshooting the final value. To the zeroth order, the current in the closed superconducting circuit is persistent (i.e. does not decay over time). However, the magnetic field can still drift as some trapped flux may leak out slowly. It’s also possible to op- erate the MPMS in oscillating mode which means the final field is achieved through a series of decreasing amplitude oscillations. This effectively forces the magnet to relax during the charging operation by cycling it through a series of smaller and smaller hysteresis loops. One can also check for magnet 170B.2. Samples s48s46s53s55 s48s46s53s56 s48s46s53s57 s48s46s54s48 s49s46s55 s49s46s56 s49s46s57 s50s46s48 s50s46s49 s50s46s50 s50s46s51 s69 s77 s85 s32 s40 s42 s49 s48 s45 s53 s41 s84s105s109s101s32s40s104s111s117s114s41 s32s72s111s108s100s101s114s44s32s49s46s51s84s44s32s53s75 Figure B.2: Left: the diagram of the holder. Right: magnet drift: An empty holder is placed into the magnetic field of 1.3 T. Within the experiment period (45 minutes), there was no obvious drift of the small signal (not shown). Therefore we can conclude that magnet drift does not make a significant contribution to our measurement. drift, by measuring the signal at a fixed temperature and field over time. In such a measurement, there’s no sign of magnet drift at 1.3 T during the test time(Fig. B.2 right panel). For more details of the device and the operation instructions, please refer to Ref. [191, 192]. B.2 Samples The sample (series number 11127a) is 180 nm thick Ga1−xMnxAs epitaxially grown on a layer of ∼ 100 nm GaAs grown by MBE on semi-insulating (SI) (100) GaAs substrate and was annealed at 280 oC for 1 hour. The SQUID measurement done by the provider is summarized in Fig. B.3 to show the effect of annealing. Its growth and characterization can be found in Section 4.2. Since we need a better measure of the bulk uniform susceptibility χ(q = 0, ω = 0) for the correct interpretation of the β-nmr experimental results, we did a series of tests on the same sample Roger used. We polished the back side of the sample (Fig. B.4) to get rid of the Indium layer, broke it into 3 small pieces and later broke the largest piece into 2. The description 171B.2. Samples s51s48 s54s48 s57s48 s49s50s48 s49s53s48 s49s56s48 s50s49s48 s45s49s48 s48 s49s48 s50s48 s32s65s115s32s103s114s111s119s110 s32s65s102s116s101s114s32s97s110s110s101s97s108s105s110s103 s77 s47 s86 s111 s108 s32 s40 s69 s77 s85 s47 s99 s109 s51 s41 s84s101s109s112s101s114s97s116s117s114s101s32s40s75s41 s84s99 s32 s32 s32s77s40s49s50s46s55s109s103s32s115s97s109s112s108s101s41s32 Figure B.3: The SQUID measurement done by the grower before and after annealing at the field of 10 G. Sample #1 #2 #3 #4 mass (mg) 37.3±0.1 2.3±0.1 7.7±0.1 12.7±0.1 thickness (mm) 0.41 0.41 0.41 0.41 area (mm×mm) 4.05×4.42 0.84×1.40 2.76×1.42 2.91×2.07 m mag GaAs of the same mass in 1.3 T (×10−5 emu) -11.16 -0.688 -2.3 -3.8 Estimated mmagMn(×10−5 emu) 19.97 1.18 3.93 6.05 Table B.1: Samples used in the SQUID measurements 172B.3. Summary of SQUID Measurements Figure B.4: Left: Back side of Ga1−xMnxAs sample before polishing. There is some In (silvery) dots on the rough surface. Middle: Sample backside after sanded on a piece of rough paper. Not much of In is removed. There are still some silvery parts. Right: Sample backside after sanding with 6000 sanding paper. No shiny dots are observable and the surface is smoother. of the resulting samples can be found in Table B.2. B.3 Summary of SQUID Measurements The Ga1−xMnxAs thin film is ferromagnetic below TC while it exhibits para- magnetism at higher temperature. The pure GaAs substrate is diamagnetic with a room temperature susceptibility χ of−3.33×10−5 cm3/mole[121], and is very weakly temperature dependent.1The magnetic moment contributed by the pure GaAs substrate in 1.3 T can be estimated (taking the largest sample (37.3 mg) as an example) by: m mag GaAs = nmolχmolH (B.2) = χmol Massmol ×H ×m = −3.33× 10−5 cm3/mol 144.64 g/mol × 13000 G× 0.037 g = −1.116× 10−4 emu. We can also estimate the saturated magnetic moment of Mn, mmagMn in each sample. Assume that every Mn atom contributes 5 µB in 1.3 T. mmagMn (an 1The variation of χ with temperature ∂χ∂T is 1.2 × 10 −7cm3/(mol*K), and the exper- imental temperature range is ∆T = 300K. Then χ only varies 1.2 × 10−7 × 300 = 3.6× 10−7 cm3/mol, i.e. a change of ∼ 1% from room temperature value (−3.33 × 10−5 cm3/mol)[105]. 173B.3. Summary of SQUID Measurements upper limit at any finite temperature) can be estimated as: m mag Mn = ρsdfilm Massmol xNA(5µB). with ρ the density of GaAs=5.32 g/cm3, s the sample area, dfilm the film thickness=180 nm, Massmol the molar mass of GaAs=144.64 g/mol, NA the Avogadro number, and µB Bohr Magneton=9.27×10−21 emu. We then calculated the signals expected from each GaAs substrate and each saturated Mn moment (Table B.2), and compared them with the measured signals collected by the SQUID. We measured the magnetic moment of all four pieces and the correspond- ing empty holders except for the 37.3mg sample. A piece of GaAs of 12.1 mg was also measured for comparison. The SQUID measurements are all done at 1.3 T and summarized in Fig. B.5. The temperature dependent term that comes up below 100 K is clearly due to the Mn doped film and compa- rable to previous measurements in Fig. B.3. However, the signal above TC is paramagnetic, and varies significantly from run to run and from sample to sample. And the signal is nearly always paramagnetic (positive moment), rather than the diamagnetic moment expected from the GaAs substrate (see horizontal dashed lines in Fig. B.5.) For these reasons, we conclude that there is a rather large, apparently temperature-independent, paramagnetic contribution coming from the sample holder (mmagholder). This is confirmed, for example, from runs using the same holder, with and without the sample. This mmagholder must exist in all the data, and the data that yields a near zero moment simply has the combination mmagholder +m mag substrate just nearly canceling. We converted the magnetization to volume susceptibility χ by dividing the signal by the film volume and the field. The results of measurements on 37.3 mg sample and 12.7 mg sample are stacked in Fig. B.6 together with the GaAs sample of 12.1 mg. For the Ga1−xMnxAs sample of 12.7 mg and the GaAs sample of 12.1 mg, the holder signal is removed and the resulting magnetization contributed only by the sample is converted to volume suscep- tibility. Take the measurement of the 12.7 mg Ga1−xMnxAs sample at 90K 174B.3. Summary of SQUID Measurements s48 s49s48s48 s50s48s48 s51s48s48 s45s49s48 s48 s49s48 s50s48 s71s97s65s115 s109 s109 s97 s103 s40 s120 s49 s48 s45 s53 s69 s77 s85 s41 s84s101s109s112s101s114s97s116s117s114s101s32s40s75s41 s32s71s97s65s115s77s110s32s51s55s46s51s32s109s103 s97s41 s48 s49s48s48 s50s48s48 s51s48s48 s48 s50 s52 s109 s109 s97 s103 s40 s120 s49 s48 s45 s53 s69 s77 s85 s41 s98s41 s71s97s65s115 s71s97s65s115s77s110s32s50s46s51s109s103 s84s101s109s112s101s114s97s116s117s114s101s32s40s75s41 s69s109s112s116s121s32s104s111s108s100s101s114 s48 s49s48s48 s50s48s48 s51s48s48 s48 s53 s49s48 s49s53 s109 s109 s97 s103 s40 s120 s49 s48 s45 s53 s69 s77 s85 s41 s99s41 s69s109s112s116s121s32s104s111s108s100s101s114 s32s71s97s65s115s77s110s32s55s46s55s32s109s103 s84s101s109s112s101s114s97s116s117s114s101s32s40s75s41 s48 s49s48s48 s50s48s48 s51s48s48 s45s51 s48 s51 s109 s109 s97 s103 s40 s120 s49 s48 s45 s53 s69 s77 s85 s41 s100s41 s32s71s97s65s115s58s77s110s32s49s50s46s55s109s103s44s32s49s46s51s84 s32s112s117s114s101s32s71s97s65s115s32s50s44s32s49s50s46s49s109s103 s32s101s109s112s116s121s32s104s111s108s100s101s114 s32s71s97s65s115s32s101s120s112s101s99s116s101s100s32s69s77s85 s84s101s109s112s101s114s97s116s117s114s101s32s40s75s41 Figure B.5: SQUID measurements of various samples at 1.3 T. The open black squares, open red circles, open blue triangles are signals from sam- ple+holder,empty holder, and pure GaAs substrate, respectively, while the blue dashed line is the expected GaAs magnetization at 1.3 T calculated with the susceptibility from Ref. [105]. 175B.3. Summary of SQUID Measurements s48 s49s48s48 s50s48s48 s51s48s48 s48 s49 s50 s32s71s97 s49s45s120 s77s110 s120 s65s115s32s51s55s46s51s32s109s103 s32s71s97 s49s45s120 s77s110 s120 s65s115s32s49s50s46s55s32s109s103 s32s71s115s65s115s32s49s50s46s49s109s103 s84s101s109s112s101s114s97s116s117s114s101s32s40s75s41 s40 s120 s49 s48 s45 s51 s32 s101 s109 s117 s47 s40 s103 s97 s117 s115 s115 s42 s99 s109 s51 s41 s41 s32 s32 Figure B.6: The signal of the holder is removed, then the magnetization only due to the sample itself is converted into volume susceptibility. The dashed red line indicate the volume susceptibility expected for GaAs. for an example. The sample signal mmagsample is (7.425±0.515)×10−6emu, and the holder signal mmagholder is (5.82439±3.62)×10−6 emu. The sample volume V is calculated using the sample mass (12.7 mg), film thickness(dfilm = 180 nm) and substrate thickness(dsub = 0.41 mm), assuming that the den- sity of the Mn doped overlayer is the same as that of the GaAs substrate (ρ = 5.32 g/cm3): V = m ρ dfilm dsub = 0.0127 g 5.32 g/cm3 0.18 µm 410 µm = 1.048× 10−6 cm3 The volume susceptibility at 90K in the field of 13000 gauss is calculated as: χ = m mag sample −m mag holder H × V = 7.425× 10−6 − 5.8243× 10−6 13000× (1.048× 10−6) 176B.3. Summary of SQUID Measurements = 1.1749× 10−4 emu/(gauss*cm3) Note that since there is no holder information for the 37.3 mg sample, it is corrected by removing the nonzero baseline at high temperature to calcu- late the volume susceptibility (open black squares in Fig. B.6). The volume susceptibility resulting from two samples nearly overlap, confirming the re- producibility of our measurements. Taking the S/N ratio into consideration, we would use the data set measured with 37.3 mg sample to calculate the volume susceptibility of the Ga1−xMnxAs film in the β-nmr experiments. In the ferromagnetic state, since the relation M = χH does not hold (due to hysteresis), it is more appropriate to consider simply the magnetization, M in the 1.3 T field-cooled measurement. This is exactly the condition of the β-nmr experiment, so it should be directly comparable. For example, at 30K, the sample signal mmagsample is (18.50 ± 0.06) × 10−5 emu, and the high temperature baseline mmagbase is (11.25 ± 0.04) × 10−5 emu. Then the magnetization is calculated as: M = m mag sample −m mag base V = (18.50− 11.25)× 10−5 3.22× 10−6 = (22.5± 0.2) emu/cm3 = (22.5± 0.2) gauss And the demagnization field is: Hdemag = −NM = −4piM = −4pi × 22.5 gauss = −282.74 gauss 177B.3. Summary of SQUID Measurements The corresponding frequency is: γHdemag = −0.63015 kHz gauss × 4pi × 22.5 gauss = −178.2 kHz As a comparison, the frequency shift at 30 K, observed in the β-nmr exper- iment, of the broadened resonance in the overlayer is -8.51 kHz with respect to the sharp resonance in GaAs substrate (Fig. 4.7). The demagnetization effect is much larger in this case (Section 4.4.3). 178Appendix C Current Injection Experimental Setup To carry out the current injection experiment, a new current injection system was needed to allow the application of electrical current to a sample during a β-nmr run under ultra-high vacuum (UHV) and cryogenic conditions. This requires 1) a new sample holder which enables the application of a current and is compatible with the existing apparatus; 2) a system which allows current injection and does not interfere with the use of the original sample holder when current injection is not required; 3) the careful selection of materials of each part (e.g. UHV compatible, non-magnetic, etc.). The new system consists of three main components: sample holder, sam- ple clamp and socket (Fig. C.1). The sample holder is made of Oxgen-free copper, because it is non magnetic, UHV compatible and of high thermal conductivity. Both the clamp and the socket are used to help make the elec- tric connection but insulate the current from the grounded copper holder. Therefore DuPont VespelTM SP–1 was selected for its low outgassing, cryo- genic compatibility, low ware for long lifetime, and similar thermal expansion coefficient to copper (50 µm/m/K) for Vespel). The current is carried by contact springs made of 0.01 inch thick beryllium copper (BeCu) strips, which is of high strength, good electrical conductivity, UHV compatible, springy and, more importantly, non magnetic. The new sample holder is adapted from the original sample holder (Fig. C.2). The top part is unchanged, and compatible with the existing appara- tus. The flat surface works as a key to align the sample when the sample is loaded into the cryostat. The sample (usually glued to a sapphire plate) 179Appendix C. Current Injection Experimental Setup Figure C.1: Three main components of the current injection system: sample holder, sample clamp, and socket. is held in a recess with a window behind to minimize the thermal mass and also β electron absorption. Compared to the original holder, the recess is extended vertically to allow space for electrical contacts. There is a lip and a recess at the bottom for the sample clamp (attached with a M2 screw) which is designed to provide clamping force on the sample and make electric connection when screwed down to the holder. Two metallic BeCu springs are held in the recesses on the clamp to carry current to the sample (Fig. C.3 Left panel). The springs are wrapped around the clamp and make electrical contact with both the sample and the socket below. The socket assembly engages the holder assembly with the clamp when they are inserted to make the electric connection. Two BeCu strips, carrying current to the springs on the clamp, are held in the socket with screws from both top and bottom. The strips are connected to a current source through the strip bottom by lead wires. The through screw holes are vented from the side of the socket to maintain the UHV environment required by the β-nmr 180Appendix C. Current Injection Experimental Setup Figure C.2: Left: original and new sample holders. Right: Details of new sample holder experiment. Two additional holes opposite the BeCu strips are reserved for the rf antenna, a diagnostic device for the spectrometer. The socket is attached by a bottom copper plate to the copper sample enclosure. A small cut-away in both the socket and the plate ensures the correct orientation of the socket. Fig. C.4 shows the assembled current injection system with a sample in the cryostat. The limited space inside the copper housing constrains the dimension of the current injection system. The spacing of the coils determines the maximum width of the sample holder and the clamp, less than 9 mm. The height of the socket is limited by the position of the Helmholtz coil. However, the socket height is kept even lower to minimize the thermal load on the cryostat. All screws used in this system are titanium M2 screws which are non magnetic. The two lead wires to the socket are Kapton insulated UHV copper leads (KAP3) from MDC that begin at SHV feedthroughs on the cryostat. These existing feedthroughs were then adapted to standard RCA bananaplug con- nectors. The total resistance of twol lead wires including the banadaplug is 1.3 Ω at room temperature. The 0937 current source is made at TRIUMF. The range of the current source is (-500 mA, +500 mA) with the resolution of 1 mA. 181Appendix C. Current Injection Experimental Setup Figure C.3: Left: the front and back side of the vespel clamp with two BeCu springs. Right: the vespel socket sitting on the bottom plate of the Copper housing. Two BeCu strips are bolted to the vespel socket with titanium M2 screws. Figure C.4: The assembled current injection system with a sample in the cryostat. 182Appendix D Sample Preparation for Current Injection Experiment This section describes how the samples were prepared for the in-situ current injection experiments detailed in Chapter 5. Gold (Au) pads for making elec- trical contact were thermally deposited on both sides of the Au/Fe/nGaAs sample by the thermal evaporator in the cleanroom at AMPEL, UBC. The evaporator is capable of depositing 4 types of thin films once the sample is loaded inside the chamber. Fig. D.1 shows the geometry of the contacts on the front (left panel) and back (right panel) side. All contacts were deposited at room temperature in high vacuum (∼ 5× 10−6 Torr). Inside the thermal evaporator, the sample was arranged upside down to face the Au source below to deposit the contacts on the front side. In order to protect the thin MBE heterostructure, we made a special holder with a set of s48s46s53s32s109s109 s51s32s109s109 s49s32s109s109 s49 s46 s53 s32 s109 s109 s52s32s109s109 s54 s32 s109 s109 s50 s32 s109 s109 s50s32s109s109 Figure D.1: The geometry of gold contacts on the front (left) and back (right) side of Au/Fe/nGaAs sample. 183Appendix D. Sample Preparation for Current Injection Experiment Figure D.2: Left: the sample holder and masks for the termal evaporation. Right: The section view of the assembled thermal evaporator sample holder. masks(Fig. D.2) under the help of P. Dosanjh from UBC. When it is loaded into the evaporator, the front surface is supported and protected by Mask 2 only touching the sample edges and leaving the center area untouched (Fig. D.2). On the front side of the sample is the 20 ML thick Au layer to protect the Fe layer from oxidation. The Au pads were deposited directly on the MBE Au layer and had a thickness ∼194 nm estimated by a quartz crystal thickness monitor. There is a window on the backside of the evaporation sample holder, which is used as the mask when evaporating the Au contacts on the backside of the sample (Fig. D.2). Before the backside Au contact is made, a very thin layer of Ti (∼ 3 nm ) was deposited. Because Au does not stick to GaAs very well, a direct deposition of Au onto GaAs would not result a long-lasting Au layer. Ti helps to smooth the unpolished GaAs backside, and improves the contact bond to GaAs[193]. Right after the Ti layer was evaporated, the back Au contact (∼195 nm) was deposited without breaking the evaporator chamber vacuum. Between the copper β-nmr sample holder and the Au/Fe/nGaAs sample, there is a 8×15×0.5 mm3 sapphire plate (one-side polished) to insulate the electrically biased sample from the conductive sample holder and connect the sample to the current source. To conduct current to the sample, a layer of gold (∼195 nm) is also thermally evaporated on the polished side of the sapphire plate. A thin layer of Ti (∼3 nm) was deposited prior to the Au layer to help gold better bond to the sapphire. The pattern of the 184Appendix D. Sample Preparation for Current Injection Experiment Figure D.3: Left: the geometry of the gold contacts on the sapphire plate. Right: The sample assembled on the sapphire plate. gold contacts pads on the sapphire is shown in left panel of Fig. D.3. The right pad is bonded to the back contact of the sample with UHV compatible silver paint (cured at room temperature), and the left pad is connected to the sample front pads via fine gold wires (0.001” in diameter). The fine gold wires were installed by a gold wire bonder in the lab of J. Folk from UBC with the assistance of M. Studer. The BeCu springs make contact with the gold pads when the sample is clamped down to the holder, making electrical contact. Therefore a small gap at the bottom of the gold pattern is required so that the gold will not be short-circuited by contacting with the copper sample holder. A picture of the sample assembled on the sapphire plate is shown in the right panel in Fig.D.3. 185

Cite

Citation Scheme:

    

Usage Statistics

Country Views Downloads
Canada 19 0
United States 16 0
Republic of Korea 13 2
China 10 0
Germany 6 12
France 4 0
Ukraine 3 0
India 2 0
Japan 1 0
Ethiopia 1 0
City Views Downloads
Unknown 31 14
Vancouver 16 0
Beijing 8 0
Ashburn 6 0
Palo Alto 3 0
Shenzhen 2 0
Redmond 2 0
Edmonton 1 0
Cheyenne 1 0
Lewes 1 0
Richland 1 0
Mountain View 1 0
Plano 1 0

{[{ mDataHeader[type] }]} {[{ month[type] }]} {[{ tData[type] }]}
Download Stats

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.24.1-0073399/manifest

Comment

Related Items