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Microwave surface resistance measurements of YBa2Cu3o6+x single crystals and melt textured slabs employing… Dosanjh, Pinder S. 2001

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Microwave Surface Resistance Measurements of Y B a 2 C u 30 6_ l_ x Single Crystals and Melt Textured Slabs Employing a Niobium Double Sp'lJt-Ring Resonator By Pinder S. Dosanjh B. Sc. University of British Columbia, 1989 A T H E S I S S U B M I T T E D I N P A R T I A L F U L F I L L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F M A S T E R O F S C I E N C E in-T H E F A C U L T Y O F G R A D U A T E S T U D I E S D E P A R T M E N T O F P H Y S I C S A N D A S T R O N O M Y We accept this thesis as conforming to the required standard T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A April 2001 © Pinder S. Dosanjh, 2001 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of Br i t i sh Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be ahowed without my written permission. Department of Physics and Astronomy The University of Br i t i sh Columbia 6224 Agricul tural Road Vancouver, B . C . , Canada V 6 T 1Z1 Date: Abst rac t The microwave surface impedance of YBa2Cu3OQ+x was measured using a new nio-bium split-ring resonator. For the first time it is shown that this resonator geometry allows one to measure both small single crystals and large area slabs employing the same resonator assembly. B y careful polishing of the niobium surfaces the niobium split-ring resonator has achieved a resolution of 0.2fiQ at 2.079GHz, about a factor of 5 better than its predessesor. Results are presented on both the a and b axis at 2.079GHz and 2.942GHz for a high quality YBa2Cu30e 5 OrthoII single crystal as well as results on two YBa2C'ii30e+x top seeded melt textured slabs. The single crystal results show significant frequency dependence over the narrow range studied, an indication that the width of the Drude peak is less than what has been observed in optimally doped YBa2CusOe+x- The scattering rates for both the a and b axis are not well described by a single rate; this is suggestive of two processes contributing to the scattering. As well, the scattering rate in the b direction seems to be impuri ty limited. Measurements on the two melt textured slabs show that changing the YiBaxCu\0^ concentration from 15-3% has little effect on the surface resistance in the superconducting state. A t 77K, the surface resistance for the best slab is only a factor of 1.3 higher than that reported for the best Tl^Ba^CaiCu^OA thin films. 1 1 Table of Contents Abstract i i Table of Contents i i i List of Figures vi List of Tables ix Acknowledgements x 1 Introduction 1 2 The High Temperature Superconductor Y B a 2 C u 3 0 6 + x 4 2.1 Growth and Crystal Structure of YBa2Cu306+ x 4 2.1.1 Detwinning 7 2.1.2 Oxygen Annealing 7 3 The Split-Ring Resonator 11 3.1 History, of the Split-Ring Resonator at U B C 11 3.2 Pb:Sn Double Split-Ring Resonator 15 3.3 Limitat ions W i t h the Previous Design 15 4 The Niobium Double Split-Ring Resonator and Experimental Probe 16 4.1 Niobium Electropolishing 16 4.2 Niobium Anodizing 18 i i i 4.3 M a i n B o d y - . . . . 20 4.4 Assembly of the Double Spi l t -Ring 21 4.5 The Top Loading Experimental Probe 23 4.5.1 Insert 23 4.5.2 Sample Mount 24 4.5.3 Chip Thermometer/Heater Mount ing Procedure 26 4.6 A x i a l Alignment 27 4.7 Measurement Electronics 28 4.8 Sapphire Plate Thickness and Resonant Frequency 30 4.9 Magnetic and Electric A x i a l F i e ld Profile 32 4.10 Probe Systematics 36 4.10.1 Frequency Drifts 38 4.10.2 Niobium Surface Ageing 38 4.10.3 Thermal Cycl ing Effects 40 5 Single Crystal Measurements and Results 42 5.1 Measurement Procedure 42 5.1.1 Background Corrections 45 5.2 Calibrat ion Technique 47 5.2.1 Reproducibili ty 50 5.3 Single Crystal Results 55 6 Melt Textured Slab Measurements 64 6.1 Melt textured crystal growth parameters 64 6.2 Measurement Technique 65 6.3 Background Corrections and Lead Calibrat ion 68 6.4 Results 71 i v 7 Conclusions 74 7.1 OrthoII results 74 7.2 Mel t textured slab results 75 7.3 Future improvements 75 7.4 Future work 76 Bibliography 78 A PbSn plating Solution and Procedure 81 A . l Pla t ing solution 81 A.2 Plat ing procedure 81 v List of Figures 2.1 A schematic of the growth set-up used for the production of high purity Y B a 2 C u 3 0 6 + T crystals 8 2.2 The crystal structure of Y B a 2 C u 3 0 6 + x showing the C u sheets and chain formation 8 2.3 Ideal oxygen contents that lead to ideal ordered phases for Y B a 2 C u 3 0 6 + x - 10 4.1 Schematic of the apparatus used for electropolishing niobium metal. . . . 19 4.2 Schematic of the apparatus used for anodizing niobium metal 19 4.3 Picture comparing the old resonator body design to the new 21 4.4 Schematic of the electronics 29 4.5 Frequency shift as a function of position for a Pb:Sn sample. The arrow points to the region of optimum uniform magnetic field for the 2.079GHz resonator 35 4.6 Frequency shift as a function of position for the Pb:Sn sample and the sapphire plate smeared with a small quantity of grease. The data for the sapphire plate has been multiplied by -1 35 4.7 Frequency shift as a function of position for a Pb:Sn sample. The arrow points to the region of optimum uniform magnetic field for the 2.9GHz resonator 37 4.8 Frequency shift as a function of position for the Pb:Sn sample and the sapphire plate smeared with a small quantity of grease. The data for the sapphire plate has been multiplied by -1 37 vi 4.9 Ageing of the niobium resonator assembly as a function of run# 39 5.1 Schematic of the double split-ring resonator showing the sapphire support posts, cutoff tube, and the sapphire plate that holds the sample 44 5.2 Sapphire and grease background for the 2.079GHz and 2.942GHz resonators. 46 5.3 Schematic of a sample in a magnetic field that is parallel to its broad face. 48 5.4 Schematic of a sample in a magnetic field that is perpendicular to its broad face 48 5.5 Plot ted is the Resistivity of pure Lead vs A ( l / Q ) 2 obtained for the Pb:Sn calibration sample for the 2.079GHz (top panel) and 2.942GHz (bottom panel) data sets 51 5.6 Variation of A ( l / Q ) for four different positions along the axis of the res-onator 53 5.7 The same data is plotted here again after each data set was multiplied such that each data set coincided with the data set taken at position zero. 53 5.8 Raw A ( l / Q ) data for the OrthoII data set 56 5.9 The b-axis surface resistance for a Y x P ^ C u s O ^ . s ) OrthoII crystal after applying thin l imit corrections 56 5.10 The a-axis surface resistance for a Y 1 B a 2 C u 3 0 ( 6 . 5 ) OrthoII crystal scaled by J2 57 5.11 The b-axis surface resistance for a YiBa2Cu30(6.5) OrthoII crystal scaled by f2 57 5.12 Low temperature 6X results plotted with 6X data obtained by Saeid K a m a l using the loop gap resonator 59 5.13 The a-axis conductivity for a Y iBa2Cu30( 6 . 5 ) OrthoII crystal 60 5.14 The b-axis conductivity for a Y 1 B a 2 C u 3 0 ( 6 5) OrthoII crystal 60 vii 5 . 1 5 The scattering rate for both the a and b-axis is plotted for two separate frequencies 6 3 6.1 Cross sectional schematic of the split-ring resonator 6 7 6 .2 A plot of A ( l / Q ) vs A f as a function of the axial position of a slab. . . . 7 0 6 . 3 Plot ted is the Resistivity of pure Lead vs A ( l / Q ) 2 obtained for the Pb:Sn calibration sample 7 0 6 . 4 Surface resistance in the normal state comparing a commercial slab, two U B C melt textured slabs, and a twinned high quality Y BaiCu^O^x single crystal 7 3 6 .5 Surface resistance in the superconducting state comparing a commercial slab, two U B C melt textured slabs, and a twinned high quality YBa2Cu^O^+x single crystal 7 3 vm List of Tables 4.1 Typica l variation of the resonant frequency for different thickness sapphire plates 31 4.2 Resonant frequency as a function of plate thickness and surface quality of the clamping surface 32 4.3 Variation of the resonant frequency between 4.2K and 1.2K for a split-ring having sanded clamping surfaces 41 4.4 Variation of the resonant frequency between 4.2K and 1.2K for a split-ring having hand polished clamping surfaces 41 5.1 Variation of the calibration constant for three separate runs 54 6.1 A comparison of the surface resistance at 77K for a commercially available melt textured slab, a thall ium thin film from STI , two U B C melt textures samples, and a U B C twinned Y Ba^Cu-iO^x single crystal 72 ix Acknowledgements First and foremost, I would like to thank my supervisor, Dr . Doug Bonn, for allowing me to persue this work. I would like to thank Dr. Walter Hardy from whom I have learned a great deal about Physics. I would also like to thank Dr . J i m Carolan for introducing be to the world of Physics. For being extremely understanding, I would like to thank my three girls, Jenna, Simrin, and K a m . x Chapter 1 Introduction Superconductivity is a fascinating phenomenon. The ability of a material to carry electri-cal current without any dissipation is something that is truly unique. After the discovery of superconductivity in 1911 by Onnes[l], it took almost half a century before an ade-quate theory was put fourth in 1957 by Bardeen, Cooper, and Shreffer[2] ( B C S theory), an indication of the true complexity of the problem. B C S theory was ground breaking because it provided a solid theoretical understand-ing of superconductivity. The theory adequately described a number of experimental results and made a number of predictions. In particular B C S theory predicts a transition temperature T c given by, Tc = QDexp(-l/X) (1.1) where QD is the Debye temperature and, A is the electron phonon coupling constant. W i t h a typical Debye temperature of a few hundred Ke lv in , and with an upper l imit for A of 0.5 (weak coupling), the maximum critical temperature would fall in the range 40-50K. It was thus established that superconductivity was, and would remain, a low temperature phenomenon. In 1964 Lit t le hypothesized that one might be able to ob-serve room temperature superconductivity in an organic material[3]. Li t t le suggested that if one could replace the normal electron-electron interaction found in B C S theory by the interaction of conduction electrons with bound electrons one could raise the super-conducting transition temperature to well above room temperature. Although a room temperature superconductor has not yet been discovered, the first organic superconductor 1 Chapter 1. Introduction 2 was discovered in 1980 having a T c of 1.2K. Six years later, in 1986, the discovery of H j T c superconductivity came as a complete surprise to the scientific community. Overnight, the maximum transition temperature had jumped from 23K (Nb 3 Ge) to an impressive 35K (Ba-La-Cu-O) . In 1987 the first "real" H j T c material, Y B a 2 C u 3 0 6 + a ; wi th a transi-tion temperature of 95K, was discovered[4]. The discovery of H j T c superconductivity re-ignited the quest for a thorough theoret-ical understanding of superconductivity at high temperatures. As well, the experimental situation was just as challenging. Whereas conventional superconductors were typically metals, and high purity samples were readily available, the new high temperature materi-als were oxides and presented a considerable challenge to the material science community. Moreover, since the superconducting transition itself is a phase transition between two states, it was important to gain an understanding of both the superconducting and normal state properties. Herein lay a number of difficulties. In the normal state the H^T C mate-rials consistently displayed a resistivity that was linear with temperature suggesting that normal fermi-liquid theory would not apply, and thus, one did not understand the normal state. W i t h upper critical fields approaching 100T it was also impossible to quench the superconductivity and observe normal state behaviour down to zero temperature. As well, the extremely short coherence lengths made tunnel junction fabrication extremely difficult. The combination of problems outlined above, combined with a multitude of others, rendered a number of conventional experimental techniques inadequate. A t U B C , the drive has been to understand the superconducting state of the high temperature superconductors by exploring the electrodynamics of YBa2Cii306+ x- The electrodynamic properties in the superconducting state can reveal information about a number of fundamental properties such as the quasiparticle excitations, structure of the gap, and scattering. A very common method for investigating the electrodynamics of materials is by microwave measurements, in particular, cavity perturbation techniques. Chapter 1. Introduction 3 However, the main difficulty with traditional cavity techniques is the large cavity volume when operating at low frequency. Given the difficulty in producing large single crystal samples, the traditional cavity techniques simply do not have the required sensitivity. A breakthrough in the technique came with the use of split ring resonators. This thesis is, in part, a continuation of this work. Chapter 2 The High Temperature Superconductor Y B a 2 C u 30 6 + x A large number of oxide superconductors have been identified[5] since the ini t ial dis-covery of superconductivity in B a - L a - C u - 0 by Bednorz and Muller[4]. However, of all H j T c materials, YBa2Cu 3 06+ x has received the most attention due to the availability of phase pure single crystals. Unlike the case for conventional superconducting metallic compounds, (or superconducting metallic elements) where single crystal growth is rela-tively straightforward 1, H j T c materials with high puri ty are rather difficult to produce. This chapter presents an overview of the growth and oxygen dynamics of Y B a 2 C u 3 0 6 + x . 2.1 Growth and Crystal Structure of Y E ^ C u s O e + i YBa2Cu3C>6+a; single crystals were grown in high density BaZr03 crucibles, a significant achievement given the difficulty in preparing B a Z r 0 3 crucibles[6] [7] [8]. Generally, due to the highly corrosive nature of the B a O - C u O flux at high temperatures, very few crucible materials can survive for extended time periods. Moreover, most commercial crucible materials, such as Y S Z , tend to form reactive byproducts that l imit the size of the crystals by continously shifting the melt composition during growth, or the crucibles themselves introduce significant impurities. Specific advantages of a B a Z r 0 3 crucible include: • The crucibles are inert to the melt. 1 S i n g l e crystal growth of any form is somewhat of a black art. T h e combinat ion of a number of elements reacting w i t h oxygen at high temperature (1000°C or more) and the incongruent mel t ing of the materials is what makes H;TC crystal growth especially difficult. 4 Chapter 2. The High Temperature Superconductor YBa2CusOQ+i 5 • Long crucible lifetime at high temperatures. • Increase purity of the crystals. • Ab i l i t y to grow more, and potentially, larger single crystals. A typical growth run first starts with packing a 10 ml BaZrOa crucible with about 26 grams of a 10 wet.% Y B a 2 C u 3 0 6 + x and 90 wet.% B a O - C u O eutectic mixture that has been calcined at 890°C to reduce the volume. The crucible is then heated to 1020°C and held at this temperature for 15h to melt the powders. Once melted, the eutectic mixture is then cooled to 1000°C and held at this temperature for 0.5h, followed by a slow cool at a rate of 0 .3-1.0°C/h to 960°C. To expose the Y B a 2 C u 3 0 6 + x crystals, the crucible is decanted at 960°C and the furnace turned off and allowed to cool to room temperature. Due to the weak adhesion at the edges of the crystal to the crucible wall, the extraction of the crystals is easily accomplished by the use of tweezers. The crystals typically have dimensions of several millimeters within the a-b plane and show remarkable crystallinity. The X-ray rocking curve of Y B a 2 C u 3 O 6 + x ( 0 0 6 ) shows a F W H M of just 0.007°, and chemical analysis performed using an I C P - M S instrument indicate that the overall purity of the crystals is between 99.99 and 99.995 at.%. However, the asgrown crystals are imperfect in two respects: twinning of the a-b axes and an oxygen content that is inhomogeneous and not well known. Bo th problems are easily overcome, first by applying uniaxial pressure within the a-b plane to detwin the crystal, and by post annealing in a pure oxygen atmosphere to accurately define the oxygen concentration. The crystal structure of Y B a 2 C u 3 0 6 + x falls under the category of an oxygen deficient layered perovskite. W i t h four elements the crystal structure is complex; however, only two structural features are of importance here: the oxygen chain formation along the b-axis which controls the doping 2 , and the two dimensional copper oxygen planes that 2 This chain formation is exclusive to the Y-Ba-Cu -0 system. Chapter 2. The High Temperature Superconductor YBa2Cu^0Q+ 6 are responsible for the superconductivity. A t an oxygen content of precisely 6.00 the oxygen chain sites are completely empty and within the a-b plane the a and b axis have equal dimension, and thus the structure is tetragonal. A t this oxygen concentration the system is also an antiferromagnetic insulator. A s oxygen atoms are added to the chain sites, holes are doped onto the two-dimensions copper oxygen planes due to a charge transfer [9] [10]. Initially as oxygen atoms are added they are randomly distributed within the chain layers. However, as more oxygen is added, the chain oxygen atoms begin to cluster forming short one-dimensional chains having lengths of about 2-3 atoms. The system at this point is st i l l tetragonal unti l an oxygen content of 6.35 has been reached. Beyond an oxygen content of 6.35 the average chain length increases and a structural transition occurs which drives the structure into an orthorhombic state. At the same time, as oxygen is added to the structure the lattice parameters are continuously affected[ll]. It is not unti l the crystal structure is actually orthorhombic that superconductivity is observed. It should be pointed out however, that right at the orthorhombic-tetragonal transition it is unclear whether antiferromagnetism and superconductivity co-exist and a large body of work exists addressing this issue both from an experimental and theoretical point of view. Once the structure is orthorhombic the crystal is also prone to twinning. Twinning occurs within the a-b plane and is a method for the crystal to decrease mechan-ical stress during the cool down stage. After growth and once cooled, the twinning wil l exist indefinitely. Whi le cooling, domains are created having the b-axis flipped by 90°, effectively averaging out the a-b plane anisotropy that is inherent for an orthorhombic crystal structure 3 . 3 A typical twinned sample will visibly display a large number of twin boundaries Chapter 2. The High Temperature Superconductor Y B a 2 C113 0 6 + x 7 2.1.1 Detwinning Detwinning of the crystals is undertaken in a dry oxygen atmosphere with the crystal sitting on a ceramic YBa 2 Cu30 6 + : ; . support while being held between two stainless steel jaws that are each covered with a thin gold sheet 4. The Y B a 2 C u 3 0 6 + x support itself sits on a stainless steel platform that is heated from below using a 600W halogen lamp. Pressure along the plane of the crystal is applied via a spring loaded plunger located behind one of the jaws. W i t h pressure continously applied to the sample the temperature of the crystal is slowly Increase while the twin structure is monitored through an optical microscope. The sample is il luminated by polarized white light and is situated so that specular reflection off the surface wil l pass through an eyepiece. One eyepiece also has a r polarizer attached to it, with the combination of polarizers highlighting the twin structure via a plurality of colours. After a successful detwinning procedure the crystal wi l l appear to have a uniform colour over it 's entire surface, an indication that at least on an optical scale, the crystal has completely detwinned. Since Y B a 2 C u 3 0 6 + x is orthorhombic it is easily verified that the axis under pressure during detwinning wil l be the a-axis of the crystal, while the other axis which was not under uniaxial pressure evolves into the b-axis. 2.1.2 Oxygen Annealing To set a well defined oxygen content the crystal is post annealed in pure oxygen. Using a tube furnace dry (high purity) oxygen gas at 1 atm is introduced into the center of a quartz tube in close proximity to where the crystal is located. This ensures that airy-evolved impurities within the quartz tube are quickly and efficiently flushed from the sys-tem. B y setting a particular temperature, the oxygen partial pressure for YBa2Cii306+.T 4 T h e gold sheet protects the Y E ^ C u s O g + x crystal from contaminat ion . G o l d w i l l work well for temperatures less than about 5 0 0 ° C . Chapter 2. The High Temperature Superconductor Y B a 2 C113 06+^ 8 (D Crucible © Ceramic roll © Porous Ceramic @ Ceramic supporter © Quartz glass rod © Furnace Figure 2.1: A schematic of the growth set-up used for the production of high purity YBa2Cii306+ x crystals. Once the growth time has expired the crucible is carefully pushed over and the remaining l iquid is allowed to drain. Figure courtesy of Ruix ing Liang. Figure 2.2: The crystal structure of Y B a 2 C u 3 0 6 + I showing the C u sheets and chain formation. The chain oxygen sites are responsible for doping the system with mobile charge carriers. Figure courtesy of Ruixing Liang. Chapter 2. The High Temperature Superconductor YBa 2 CU3 06+: 9 is well understood and once the crystal has equilibrated wi th the surrounding tempera-ture its oxygen content wi l l be well defined. Quenching the crystal, by removing it from the furnace, wi l l lock-in that oxygen content. The oxygen phase diagram for Y B a 2 C u 3 0 6 + x is extremely complicated when oxygen ordered phases are taken into account. Although the procedure outlined above works well for almost fully oxygenated Y B a 2 C u 3 0 6 + x , it fails when trying to set oxygen levels close to the orthorhombic-tetragonal phase boundary due to oxygen phase separation[12]. Near this boundary one must set the oxygen content such that the chain oxygen is able to order into full and empty chains only. For example, the OrthoII phase has alternating full and empty chains, and the OrthoII I phase has two full chains separated by one empty chain. Figure 2.3 illustrates the ideal ordering phases and the ideal oxygen concentration required to realize such ordering. To achieve these ordered phases experimentally one must first set the overall oxygen concentration correctly and then anneal the crystal at low temperature (50-100°C) for a sufficient time. W i t h high purity crystals, such as those grown in BaZrOs, the high oxygen mobil i ty 5 allows one to achieve such ordering in a reasonable time and produce highly ordered OrthoII samples[13]. 5 T h i s high mobility is a direct consequence of the high purity of the crystal. As an example, small amounts of aluminum, which will sit on the copper chain site, can decrease the oxygen mobility by a few orders of magnitude without significantly lowering T c Chapter 2. The High Temperature Superconductor YBa2 C113 10 T (x<0.3) • o o o o o o o o * • (^•••••••o«o»o»o»o» o o o o o o o o o * •o»o»o»o»o»o»o«o»o» o o o » o o o » o o •••o»o«o»o»o»o»o»o» o o o » o » » o o o •o«o«o»o»o«o»o»»»o» o o o » o o o o » » O i l (x=0.5) • o » o » o » o « o •o»o»o»o»o»o»o»o»o« • o « o » o » o » o •o«o«o»o»o«o»o»o»o» • o » o « o « o » o •o»o»o»o»o»o«o»o»o« • o « o « o » o » o •o»o»o»o»o»o»o»o»o» • o # o # o # o < i o OV (x=0.6) • • o » o » « o « o •o»o«o»o«o»o»o»o»o» • • o » o » » o « o •o»o«o»o»o»o»o«o»o« • • o » o » . » o » o •o»o«o»o»o»o»o»o»o» • • o » o » » o « o •o»o«o»o»o»o»o«o»o» • • o » o « » o * o OI (x=l) o»o»o»o»o»o«o«o«o» • • • • • • • • • o«o»o»o»o»o«o«o»o» • • • • • • • • • o«o«o»o«o»o»o»o»o» • • • • • • • • • o»o»o«o»o»o«o»o»o» OIII (x=0.67) • 0 « « 0 « « D « o»o»o«o»o»o«o»o»o» • o « » o » « o » o»o»o»o»o»o»o»o»o» • o # « o * « o « o»o»o»o«o«o«o«o»o» • o « « o « « o * o»o«o»o»o»o»o»o»o» • o « « o « « o * OVIII (x=0.625) • o « o « « o « « o»o»o«o»o»o»o»o»o» • o » o » « o » » o«o»o«o»o»o«o«o»o» • o « o « * o « « o»o»o«o»o»o»o»o»o» • • • • • • o«o»o»o»o»o«o»o»o« • o « o « # o « « Figure 2.3: Ideal oxygen contents that lead to ideal ordered phases for Y B a 2Cu30 6 + ; c. Below x=6.3 the system is tetragonal and non-superconducting. Chapter 3 The Split-Ring Resonator The split-ring resonator has proved to be a very useful tool for studying the electrody-namics of the high temperature superconductors. The ability to measure the microwave surface resistance with high precision on small samples is challenging. Cavi ty perturba-tion techniques have been around for a very long time and one of the first experiments performed on Y P ^ C u s O e + z was the measurement of R s . Unfortunately the crystals available at the time were only l m m x l m m at best, and posed a considerable challenge for cavity perturbation techniques given the extremely low filling factors. In fact the best resolution early on was only about 400micro-ohms at 10GHz[14][15], masking the won-derful underlying physics. It was not until the Pb:Sn plated copper split-ring resonator was used explicitly for small superconducting samples that the instrument resolution al-lowed one to probe the electrodynamics of H j T c wi th any real precision. In this chapter we take a brief look at the early days of the split-ring resonator at U B C and its developj-ment and evolution as a key tool for exploring the electrodynamics of high temperature superconductors. 3.1 History of the Split-Ring Resonator at U B C The term "split-ring resonator" was first coined by Hardy and Whitehead[16] at U B C . The init ial reason for development of the split-ring resonator was the lack of resonators in the 200MHz-2GHz frequency range, having large filling factors, suitable for studying atomic Hydrogen at low temperatures[17][18]. A key advantage of the split-ring design 11 Chapter 3. The Split-Ring Resonator 12 was the uniform magnetic field produced within the bore region. In contrast, a conven-tional cavity resonator exhibits a uniform magnetic field over a very small region within its volume, l imit ing the size of the sample, which in turn is reflected in low filling factors. The split-ring design thus provides a solution for fabricating a resonator that has a large filling factor, operating in the range of 200MHz to a few G H z , while maintaining a high Q. In early 1979, the split-ring resonator was successfully employed for one of the first1 magnetic resonance studies of an atomic hydrogen gas at liquid-helium temperatures [18]. These init ial studies lay the foundation for understanding the interactions at low temper-ature of atomic hydrogen[19], eventually leading to the development of the all-cryogenic hydrogen maser[20][21]. The split-ring resonator used for the hydrogen maser was a copper resonator with a typical Q of 50000 at 0.5 K . In 1987 an undersized version of the U B C recirculating cryogenic hydrogen maser was demonstrated to have short term stability comparable to the best hydrogen masers of the time, with expectations that a full version would have an order of magnitude better stability[21]. It was not unti l 1992 that the split-ring resonator was again used at U B C . Doug Bonn and Walter Hardy initiated a program of exploring the microwave properties of the then recently discovered high temperature superconductors using the spilt-ring res-onator. Once again the choice of employing the split-ring resonator arose from a physical constraint of small single crystal samples 2 It was evident from the start that in order to measure extremely low loss samples the Q of the resonator needed to be higher than l x l O 6 . To achieve such high Q's the 1 A paper by S. Crampton et al appearing in the same journal as [18] was the second observation of magnetic resonance at low temperatures 2 B y 1990 the compound YBa2Cu30e+ x had been identified but large single crystal samples could not be grown. The largest samples at the time had dimensions of approximately 0.5mmx0.5mmxl0/im rendering perturbation measurements using conventional cavities impossible. Even to this day high purity YBa2Cu30e+ x single crystals suitable for cavity perturbation methods are no larger than about 1.5mmxl.5mmx50/im at the extreme, making them ideal for the split-ring resonator. Chapter 3. The Split-Ring Resonator 13 split-ring resonator itself needed to be manufactured using a very low loss material. The solution adopted to achieve such high Q's was to electroplate a copper split-ring wi th lead. One key problem that had to be overcome was the quick oxidation of a pure lead surface exposed to air. To deal with this problem the copper surfaces were electroplate wi th a Pb:Sn alloy. To stop, or greatly decrease the oxidation rate of pure lead only about a 5% substitution of t in for lead was required. This low t in concentration also ensured that the transition temperature remained high, maximizing the attainable Q at 1.2 K . For the case where the split-ring required Pb:Sn plating, the resonator needed to be built from three separate pieces which were then assembled to form the actual resonator. The need for the assembly arose from problems encountered when trying to electroplate a very narrow gap region. The average gap spacing for the Pb:Sn split-ring resonator was approximately 0.050"-0.100" making it impossible to cover all of the copper surface within the gap region. One of the main problems encountered when assembling a split-ring resonator from a number of individual pieces was the introduction of weak link problems at the joints. This problem with the design was never completely overcome, although, if the resonator was fastened tightly the weak link problems could be significantly reduced. Nevertheless, the sensitivity of this early Pb:Sn split-ring resonator was sufficient to shed new light on the electrodynamics of high temperature superconductors. Reference [22] outlines in detail the performance characteristics of a Pb:Sn plated copper split-ring resonator, as well as procedures for measuring Q's with high precision. Using the Pb:Sn plated split-ring resonator Bonn et al[23] were able to study the electrodynamics of the quasi-particles below T c in a high quality Y 1 B a 2 C u 3 0 ( 6 9 5 ) single crystal. The results were very unexpected, revealing a thermally excited quasiparticle scattering rate that rapidly decreased below T c . This rapid drop in the scattering rate was manifested in a broad peak like feature, centered around 35K, found in the surface Chapter 3. The Split-Ring Resonator 14 resistance and was attributed to a competition between the normal fluid density and the scattering rate. It was also postulated at the time that the addition of impurities would decrease the surface resistance rather than increasing the surface resistance as intuition would suggest. By systematically doping high purity Y B a 2 C u 3 0 6 + x single crystals with impurities such as Zn, and Ni, it was subsequently proven by Bonn and co-workers that indeed, the surface resistance of YBa 2 Cu306+:E decreased with the addition of such impurities3[24, 25, 26, 27, 28, 29]. At about the same time as the experiments of Bonn, another experiment was under-way at U B C to address the problem of resolving the underlying symmetry of the high temperature superconductors. Using a novel split-ring resonator, Hardy et al[30] were able to measure the London penetration depth (A) of YBa 2 Cu306+! to great precision4. With a single crystal sample held rigidly in a uniform magnetic field of the split-ring (or loop gap) resonator, the frequency was accurately recorded as the sample temper-ature was changed. The corresponding frequency shift was mapped to a change in the penetration depth and thus the temperature dependence of the penetration depth was determined. What was strikingly evident was the linear temperature dependence found at low temperature, which was in complete contrast to the expected temperature depen-dence of a conventional s-wave superconductor and was thus one of the first pieces of evidence suggesting an unconventional gap symmetry. In fact, the linear temperature dependence was consistent with a gap symmetry that was d-wave in nature. A number of experiments now have solidified the notion that the gap symmetry of Y B a 2 C u 3 0 6 + I is d-wave[31]5. 3 T h i s was an impor tan t achievement because i t proved that the lower microwave loss measured i n t h i n films was due to impuri t ies found i n the films rather than the films being of higher qual i ty than the U B C single crystals . 4 Reference [30] was one of the ten most ci ted papers of the year. 5 Reference [31] is an excellent overview of experiments t ack l ing the question of the pa i r ing symmetry i n the cuprate superconductors w i t h an emphases on phase sensitive techniques Chapter 3. The Split-Ring Resonator 15 The next set of experiments performed at U B C employing the split-ring were under-taken by David Morgan as part of a P h D thesis [32]. Morgan was measuring the flux flow resistivity of YBa2Cu306+ x at 5.4GHz using a copper split-ring, operating at 4.2 K , in a magnetic field. Since the flux flow resistivity measurements were all performed in the normal state, a cooled copper cavity had sufficient resolution 6 3.2 Pb:Sn Double Split-Ring Resonator Most recently, Gowe[33] designed and tested a split-ring resonator that overcame the weak link problems encountered in the original Pb:Sn split-ring configuration[22]. This new design was based on two half cylinders, freely supported via two sapphire rods within a Pb:Sn plated copper cutoff tube, clamping a thin sapphire plate. B y adopting the double split-ring design Gowe was able to measure the microwave surface resistance of low loss Tl^Ba^C'a^Ci^OA films with a resolution of lfxQ at 2 .4GHz and 5/iCl at 910MHz. 3.3 Limitations With the Previous Design Gowe's design overcame a number of assembly and weak link problems, however, the experimental apparatus still had a number of limitations. In particular, the Q quickly degraded from ageing of the Pb:Sn plated copper ring set and accurate data at low temperatures was rather difficult. Also, the design of the apparatus allowed easy rotation of the sample making it difficult to unload and load a sample while maintaining an accurate orientation. In addition, the design of the cutoff tube was such that the thermal link to the Helium bath occured via a grease thermal boundary. The present work has addressed these issues in an effort to improve upon the double split-ring design. 6 O f course it would not be possible to use a Pb:Sn plated copper resonator in a magnetic field exceeding the lower critical field of the Pb:Sn alloy. Chapter 4 The Niobium Double Split-Ring Resonator and Experimental Probe One of the main problems with traditional Pb:Sn plating is aging of the plated surface. A typical Pb :Sn plated split-ring resonator may achieve a Q of 5 x l 0 6 at 1.2 K but such a Q can only be sustained for a few temperature cycles. The Pb:Sn plated surface also grows in a random fashion and, consequently, is very porous. This porosity of the plated film results in a resonant base frequency that continously drifts at 1.2 K on the order of lOOHz/min . Frequency drifts of this nature are caused by the decreasing effective volume of the resonator due to slow creep of the porous Pb:Sn surface under compression. A n inspection of the clamping surfaces after a cool down wil l clearly display shiny patches over areas that were in contact with the sapphire plate, an indication that the Pb:Sn surface has been physically modified. In an attempt to address the problem of Pb:Sn surface aging and resonant frequency creep, a double split-ring resonator was machined from niobium metal. This chapter details the assembly, and characteristics of the niobium double split-ring resonator. 4.1 Niobium Electropolishing Machined niobium rings without careful surface preparation exhibit a Q of only 3-4xl0 5 at 1.2 K[33]. This low Q results from damage to the niobium metal which propagates several tens of micrometers into the material. It is therefore necessary to remove this dam-aged material without inducing further mechanical damage. This was accomplished by electropolishing the surface in a solution of H 2 S 0 4 and HF[34]. Figure 4.1 is a schematic 16 Chapter 4. The Niobium Double Split-Ring Resonator and Experimental Probe 17 of the electropolishing apparatus. The electropolishing solution was placed in an aluminum container which also acted as the cathode for the electropolishing process. Electropolishing began by first thoroughly cleaning the niobium with trichloroethane, followed by an acetone rinse, finishing with a rinse in ethanol. A tapered niobium rod was used to make electrical contact to the rings by wedging the rod into the blind support hole located on the outside surface of the ring. Using a niobium rod as a method for holding the ring in solution ensures solution pur i ty 1 . Otherwise contamination of the solution would quickly decrease the life of the solution. The niobium is then immersed into the etch solution with the rings having the flat clamping surface held almost vertically. Placing the rings vertically ensures that bubbles formed during the etch process do not get trapped anywhere along the clamping surface. The first polishing attempt resulted in deep etch pits on these surfaces, a direct result of placing the flat regions of the ring horizontally in the polishing solution and trapping bubbles on the underside of the niobium ring. Once the material had been immersed in the solution and all electrical contacts checked, the voltage was set to 9V. During the etch process the current oscillates as layers of metal are oxidized and then removed. Removal of 2-300 microns of material re-quires approximately 30 minutes after which time the surface of the niobium was smooth and almost all of the machine marks had disappeared. Immediately following completion of the polishing cycle the rings were removed from the polishing solution and rinsed with an aqueous neutralizing solution to remove all traces of H F . It is important that one take care and remove any H F solution trapped in behind the tapered niobium rod. Having neutralized any H F acid, the rings were then gently lifted using a Teflon tweezer and placed into an acetone bath for safe keeping. Following the polishing process the surface ' A tapered a l u m i n u m rod wi l l also suffice and is a more pract ical solut ion as pointed out to the author by D a v i d B r o u n . Chapter 4. The Niobium Double Split-Ring Resonator and Experimental Probe 18 of the niobium was anodized to create a stable protective oxide barrier. 4.2 Niobium Anodizing M u c h like aluminum metal, niobium metal wil l oxidize rapidly in air. This oxidation process generates N b O filamentary patterns which contribute to weak link problems when exposed to R F fields. One mature industry that extensively makes use of Nb in R F applications is the particle accelerator industry. In accelerator applications, super-conducting Nb cavities at R F frequencies are routinely employed and these cavities have been extensively investigated. Thus, a large body of information exists detailing methods for preparing highly stable, R F compatible, Nb surfaces. One such method for overcom-ing weak link problems is the deliberate generation of a stable N b 2 0 5 oxide layer through anodic oxidation[35]. This protective N b 2 0 s layer has proved to provide a stable surface in R F fields and has helped not only in improving the power handling capabilities of the treated Nb cavity but also the Q of the cavity. Another secondary benefit of a surface oxide layer is the protection it provides from further oxidation of the underlying material. To take advantage of this protective oxide layer, the niobium rings were anodized in a solution of distilled water containing 10% N H 4 0 H by weight as shown in Figure 4.2. Again, a niobium tapered rod was used to suspend the niobium ring within the N H 4 O H solution, in this case without considering orientation effects. The current for the anodizing was supplied by a Keitheley Current source and voltage monitored by an H P multi meter. The anodizing required a current of 2mA for a duration of approximately 4 minutes. During the growth of the oxide layer the voltage steadily increased as the layer grew thicker, thus providing a useful tool for monitoring the growth process. During the anodizing process, the colour of the niobium rings gradually turned from gold to a brilliant blue, an indication that the N b 2 0 s surface was actually oxygen deficient since Chapter 4. The Niobium Double Split-Ring Resonator and Experimental Probe 19 + Figure 4.1: Schematic of the apparatus used for electropolishing niobium metal + Current Source Figure 4.2: Schematic of the apparatus used for anodizing niobium metal. The tapered end of the niobium rod is pressed into place and acts as one electrode during the anodizing procedure. Chapter 4. The Niobium Double Split-Ring Resonator and Experimental Probe 20 stoichiometric ND2O5 should in fact be transparent. For all surface treatments, the current was turned off when the voltmeter read approximately 30V, coinciding with a lack of any further colour change. Other than the crude voltage criteria mentioned above and visual observation of the colour, no further attempt was made to characterize the oxide surface layer. As a precautionary note, we point out that niobium metal is one of the most difficult materials to machine because of its extreme softness. Thus, after preparing a set of niobium rings by electropolishing and subsequent anodizing, it is advisable to ensure that the rings do not collide wi th one another or with any hard surface. It is especially important that the sharp edges found on the flat clamping surfaces never be deformed. Bumping the edge 2, by dropping the ring for example, can easily provide a point of stress when clamping a sapphire plate between a set of rings and may result in plate breakage. Kimwipes (a brand of low-lint cellulose tissue) should also be used with caution since the Kimwipe surface is abrasive and may leave scratches. 4.3 Main Body The main body, or resonator housing, is a cutoff tube that has the split-ring pair sus-pended within its bore. Although the old probe design works well, it does have a number of limitations which have been addressed. Figure 4.3 is a comparison of the old design to the new. The new main body is relatively unchanged from the previous design: the diameter and length of the cutoff tube, position of the coupling holes, and placement of the coaxial lines have not been altered. The placement of the vacuum can, however, has been altered in order to make this new design more efficient at cooling the rings. B y 2 I t is important to stress this point. D u e to the softness of the metal , two rings in the same container can cause damage to each others edges. Chapter 4. The Niobium Double Split-Ring Resonator and Experimental Probe 21 designing the vacuum can to bolt onto the main body, the entire assembly is more effi-cient, compact, and lighter than the old design. As well, due to a decreased resonator to thermal bath distance, and the elimination of one thermal boundary, resonator warming effects for temperatures higher than 50 K have been reduced. New Design Old Design Figure 4.3: Picture comparing the old resonator body design to the new. 4.4 Assembly of the Double Spilt-Ring Because the main body of the resonator was machined from copper it was necessary to electroplate the bare copper surface with a layer of Pb:Sn (see the appendix). Once the body had been plated it was placed into a vacuum oven set at 120C for 20-30 minutes to thoroughly dry the electroplated layer. A longer bake time tends to discolour the Pb:Sn surface and also results in degraded performance. A s a precaution the baked pieces are assembled together, without the rings, and mounted onto the microwave probe Chapter 4. The Niobium Double Split-Ring Resonator and Experimental Probe 22 and evacuated to low pressure. The probe was allowed to pump overnight and was then disassembled and made ready to accept the rings. To assemble the rings, one first places one of two sapphire rods into one of the two sapphire support holes. No grease was applied directly to the ends of the sapphire rod 3 . The sapphire rod was followed by a Pb:Sn plated copper plug that has greased ends for thermal contact. Next, a set screw with greased threads was placed just in behind the plug and screwed in such that the sapphire post protrudes approximately 2-3 mm into the cutoff tube. The entire assembly could then be held with the protruding sapphire post set in a vertical position and the cutoff tube horizontal. W i t h a set of Teflon tweezers one of the niobium rings was placed over top of the sapphire post such that the clamping surface of the rings was also horizontal. To make thermal contact to the ring itself, grease was sparingly applied to the bottom of the support hole before the ring was mounted on the sapphire post. Whi le mounting, slowly rocking and slightly spinning the ring wil l help seat the ring properly over the sapphire post. Then, a clean sapphire plate was lowered onto the exposed flat surface of the ring such that the clamping surface of the ring was more or less in the center of the plate. Placement of the top ring is the most difficult step due to the narrow dimensions of the cutoff tube. Here again, it was critical to ensure that the ring did not fall off of the sapphire plate because such a fall would likely result in either the plate breaking or a corner of the ring hitt ing the Pb:Sn plated copper body causing damage to the edge. However, if one is careful, the second ring can be gently placed on the sapphire plate without excessively moving the plate or spinning the underlying ring. For thermal contact, a minute quantity of grease was applied to the bottom of the support hole. To secure the second ring, the second sapphire support rod was dropped in from the top of the main body and the second ring gently nudged 3 A Pb:Sn plated surface quickly degrades when in contact with grease. B y not having any grease on the sapphire rod before insertion we ensure a grease free area around the region where the sapphire rod enters the cutoff tube. Chapter 4. The Niobium Double Split-Ring Resonator and Experimental Probe 23 about unti l the sapphire rod fell into the support hole. Once again, the sapphire rod was followed by a greased Pb:Sn plated copper plug and a greased set screw. Following the predescribed procedure the double split-ring assembly is ready for alignment and final tightening. 4.5 The Top Loading E x p e r i m e n t a l P r o b e One of the main limitations of the existing probe was its inabili ty to reach sample tem-peratures lower than 15K. Data at lower temperatures was possible with the addition of helium into the sample space, but the benefits of being able to take such data are marred by the procedural inefficiencies that are a direct result of such action. Specifically, there is an increase in total run time (of about 3-5 hours) that is a consequence of waiting for temperature stability after adding the exchange gas; there is also a shift in the resonant frequency of the rings; and a decrease in the Q makes it necessary to unload the sample at each temperature to accurately establish the unloaded Q. Faced with the problems outlined above, a new experimental probe was designed and built to overcome some of these limitations. The new probe is able to reach lower temperatures then its predecessor and, importantly, allows the abili ty to load and unload the sample without introducing sample rotation. The sections below outline in more detail each of the modifications. 4.5.1 Insert The new insert is designed around a length of 1 /8" stainless steel rod with a wall thickness of 0.030", an approximate halving of the cross sectional area of the previous insert. Five copper radiation baffles, each having a small hole for feeding wires 4 , are evenly spaced 4 E a c h hole was debured and all edges around the hole coated with a thin layer of 2850 black stycast to ensure that a smooth surface was present when pulling wires through each baffle Chapter 4. The Niobium Double Split-Ring Resonator and Experimental Probe 24 down the length of the tube. A 1/4" brass rod soldered to the top end of the S.S. tube provides the sealing surface and houses a miniature connector on its end. Three pairs of 0.005" brass wires provide connections to the heater and Cernox thermometer. Each pair has been carefully fed through the baffles and thermally secured to the S.S. tube with dilute G . E . varnish. A t the bottom of the stainless steel tube is a copper cold stage. This copper stage is anchored to the pumped helium bath via a two inch length of copper braid. The braid itself is soldered to copper securing blocks at each end. W i t h just one thermal anchor the minimum attainable temperature for this probe is 2K. For centering and rigidity each end of the cold stage is fitted with six beryll ium copper spring loaded fingers providing the only contact to the actual probe other than the clamping mechanism at the top of the probe and the copper braid at the bottom. This is one of the modifications that was markedly different than the previous design. Although the existing insert incorporated 3 spring loaded fingers for thermal contact to the bath, only the bottom finger was responsible for cooling the sample. This was determined by systematically removing the top two fingers and verifying that the absolute attainable temperature was not affected5. 4.5.2 Sample Mount For easy handling and mounting of samples under a microscope, the sample mount is designed to unscrew from the cold stage. The sample mount comprises a copper body that houses a male micro-connector 6, a quartz tube' for sustaining a temperature gradient, and a sapphire block[15]. For electrical contact three pairs of brass wires have been 5These tests were conducted without pumping the bath. 6 T h e connector is available from Samtec. The connector used here was found in a free sample kit that can be obtained from the manufacture, see their web page : www.samtec.com. 'This is an N M R tube from Wilmad with an outside diameter of 4.97mm. Chapter 4. The Niobium Double Split-Ring Resonator and Experimental Probe 25 soldered to the micro-connector wi th i nd ium 8 and thoroughly cleaned using ethanol to remove all remaining flux. For good axial alignment the ends of the quartz tube were polished by setting the tube with crystal bond into a hole in an aluminum block. B y inching the tube out beyond the polishing plane of the block and polishing off the excess it was possible to produce a tube that had flat parallel edges. The sapphire block is a semi-circular piece glued to one end of the quartz tube such that a thin sapphire plate can be positioned exactly along the probe axis. The sapphire plate used for mounting the sample is typically 1" in length, approximately 0.1" in width and 0.004" thick. It is mounted onto the sapphire block with a small quantity of grease for thermal contact and then visually aligned. A few drops of G . E . varnish, over top of the sapphire plate and block, prevents the plate from moving. For temperature control the sapphire block is equipped with one bare Cernox chip thermometer 9 and one lkQ chip heater. Both are mounted with dilute G . E . varnish to provide good thermal contact. The other end of the tube is glued to a sapphire plate which in turn is glued to a copper housing. The sapphire plate is necessary because mounting the quartz tube directly to a copper surface tends not to work due to the large thermal mismatch between quartz and copper. The wires are secured to the quartz tube with dilute G . E . varnish and the ends soldered, once again using i n d i u m 1 0 , to the heater and thermometer leads. In order to protect the chip devices from falling objects, the leads that are attached to the chip devices have been bent up and over each device into a cage-like structure before being soldered to the brass wires. Mounting of a sample to the end of the sapphire plate is performed under a microscope. The sample is first cleaned in heptane, and then quickly rinsed in acetone to remove any 8 W h e n using Ind ium it is impor tan t that the t i p temperature be set jus t above the mel t ing point of i nd ium; usual ly 6 5 V on a Var iac for a 100W t i p is a good s tar t ing point . 9 T h e Lakeshore Cernox chip thermometer was cal ibra ted in house employing a Q u a n t u m Design S Q U I D magnetometer v i a the S Q U I D ' s u t i l i ty insert. 1 0 T h e best flux for pure Ind ium is F l u x # 2 from the Ind ium Corpora t ion solder k i t . Chapter 4. The Niobium Double Split-Ring Resonator and Experimental Probe 26 grease. Using a small drop of silicone grease, the sample is then gently secured on the end of the sapphire plate. Rotat ing the sample and sliding it back and forth wil l provide good adhesion. To mount the entire assembly onto the insert, the threads on the copper housing are first cleaned with ethanol and a fresh layer of grease is applied. It is important to re-apply grease to the threads each time the mount is screwed into the cold stage to ensure good thermal contact. Wi thout a fresh layer of grease the minimum attainable temperature wil l likely be at least 1 K higher, or problems wil l arise with temperature regulation and stability. 4.5.3 C h i p Thermometer /Hea te r M o u n t i n g Procedure The following procedure for mounting small chip devices using G . E . varnish is one that has been developed by trial and error over the past few years. Although it may be possible to use an alternative method for mounting devices, this procedure has provided consistent and reliable results. It is critical that the thickness of the G . E . varnish layer be as thin as possible to help minimize thermal gradients. To achieve optimum results, the G . E . varnish was first diluted with Ethanol in a 10:1 ratio to produce a very dilute solut ion 1 1 . Extremely dilute G . E . varnish has a number of advantages: it is more elastic and less prone to cracking, and the reduced surface tension of the mixture allows the solution to penetrate more effectively into tight spaces. Next, the surface of the sapphire was carefully cleaned with ethanol and any dust was brushed off. Each chip was prepared such that the chip was able to "stand" on a flat surface with the leads attached. The Cernox chip thermometer has four gold leads approximately 5-7mm in length, while the chip heater has two brass leads of about the same length. Each chip required careful bending of each lead such that 1 I T h e usual solvent for G . E . varnish is a 50/50 solut ion of ethanol and toluene. However, using ethanol alone works just as well and avoids toluene fumes. Chapter 4. The Niobium Double Split-Ring Resonator and Experimental Probe 27 the entire assembly was stable and freely standing. This procedure is a good method for eliminating mechanical stress at each contact. W i t h a pair of clean tweezers 1 2 the balanced chip was then set atop the sapphire block close to the area that would permanently accept the chip. Whi le working under a binocular microscope a small drop of diluted G . E . varnish was placed on the sapphire block and quickly, the balanced chip was picked up with tweezers and placed on top of the varnish. It is important not to disturb the chip once it has made contact wi th the drop. If the chip wanders from the intended location and its position must be altered, it is advisable to completely remove the chip, clean all surfaces and start again. Initially the chip wil l sit very high off the sapphire block, and the temptation is to apply pressure. However, this is not the approach that should be taken to ensure good thermal contact. Instead the chip should not be disturbed, as the drop dries it wi l l slowly draw the chip to the sapphire surface and eventually secure it in place with a very thin layer of varnish. One final note, to avoid dislodging the chip, it is a good idea not to expose the chip to vacuum for at least 6-12 hours after the ini t ial mounting. If the varnish layer remains wet, a vacuum wi l l introduce bubbles beneath the chip and greatly reduce the thermal contact between the chip and sapphire block. 4.6 Axial Alignment Alignment of the rings within the bore must be done visually. When tightening the set screws, the tendency is for the rings to spin about the clamping axis. In order to avoid rotation of the rings, one of the rings must be held in place by applying pressure in the counter clockwise direction while the set screw is turned. Usually a few attempts wil l be required to achieve satisfactory alignment. For measurements of samples placed outside 1 2 U s i n g an ethanol soaked K i m w i p e to wipe the ends of the tweezers is adequate and w i l l allow easy release by e l imina t ing any st icky residue. Chapter 4. The Niobium Double Split-Ring Resonator and Experimental Probe 28 the bore the alignment procedure is straightforward and not cri t ical . As long as the axis of the rings is within a few degrees of the cutoff tube axis the rings are adequately aligned. As well, the tightening of the set screws in this case can be done on the work bench without having to mount the resonator on the end of the probe. When the measurement involves placing a sample within the bore, the alignment must be performed with the sample mounted on its sapphire plate, the resonator bolted to the probe, the top loading assembly inserted into the probe, and the sample in close proximity to the top of the resonator. W i t h the vacuum can off and the end plate on the cutoff tube removed, the resonator assembly can easily be rotated about the clamping axis. As well, the entire structure can readily be moved up and down in small increments while the sapphire plate is in place. Having the vertical and rotational degrees of freedom the sample can be visually aligned in approximately 10 minutes such that, when inserted, the sample wil l make its way down between the sapphire plate and one of the rings. It is important that the sample be moved in towards the resonator in small steps to avoid hit t ing the clamped Sapphire plate or the resonator walls. It is also important that the sample clears the walls of the rings over its entire range of travel within the bore. 4.7 Measurement Electronics The measurement electronics are relatively straight-forward for this experiment. A mi-crowave signal is generated by an HP83630A Synthesized Sweeper and fed down into the low temperature probe via a stainless steel 9/64" diameter coax. The end of the coax is fitted with a loop of tinned copper wire that provides magnetic coupling to the resonator through a coupling hole (see Figure 4.4). The output signal, which wil l be the transmitted signal, is also picked up via a 9/64" stainless steel coax looped at its end. The output signal is then extracted at the top of the probe and fed into a microwave Chapter 4. The Niobium Double Split-Ring Resonator and Experimental Probe 29 Trigger Signal _L H P 83630A Synthesizer GPIB Computer A GPIB Conductus LTC20 Temperature Controller 1 Input Coax (Si GPIB AID Converter Microwave Microwave Amplifier Detector Output Coax Figure 4.4: Schematic of the electronics. Chapter 4. The Niobium Double Split-Ring Resonator and Experimental Probe 30 amplifier followed by a crystal detector. The output of the detector is a D C voltage which is amplified by a final D C amplifier. The output signal is next digitized with a 12bit A / D converter. Temperature control is maintained by a Conductus L T C 2 0 temper-ature controller. Figure 4.4 is a schematic of the probe including the input and output electronics. W i t h the collection of electronics described above, two methods exist for acquiring data. If a sample under investigation is placed into a perfectly homogenous field then measurements in the frequency domain wil l allow one to determine both the Q of the resonance and the center frequency simultaneously by fitting the Lorentzian lineshape of the acquired signal. If however, the sample is placed into a region where the field is not homogenous, then, as the sample moves microscopically in the field, the center frequency of the resonance wil l shift accordingly. Dur ing data acquisition this translates into not being able to record a clean Lorentzian lineshape and hence both the determination of the center frequency and Q of the resonance wi l l be in error. In this case clean data is st i l l possible if one acquires the data in the time domain; where accurate values for the Q are easily attainable but at the expense of not being able to determine the center frequency with acceptable accuracy for precision A A measurements. 4.8 Sapphire Plate Thickness and Resonant Frequency There are two methods for changing the resonant frequency of the split-ring resonator. The frequency can be tuned by changing the actual size of the rings or by changing the thickness of the dielectric. For easy assembly, the latter choice is preferable since it is difficult to assemble the rings if they are larger than the standard 1cm diameter ring set. Also, larger rings wil l necessarily have a larger effective cavity volume and require a larger sample to maintain an equivalent signal to noise ratio. W i t h a reasonable choice of Chapter 4. The Niobium Double Split-Ring Resonator and Experimental Probe 31 plate thickness, the resonant frequency can be conveniently tuned from 1.7GHz to about 4 G H z wi th ease. Table 4.1 lists the measured resonant frequency of a split-ring pair wi th different plate thicknesses. Plate Thickness (Inches) Resonant Frequency (MHz) 0.002 1791.318815 0.004 2182.945980 0.012 2940.335967 Table 4.1: Typica l variation of the resonant frequency for different thickness sapphire plates. The quality of the clamping surface can also change the resonant frequency of a split-ring, albeit not to the same extent as altering the plate thickness. The lowest attainable frequency for a ring set occurs when one has produced the smoothest clamping surface. If the clamping surfaces are extremely well polished the resonant frequency for a 1cm ring set, assembled with a 0.002" sapphire plate, is 1795MHz. After electropolishing the resonator surfaces, the resonant frequency quickly moves up to 1936MHz due to rough-ening of the surface and hence the development of a gap region that has two dielectric media, sapphire and vacuum. One important point to mention is the narrow margin between the resonant frequen-cies found for a ring set assembled wi th a 0.002" sapphire plate having large pits on the clamping surfaces and a ring set assembled wi th a 0.004" sapphire plate having very small pits on the clamping surfaces. From Table 4.2 we see that this difference is only about 110MHz. Thus, if one is careful in preparing the clamping surfaces it may be possible to avoid having to use the very fragile 0.002" sapphire plates. Chapter 4. The Niobium Double Split-Ring Resonator and Experimental Probe 32 Plate Thickness (Inches) Surface Quali ty Resonant Frequency (MHz) 0.002 small pits 1791.318815 0.002 large pits 1935.586200 0.004 very small pits 2043.781324 0.004 small pits 2183.240240 0.004 large pits 2242.423695 Table 4.2: Resonant frequency as a function of plate thickness and surface quality of the clamping surface. 4 .9 Magnetic and Electric Axia l Field Profile W i t h careful alignment, the split ring resonator is capable of measuring samples that are placed within the bore of the resonator or just above the bore. For each case it is important that the electric and magnetic field profiles be well characterized. When measuring small single crystal samples that can be accommodated within the bore of the resonator, the critical parameter that determines the quality of the acquired signal is the magnetic field homogeneity. The more homogenous the external field the less one needs to worry about microphonics, and the impact they have on the Lorentzian lineshape when measuring the frequency response. To minimize microphonics, it is important to place the sample at a location within the bore of the resonator that provides the greatest magnetic field homogeneity. In the case of large samples that are placed just outside the bore, the quantity that one wants to minimize is the electric field strength near the sample. The electric field within the gap region is relatively high and this field can introduce spurious frequency shifts and hence errors in determining Af when the sample is brought in close proximity to the bore. In general, when a sample starts to interact with the magnetic field of a resonator the rearrangement of the field profile wi l l shift the resonant frequency fo. If the sample is metallic the tendency wi l l be to shift the frequency higher due to the effective decrease Chapter 4. The Niobium Double Split-Ring Resonator and Experimental Probe 33 of the cavity volume as currents shield the interior of the sample. For samples that are dielectrics, for example high puri ty sapphire, the frequency shift is in the opposite direction. In this case the frequency shifts down, relative to the resonant frequency fo, due to the effective increase of the cavity volume, a consequence of the larger dielectric constant. Thus, to map the axial magnetic field of the split-ring resonator we make use of a metallic or superconducting sample and monitor the frequency shift as the sample is inserted into the resonator. The total frequency shift in this case wil l depend upon the volume of the sample as well as the field homogeneity. Likewise, to map the electric field one can simply measure the frequency shifts caused by a dielectric sample as it is incrementally lowered into the bore. In practice, measuring the axial electric field is somewhat difficult since the dielectric sample that one uses to explore the electric field needs to be held such that the overall frequency shift from the background is small. Conversely, using a thin sapphire plate to hold a metallic sample is not a problem since the relative contribution to the frequency shift from the dielectric itself is small. It is important to keep in mind that the results from a dielectric plate as employed here wil l not truly reflect the electric field profile, and only provide an indication of how extended the electric field actually is along the resonator ax i s 1 3 . For the experiments, a Pb:Sn sample was used to probe the axial magnetic field. To mimic a thin YBa2Cu3C>6+x crystal a small piece of Pb:Sn was clamped between two stainless steel pistons and pressed thin. The thickness of the pressed Pb:Sn platelet was approximately 20-30/im with a surface area of about 1mm 2 . Frequency shifts from the axial electric field were measured using just the sapphire plate smeared with a small quantity of grease. Although the grease wil l contribute to the overall frequency shift, the contribution is small and was ignored for these measurements. The electric and magnetic 1 3 T h i s arises since the dielectric sample is not of smal l dimensions relative to the bore of the resonator. T h e frequency shift w i l l reflect an integrated cont r ibu t ion from the length of the plate that is interact ing w i t h the electric field. Chapter 4. The Niobium Double Split-Ring Resonator and Experimental Probe 34 field profile was measured for two resonator assemblies: one having a resonant frequency at 2.079GHz and the other at 2.942GHz. 2.079 G H z Split-Ring Resonator To map the axial magnetic field profile the frequency of the resonator was recorded at discreet intervals as the Pb:Sn sample was moved into the resonator. The measurements were initiated with the sample moved into the unload position and subsequently recording the unloaded Q and resonant frequency accurately. The sample was next moved into the resonator in approximately 0.5 mm increments and the loaded Q and center frequency were recorded once again (although the Q is measured along with the center frequency, it is not required for determining the field profile). Initially, since the magnitude of the magnetic field is small the frequency shifts are only on the order of lOOHz/mm at a position of 20mm, however, the maximum gradient at a position of 9mm (this number is wrong must get the correct position) is 7 5 K H z / m m . It is in this region that measurements are most difficult due to microphonics. Because of the extreme sensitivity to sample vibrations near the bore of the resonator each data point required a settling time of approximately 15 minutes. Figure 4.5 is a plot of the frequency shift as a function of position for a split-ring mounted with a 0.004" inch sapphire plate and having a resonance at 2.079 G H z . From the plot we see that a region around 2.5mm exhibits the least frequency dependence and is the location at which the YBa2Cu306+a; and calibration samples were placed. For the electric field profile the sapphire plate was smeared with a small quantity of grease and moved into the bore as described above. Due to the dielectric constant the frequency shift is in the opposite direction and hence the absolute value is plotted. Figure 4.6 shows both the magnetic and electric field profiles. Due to the nature of the split-ring resonator, electric fields are confined to the gap region and this is apparent in Figure 4.6. Chapter 4. The Niobium Double Split-Ring Resonator and Experimental Probe 35 3.0 -2.5 -5 2.0 r c 1.5 r 1.0 8" 0-5 I— 1 0.0 I sample positiori (2.5 mm) oco 5 10 15 Sample Position (mm) O 20 Figure 4.5: Frequency shifts as a function of position for a Pb:Sn sample. The arrow points to the optimum region of uniform magnetic field for the 2.079GHz resonator. 3.0 2.5 . 2.0| < e 1-5 1 -E ?r 0.5 0.0 O PbSn Sample • Bare Sapphire Plate With Grease o o ; . O ' °^~r~Er o c o 5 10 15 Sample Position (mm) O 20 0.30 0.25 0.20 0.15 0.10 0.05 0.00 Figure 4.6: Frequency shift as a function of position for the Pb:Sn sample and the sapphire plate smeared with a small quantity of grease. The data for the sapphire plate has been multiplied by -1. Chapter 4. The Niobium Double Split-Ring Resonator and Experimental Probe 36 In fact, the sapphire plate does not register any frequency shift at all unti l the plate reaches 9mm unlike the magnetic field which started to register a shift at approximately 20mm. 2.942 GHz Split-Ring Resonator Figure 4.7 is a plot of the magnetic field profile for the 2.942GHz resonator. The sample position has changed to 3.1mm from 2.5mm as was found for the 2.079GHz resonator. This small discrepancy is probably due to the accuracy to which the bl ind support holes have been drilled. One striking feature apparent in Figure 4.8 is the actual field profile which is significantly different than the profile measured for the 2.079GHz resonator. The data shows a stronger magnetic field just outside the bore, spanning about a 2mm region. Although there is no clear indication of what could cause such a profile, this data suggests that a larger gap may drastically alter the magnetic field profile. This was tested with a 0.045" sapphire plate, the results indicated that the normal split-ring mode for this geometry where the magnetic field is confined to the bore and the electric field to the gap did not exist. The skewed magnetic field profile displayed in Figure 4.8 might be the onset of a different mode of oscillation. The center frequency for this particular resonator was 6.5GHz, and suggests that the maximum resonant frequency for the split-ring mode having a uniform magnetic field down it's bore lies somewhere between 2.9GHz and 6.5GIiz for the 1cm ring set or, alternatively, between a plate thickness of 0.012"-0.045". 4.10 Probe Systematics There are a number of systematic effects that govern the overall performance of the ex-perimental apparatus. The degree to which the center frequency drifts over time wil l l imit the resolution to which one can measure A A accurately. The ageing of the Nb and copper Chapter 4. The Niobium Double Split-Ring Resonator and Experimental Probe 37 2.0 h 1 1.5 1 C/5 1.0 L 0.5 p. 0.0 —1 1 1 r Q Onmi o C Z 7 sample position (3.1mm) o O O O O O O 5 10 15 Sample Position (mm) 20 Figure 4.7: Frequency shifts as a function of position for a Pb:Sn sample. The arrow points to the optimum region of uniform magnetic field for the 2.9GHz resonator. 2.0 1.5 < Z 1.01 0.5 h 0.0 O • • O O O • • o O PbSn Sample • Bare Sapphire Plale With Grease o o o o o o 5 10 15 Sample Posi t ion (mm) 20 | 0.8 -n 0.6 I | 0.4 £ > I 0.2 P" c 0.0 Figure 4.8: Frequency shift as a function of position for the Pb:Sn sample and the sapphire plate smeared with a small quantity of grease. The data for the sapphire plate has been multiplied by -1. Chapter 4. The Niobium Double Split-Ring Resonator and Experimental Probe 38 plated surfaces wil l determine how the Q changes over time and effectively determines the life of the resonator. Over the short term, thermal cycling effects determine the life of a particular calibration factor. As the resonator assembly is temperature cycled the set screws tend to loosen the assembly and decrease the rigidity of the resonator; this results in an increased standard deviation for each Q measurement and determines how often the set screws need to be re-tightened. Each of the effects mentioned above have been investigated and the results are presented below. 4.10.1 Frequency Drifts For this experimental probe there are two main contributors to frequency drifts. The first is the drift of the center frequency after the Helium bath is close to 1.2K but the system has yet to stabilize, and this drift is due to the effective volume of the resonator decreasing during cooling. The stabilization time can range anywhere from 30-45 minutes once the main valve to the pumping line has been opened. Once stable, the center frequency varies by 1-2 H z / m i n on average for rings that have been clamped with reasonable torque. This rate is extremely dependent on how the rings are tightened, and can be as low as l O H z / H r . The second contribution to frequency drift occurs when the sample is placed into the load position. In this case the drift is due to the insert changing its length due to mechanical relaxation. A t first the frequency drifts rapidly, about lOOHz/min, and then slows down to almost l H z / m i n over the course of about one half hour after which time the rate picks up again and wi l l take 2-3 hours to stabilize. 4.10.2 Niobium Surface Ageing Even with the protective oxide layer the niobium surface does degrade over time, a consequence of the porous nature of the oxide layer. W i t h a starting Q of 9 x l 0 6 a typical resonator assembly wil l exhibit a Q of approximately 5 x l 0 6 after about 5 months of Chapter 4. The Niobium Double Split-Ring Resonator and Experimental Probe 39 operation. Figure 4.9 is a plot of the Q of the resonator as a function of time. The points represent individual cool downs and do not reflect equal time intervals. Between runs, the resonator was stored in air without taking measures to reduce exposure to water vapour. The degradation of the Q, of course, is due to both the ageing of the niobium and the Pb:Sn plated copper surfaces. The relative contribution of each was not investigated. 10 9 8 7 6 5 4 3 ~1—'—I 1 —i—•—r o o o o o -J i I i I i I i L _ i L . _1_ 0 2 4 6 8 10 12 14 16 Run # Figure 4.9: Ageing of the niobium resonator assembly as a function run#. The last point on the graph represents approximately a 5 month time span following the ini t ial assembly of the ring set. The drop in Q to 2 .7x l0 6 was due to a small quantity of grease that had run down into the gap region. When the Q of a resonator has dropped to levels that are unacceptable, the resonator can be readily rejuvenated by re-etching the rings and re-plating the copper housing. Although the plating procedure is identical to the procedure outlined in the appendix, the procedure for the niobium etch is somewhat simpler. Since damage as a result of machining was previously removed, the degraded surface layer on the aged rings is relatively thin. In fact, all that is required is a quick dip in a weak H F solution to remove this dead layer, after which one can re-anodize the fresh surface. Chapter 4. The Niobium Double Split-Ring Resonator and Experimental Probe 40 4.10.3 Thermal Cycling Effects One last point to consider is the effect of thermal cycling on the rings. Each thermal cycle tends to loosen the set screws that are applying pressure on the sapphire posts. Each cycle also tends to increase the time over which frequency shifts subside and after approximately four temperature cycles the rings must be re-tightened. Table 4.3 below lists 3 consecutive runs that detail the typical variation in the resonant frequency between 4.2K and 1.2K. The clamping surface of the rings were polished flat using 1200 grit sandpaper before etching. The typical variation from run to run can be as much as 20MHz, while the typical average variation between 4.2 K and 1.2 K is about 6400Hz. Table 4.4 is a similar comparison for a set of rings that have had the clamping surfaces carefully hand polished using 30/zm, 6fim, and 1/xm Diamond polishing pastes respec-tively. This three step procedure was sufficient for producing a smooth flat surface. Also, polishing was undertaken on a set of rings that had previously been etched. The polish-ing was then followed by an etch to remove any surface damage on the clamping surface, while being careful not to introduce large etch pits. We see from the table that the resonant frequency of the rings can change only as much as 1.6MHz, while the change from 4.2K to 1.2K for any given run is just 3800Hz on average. This difference between the two sets of data clearly indicates that polished and flat clamping surface are a key criteria for producing a stable resonator. W i t h the combined modifications presented here the niobium double split-ring res-onator has achieved a resolution of about 0.2 f.iQ at 2.079GHz. This is about a factor of 5 better than the previous design. Chapter 4. The Niobium Double Split-Ring Resonator and Experimental Probe 41 R u n # 4.2K 1.2K 1 2251.936631 M H z 2251.926141 M H z 9226 Hz 2 2242.423695 M H z 2242.419691 M H z 4004 Hz 3 2260.350720 M H z 2260.344845 M H z 5875 Hz Table 4.3: Variation of the resonant frequency between 4.2K and 1.2K for a split-ring having sanded clamping surfaces. R u n # 4.2K 1.2K 1 2942.387850 M H z 2942.391543 M H z 3693 Hz 2 2940.779968 M H z 2940.783873 M H z 3905 Hz 3 2941.218069 M H z 2941.221854 M H z 3785 Hz 4 2940.331960 M H z 2940.335967 M H Z 4007 Hz Table 4.4: Variation of the resonant frequency between 4.2K and 1.2K for a split-ring having hand polished clamping surfaces. Chapter 5 Single Crystal Measurements and Results The niobium double split-ring resonator was recently employed for microwave surface resistance measurements of an optimally doped single crystal of Y B a 2 C u 3 0 6 + x (labeled YPH)[36] . These results were obtained with the "old" experimental probe by incremental additions of helium gas to reach temperatures less than 15K. This approach is not feasible if one needs accurate data at low temperatures. This chapter presents results obtained on a high purity OrthoII, YBa2Cu 30 6.5o, single crystal for both the a and b axis. The OrthoII crystal, labeled Y P Q , was measured wi th the new top loading probe at 2.07GHz, and at 2.95GHz with accurate results obtained down to 2 K . The chapter also details the measurement procedure and calibration method. 5.1 Measurement Procedure W i t h the sample mounted on the sapphire plate, the resonator bolted to the end of the probe, and the insert in place, the probe is pumped out over a period of approximately 2 hours resulting in a base pressure close to 5 x l O _ 6 T o r r . Whi le the probe is being evacuated, the Dewar set that wi l l house the probe must also be prepared for cooling. The set consists of two vacuum insulated glass flasks or Dewars, one that holds the L N 2 and another that holds the LHe . Since helium gas at room temperature can migrate through the glass wall of the Dewar and into its vacuum jacket one must always pump 42 Chapter 5. Single Crystal Measurements and Results 43 out the vacuum jacket of the inner Dewar prior to cool down 1 . W i t h the pump still attached to the probe, the resonator assembly is pre-cooled wi th L N 2 before placing the probe into the dewar. After the probe has been inserted into the dewar, the coaxial, thermometer and heater connections are made and the temperature is monitored. Once the temperature has reached 100K or less the L H e transfer can be started. W i t h the dewar filled wi th L H e the resonance is found and its Q and center frequency are determined. The helium bath can now be pumped down to 1.2 K . As described in Chapter 3, the system requires at least 1 hour to reach thermal equilibrium before meaningful data can be taken. When the system is stable, the unloaded Q of the resonator is measured and recorded by computer. The sample is then lowered into the resonator and placed into the region having the most uniform field as determined in Chapter 3. After the sample has been inserted, another 2 hours is required to establish a stable frequency. Usually just before the 2 hour wait period has expired the L N 2 is topped up and wil l not need to be filled again for the remainder of the experiment. After the 2 hour stabilization period data acquisition can commence. For measurements in frequency domain, the above waiting period is essential, while for time domain measurements the frequency is not important and the waiting time can be reduced. Sti l l , for time domain measurements, it is a good idea to allow the resonator itself to stabilize before a sample is moved into the load position. The raw data consists of Q and frequency values at a number of predetermined tem-peratures. A l l data is taken by computer and stored 2. The data file typically wi l l have 5 points at each temperature that need to be averaged and then converted to A(l/Q) val-ues using the unloaded Q of the resonator. A t this time, frequency shifts from the lowest J O n e good method to ensure that almost a l l of the hel ium gas has been removed from the jacket is to backfi l l the jacket w i t h a smal l quant i ty of dry nitrogen gas and then p u m p out the mix ture . Repea t ing this process two or more t imes is usual ly more than adequate and is a s tandard procedure in the lab. 2 T h e da ta acquisi t ion program was wr i t t en by Saeid K a m a l . Chapter 5. Single Crystal Measurements and Results 44 Figure 5.1: Schematic of the double split-ring resonator showing the sapphire support posts, cutoff tube, and the sapphire plate that hold the sample. The loops threading the bore of the resonator are meant to represent the B fields. Since the cross section of the sample is minimized in this geometry, the fields within the bore of the resonator are very weakly perturbed. The top and lower panel illustrate the sample unload and load positions respectively. Chapter 5. Single Crystal Measurements and Results 45 temperature data point are also determined. Mul t ip l ica t ion of the A ( l / Q ) values by a constant (which is dependent upon the resonator/cavity volume) is all that is required to calibrate the data set. 5.1.1 Background Corrections For samples that have low loss at low temperatures it is important to correct the raw A ( l / Q ) data for losses associated with the grease and sapphire plate. For each resonator this was done by placing a small quantity of grease on the end of the sapphire plate and then performing a complete loss measurement from 2 to 160K. Figure 5.2 is a plot of the results for the grease and sapphire plate. A t temperatures below 50K the contribution of the background is relatively small. This is expected since sapphire is a low loss material and the quantity of grease employed is very small. However, above 50 K the loss appears to increase fairly rapidly and cannot arise from the grease or sapphire plate 3 . In fact, the increase in A(l/Q) at high temperature is the result of heating of the liquid helium bath which increases the base operating temperature of the resonator and decreases its Q. Measuring A(1/<Q) of the grease and sapphire plate from 2 K to 160K is an effective method for taking all background contributions into account. A l l data obtained was corrected for background effects by first using a polynomial to fit the A ( l / Q ) data and then the fitted curve was used to subtract the raw A(l/Q) results for each sample under investigation. We note that this correction is very minor for the OrthoII sample since the Tc is near 50K where background corrections are essentially negligible. 3 T h i s is assuming that bo th the grease and sapphire plate have not been contaminated. A t t imes the loss at low temperature from the sapphire and grease can easily be a few t imes larger i f contaminat ion occurs. Chapter 5. Single Crystal Measurements and Results 46 0 20 40 60 80 100 120 140 160 Temperature (K) Figure 5.2: Sapphire and grease background for the 2.079GHz (top panel) and 2.942GHz (bottom panel) resonators. Chapter 5. Single Crystal Measurements and Results 47 5.2 Calibration Technique The calibration constant for the resonator is calculated from perturbation theory[37]. For our geometries, one obtains: T - 2 A { Q ) = 2VA1 —) ( 5 1 ) gation constant, c is the half thickness of the sample, Vs is the volume of the sample, and Vc the effective volume of the cavity. We note that the above equation is valid for geometries where the demagnetizing factors are small, and the sample is located within a uniform magnetic field. In particular the equation above works well for a thin rectangular slab placed in a magnetic field with its broad face parallel to the field as shown in 5.3. A solution for the rectangular slab placed in a uniform magnetic field perpendicular to its broad face is a much more complicated problem and equivalent cavity perturbation equations do not exist. Recently, the magnetic moment for a slab in the perpendicular geometry has been calculated by Brandt [38]. For small 7c we can take tanh(7c) to be 1 and simplify the right hand side of equation Substituting for the low frequency propagation constant of a metal using 4 , where the skin depth 8 can be written in terms of the resistivity p of the metal, 4 F o r a superconductor the propagat ion constant would be 7 = were A is the penetrat ion depth for the mater ia l . 5.1. (5.2) Chapter 5. Single Crystal Measurements and Results 48 Figure 5.3: Schematic of a sample in a magnetic field that is parallel to its broad face. The geometry shown here has the least demagnetizing effects. Penetration of the field into the surface is not shown. Figure 5.4: Schematic of a sample in a magnetic field that is perpendicular to its broad face. This geometry has the largest demagnetizing effects. Penetration of the field into the surface is not shown. Chapter 5. Single Crystal Measurements and Results 49 S = M (5.4) we arrive at the following: f 2 V Q / 1 2V C V 2 c V ^ 2c)j nou J { ' Equating the imaginary components on each side of equation 5.5 and substituting c=d/2 (d is the thickness of the sample) we can write wi th A being the area of the sample. Our calibration sample is a P b sample with about a 5% Sn impurity. We can express the resistivity as a sum of the resistivity for pure Pb and a temperature independent term due to impuri ty scattering. We can then express the quantity A(l/Q) as l\ A 2 {pn + A . ) Examining equation 5.7, the only unknown quantities are the volume of the cavity and the impurity resistivity of the Pb:Sn sample assuming that the resistivity of pure P b is known. Squaring both sides of equation 5.7 we finally arrive at the following, l2 T / 2 [P + PO Vc /.L0u Pb:Sn-l Equation 5.8 is in a useful form since it explicitly states that a plot of the square of the A ( l / Q ) values determined from the Pb:Sn sample vs the resistivity of pure P b 5 , for each temperature measured, the slope m (obtained from a least square fit) wi l l determine 5 T h e resist ivi ty of pure P b was obtained from the exis t ing l i terature Chapter 5. Single Crystal Measurements and Results 50 the effective cavity volume (see Figure 5.5). Moreover, the intercept of the linear fit wil l determine the impuri ty resistivity po for the Pb :Sn sample. Given that it is a difficult matter to determine the actual amount of Sn in our sample, this method of determining the effective cavity volume precludes the need for independently determining the actual resistivity of the calibration sample. The effective cavity volume is thus given by Once the effective resonator volume has been determined the surface resistance of an unknown sample S, having an area A s can be found from 5.2.1 Reproducibility There are a number of factors that govern the reproducibility of the measurement system. However, the main factor is the reproducibility of the sample position when the insert is removed from the probe, the sample mount unscrewed and then the entire sample assembly remounted. Although in principal the bottom beryll ium copper springs on the cold stage should be able to accurately center the sapphire plate, in practice the sample position does change. A number of tests were undertaken to establish the degree to which the calibration is dependent on sample position and how the calibration constant itself varies between reassembly of the resonator. To establish the variation of the calibration constant on the axial position of the sample, five measurements were performed with a Y P ^ C u s O e + a ; sample located within the bore of the resonator. Setting the zero position as the optimum position determined from the axial field profile, the sample was systematically moved out of the resonator (5.9) (5.10) Chapter 5. Single Crystal Measurements and Results 51 [A(l/Q)f Figure 5.5: Plot ted is the Resistivity of pure Lead vs A(l/Q)2 obtained for the Pb:Sn calibration sample for the 2.079GHz (top panel) and 2.942GHz (bottom panel) data sets from 10K (bottom left data point) to 130K (top right data point). The line is a least squares fit to the data from which the slope determines the cavity volume. The linearity of the data strongly supports a temperature independent calibration constant. . Chapter 5. Single Crystal Measurements and Results 52 wi th measurements taken at 0.6mm, 1.9mm, and 2.8mm. Two measurements were taken at 0.6mm to check the reproducibility of loading and unloading the sample while the probe was kept at low temperature. Figure 5.6 displays the raw A ( l / Q ) data obtained for the five data sets. The two data sets taken at a position of 0.6mm agree very well at all temperatures and confirm that the sample position does not change significantly as the sample is loaded and unloaded several times. Figure 5.7 is a plot of the same data sets shown in figure 5.6 multiplied by 1.04, 1.08, and 1.16 for the corresponding positions of 0.6mm, 1.9mm, and 2.8mm respectively. It is clear from figure 5.7 that as the sample was eased out of the region of uniform magnetic field the effective calibration of the cavity changed by 4%, 8%, and 16% for each of the positions. The discrepancy at higher temperatures for the data taken at a position of 2.8mm is likely due to the more divergent magnetic field as one moves further out of the bore. The results above clearly indicate that within a single experimental run, the axial position of the sample is very reproducible, and further, that an axial positioning error of 0.6mm will at most change the calibration by no more than 4%. Given the design of the apparatus, an error in the axial position of the sample is largely limited by the reproducibility of mounting the sample at a particular location, on the end of the sapphire plate. Since all samples were mounted using a binocular microscope, it is estimated that an error in the axial position of the sample cannot be more than about 0.3mm between successive removal and replacement of the insert, and hence, the calibration cannot be affected by more than 2%. A further question is the following; How reproducible is the sample position within the plane of the resonator, at a particular axial position, when the sample and insert, while the sample remains on the sapphire plate connected to the low temperature stage, is removed entirely from the probe and then re-mounted? As a way of determining Chapter 5. Single Crystal Measurements and Results 53 8.0x10 6.0x10 4.0x10 2.0x10 1 ' 1 ' 1 1 1 Zero o 0.6mm V •0.6mm 1.9mm 2.8mm -- -1 . 1 I I 20 30 Temperature (K) 40 Figure 5.6: Variat ion of A ( l / Q ) for four different positions along the axis of the resonator. The solid line represents a second data set taken at a position of 0.6mm to check the reproducibility of the data after repeatedly unloading and loading the sample a number of times during the course of a single experiment. 8.0x10 6.0x10 4.0x10 2.0x10 • Zero o 0.6mm 0.6mm v 1.9mm 2.8mm -I 10 20 30 Temperature (K) 40 Figure 5.7: The same data is plotted here again after each data set was multiplied such that each data set coincided with the data set taken at position zero. The data sets at positions 0.6mm. 1.9mm, and 2.8mm were multiplied by 1.04, 1.08, and 1.16 respectively. Chapter 5. Single Crystal Measurements and Results 54 the extent to which a sample can be re-positioned within the plane of the resonator, at a defined axial position, two measurements were performed on two different Pb:Sn samples 6, which were also used to calibrate the data at 2.079GHz. Typica l ly for calibration runs, a piece of Pb :Sn was cut to approximately the same dimensions as the crystal under study from a thicker piece of Pb:Sn which had been placed between two stainless steel pistons and pressed thin. The resulting thin Pb:Sn sheet was sized and mounted onto the end of the sapphire plate. Data were then acquired as described above and A(l/Q) values determined as before. Table 5.1 shows the calibration results for three lead samples taken from two resonator assemblies. Lead sample ^ 2 and #3 were both measured in the same resonator assembly while sample #1 was used to calibrate a different assembly. Comparing the results from sample #2 and #3 we conclude that variations from the sample position, within the plane of the resonator bore, are on the order of 5%. Unfortunately, without collecting more statistics, we cannot draw a conclusion about the variability of the calibration constant between successive re-builds being l imited to only 5% as suggested by the data. Thus, calibration of each resonator assembly is still prudent. P b Sample # Resonator Frequency Area Vc 1 2076.032876 M H z 1.142 mm2 66 .65x l0" 9 ?n 3 2 2046.451782 M H z 0.957 mm2 65 .96x l0 - 9 ?n 3 3 2045.763706 M H z 0.507 mm2 62 .65x l0" 9 ?n 3 Table 5.1: Variation of the calibration constant for three separate runs. The resonator was completely taken apart and re-assembled after measuring sample #1. Sample #2 h 3 were both measured using the same resonator assembly. 6 T h e ideal solut ion is of course to measure the same sample wi thout a l ter ing its posi t ion on the sapphire plate. T h i s was not done here, and thus the result of this test is flawed due to an error i n sample placement. However, this error is l im i t ed to about 2% as discussed i n the text . Chapter 5. Single Crystal Measurements and Results 55 5.3 Single Crystal Results The Y i B a 2 C u 3 0 ( 6 5 ) single crystal ( Y P H ) was measured at two frequencies: 2.07GHz and 2.942GHz in both the a and b directions. For each resonator assembly the resonator was tightened in place and then not tightened or adjusted unti l the end of the measurement cycle. One complete measurement cycle involves a number of steps. First , the sapphire plate with a small quantity of grease was measured. Next, the calibration sample was removed and the YBa 2 Cu306+ x crystal requiring investigation mounted 7 . For each res-onator assembly, the a-axis was measured followed by warming of the probe to room temperature and rotation of the sample for measurement of the b-axis. Once the raw data had been collected A(l/Q) values were calculated and background corrections taken into account. Figure 5.8 shows the raw A(l/Q) data obtained at 2.942GHz for the b-axis of Y P H . We see that in the normal state the data is non-monotonic as one passes through the superconducting transition region. This effect is due to the microwave magnetic field penetrating through the entire sample once the skin depth exceeds the thickness of the sample. To correct the data in the normal state thin l imit corrections have been applied 8 and as an example the corrected b-axis surface resistance is presented in Figure 5.9. As a method of comparing results at different frequencies we can scale the data by f2 for both the a and b-axis. Figure 5.10 and Figure 5.11 are the scaled data sets for the a and b-axis respectively. It is apparent that the data scales very well above about 15 K , but below this temperature the data displays a frequency dependence. If the resonator has been carefully assembled, and a sufficient time has elapsed once the sample has been moved into the load position, it is possible to extract the temperature ' E a c h t ime a sample was removed a very smal l quant i ty of grease was added to the end of the sapphire plate to approximately compensate for the smal l amount of grease lost. 8 T h e raw A(l/Q) da ta was analyzed using a M a t h C a d file wr i t ten by Saeid K a m a l . Chapter 5. Single Crystal Measurements and Results 56 Figure 5.8: Raw A(l/Q) data for the OrthoII data set. The sample looks thin in the normal state and thin l imit corrections are necessary. Figure 5.9: The b-axis surface resistance for a Y 1 B a 2Cu30( 6. 5) OrthoII crystal after-applying thin limit corrections. Chapter 5. Single Crystal Measurements and Results 57 10 20 30 Temperature (K) 40 50 Figure 5.10: The a-axis surface resistance for a YiBa2Cu30 (6 5) OrthoII crystal scaled by p . Two frequencies are shown: 2.079GHZ and 2.942GHz. 10 20 30 Temperature (K) 40 50 Figure 5.11: The b-axis surface resistance for a YiBa2Cu30( 6 5 ) OrthoII crystal scaled by p . Two frequencies are shown: 2.079GHZ and 2.942GHz. Chapter 5. Single Crystal Measurements and Results 58 dependence of the penetration depth from the frequency shift data. We once again employ cavity perturbation results as outlined earlier in the chapter. Equating the real components on either side of equation 5.5 we can write, A f V3 ( 1 2p \ , and calibration of the frequency shift is a matter of using the same Vc calculated for the loss measurements. Figure 5.12 is a comparison between the penetration depth obtained from the loop gap resonator 9 operating at 1GHz and the present double split-ring resonator at 2.942GHz for both the a and b-axis. From the top panel it is clear that a discrepancy exists between the results, the bottom panel is a plot of the 1GHz data set multiplied by a 14% correction. The origin of this discrepancy has not yet been resolved although the present data is more consistent with data obtained by Bidinosti[39][40] and is an indication that an error exists in the determination of the sample thickness 1 0 . Nevertheless, applying this 14% correction, the two data sets agree very well (bottom panel of figure 5.12) and exhibit the same temperature dependence. W i t h i n the context of a two-fluid model and in the l imit of local electrodynamics we can relate, below Tc, the surface resistance to the conductivity as follows: p02UJ2\A(T) where A(T) is the temperature-dependent penetration depth. Figure 5.13 and 5.14 show the conductivity as calculated using equation 5.12 for both the a and b axis respec-tively. The quantity 0\ is inversely related to the cube of the temperature-dependent 9 C o u r t e s y of Saeid K a m a l 1 0 A t the t ime of wr i t ing , sample Y P H was unavailable for an accurate thickness measurement. If an accurate thickness can be obtained it would provide an oppor tun i ty to compare three A A data sets obtained from three completely different experiments Chapter 5. Single Crystal Measurements and Results 59 Temperature ( K ) Figure 5.12: The top panel shows low temperature 6X results plotted with <5A data obtained by Saeid K a m a l using the loop gap resonator. The lower panel is the same data after the S\ results have been multiplied by 1.18. The discrepancy between the two data sets is not understood. However, the temperature dependence of the 2.942GHz data set is very close to that obtained using the loop gap resonator. Chapter 5. Single Crystal Measurements and Results 60 • 2.079 G H z O 2.942 G H z a o U 20 30 40 Temperature (K) Figure 5.13: The a-axis conductivity for a Y i B a ^ C u ^ O ^ . s ) OrthoII crystal. Two frequen-cies are shown: 2.079GHZ and 2.942GHz. E O Cl o u 2.079 G H z 2.942 G H z 10 20 30 40 Temperature (K) Figure 5.14: The b-axis conductivity for a YiBa2Cu30(e.5) OrthoII crystal. Two frequen-cies are shown: 2.079GHZ and 2.942GHz. Chapter 5. Single Crystal Measurements and Results 61 penetration depth and thus requires an accurate value for the zero temperature penetra-tion depth, A(0). Al though A A has been determined down to low temperature from the measured frequency shift as presented here, and is well known from cavity perturbation results from low temperature (1.2K) to just below Tc using the loop-gap resonator, A(0) is not well known and must be inferred from other measurements. For the results here 2600A was chosen as the zero temperature penetration depth for the a-axis, and 1 8 0 0 A for the b-axis. ai represents the conductivity of the thermally excited quasiparticles and using a generalized two-fluid model we can extract the quasiparticle lifetime from ^ = lJmx"{T)T^SkrJ = ^ <0>*"<T)T7SW ( 5 1 3 ) where x „ = l - a ; s = l - ( A ( 0 ) / A ( T ) ) 2 is the normal fluid fraction. Figure 5.15 is a comparison of the quasiparticle scattering rate for the a and b-axis for Y P Q . We see that below T c the scattering rate drops rapidly due to a loss in the normal fluid density as the condensate density increases, and the peak in (j\ at low temperature is a direct consequence of competition between the scattering rate and the disappearance of the normal fluid. Above about 12 K the scattering rate is well described by a T2'a dependence as is apparent in the lower panel of Figure 5.15. The data at lower temperatures indicate that the results cannot be explained by a single scattering rate and is suggestive of a two rate scattering process. Although the Drude model is not an adequate model to accurately represent the data, we can never the less draw the following conclusion. If we compare the a and b-axis scat-tering rate below about 10 K we see that the scattering rate in the b-axis levels oft at low temperature. In contrast, the scattering rate in the a-direction is linear at low tempera-ture and shows no hint of leveling off. One explanation for the discrepancy between the Chapter 5. Single Crystal Measurements and Results' 62 a and b-axis results at low temperature may be the role of oxygen defects along the one dimensional chains which act as scattering centers and result in a temperature indepen-dent scattering rate at the lowest temperatures. A detailed spectroscopic study of this OrthoII sample is currently underway and the results wi l l be reported elsewhere[41]. Chapter 5. Single Crystal Measurements and Results 63 20 30 Temperature (K) 1 ' o 2 G H z a-axis / ° 2 G H z b-axis * 3 G H Z a-axis -/ 3 G H z b-axis df : : • - s « i - " D Q D - D o° B o o ° 10 Temperature (K) Figure 5.15: The scattering rate for both the a and b-axis is plotted for two separate frequencies. The lower panel is a log-log plot of the same data accentuating the low temperature behaviour. A t temperatures higher than about 20K the data follows a power law with exponent 2.75. The a-axis scattering rates appear to be linear at low temperature while the b-axis shows a scattering rate that seems to be impuri ty limited. Chapter 6 Melt Textured Slab Measurements For microwave applications, the surface resistance is a key quantity which wi l l determine in part, the performance of any microwave device. To date, r L T c microwave devices have been developed employing thin film techniques or thick H j T c films on insulating ceramics. Although early attempts were made at developing devices from bulk ceramic samples, the large microwave losses found in such devices due to grain boundaries quickly proved the technique inadequate. To overcome grain boundary problems one is immediately handed the task of producing a bulk material that is essentially a single crystal. The most promising technique for producing bulk single-crystal-like samples has been the top-seeded melt growth technique. Large melt textured crystals have been success-fully grown and optimized for magnetic levitation using this technique. In this chapter we explore the possibility of producing bulk melt textured crystals optimized for microwave applications by minimizing the surface resistance. 6.1 Melt textured crystal growth parameters The samples were prepared from a mixture of YBa2CusOe+x containing an excess of YzBaiCuiOe+x. The powder was pressed into a pellet under 300 M P a of hydrostatic pressure. The result is a starting pellet that is approximately 1.2 cm in diameter and height. A NdBa2Cu306+x crystal, which has a slightly higher melting temperature, placed at the center of the top surface is used as a seed crystal. A typical growth consists of heating and cooling the pellet in a multi step process requiring approximately 5 days. 64 Chapter 6. Melt Textured Slab Measurements 65 Usually, the resulting melt textured crystal is predominately single domain exhibiting a Tc of 93 K (determined by S Q U I D magnetometry) and a rocking curve of 0.4-0.7 degrees for the c-axis. For the microwave measurements, the melt textured sample was cut into square slabs wi th approximate dimensions of 5mmx5mm and a thickness of 0.5mm. Once cut, one surface of the slab was polished using 6, 3, and 0.1 micron diamond pads respectively to produce a near mirror like finish 1 . Mount ing of the slab for measurements was accom-plished by sticking the unpolished surface of the slab onto the end of a 1/8" sapphire rod using a small quantity of grease. The sapphire rod itself was epoxyed into a copper housing fitted with a heater and thermometer allowing the sample temperature to be varied from 15 K to 160 K . As mentioned earlier, a low temperature limit of 15 K was unavoidable when using the original insert. 6.2 Measurement Technique In the case of large samples that cannot be placed into the bore of the resonator, the alternative method for measuring R s is to place the sample just outside the resonator. There are however a number of drawbacks to this approach. Because the sample is located in a field that is spatially inhomogeneous, the calibration factor wil l depend upon the exact axial position of the sample. Also, small changes in sample position caused by thermal effects will lead to shifts in the resonant frequency. We should note as well that it is impossible to measure anisotropy in the plane perpendicular to the axial field since induced currents wi l l be circular in nature. The measured loaded Q wil l thus reflect a spatially averaged loss of the exposed plane. However, for the case where we have isotropic samples or samples that are heavily twinned 2 , averaging effects are 1 T h e samples have a l l been grown, pol ished and characterized by R u i x i n g L i a n g and Dar ren Peets 2 T h i n film and melt textured samples are always heavily twinned Chapter 6. Melt Textured Slab Measurements 66 inconsequential. The resonator used for these measurements is the same resonator used for the single crystal measurements which was bolted onto the old experimental probe 3 A typical measurement of the surface resistance involves first measuring the unloaded Q of the resonator and then moving the sample into the magnetic field to a particular location just above the resonator. As the sample is moved into the resonator the resonant frequency wi l l move higher and the Q of the resonator wi l l drop, reflecting power absorbed by the sample. A 3 M H z shift was chosen as an adequate perturbation and one that would allow enough sensitivity for the required measurements. Once the required frequency shift has been established it is important that the system be allowed to equilibrate for a minimum of 2 hours to allow for thermal equilibrium of the insert 4 . A t times, while trying to establish a particular frequency shift, the target frequency is unavoidably overshot and the insert must be moved away from the resonator a fraction of a millimeter to compensate for the overshoot. It was noted experimentally that if the insert is pulled up by a fraction of a millimeter when an overshoot occurs, the system requires a much longer time for the frequency drifts to subside. If an overshoot occurs, the better alternative, to ensure that the system reaches equilibrium quickly, is to move the sample to the unload position and attempt to set the desired frequency shift in one motion. For the measurements, starting from the lowest temperature possible of 15K and waiting a sufficient time, the loaded Q was measured at predetermined temperatures up to 160K. A t each temperature, 5 sweeps were taken and the results averaged. During the course of the experiments the l iquid helium bath was not regulated. Once the raw Q values were recorded the quantity A(l/Q) was calculated. 3 Measurements of samples placed outside the bore can certainly be performed w i t h the new probe i f a new sample holder is constructed that can support a heavy sample. 4 T h e 2 hour wai t t ime exercised for these measurements is not adequate for accurate frequency shift measurements, but accurate loss measurements could be performed. Chapter 6. Melt Textured Slab Measurements 67 Figure 6.1: Cross sectional schematic of the split-ring resonator illustrating load and unload positions for a typical slab measurement. The field profile shown in the diagram has not been calculated and is simply for illustration purposes only. Chapter 6. Melt Textured Slab Measurements 68 6.3 Background Corrections and Lead Calibration Before the data on the sample can be used any background corrections must be taken into account. The main background problem is again the change in the bath temperature as the sample is heated. The unloaded Q of the resonator is stable up to a sample temperatures up to about 50K, above which enough heat is being evolved into the bath that the unloaded Q of the resonator begins to monotonically decrease. To correct the raw data we must again measure the unloaded Q of the resonator as a function of sample temperature.. However, for this particular geometry one does not need to measure the contribution from the sapphire rod since the grease and sapphire interact only very weakly with the magnetic field (see Figure 6.1). Instead the temperature regulation is turned off at high temperature and the unloaded Q was recorded on the fly as the system cooled. The raw data was then corrected by taking this temperature dependent variation of the base Q into account. The calibration constant is once again accomplished by measuring a piece of Pb:Sn in the normal state. First, a piece was cut to dimensions that are similar to the actual samples that have been measured. One broad face of the sample was then cleaned by sanding the surface with fine emery cloth and then wiped with an ethanol soaked kimwipe. The edges of the sample were then cut with a sharp razor blade to expose clean surfaces. Before mounting, the Pb:Sn sample was quickly cleaned once more in an ethanol bath. Unlike the calibration for single crystals, the Pb:Sn sample was not thinned since the induced currents wi l l only flow on one face of the sample. The calibration run is exactly like that for a single crystal. The unloaded Q of the resonator was accurately determined after the resonant frequency had stabilized. The Pb:Sn reference was then moved in towards the resonator until the resonant frequency had shifted by 3 M H z which set the calibration sample at the same frequency shift, or position, as the samples requiring Chapter 6. Melt Textured Slab Measurements 69 calibration. Data acquisition was then initiated after a 2 hour wait period which, as before, was required for the system to equilibrate. The cavity perturbation equations used for analyzing the single crystal measurements were derived assuming that the sample resided within a region of uniform magnetic field. The relationship between A(l/Q) and A f is such that the ratio of the two is proportional to the ratio of the sample volume, to that of the cavity; both are well defined quantities. W i t h a well defined geometry the effective cavity volume can be readily calculated from the slope of A(l/Q)2 versus p(T), where p(T) is the resistivity of pure lead, as described earlier. However, the perpendicular geometry used for the present measurements is not well defined. Fortunately, a method does exist that wil l allow us to calibrate raw A(l/Q) data acquired using this geometery. If we go back to equation 5.1 and simplify, we can relate both A ( l / Q ) and A f to the skin depth 8. f 2 \Q 2VC (6.1) Thus, — oc c — 8 (6.2) and A( l /Q)oc<5 (6.3) Figure 6.2 is a plot of A ( l / Q ) versus A f at a number of axial positions reflected by a particular frequency shift for each position. The linear relationship evident in Figure 6.2 verifies that A ( l / Q ) and A f are indeed proportional, and the slope of this curve is the proportionality constant needed to analyze the data. If we now fix the position of the sample at a frequency shift of 3 M H z and measure A ( l / Q ) as a function of temperature Chapter 6. Melt Textured Slab Measurements 70 0 l x l O 6 2 x l 0 6 3 x l 0 6 4 x l 0 6 5 x l 0 6 Af (Hz) Figure 6.2: A plot of A ( l / Q ) vs A f as a function of the axial position of a slab. The fact that the data is very well described by a linear fit is critical since this shows that A ( l / Q ) is proportional to A f . A l l data have been taken at a fixed temperature. 1.0x10 8.0x10 1 6.0x10" 4.0x10 2.0x10 5 . 0 x 1 0 " 1.0x10"'° 1.5x10"'° 2.0x10'10 A(i/Qr Figure 6.3: Plot ted is the Resistivity of pure Lead vs A(l/Q)2 obtained for the Pb:Sn calibration sample. The results are much like those obtained for samples placed in a uniform magnetic field. Chapter 6. Melt Textured Slab Measurements 71 we can check to see i f the calibration constant is temperature independent. Figure 6.3 is a plot of the resistivity of pure lead versus [ A ( l / Q ) ] 2 and once again a linear dependence is evident, pointing to a temperature independent calibration constant. 6 .4 Results Figure 6.4 and 6.5 display calibrated results for 4 samples. As a way of providing upper and lower limits for the surface resistance a commercial melt textured sample 5 and a twinned YBa2CusOe+x single crystal were measured. Two melt-textured samples have been measured with varying amounts of Y2Ba,iCuiO(6+$y. one sample had a 211 concen-tration of 15% (P6-58), the other was produced with a Y2BaiCuiO^+s~j concentration of 3%(P6-69). In the normal state we see that as the YzBaiCuiO^+g-) concentration is increased the normal state resistivity of the slab increases accordingly. However, in the superconducting state the difference between P6-58 and P6-69 is relatively small. The main effect of having a high Y^BaiCuyO^s) concentration is to introduce more temperature dependence, whereas sample P6-58 has a surface resistance that is much less temperature dependent. It is interesting to compare these results to state-of-the art Tl2Ba2Ca,iGu20& films from Superconductor Technologies Inc. (STI)[42]. Table 6.1 compares the surface resistance measured at 77 K (2.079GHz) for the commercial melt textured sample, a U B C twined single crystal, the two U B C melt textured samples, and an STI Tl2Ba2Ca1Cu20A thin film. Although the results at 77 K are all well above the surface resistance for a pure twinned single crystal the comparison between the U B C melt textured samples and the STI film is very encouraging. Compared to P6-69 with a Y2BaiCuiO(p+s) concentration of 15% the STI sample is only a factor of 1.3 better. For the surface resistance P6-58 is only about 30% higher than that of the S T I thin film. 5 T h i s commercia l pellet had been opt imized to achieve a m a x i m u m cr i t ica l current and was not op t imized for microwave surface resistance. It is inc luded here as a reference point only. Chapter 6. Melt Textured Slab Measurements 72 A s a preliminary test, a double split-ring structure was fabricated from an early melt textured pellet 6 and tested. A 0.004" sapphire plate was used for the dielectric spacer and the Y Ba2Cu^O&+x rings replaced the 2GHz Niobium ring set. The resonator was then cooled to 4.2 K and a Q of 50000 was measured 7. It is expected that a double split-ring pair manufactured from a pellet that has properties like those measured for sample P6-58 should exhibit a much higher Q at 4.2 K . As well, since sample P6-58 has very little temperature dependence in its surface resistance from 4.2 K to 77 K , the Q at 77 K should not be much lower than at 4.2 K . As a final note, given the low surface resistance measured for the best U B C melt textured samples at 77 K , it maybe be possible to manufacture resonators and filters that are competitive with current state of the art thin film devices. Sample Rs (/j.Q) @ 77K & 2GHz Commercial Slab 157 U B C Slab P6-58 (15% 211) 46.4 U B C Slab P6-69 (3% 211) 28.6 STI Tl2Ba2Ca1Cu20A film (scaled to 2GHz) 21.7 U B C Twinned Single Crystal 1.5 Table 6.1: A comparison of the surface resistance at 77K for a commercially available melt textured slab, a thall ium thin film from STI, two U B C melt textures samples, and a U B C twinned Y Ba2CuzO§+x single crystal. T h e pellet was machined into a double spl i t - r ing pair by R u i x i n g L i a n g ' T h e surface resistance of this par t icular sample, from which the r ing set was machined, was not measured and is l ikely much worse than sample Y2BaiCu\0^+Sy Chapter 6. Melt Textured Slab Measurements 73 CJ u 3 00 100000 80000 60000 40000 20000 0 O P6-58 O P6-88 O Commercia l Sample^ A Single Crystal 0 20 40 60 80 100 120 140 160 Temperature (K) Figure 6.4: Surface resistance in the normal state comparing a commercial slab, two U B C melt textured slabs, and a twinned high quality YBO,2CU30Q+X single crystal. 140 120 A 100 c C3 Oi u 3 OO • P6-58 O P6-88 O Commercia l Sample ^ A Single Crystal O o 0 10 20 30 40 50 60 70 80 90 Temperature (K) Figure 6.5: Surface resistance in the superconducting state comparing a commercial slab, two U B C melt textured slabs, and a twinned high quality YBa2Cu3OQ+x single crystal. Chapter 7 Conclusions A new top loading probe as well as a Niobium double-split ring resonator assembly have been developed and employed for exploring the electrodynamics of a high purity YBa2Cu30e+x OrthoII single crystal as well as bulk YBa2Cu306+ x melt textured slabs. With careful attention to the polishing procedure and the use of Niobium metal for the ring material it has been demonstrated that this new apparatus is capable of measuring the complex surface impedance of small H j T c single crystals with high precision. Once properly assembled, a resolution of 0.2/j,Q, for the surface resistance, and a frequency stability of l O H z / H r for the most stable resonator was achieved. It has also been shown that surface resistance measurements on large area samples can be performed using the same resonator assembly. This dual capability, combined with the tunability through the choice of the sapphire plate thickness, makes this apparatus extremely versatile. 7.1 OrthoII results The high purity OrthoII single crystal was measured at 2.079GHz and at 2.942GHz in the a and b directions. The peak observed at about 35K in the optimally doped single crystals has shifted down in temperature to just under 10K. As well, the sample displays significant frequency dependence over the relatively narrow range studied here, suggesting that the width of the Drude peak is less than that found in optimally doped Y B a 2 C u 3 0 6 + x . By achieving greater frequency stability over previous top loading split-ring designs, 74 Chapter 7. Conclusions 75 the temperature dependence of the penetration depth could also be measured down to 2 K . W i t h both the penetration depth, and surface resistance, a scattering rate was extracted from the data. In the b direction, at low temperature, the scattering rate seems to be impurity limited, likely caused by scattering off oxygen vacancies along the chains, while the a axis results show a linear temperature dependence. A t temperatures higher than approximately 20K the scattering rate is well described by a T 2 " 5 temperature dependence for both directions. 7.2 Melt textured slab results Surface resistance results for two melt textured slabs have been presented and compared. Varying the Y 2 B a 1 C u 1 0 ( 6 + x ) concentration from 15% to 3% has little impact on the low temperature behaviour of the surface resistance other than the 3% Y 2 B a i C u i 0 (6+ x ) sample displaying a little less temperature dependence below 77K. A t 77K the best melt textured slab has a surface resistance that is only a factor of 1.3 higher than state-of-the-art thall ium thin films. Preliminary results on a YBa2Cu306+ x double split-ring resonator have been very encouraging. A t 4 .2K the Q for the Y B a 2 C u 3 0 6 + T split-ring resonator housed in a Pb:Sn plated copper cutoff tube was approximately 50,000. Although this is a rather low Q relative to the Niobium rings, it is never the less competitive with current, packaged, H j T c thin film devices. 7.3 Future improvements Although the apparatus in its present state has performed exceedingly well, a number of improvements can be made to enhance the low temperature operation as well as improving the overall sensitivity. They are : Chapter 7. Conclusions 76 1. Regulation of the helium bath during data acquisition. The stability of the probe should increase with bath regulation, and in particular the change in bath temperature at the higher sample temperatures can be suppresed. 2. A new copper window cover wi th a method for attaching the copper braid to the cover would help achieve a lower base temperature. 3. Addi t ion of another copper braid to help reach 1.2K. Currently, 2 K is about the lowest attainable temperature; another braid close to the bottom of the insert would allow operation down to 1.2K. 4. A new probe tip capable of supporting large area samples. The probe tip used for the melt textured slabs can only be used wi th the original insert which cannot be operated at temperatures less than 15K without the addition of an exchange gas. 5. Addi t ion of another support hole on each half ring. This would allow tightening of each ring without introducing rotation as well as help improve the alignment of the ring set relative to the axis of the cutoff tube. 6. A re-design of the fingers on the cold stage. A t present, the fingers are not as tight against the inside of the S.S. tube as originally planned due to an alteration in the design during construction. The original fingers provided to the shop did not survive the ini t ial design and a substitution was made. 7. Replace the Pb:Sn plated copper tube with a niobium cutoff tube. This should help increase the lifetime of the resonator assembly as well as consistently achieving higher Q's over the current cutoff tube. 7.4 Future work For single crystal samples, going further into the underdoped region has a high priority. Currently an underdoped Y B a 2 C u 3 0 6 + x sample with a T c of 5K has been prepared and Chapter 7. Conclusions 77 is ready to measure. As well, exploring the frequency dependence of the c-axis might be interesting, especially since the relative contribution of the c-axis increases as one decreases the doping. From the results on melt textured slabs obtained thus far, it seems likely that one should be able to produce samples that have a surface resistance at 77K that are com-petitive with current state-of-the-art thin films. The next obvious task is to build a real microwave device, such as a filter or resonator, employing bulk melt textured materi-als. 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Appendix A PbSn plating Solution and Procedure A . l Plating solution The following recipe wi l l yield 1.5 Liters of plating solution • 240 m L P b ( B F 4 ) 2 Solution • 1200 m L Disti l led H 2 0 • 60 m L Glue (this is 60mL of water with 0.75grams of glue) To charge the solution with about 5% Sn the following is required: • C a t h o d e ^ : Stainless steel electrode. • Anode ( + ' : High purity Sn electrode. • Copper removal : R u n cell for about 30 minutes at 30mA to remove any Copper in solution. • Sn Charging : Run cell for about 90 minutes at 650 m A to charge solution with approximately 5% Sn. A.2 Plating procedure 1. Soak in Trichloroethylene for 30 minutes. Rinse in Acetone, then warm water, then distilled water. 81 Appendix A. PbSn plating Solution and Procedure 2. If bare copper, etch briefly in C u etch. Rinse in water, then distilled water. Otherwise go to step 3. 3. Soak in N a O H for 30 minutes. Rinse well in warm water, then distilled water. 4. If bare copper, etch briefly in Lead stripper. Rinse in water, then distilled water. Otherwise go to step 5. 5. Plate at 3 0 m A / c m 2 . 6. Rinse quickly with distilled water. 7. Rinse thoroughly with Acetone. 8. Blow dry with dry Nitrogen gas. 

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