Science, Faculty of
Physics and Astronomy, Department of
DSpace
UBCV
Balandeh, Shadi
Doctor of Philosophy - PhD
University of British Columbia
Hole doped bismuth perovskite is one of the rare examples of a three-dimensional high transition temperature superconducting oxide (Tc = 34 K) without a transition metal cation. The undoped compound, BaBiO₃, also shows closely interlinked electronic and structural phase transitions and a controversial insulating mechanism. Understanding the electronic structure of the parent compound, BaBiO₃, can give valuable insight into both its superconducting mechanism, in particular, and into the physics of the perovskites family, in general. In this work, we first grow high-quality single crystals of BaBiO₃ by congruent melting technique and characterize the crystals with x-ray di ffraction, x-ray photoemission, and transport properties measurements. We then investigate the electronic structure of the material from both theoretical and experimental perspectives. Experimentally, we study the crystals through x-ray absorption, x-ray emission, and photoelectron spectroscopies. X-ray spectroscopy verfi es the results of density functional theory (DFT) regarding the overall band structure featuring strong O 2p character of the empty anti-bonding combination of the hybridized Bi 6s and O 2p states. We also develop a routine to successfully clean the sample's surface in order to achieve the intrinsic O 1s x-ray photoemission spectrum. Finally, we employ the "exact diagonalization single cluster con figuration interaction" method to investigate the ground state electronic structure of the material and to understand the measured O 1s x-ray photoemission result. From the analysis of the core level line shapes, we conclude that the dominant O 2p-Bi 6s hybridization energy scale determines the low energy scale electronic structure. We also find that for a wide range of electronic parameters, the holes reside primarily on the ligand oxygen anions rather than the bismuth cation consistent with the band structure calculation but contrary to what is traditionally assumed for this material. This analysis provides further insight into the importance of self-doped oxygen 2p states in this high Tc family of oxides.
Experimental and Theoretical Studyof The Electronic Structure ofSingle-crystal BaBiO3byShadi BalandehB.Sc., Sharif University of Technology, 2011M.Sc., The University of British Columbia, 2013A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinThe Faculty of Graduate and Postdoctoral Studies(Physics)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)August 2018c© Shadi Balandeh 2018The following individuals certify that they have read, and recommendto the Faculty of Graduate and Postdoctoral Studies for acceptance, thedissertation entitled:Experimental and Theoretical Study of The Electronic Structure ofSingle-crystal BaBiO3submitted by Shadi Balandeh in partial fulfillment of the requirementsfor the degree of Doctor of Philosophy in Physics.Examining Committee:Supervisor: Prof. George A. SawatzkySupervisory Committee Member: Prof. Doug BonnSupervisory Committee Member: Prof. Mona BerciuSupervisory Committee Member: Prof. Mark Van RaamsdonkUniversity Examiner: Prof. Srikantha PhaniUniversity Examiner: Prof. Sarah BurkeiiAbstractHole doped bismuth perovskite is one of the rare examples of a three-dimensional high transition temperature superconducting oxide (Tc = 34K) without a transition metal cation. The undoped compound, BaBiO3,also shows closely interlinked electronic and structural phase transitions anda controversial insulating mechanism. Understanding the electronic struc-ture of the parent compound, BaBiO3, can give valuable insight into bothits superconducting mechanism, in particular, and into the physics of theperovskites family, in general.In this work, we first grow high-quality single crystals of BaBiO3 by con-gruent melting technique and characterize the crystals with x-ray diffraction,x-ray photoemission, and transport properties measurements.We then investigate the electronic structure of the material from boththeoretical and experimental perspectives. Experimentally, we study thecrystals through x-ray absorption, x-ray emission, and photoelectron spec-troscopies. X-ray spectroscopy verifies the results of density functional the-ory (DFT) regarding the overall band structure featuring strong O 2p char-acter of the empty anti-bonding combination of the hybridized Bi 6s andO 2p states. We also develop a routine to successfully clean the sample’ssurface in order to achieve the intrinsic O 1s x-ray photoemission spectrum.Finally, we employ the “exact diagonalization single cluster configurationinteraction” method to investigate the ground state electronic structure ofthe material and to understand the measured O 1s x-ray photoemissionresult. From the analysis of the core level line shapes, we conclude that thedominant O 2p-Bi 6s hybridization energy scale determines the low energyscale electronic structure. We also find that for a wide range of electronicparameters, the holes reside primarily on the ligand oxygen anions ratherthan the bismuth cation consistent with the band structure calculation butcontrary to what is traditionally assumed for this material. This analysisprovides further insight into the importance of self-doped oxygen 2p statesin this high Tc family of oxides.iiiLay SummaryIn this work, we study the electronic structure of BaBiO3 which is the parentcompound of a family of materials with unusual physical properties includingsuperconductivity. To study this, high-quality single crystals are requiredthe growth of which was the first task of this project. We then used severalx-ray spectroscopy techniques sensitive to the electronic structure and useda model calculation to interpret the experimental findings.It is generally assumed that in BaBiO3 the oxygen does not play a promi-nent role in determining the physical properties of the material such as elec-trical conductivity and magnetic susceptibility. However, we find evidenceto show otherwise. We show it is, in fact, the oxygen electronic states thatdictate these interesting physical and electronic behaviours.ivPrefaceThis thesis is mainly based on one published paper [Experimental and theo-retical study of the electronic structure of single-crystal BaBiO3[1] by ShadiBalandeh, Robert J. Green, Kateryna Foyevtsova, Shun Chi, OleksandrFoyevtsov, Fengmiao Li, and George A. Sawatzky, Phys. Rev. B 96, 165127- Published 13 October 2017 ] for which I was responsible for all majorareas of crystal growth, data collection, analysis, creating the plots andmanuscript composition under supervision and guidance of my supervisor,Prof. Sawatzky, and with assistance from the other co-authors. Dr. RobertGreen, in particular, played an essential role in aiding me in doing the ex-periments at the Canadian Light Source (CLS) and also in the use of theQuanty program for the computational results of the chapter 5.For this work, I have carried out the experiments partly at the StewartBlusson Quantum Matter Institute at the University of British Columbiaand partly at the Canadian Light Source (CLS) research facility. In chapter2, the reciprocal map x-ray diffraction and resistivity measurements havebeen carried out by Dr. Oleksandr Foyevtsov. In chapter 3, the DensityFunctional Calculations have been done by Dr. Kateryna Foyevtsova. Therest of the experiments and calculations have been done by me. In chapter5, the computations have been done via Quanty program developed by M.Haverkort et al.vTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . viList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . xviDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii1 Bismuthates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Electronic structure . . . . . . . . . . . . . . . . . . . . . . . 11.1.1 Bismuthates and Nickelates . . . . . . . . . . . . . . . 51.2 Crystal Structure . . . . . . . . . . . . . . . . . . . . . . . . 71.3 Superconductivity . . . . . . . . . . . . . . . . . . . . . . . . 81.3.1 Bismuthates and Cuprates . . . . . . . . . . . . . . . 92 BaBiO3 Single Crystal Growth . . . . . . . . . . . . . . . . . 122.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.2 Single Crystal Growth Procedure . . . . . . . . . . . . . . . 152.3 Characterization . . . . . . . . . . . . . . . . . . . . . . . . . 272.3.1 X-ray Photoemission Spectroscopy . . . . . . . . . . . 272.3.2 X Ray Diffraction . . . . . . . . . . . . . . . . . . . . 332.3.3 Resistivity . . . . . . . . . . . . . . . . . . . . . . . . 422.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44viTable of Contents3 X-ray Absorption and Resonant X-ray Emission Spectroscopy453.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 453.1.1 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . 473.1.2 Detection Techniques . . . . . . . . . . . . . . . . . . 513.1.3 REIXS Beam-line at CLS . . . . . . . . . . . . . . . . 533.2 Oxygen K-edge XAS Results . . . . . . . . . . . . . . . . . . 553.3 Oxygen K-edge RXES Results . . . . . . . . . . . . . . . . . 593.4 Theoretical Interpretation of The Experiment . . . . . . . . 603.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 664 X-ray Photoemission . . . . . . . . . . . . . . . . . . . . . . . . 674.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 674.1.1 XPS detection technique . . . . . . . . . . . . . . . . 704.1.2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . 704.1.3 XPS, core levels and satellites . . . . . . . . . . . . . 724.2 XPS Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 734.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 805 Exact Diagonalization Cluster Model . . . . . . . . . . . . . 815.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 815.1.1 Atomic Model . . . . . . . . . . . . . . . . . . . . . . 825.1.2 Crystal Field Model . . . . . . . . . . . . . . . . . . . 845.1.3 Ligand Field Model . . . . . . . . . . . . . . . . . . . 885.2 Computations . . . . . . . . . . . . . . . . . . . . . . . . . . 915.2.1 Cluster . . . . . . . . . . . . . . . . . . . . . . . . . . 915.2.2 Model Hamiltonian . . . . . . . . . . . . . . . . . . . 915.3 Ground-State Spin Calculation . . . . . . . . . . . . . . . . . 965.4 Hole Distribution Calculation . . . . . . . . . . . . . . . . . . 975.5 XPS calculation . . . . . . . . . . . . . . . . . . . . . . . . . 1005.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1036 Summary and Future Work . . . . . . . . . . . . . . . . . . . 1046.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1046.2 Future Works . . . . . . . . . . . . . . . . . . . . . . . . . . 1056.2.1 Further Characterization of the Single Crystals . . . 1056.2.2 Electron Doped Material . . . . . . . . . . . . . . . . 1056.2.3 Resonant Photoemission Measurements . . . . . . . 1066.2.4 Pair Distribution Function Measurements . . . . . . . 106viiTable of ContentsBibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107AppendicesA BaBiO3 Bragg Reflections . . . . . . . . . . . . . . . . . . . . 117viiiList of Tables2.1 BaBiO3 lattice parameters in I2/m symmetry taken from Ref.[2] and used to simulate the powder diffraction pattern in Fig.2.7. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222.2 The atomic ratios of the grown single crystal given by theXPS measurement (Fig. 2.14 ). The accuracy of the resultsderived from this technique (described in the text) is within5%. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322.3 BaBiO3 single crystal lattice parameters measured at tem-peratures 90 K and 210 K. . . . . . . . . . . . . . . . . . . . . 352.4 The R value for different Bragg reflection pairs. R is definedin Eq. 2.19 and is indicative of contribution from differentcrystal domains. This result implies that the given crystalwas 13% twinned. . . . . . . . . . . . . . . . . . . . . . . . . 424.1 The relation between quantum numbers, atomic notation andx-ray notation for the first few energy levels [3]. j is the totalangular momentum quantum number which takes |` − s| ≤j ≤ |`+ s| values where s = 1/2 for electrons. . . . . . . . . . 69ixList of Figures1.1 Top: Density of states of a compressed and expanded BiO6octahedron projected on to the Bi-6s orbital and combina-tions of the O-pσ orbitals for SrBiO3 structure from Ref.[4]’s DFT(LDA) calculations [4, 5]. Bottom: The octahe-dron with O-pσ orbitals at the corners hybridized throughnearest-neighbor hopping integrals of −t and the correspond-ing eigenstates in the table for different symmetries [4] . . . . 31.2 DFT(LDA) band structures of BaBiO3 and SrBiO3 calculatedwith a supercell of dimensions√2a×√2a×√2a. The bandstructures are almost identical around the Fermi energy ex-cept for a larger gap in SrBiO3 due to its more prominentstructural distortions. The Fermi energy is set to zero [4]. . . 41.3 a: Mott-Hubbard insulators where the gap is determined bythe Coulomb energy U versus c: charge-transfer insulatorswhere the gap is determined by ∆ which is smaller than U .b: charge fluctuations corresponding to the energies ∆ andU . The blue and red orbitals represent the ligand oxygen p,and the transition metal d orbitals, respectively [5, 6]. . . . . 51.4 The schematic illustration of the perovskite nickelate (on theleft) and bismuthate (on the right) electronic structures. Inthe bismuthate, the deep Bi-6s states with the A1g symme-try hybridize strongly with the combination of the O2p stateswith the same symmetry. Consequently, the state of A1g sym-metry and mainly O2p character are pushed above the Fermilevel. In the nickelate, the situation is similar but the cationstates are the Ni-3d states with the Eg symmetry which againmix with the O2p states with the same symmetry [5]. . . . . 6xList of Figures1.5 The crystal structure of perovskite BaBiO3. The green ballsat the corners of the octahedra represent the oxygen anions.The black and white balls at the centers of the octahedrarepresent the bismuth cations in expanded and collapsed oc-tahedra, respectively [4]. . . . . . . . . . . . . . . . . . . . . 71.6 Summary of BaxK1−xBiO3 properties taken from Ref. [7]. . 91.7 The phase diagrams of top: Ba1−xKxBiO3 and bottom: BaBi1−xPbxO3compounds. Due to the lack of phase purity for BaBi1−xPbxO3samples and hence the non-conclusive results the BaBi1−xPbxO3phase diagram is perhaps only qualitatively correct [7]. . . . 102.1 An overview of the most used crystal-growth techniques [8].These techniques fall into four main categories: solid-stategrowth, vapour phase growth, melt growth and solution growth.In this work a combination of solid-state+melt growth was ul-timately used to grow BaBiO3 crystals. . . . . . . . . . . . . 142.2 Temperature-steps for the BaBiO3 single crystal growth asgiven by Ref. [9]. (The highest temperature of 1010◦ C inthe plot has to be an error. Based on the text and the BaBiO3melting temperature of 1040◦ C, it has to be 1100◦ C.) . . . 172.3 First growth attempt and its Laue-gram. The result was notsingle crystal. (unsuccessful) . . . . . . . . . . . . . . . . . . 182.4 The construction of the furnace (top) with the insulatingceramic disk (bottom) to introduce a temperature gradientalong the crucible for the second attempt. . . . . . . . . . . 192.5 Second growth attempt and its Laue-gram. Here the previ-ous procedure was repeated but a temperature gradient wasalso introduced along the crucible. The result was not singlecrystal. (unsuccessful) . . . . . . . . . . . . . . . . . . . . . . 202.6 Third growth attempt and its Laue-gram. Here the previ-ous procedure was repeated but the calcined powders wasground and homogenized before the melt. The result wasgolden brown as expected for BaBiO3 but not single crystal.(unsuccessful) . . . . . . . . . . . . . . . . . . . . . . . . . . 212.7 Simulated (top) and measured (bottom) BaBiO3 powder diffrac-tion patterns with Cu-Kα X-ray source. . . . . . . . . . . . . 232.8 The thermal process for the BaBiO3 singe crystal meltinggrowth. The red arrow indicates the slow cooling step fromabove the melting point to the below. . . . . . . . . . . . . . 24xiList of Figures2.9 Fourth growth attempt and its Laue-gram. The melting pro-cedure was performed on BaBiO3 powder which had been syn-thesized in advance through solid-state reaction. The resultwas 1× 1 mm2 plates of BaBiO3 single crystals. ( successful). 252.10 Fifth (final) growth attempt. Increasing the melt surface areaby using a wider crucible (25 mm OD) resulted in growingbigger single crystals. (successful) . . . . . . . . . . . . . . . 262.11 X-ray back-reflection Laue-gram of the grown crystal with thex-rays oriented along the [100] crystallographic direction in acubic unit cell. . . . . . . . . . . . . . . . . . . . . . . . . . . 262.12 A carbon 1s x-ray photoemission spectrum with the back-ground signal corrected using the top: linear and bottom:Shirley algorithms. The figures are taken from Ref. [10] andthey have been modified slightly by adding the labels. . . . . 302.13 Omicron Multi-probe MXPS system at the Surface ScienceFacility of the REIXS beam-line at the Canadian Light Source(CLS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312.14 X-ray photoemission spectrum of BaBiO3 single crystal atroom temperature . . . . . . . . . . . . . . . . . . . . . . . . 322.15 A schematic representation of a two-dimensional crystal lat-tice. An incident beam hitting the crystal undergoes a con-structive (in phase) diffraction when the path difference isequal to an integral multiple of the wavelength: nλ = 2dsinθ.(Bragg’s law) . . . . . . . . . . . . . . . . . . . . . . . . . . . 332.16 X-Ray Diffraction pattern on a grown BaBiO3 single crystalwith the “as grown” surface facing. . . . . . . . . . . . . . . 362.17 Schematic illustration of the coplanar diffraction geometry.n is the normal to the sample surface and nφ is the normalto the diffracting lattice planes. αi and αf are the angles ofincident and exit. ω is the angle between the incident beamand the diffracting lattice planes, ω = αi + φ. . . . . . . . . 382.18 Reciprocal space maps of crystal BaBiO3 top: around (110)and (002) and bottom: around (220) and (004) Bragg diffrac-tions. The axes are in reciprocal lattice unit (r.l.u) which isλ2dhklwhere λ = 1.54059A˚. . . . . . . . . . . . . . . . . . . . 402.19 Reciprocal space maps of crystal BaBiO3 top: around (330)and (006) and bottom: around (440) and (008) Bragg diffrac-tions. The axes are in reciprocal lattice unit (r.l.u) which isλ2dhklwhere λ = 1.54059A˚. . . . . . . . . . . . . . . . . . . . 41xiiList of Figures2.20 Schematic representation of the 4-probe resistivity measure-ment using a lock-in amplifier. . . . . . . . . . . . . . . . . . 432.21 Resistivity measurement of BaBiO3 crystal. An abrupt changein slope, i.e. activation energy (Ea), happens at T = 233 K. 433.1 The three main regions of an x-ray absorption spectrum [11]. 473.2 The schematic representation of x-ray photoemission/absorption,normal and resonant emission processes.[12] . . . . . . . . . . 523.3 Some standard XAS detection techniques. The blue regionsqualitatively represent the detection depths of each technique.[11] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 533.4 XAS machine at the REIXS end-station at CLS [13]. . . . . . 553.5 Some specifications of the REIXS beam-line end-station atCLS [14]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 553.6 Oxygen K-edge XAS of single-crystal BaBiO3 top: measuredat 20 K and 400 K with vertical polarization. bottom: withpolarizations perpendicular (vertical) and parallel (horizon-tal) to the sample surface plane at room temperature. Nosignificant temperature or polarization dependence is observed. 573.7 The reproducibility of the top: TEY and bottom: TFY sig-nals are tested for the oxygen K-edge XAS of single-crystalBaBiO3. The measurements are repeated after 24 hours whilesample was kept in vacuum. The TFY is found reproducibleover time unlike the TEY. . . . . . . . . . . . . . . . . . . . 583.8 Main: oxygen K-edge resonant x-ray emission spectra on asingle crystal of BaBiO3 at three different Resonant IncidentEnergies (RIE). Inset: oxygen K-edge XAS spectrum. Thered dots show the resonant incident energies used for theRXES measurement. . . . . . . . . . . . . . . . . . . . . . . . 603.9 Oxygen K-edge RXES and XAS spectra measured on a BaBiO3single crystal and the DFT(LDA) oxygen p projected densityof states of BaBiO3. The energy has been shifted by -528.5eV for the experimental axis to facilitate comparison with thecalculation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 623.10 Oxygen K-edge XAS compared to oxygen p projected densityof unoccupied states from top: DFT(LDA). middle: DFT(LDA)and the XSPEC package which takes into account the transi-tion probabilities in calculating the intensity. bottom: DFT(LDA) on a 2× 2× 2 supercell with a core-hole. . . . . . . . 65xiiiList of Figures4.1 XPS spectrum of lead illustrating schematically how excitingelectrons from each orbital can give rise to a distinct peak inthe spectrum [3]. Those electrons that are excited and leavethe surface without an energy loss produce the characteristicpeaks and those that undergo inelastic scattering and energyloss processes contribute to the background. . . . . . . . . . 684.2 Schematic presentation of the core 1s XPS process . . . . . . 694.3 This shows how at a low electron take off angle (grazing) thesurface sensitivity is enhanced and the thin oxide layer on thesilicon is more dominant [15]. . . . . . . . . . . . . . . . . . 714.4 Core 1s XPS spectra of elements with the atomic numbersof 3 to 9. The binding energy increases with increasing theatomic number [16, 17]. . . . . . . . . . . . . . . . . . . . . . 734.5 Oxygen 1s XPS of O2 and H2O in their gas phase. O2 isparamagnetic with two unpaired electrons in its valence shell.The core-hole created through the XPS process can interactwith these and gives two non-degenerate states observed asthe two XPS lines. H2O is diamagnetic with all its valenceelectrons paired; therefore, it gives one single XPS peak.[17, 18] 744.6 Oxygen 1s and carbon 1s XPS spectra after our first attemptin cleaning the surface of the single crystal BaBiO3. . . . . . 764.7 Oxygen 1s and carbon 1s XPS spectra at different stages ofour cleaning procedure on the single crystal BaBiO3. Theremoval of the carbon peak confirms the effectiveness of theprocedure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 784.8 Oxygen 1s and carbon 1sXPS spectra of single crystal BaBiO3after the optimized cleaning procedure described in the text.The oxygen spectrum loses most of its structure with the pro-gression of the cleaning but remains slightly asymmetric. . . . 795.1 d orbitals in various crystal field symmetries. The specificsymmetry of the ligands affect the energy levels of the metalion [11]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 855.2 The arrangement of d electrons in the ground state of an octa-hedral complex following the Hund’s rules. N is the numberof distinct pairs of electrons with parallel spins. The crystalfield potential here is the energy difference between the t2gand the e1g orbitals. . . . . . . . . . . . . . . . . . . . . . . . 87xivList of Figures5.3 A schematic representation of a: σ and b: pi bonding and anti-bonding molecular orbitals of p orbitals. The figure is takenfrom Ref. [19] and has been modified slightly by adding thesigns. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 905.4 The model single cluster of BaBiO3 with six oxygens at thecorners and a bismuth atom at the center. . . . . . . . . . . . 925.5 A schematic presentation of the involved hybridization termsin our model Hamiltonian. There are bismuth s orbital at thecentre and oxygen p orbitals at the corners of the octahedron.a: tOp−Bi6s =√6tspσ. b: σ and pi oxygen p hopping terms. c(and a): tpp = 1/2(tppσ − tpppi). d: t′pp = 1/2(tppσ + tpppi)[1]. . 945.6 The total spin of the ground state as a function of crystalfield energy (ECF ) and oxygen-bismuth hybridization energy(tspσ) for U = 3 eV. The first arrow indicates that we needto turn on the ECF , so that for tspσ=0 we get the correcttriplet ground state for a bismuthless octahedron with twoholes. The second arrow shows we have to increase the tspσenergy so that we achieve the expected low spin ground statewhen the bismuth is present. . . . . . . . . . . . . . . . . . . 975.7 The average number of holes as a function of a: Bi 6s/O phybridization energy (tspσ) for ∆ = −4 eV. and b: the chargetransfer energy ∆ for tspσ = 2.1 eV. For a large range ofparameters, holes reside primarily on the ligand oxygens. . . 995.8 Calculated oxygen 1s XPS spectra with all the hybridizationterms set to zero for different core-hole potential (Q) values.The curves are shifted along the “Intensity” axis. . . . . . . 1015.9 Calculated oxygen 1s XPS spectra for different Bi 6s/O p hy-bridization energies (tspσ), for tpppi = −0.04eV, tppσ = 0.63eV, U = 3 eV, Q = 3.6 eV, and ECF = 1 eV. Multiplets losetheir intensities significantly with turning on the bismuth-oxygen hybridization. The curves are shifted along the “In-tensity” axis. . . . . . . . . . . . . . . . . . . . . . . . . . . . 102A.1 The constructive Bragg reflections for monoclinic BaBiO3with lattice parameters given in table 2.1 for 17.68◦ ≤ 2θ ≤63.29◦ calculated via Vesta program. To be continued on thenext two pages. . . . . . . . . . . . . . . . . . . . . . . . . . . 118xvAcknowledgementsFirst and foremost, I would like to express my sincere gratitude to my su-pervisor Professor George A. Sawatzky for his continuous support, patience,motivation, and immense knowledge. I could not have imagined having abetter mentor and advisor for my Ph.D. study. His strong work ethic, never-ending passion for knowledge, and his genuine care for the people aroundhim have provided me with the best example of a great professional andhuman being.Besides my supervisor, I would like to thank the rest of my thesis com-mittee: Prof. Dough Bonn, Prof. Mona Berciu, and Prof. Mark VanRaamsdonk for serving as my committee members and for their insightfulcomments, encouragement and the stimulating discussions. I would like to,especially, thank Prof. Dough Bonn for giving me the opportunity to jointhe crystal growth laboratory and for his help and guidance through out thecrystal growth project. I also thank Dr. Shun Chi for his tremendous helpthroughout the same project.My sincere thanks also go to Dr. Robert Green without whom this workwould not have seen the light. I would like to thank him for his contin-uous support and mentorship throughout the synchrotron x-ray measure-ments and also the exact diagonalization calculations. I sincerely thank Dr.Kateryna Foyevtsova for supporting the band structure calculation aspectof this work. I also thank Dr. Oleksandr Foyevtsov, Dr. Fengmiao Li, Dr.Ronny Sutarto, Dr. Ilya Elfimov, and Mr. Arash Khazraei for their precioussupport at different stages of this work.And last but not least, I gratefully thank the Stewart Blusson quantumMatter Institute and the University of British Columbia for providing mewith a vast number of resources throughout my study.xviDedicationDedicated to my husband, Ehsan, for his continuous love and patience, andto my family and friends for their encouragement and support.xviiChapter 1BismuthatesBaBiO3 was first made and introduced in 1963 [20]. It is a diamagneticinsulating perovskite compound with a reddish brown colour. From thebeginning, its physics attracted attention due to its insulating mechanismwhich was believed to be the charge disproportionation of Bi+4 into Bi+3and Bi+5. This description has been challenged recently both experimentallyand theoretically.In 1975, it was discovered that the material becomes superconductingwith the critical temperature of 13K when doped with holes by partiallysubstituting bismuth with lead [21]. Later in 1988, a higher Tc of 34Kwas discovered for another hole doped compound by partially substitutingbarium with potassium [22]. It is one of the highest critical temperaturesdiscovered for a three-dimensional compound without a transition metalion. Despite this remarkable Tc, there have been many relatively quietyears regarding the bismuthate perhaps due to the revolutionary discoveryof cuprates’ superconductivity at about the same time in 1986 [23]. In thischapter, we review some of the key properties of the material and the maintheories around them.1.1 Electronic structureFrom the beginning, it was generally believed that BaBiO3 is a valance-skipping compound with the true structure of Ba2Bi+3Bi+5O6. The mainreasoning is that the nominal Bi+4 is not an energetically stable oxida-tion state for the bismuth atom. The electron configuration of bismuth is[Xe]4f145d106s26p3; therefore, it would either lose its three p electrons orthe three p plus its two 6s electrons “skipping” the +4 state.This conclusion was later supported by two important observations.First, the material was found to be insulating with a direct and an indi-rect gap of about 2 eV and 0.25 eV, respectively [21, 24], and then in 1976neutron diffraction found two distinct Bi-O bond lengths of 2.28 A˚ and 2.12A˚ [2, 25]. BaBi+4O3 has to be metallic due to the half-filled 6s band. Theabove “charge-disproportionation” of bismuth cation into the +3 and +511.1. Electronic structurestates was able to explain the insulating behaviour and also the two differ-ent Bi-O bond lengths.However, the above charge-disproportionation picture has been ques-tioned recently by several experiments as well as band structure calcula-tions. Band structure calculations do not find a significant charge transferbetween the two bismuth sites[4, 26, 27]. X-ray photoemission measurementsalso don’t give conclusive evidence for two different bismuth oxidation states[28–31]. Doubling the unit cell by the structural “bond-disproportionation”has been proposed as an alternative insulating mechanism by opening up agap similar to the Peierls distortion mechanism but for a three-dimensionalstructure [4, 32, 33]. In this picture, every other octahedron expands andcollapses in a rock-salt pattern distortion.The band structure calculation using density functional theory (DFT)shows how the strong hybridization between the deep Bi 6s and the O 2pbands pushes the O 2p anti-bonding orbitals with A1g symmetry above theFermi energy [4]. Then due to the above bond- disproportionation distortion,pairs of oxygen holes form A1g molecular orbitals around the Bi sites in thecollapsed or short-bonded octahedra. Fig. 1.1 presents the density of statesof SrBiO3 projected onto the Bi-6s orbital and A1g combinations of the O-pσorbitals for the compressed and expanded BiO6 octahedra. The image hasbeen reproduced by Ref. [5] from DFT calculation of Ref. [4]. As shown inFig. 1.2 band structure calculation finds the electronic structure of SrBiO3to be very similar to BaBiO3. The main difference is the larger gap in theSrBiO3 due to a larger structural distortion [4].Fig. 1.1 shows that states of mainly O-2p character with A1g symmetrygenerate a strong conduction band in the compressed octahedron. This bandis much less prominent for the expanded octahedron. This demonstrates thebond-disproportion action which is due to the role of the oxygen 2p holesand not the typically believed charge disproportionation of the bismuths.In this picture, bismuths are all +3 and the other remaining hole resideson the three oxygen anions. This is a very different description electroni-cally and hasn’t yet been accepted unanimously by the community [7]. Oneobjection is that the evidence for holes on the oxygens should clearly appearin experiments like O 1s x-ray photoemission; however, the existing resultshave not been conclusive [27, 28, 30, 31, 34]. In this work, we try to addressthis controversy by studying the electronic structure of oxygen anions ex-perimentally with x-ray spectroscopy measurements and theoretically usingexact diagonalization cluster calculations.21.1. Electronic structureFigure 1.1: Top: Density of states of a compressed and expanded BiO6octahedron projected on to the Bi-6s orbital and combinations of the O-pσ orbitals for SrBiO3 structure from Ref. [4]’s DFT(LDA) calculations[4, 5]. Bottom: The octahedron with O-pσ orbitals at the corners hybridizedthrough nearest-neighbor hopping integrals of −t and the correspondingeigenstates in the table for different symmetries [4] .31.1. Electronic structureFigure 1.2: DFT(LDA) band structures of BaBiO3 and SrBiO3 calculatedwith a supercell of dimensions√2a×√2a×√2a. The band structures arealmost identical around the Fermi energy except for a larger gap in SrBiO3due to its more prominent structural distortions. The Fermi energy is setto zero [4].41.1. Electronic structureFigure 1.3: a: Mott-Hubbard insulators where the gap is determined bythe Coulomb energy U versus c: charge-transfer insulators where the gapis determined by ∆ which is smaller than U . b: charge fluctuations corre-sponding to the energies ∆ and U . The blue and red orbitals represent theligand oxygen p, and the transition metal d orbitals, respectively [5, 6].1.1.1 Bismuthates and NickelatesThe above breathing type lattice distortion is similar to the one in thenickelate perovskite where every other octahedron expands and compressesalternatively. Nickelate perovskite, RNiO3, R= Rare earth, is known as acharge transfer insulator [35] . In correlated transition metal compounds,the charge transfer energy, ∆, is defined as the energy required to movean electron from a ligand oxygen 2p orbital to the cation 3d orbital or,equivalently, the energy cost for the transition p6dn → p5dn+1.As opposed to the Mott-Hubbard insulators, charge transfer insulatorshave a smaller charge transfer energy than the Coulomb energy Udd andtherefore the gap is determined by ∆, not U . The distinction between thesetwo types of insulators is schematically presented in Fig. 1.3. This wasfirst introduced in the Zaanen-Sawatzky-Allen (ZSA) theory in 1985 [6]. Inrecent years, it has been shown that nickelates are in fact negative chargetransfer insulators meaning that the p5dn+1 state has a lower energy thanthe p6dn state, so the ground state is better described as Ldn+1 where Ldenotes a hole on the ligands [6, 35, 36].Even though the above description is focused on strongly correlated tran-sition metal compounds, the non-strongly-correlated bismuthates show simi-lar behaviours to the negative charge transfer compounds like nickelates. Asmentioned above, both materials exhibit similar breathing type distortion51.1. Electronic structureFigure 1.4: The schematic illustration of the perovskite nickelate (on theleft) and bismuthate (on the right) electronic structures. In the bismuthate,the deep Bi-6s states with the A1g symmetry hybridize strongly with thecombination of the O2p states with the same symmetry. Consequently, thestate of A1g symmetry and mainly O2p character are pushed above the Fermilevel. In the nickelate, the situation is similar but the cation states are theNi-3d states with the Eg symmetry which again mix with the O2p stateswith the same symmetry [5].with alternating expanded and compressed octahedra responsible for theirinsulating phase.In nickelates, the hybridization situation is also very similar to bis-muthates except that in nickelates the Ni-d states are playing the role, soit is the Eg symmetry of the molecular orbitals involved rather than theA1g symmetry states. In other words, in nickelates, the Eg symmetry Ni-dbands hybridize strongly with the Eg symmetry oxygen p states which resultsin the anti-bonding oxygen hole states with the Eg symmetry. They thenform molecular orbitals with the same symmetry around the short bondedNi cations in the compressed octahedron [5] similar to what happens inthe bismuthates. The schematic similarities of the electronic structure ofthese two perovskites are shown in Fig. 1.4. The fact that these two per-ovskites exhibit striking similarities even though they have very differentcations demonstrates the importance of the role of oxygen in describing theelectronic properties of perovskites.61.2. Crystal StructureFigure 1.5: The crystal structure of perovskite BaBiO3. The green balls atthe corners of the octahedra represent the oxygen anions. The black andwhite balls at the centers of the octahedra represent the bismuth cations inexpanded and collapsed octahedra, respectively [4].1.2 Crystal StructureThe structure of the perovskite BaBiO3 has been determined using x-rayand neutron powder diffraction techniques over temperatures from 4.2 K to973 K [7, 37] where it goes through three main structural transitions. Thematerial is monoclinic at temperatures from 4.2 K to 430 K; however, thespace group changes from P2/m to I2/m at about 140 K. Then at about430 K, it transitions to a rhombohedral structure in the R3 space groupup until 820 K where it finally becomes cubic in the Pm3m space group.As mentioned before, the neutron diffraction also finds two different Bi-Obond lengths of 2.28 A˚ and 2.12 A˚ or two distinct, expanded and collapsed,octahedra in the material at room temperature[2, 37]. The structure atroom temperature is illustrated in Fig. 1.5.For perovskite compounds, ABO3, the Goldschmidt tolerance factor t isdefined as:t =rA + r0√2(rB + r0)(1.1)where rA, rB, and rO are the radii of the cation A, cation B and theoxygen anion, respectively. The deviation from 1 of t signifies the amount of71.3. Superconductivitydistortion in the lattice from an ideal cubic structure. The further apart thetolerance factor from 1, the more distorted the structure is. The tolerancefactor for BaBiO3 is less than 1 at about 0.9 which results in tilted octahedraand a distorted perovskite structure [38, 39].1.3 SuperconductivityThe fact that BaBiO3 is a diamagnetic insulator motivated people to look foran insulator-to-metal transition in BaBixPb1−xO3 compounds since BaPbO3was a well-known metal. This search, more than a decade later, in 1975,led to the discovery of superconductivity in the hole doped BaBixPb1−xO3,for x = 0.05− 0.3, with the highest transition temperature of Tc= 13 K forx=0.3 [21]. It was the highest observed Tc for a material with no transitionmetal until 1988 when interestingly the record broke by the same family ofmaterial, BaxK1−xBiO3, with the highest Tc of 34 K for x=0.35 [22]. Thiswas a remarkable discovery mainly because it was the highest observed Tc fora three-dimensional material with no transition metal and with a minimalelectronic density of states around the Fermi level [40].The phase diagrams of BaxK1−xBiO3 and BaBixPb1−xO3 compoundsare shown in Fig. 1.7 [7]. The lead doped compound generally has morecomplex and less understood phase relationships mainly due to the lack ofphase purity at different x values. In general, the tetragonal phase is identi-fied as the superconducting phase for x = 0.05−0.3 [37]. However, mixturesof tetragonal and orthorhombic structures are almost always detected forthose values of x [37, 41]. A recent ultrafast experiment also reports find-ing evidence for the coexistence of CDW order and superconductivity forthe underdoped BaBixPb1−xO3 composition[42]. This is especially notablesince CDW correlations have also been recently observed for some under-doped cuprate materials[43, 44]. This gives more evidence for the possiblecommonalities between the physics of these two superconducting families.Understanding the phase relationships of the potassium substituted com-pound, BaxK1−xBiO3, is less complicated thanks to the availability of themore high-quality single phase crystals. When the potassium is substitutedfor barium, the tolerance factor t increases from t = 0.9 for the pure com-pound because K1+ is larger than the Ba2+. Thus, the doped material getsless distorted and ultimately becomes cubic at room temperature. However,it was later observed that the structure at the superconducting temperaturesis, in fact, tetragonal (I4/mcm) with tilted octahedra [45]. The summaryof BaxK1−xBiO3 properties is presented in table 1.6.81.3. SuperconductivityFigure 1.6: Summary of BaxK1−xBiO3 properties taken from Ref. [7].There have been some other superconducting compositions discoveredin this family such as SrxK1−xBiO3 and BaxRb1−xBiO3 with the highestTc’s of 12 K and 29 K [46, 47], respectively. These are all s-wave super-conductors and their superconductivity mechanism is generally attributedto the bipolaronic situation implicit in the said CDW or the charge/bonddisproportionation picture[48–51].1.3.1 Bismuthates and CupratesBismuthate perovskites have some notable similarities with some other in-teresting electronic materials such as nickelates, which was discussed in theprevious section, and also with the high-Tc cuprate superconductors. Boththese high-Tc superconductors are described by strongly hybridized bandsof the ligand O 2p and the cation valence states about the Fermi level (Cu3d for the cuprates and Bi/Pb 6s for the bismuthates).However, in cuprates the hybridization is mainly between the Cu 3d(x2−y2) and the oxygen 2p states formed from the four ligand oxygen atoms, whilein the bismuthate it is between the spherically symmetric Bi/Pb 6s states91.3. SuperconductivityFigure 1.7: The phase diagrams of top: Ba1−xKxBiO3 and bot-tom: BaBi1−xPbxO3 compounds. Due to the lack of phase purityfor BaBi1−xPbxO3 samples and hence the non-conclusive results theBaBi1−xPbxO3 phase diagram is perhaps only qualitatively correct [7].101.3. Superconductivityand the 2p orbitals of the six ligand oxygens [52, 53]. In both cases, thisstrongly hybridized band splits and opens up a gap giving rise to an insu-lating state. However, while in the diamagnetic bismuthates it is due to theabove CDW or bipolaronic type of ordering, in cuprates, the large on-sited − d Coulomb repulsion causes the un-doped material with configurationd9(s = 1/2) and a full O 2p band (i.e. a positive charge transfer gap) toform local moments which at low temperatures form a stable antiferromag-netic ordered structure and a conductivity gap is determined by the positivecharge transfer gap. Upon hole doping however the holes go into a linearcombination of O 2p orbitals of dx2−y2 symmetry strongly hybridizing withthe Cu 3d orbital of the same symmetry and together these two holes (oneon Cu and One on O 2p) form a singlet and form a metallic state.The hole-doped cuprates and bismuthates both have a low density ofstates around the Fermi level compared to their superconducting criticaltemperatures [52]. Perhaps that is why the bismuthate superconductorshave also been often categorized as “unconventional” or “possibly uncon-ventional” superconductors [7]. However, a more recent modified calculationclaims that they find a high Tc consistent with their “correlation-enhancedelectron-phonon coupling” model[51].11Chapter 2BaBiO3 Single CrystalGrowthIn this chapter, we discuss how we developed a routine to grow single crystalsof BaBiO3 with sizes up to 3 × 3 × 1 mm3. We also present the results ofthe characterization techniques used to measure their chemical compositionand their structural and transport properties.2.1 IntroductionA single crystal or monocrystalline solid is typically defined as a materialthat maintains translational symmetry over macroscopic distances of biggerthan 100 µm. It requires an absence of defects associated with grain bound-aries. Because entropic effects favour the presence of such imperfections,perfect single crystals of reasonable macroscopic sizes are rare in nature,and are also challenging to make in the laboratory[54][55].Single crystals are preferred and sometimes necessary for structural de-termination or intrinsic property studies. For instance, in conductivity mea-surements, insulating grain boundaries can give rise to semiconducting prop-erties for metallic oxides resulting in inconclusive outcomes. Even in ourspecific case of bismuthates, initially, the resistivity of the BaxK1−xBiO3polycrystalline samples above Tc found to decrease with increasing temper-ature. However later, resistivity measurements on the single crystal samples,showed the resistivity indeed increases with increasing the temperature asexpected for a metal[7][56].Many crystal growth techniques have been developed over the years.Each of these techniques has its advantages and disadvantages and is usedbased on the properties of the material and the application requirements.These techniques can be categorized into the four following main methods[8]:• Solid State Growth: From a mixture of solids with no melting involvedsuch as Strain Anneal and Sintering techniques. These techniques usu-122.1. Introductionally result in polycrystalline materials with at best tiny single crystalregions.• Vapour Phase Growth: From solid to gas (vapour) to crystal. Thesedeposition techniques can be made on a lattice matched single crystalsubstrate resulting in epitaxial thin film growth such as Pulsed LaserDeposition (PLD) and Molecular Beam Epitaxy (MBE) techniques.This method can also be used for growing bulk single crystals.• Melt Growth: From solid to liquid to crystal. In these techniques, thepolycrystalline material is heated in a non-reacting crucible to aboveits melting point and then is slowly cooled down to form crystals.Various additional steps can be taken to enhance the crystal formationand quality such as inserting a seed crystal into the melt and pullingand rotating the seed to form a crystallization centre, or employinga temperature gradient along the crucible which are known as theCzochralski and Bridgman techniques, respectively.• Solution Growth: In these techniques, a saturated solution is preparedby dissolving the components of the desired crystal in a solvent at atemperature above the saturation temperature. Then the supersatu-rated solution is cooled down for the crystal to precipitate. Crystal-lization can happen by spontaneous nucleation or can be enhanced byusing a seed.In growing the bismuthate single crystal, the electrochemical method(solution growth) has often been used and proven successful in growing thesuperconducting BaxK1−xBiO3 crystals as big as 5 × 4 × 3 mm3 [57][58].In this technique typically a mixture of Ba(OH)2.8H2O and Bi2O3 powdersis used in molten KOH where the weight ratio of barium hydroxide andthe potassium hydroxide determines the amount of potassium substitution.However, due to the involved potassium, this technique is not suitable forgrowing pure BaBiO3 single crystal which is the material of our main interestin this study as the parent compound.There are not as many studies on growing the parent BaBiO3 single crys-tals compared to its doped superconducting compounds. However, floatingzone [59] and molten flux techniques [9] have been reported to be successfulin growing such single crystals. The floating zone method requires specificequipment which was not available in our laboratory at the time. Moreover,the referred report [59] lacks any stoichiometry or detailed structural anal-ysis to judge the quality of the resultant crystals. Therefore, we took the132.1. IntroductionFigure 2.1: An overview of the most used crystal-growth techniques [8].These techniques fall into four main categories: solid-state growth, vapourphase growth, melt growth and solution growth. In this work a combinationof solid-state+melt growth was ultimately used to grow BaBiO3 crystals.other approach of slow-cooling the molten mixture by I. Shiozaki and H.Ishii [9] as a guidance to start. As shown below, we realized this recipe doesnot give us our desired big high-quality single crystals either. Therefore wemade some modifications to be able to achieve our desired result.Growth from the melt by solidification is one of the oldest and also mostused single crystal techniques for growing large single crystals. The firstsystematic study of such crystal growth was carried out by Tamman in 1899.He tracked the rate of the crystal solidification of an augite compositionfrom its melt. He found with decreasing the temperature of the melt, thecrystallization rate increases to a maximum and then decreases. A morerigorous theory was developed later by Volmer and Marde in 1931 [60]. Themelting technique is most useful and straightforward for materials that melt142.2. Single Crystal Growth Procedurecongruently.Congruent melting, which is contrasted with the incongruent melting,is the thermal behaviour of intermediate compounds in a temperature-composition phase diagram. An intermediate compound is a combinationof the end members of the phase diagram between the two solids. Congru-ent melting is when one solid phase transforms to another solid phase anda liquid phase both of the same chemical compositions as of the originalcomposition.Two main factors control the size and purity of the resultant single crys-tal: nucleation rate and growth rate. If nucleation is rapid compared tothe overall growth, small single crystals or polycrystalline samples will re-sult. On the other hand, if the nucleation is slow and the growth is fastlarge single crystals will form. However, note that defect concentrationtends to increase with increasing the growth rate. Therefore, in order to gethigh-quality crystals with a reasonable size, both the growth rate and thenucleation rate should remain small.There are several techniques within the melt-growth category to lowerthe nucleation rate by limiting the number of nucleation sites: slow coolingthe melt, introducing a temperature gradient, introducing a seed crystal,and moving the crystal-melt interface [61]. In this work, we start by solid-state sintering in order to synthesize the starting polycrystalline BaBiO3,and then the single crystal is grown by slow cooling the congruent-melt.The development of this procedure is explained below.2.2 Single Crystal Growth ProcedureFirst AttemptBaCO3(99.9%) and Bi2O3(99.9%) powders were mixed in the stoichiometricmolar ratio of 2:1 based on the Eq. 2.1.1The mixture was then ground thoroughly until a fine homogenous mix-ture was achieved.According to Material Safety Data Sheet (MSDS), bismuth trioxide is“slightly hazardous in case of eye contact (irritant), of ingestion, of inhala-tion” and barium carbonate is “hazardous in case of skin contact (irritant),1 It has been suggested that adding a 10% excess barium to the starting mixture helpsavoid self-strain in the crystals [9]. For the first three attempts, we used the two mixtures(the stoichiometric, and the Ba-rich) at two separate crucibles but with the other exactsame conditions, we did not observe any difference, so we proceeded with the stoichiometricmixture.152.2. Single Crystal Growth Procedureof eye contact (irritant), of ingestion, of inhalation”. Therefore, propersafety measures have to be taken in handling and storing these chemicalmaterials. The grinding must be performed in a cool well-ventilated area.2BaCO3 + Bi2O3 +12O2 → 2BaBiO3 + 2CO2 (2.1)The resulting powder was calcined in still air in a furnace at 850◦ C for5 hours in a 10 mm Outer Diameter (OD) alumina crucible. A home-madetube furnace with a Lindberg digital controller with the maximum availabletemperature of 1200◦ C was used. No temperature gradient over the lengthand width of the crucible was detected. Note, the furnace was calibratedusing a K-type standard thermocouple before each attempt. All the tem-peratures mentioned here are the true temperatures after the calibration,not the read numbers.The mixture was heated at the centre of the furnace to a temperaturehigher than the BaBiO3 melting point of 1040◦ C[62] and then was cooleddown slowly with the rates given in Figure 2.2 following the reference[9]. Asshown in Fig. 2.3, this attempt was not successful in growing BaBiO3 singlecrystals as the Laue diffraction result suggests.In x-ray Laue diffraction technique, the sample is irradiated by an x-ray beam of continuous wavelength (“white” x-ray) while held stationary.The crystal reflects beams for which the Bragg condition is satisfied anda constructive diffraction takes place. The diffraction pattern of a singlecrystal should be a series of spots with information about its orientationand symmetry. The Laue method is convenient for a rapid assessment of agrown crystal.162.2. Single Crystal Growth ProcedureFigure 2.2: Temperature-steps for the BaBiO3 single crystal growth asgiven by Ref. [9]. (The highest temperature of 1010◦ C in the plot has to bean error. Based on the text and the BaBiO3 melting temperature of 1040◦C, it has to be 1100◦ C.)172.2. Single Crystal Growth ProcedureFigure 2.3: First growth attempt and its Laue-gram. The result was notsingle crystal. (unsuccessful)Second AttemptTrying to understand what the problem was in the last growth, we noticedin the reference paper [9] there was a temperature difference of about 3◦/cmalong the length of the crucible that was not included in our growth. In-troducing a temperature gradient is, in general, a well-known part in manycrystal growth techniques such as in Bridgman or Zone Melting methods.The idea is that when we start cooling down, the lower part of the meltwith a lower temperature reaches the melting point sooner and thereforecrystallizes earlier and then it can induce nucleation in the upper part ofthe melt.Therefore, for the second attempt, we tried to apply such a gradient. Inorder to introduce this temperature gradient over the length of the cruciblewe designed and made a sloped insulating ceramic disk with a 7 cm outerthickness at the furnace wall and 1 cm inner thickness around the crucible.It is shown in Fig. 2.4. This way we achieved a temperature difference ofabout 9◦ C across the bottom two centimetres of the crucible.182.2. Single Crystal Growth ProcedureFigure 2.4: The construction of the furnace (top) with the insulating ce-ramic disk (bottom) to introduce a temperature gradient along the cruciblefor the second attempt.The rest of the procedure was the same as the first try. As shown inFig. 2.5, the growth was not successful either and the result was almost thesame as the previous attempt. As realized later, that is because the crystal192.2. Single Crystal Growth Proceduregrowth happens only at the top one to two millimetres of the melt due tothe required air and oxygen exposure. Therefore, the temperature gradientdoes not help in this growth. The sloped disk was removed for the nextattempts.Figure 2.5: Second growth attempt and its Laue-gram. Here the previousprocedure was repeated but a temperature gradient was also introducedalong the crucible. The result was not single crystal. (unsuccessful)Third AttemptFor this growth, we realized the calcined mixed powder does not look ho-mogenous after being taken out of the furnace. It was dark grey with someshimmery brown patches. In order to start with a more homogeneous ma-terial we broke and ground the calcined tablet until it looked homogenousand then started the growth as before.As shown in Fig. 2.6, the Laue pattern again was indicative of an un-successful growth in terms of growing a single crystal; however, the resultwas golden brown and shiny as BaBiO3 has to be[7, 62]. We concluded thatwe are on the right path and perhaps we have to modify this “pre-reaction”step further.202.2. Single Crystal Growth ProcedureFigure 2.6: Third growth attempt and its Laue-gram. Here the previousprocedure was repeated but the calcined powders was ground and homoge-nized before the melt. The result was golden brown as expected for BaBiO3but not single crystal. (unsuccessful)Fourth AttemptFrom the previous attempt, we learned that the starting material has to bemore homogeneous, and heating up the Bi2O3 and BaCO3 mixture at 800◦C for 5 hours, as suggested by the Ref. [9], does not give us that. Therefore,we decided to make sure we are starting with homogeneous single phaseBaBiO3 powder before the melting step. It turned out this is a crucial stepfor a successful single crystal growth.To achieve that, we again mixed powders of BaCO3 (99.9%) and Bi2O3(99.9%) in the stoichiometric molar ratio of 2:1 (10.000 g and 11.806 g,respectively) and ground them patiently. The mixture then was sinteredfor 20 hours at 800◦ C. Then we took out the calcined tablet, broke it andground it thoroughly before putting it back in the furnace at 800◦ C foranother 20 hours.The final result did not look black and patchy anymore but all shimmerybrown which was desired. It was again ground finely and was confirmed212.2. Single Crystal Growth Procedurequalitatively by X-Ray Diffraction (XRD) test to be monoclinic BaBiO3powder to make sure the solid-state reaction between the starting powderswas successful prior to the melt procedure. A more detailed and quantitativeanalysis was intended to be carried out on the final crystals.The measurement was performed using Philips X’pert X-ray diffrac-tometer at Advanced Materials Process Engineering Laboratory (AMPEL),UBC. The XRD result is shown in Fig. 2.7 and is compared to the corre-sponding simulated pattern. The simulation has been done using the Vestaprogram with the lattice parameters given in table 2.1 from the Sleight andCox paper [2]. BaBiO3 powder XRD pattern is quite complicated with morethan 100 peaks in the 20◦ < 2θ < 60◦ range. These peaks are given explicitlyin Appendix A for the same calculation. 2θ is the angle between the incidentbeam and the diffracted beam. Physics of an XRD experiment is explainedin more detail in section 2.3.2 where the single crystal XRD results on thefinal crystals are presented.a b c α β γ6.181 A˚ 6.136 A˚ 8.670 A˚ 90.000◦ 90.170◦ 90.000◦Table 2.1: BaBiO3 lattice parameters in I2/m symmetry taken from Ref.[2] and used to simulate the powder diffraction pattern in Fig. 2.7.222.2. Single Crystal Growth Procedure 20 25 30 35 40 45 50 55 60Intensity (a.u)2 theta (degree)Simulated 20 25 30 35 40 45 50 55 60Intensity (a.u)2 theta (degree)MeasuredFigure 2.7: Simulated (top) and measured (bottom) BaBiO3 powderdiffraction patterns with Cu-Kα X-ray source.After synthesizing the BaBiO3 powder, we started the melt growth withthe following rates and temperatures:232.2. Single Crystal Growth Procedure25◦C180◦C/h=====⇒ 955◦C(20h) 60◦C/h====⇒ 1085◦C(20h)0.5◦C/h=====⇒ 1015◦C(10h) 300◦C/h=====⇒ 25◦CThe temperatures and steps were also slightly modified compared tothe reference temperature profile [9]: The cooling rate was decreased from4◦ C/h between the temperatures 1100◦ C and 750◦ C to 0.5◦ C/h between1085◦ C to 1015◦ C and the stabilization constant-temperature intervals wasincreased in time in order to allow for growing bigger single crystal domains.The steps are shown in Fig. 2.8. This procedure takes about 190 hours inaddition to the two 20-hour prior solid-state reactions. 0 200 400 600 800 1000 1200 0 20 40 60 80 100 120 140 160 180 200Temperature (Celsius)Time (hour)Figure 2.8: The thermal process for the BaBiO3 singe crystal meltinggrowth. The red arrow indicates the slow cooling step from above the melt-ing point to the below.With the above procedure, we succeeded to grow 1 × 1 mm2 plates ofBaBiO3 single crystals from the surface as was confirmed by the Laue diffrac-tion test. The result is shown in Fig. 2.9.From the observation that the single crystal growth had only happenedat the surface, we concluded that in order to get bigger single crystals weneed to increase the surface area by using a wider crucible to enhance theoxygen exposure which was essential for a successful growth. This was thechange we considered for the next growth.242.2. Single Crystal Growth ProcedureFigure 2.9: Fourth growth attempt and its Laue-gram. The melting pro-cedure was performed on BaBiO3 powder which had been synthesized inadvance through solid-state reaction. The result was 1 × 1 mm2 plates ofBaBiO3 single crystals. ( successful).Final AttemptWe learned so far that in order to grow BaBiO3 single crystals througha melting or self-flux procedure we must start with the BaBiO3 powder.Moreover, to synthesize the powder, we should mix and grind stoichiometricratio of BaCO3 and Bi2O3 powders and sinter the mixture twice at 800◦ Cfor 20 hours each. We need to grind the mixture thoroughly in between,too.We also learned that having a temperature gradient does not help withthe result since the crystals form on the surface. That is why this time,we followed the above procedure, as described in the previous attempt, andonly changed the size of the crucible from a 10 mm OD to a 25 mm ODto increase the oxygen (air) exposure. As shown in Fig. 2.10, this way wemanaged to grow BaBiO3 single crystals of sizes up to 3× 3× 1 mm3.252.2. Single Crystal Growth ProcedureFigure 2.10: Fifth (final) growth attempt. Increasing the melt surface areaby using a wider crucible (25 mm OD) resulted in growing bigger singlecrystals. (successful)Figure 2.11: X-ray back-reflection Laue-gram of the grown crystal with thex-rays oriented along the [100] crystallographic direction in a cubic unit cell.262.3. Characterization2.3 CharacterizationPreviously, it was explained how we developed a routine to grow BaBiO3single crystals of sizes up to 3 × 3 × 1 mm3. The starting powder wasconfirmed by XRD to be BaBiO3, and the final crystals were confirmedby Laue diffraction to be single crystals. After these preliminary tests, wecharacterize the crystals in more detail using X-ray Photoemission Spec-troscopy (XPS), single crystal XRD, and resistivity measurements to studythe chemical composition, their crystal structure, and their transport prop-erties, respectively.2.3.1 X-ray Photoemission SpectroscopyIn order to find the chemical composition of the grown single crystals, weused XPS. Through XPS, we measure the number of electrons ejected fromthe surface when irradiated with a beam of x-rays. The measured spectrumincludes a background signal and a set of resonance peaks. Each elementin the few nanometers of the sample surface produces a set of peaks atcharacteristic binding energies corresponding to the electron configurationof the atom. The physics of this process is explained in more detail inchapter 4.In XPS when a sample is homogeneous the number of detected photo-electrons per second in a specific peak is determined by:I = nfσθyλAT (2.2)where n is the number of atoms of the element per volume unit, f is thex-ray flux, σ is the photoelectric cross section for the given atomic orbital,θ isthe angular efficiency factor, y is the photoelectric process efficiency factor,λ is the mean free path of the photoelectrons in the sample, A is the area ofthe sample from which the photoelectrons are emitted, and T is the detectionefficiency factor.n =IfσθyλAT→ n1n2=I1/S1I2/S2(2.3)where S is called atomic sensitivity factor. This equation implies thenumber of electrons recorded in a given state is proportional to the num-ber of the corresponding atoms. It makes XPS a suitable tool to find thechemical composition. Finding the area enclosed by each characteristic peakis the primary way to find the number of excited electrons and hence the272.3. Characterizationcorresponding chemical composition when the appropriate sensitivity fac-tors are given [15]. There are many XPS softwares available that calculatethese chemical compositions for a given spectrum. We used CasaXPS forthis purpose.As will be discussed in more detail in chapter 4, an XPS spectrum con-sists of some intrinsic peaks sitting on a background signal.This “background” intensity has to be removed from the spectrum priorto finding the chemical composition of the material. A very crude approachto generate this background uses a simple linear approximation by interpo-lating the intensities at either end of an energy interval as:L(E) = I1(E2 − E)(E2 − E1) + I2(E − E1)(E2 − E1) (2.4)where E1 and E2 are ends of an energy interval and I1 and I2 are theircorresponding intensities. However, the background shape often depends onthe material and the energy. Therefore, a more complex approach is requiredto account for it such as the Shirley algorithm [63]. It is an iterative approachto construct a background by using information about the spectrum.After irradiating the sample with x-rays, the excited electrons may un-dergo inelastic collisions within the sample which alter their kinetic energies.They also can produce a multitude of low energy electron-hole excitations orso called secondary electrons. These two processes produce an energy-lossbackground plus a background due to the secondary electrons.Because of the broad range in the energy loss and the secondary back-grounds a seemingly smooth background results at energies well below thepeaks in the XPS spectrum. This background signal however only starts atthe energies corresponding to zero-loss photoelectrons with kinetic energiesless than the photoelectrons’ kinetic energy. We can describe the variationof their intensities within a peak by composing a peak out of a continuousseries of delta functions each one being followed at a lower kinetic energyby a step function of a height proportional to the intensity of that deltafunction. The total background within the peak shape is the integral overenergy of those delta functions and the stepwise contribution which resultsin an “S”-like shape background as shown in Fig. 2.12. This procedure iscalled the Shirley background procedure.The n-th iteration of the constructed Shirley background (Bn(E)) andthe n-th scattering factor (κn) are given by:282.3. CharacterizationB1(E) = κ1∫ E1EdE′(I(E′ − I1),B2(E) = κ2∫ E1EdE′(I(E′ − I1 −B1(E′))...Bn(E) = κn∫ E1EdE′(I(E′ − I1 −Bn−1(E′)) (2.5)andκn =I2 − I1∫E1E2dE′(I(E′)− I1 −Bn−1(E′))(2.6)The binding energies E1 and E2 and the intensities I1 and I2 correspondto the two selected points, one at an energy above and one below the peak,as shown in Fig. 2.12 for a carbon 1s spectrum. Note E2 is smaller than E1.Equation 2.6 guaranties at each iteration the scattering factor κ is chosenso that the background goes through the other point (E2, I2). This iterativeprocess continues until the background value, Bn, converge[10].292.3. CharacterizationFigure 2.12: A carbon 1s x-ray photoemission spectrum with the back-ground signal corrected using the top: linear and bottom: Shirley algo-rithms. The figures are taken from Ref. [10] and they have been modifiedslightly by adding the labels.302.3. CharacterizationThere are many commercial software packages available to construct abackground intensity using different algorithms and subtract it from the XPSspectrum. We picked Shirley background algorithm and used the CasaXPSsoftware for this purpose.The XPS measurements are performed using an Omicron Multi-probeMXPS machine with an energy resolution of 0.4 eV at the Surface ScienceFacility of the REIXS beam-line at the Canadian Light Source (CLS). Thesystem is shown in Fig. 2.13 which consists of two sources and one analyzer:• Sources: XM 1000 and DAR 400. XM1000 generates monochromaticx-ray with Al Kα (hν = 1486.6 eV) which is used for our experiments.DAR 400 produces none-monochromatic x-ray with Mg Kα (hν =1253.6 eV) and Al Kα (hν = 1486.6 eV) anodes. The diameter of themonochromatic x-ray beam is ≤ 0.75 mm.• Analyzer: EA 125 SPHERA. It is a hemispherical analyzer which ismounted at 37◦ from the horizontal and 83◦ from the x-ray monochro-mator.The crystal has been efficiently cleaned to remove surface contaminationusing the cleaning procedure described in chapter 4.Figure 2.13: Omicron Multi-probe MXPS system at the Surface ScienceFacility of the REIXS beam-line at the Canadian Light Source (CLS)312.3. CharacterizationThe XPS result is shown in Fig. 2.14 and the corresponding atomicratios are given in table 2.2. The atomic ratios are calculated by findingthe enclosed area under the Ba 3d5/2, Bi 4d5/2, and O 1s peaks and theircorresponding relative sensitivity factors. 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000 300 400 500 600 700 800Bi 4d 5/2Bi 4d 3/2O 1sBi 4p 3/2Ba 3d 5/2Ba 3d 3/2Bi 4p 1/2C 1sIntensity (a.u)Binding Energy (eV)Figure 2.14: X-ray photoemission spectrum of BaBiO3 single crystal atroom temperatureElement At%Ba 19 ± 1Bi 19 ± 1O 62 ± 3Table 2.2: The atomic ratios of the grown single crystal given by the XPSmeasurement (Fig. 2.14 ). The accuracy of the results derived from thistechnique (described in the text) is within 5%.322.3. Characterization2.3.2 X Ray DiffractionIn real space, crystalline solids consist of series of planes of regularly spacedatoms separated by the distance d. When a beam of light hits these planes,there is a strong constructive interference of the reflected beams from thesurface and the various layers if the path difference is integer multiple of theincident beam’s wavelength. As explained below, this results in a formulatedcondition known as Bragg’s law.Figure 2.15: A schematic representation of a two-dimensional crystal lat-tice. An incident beam hitting the crystal undergoes a constructive (inphase) diffraction when the path difference is equal to an integral multipleof the wavelength: nλ = 2dsinθ. (Bragg’s law)As illustrated in Fig. 2.15, when a beam of rays hits a crystal, somereflect along AD by the first plane and some transmit and get reflected bythe second plane along BC. The path difference between these two equals:path difference = (AB + BC)− (AD) (2.7)These beams will undergo constructive interference, if and only if:path difference = nλ, (2.8)where, n is a positive integer and λ is wavelength of the incident wave.Based on a simple trigonometry in Fig. 2.15:332.3. CharacterizationAB = BC =dsinθAC =2dtanθAD = ACcosθ ⇒ nλ = 2dsinθ (2.9)For each lattice system, the inter-planar distance d can be expressed interms of the Miller indices (h, k, l) for each set of planes. For the simplestcase of a cubic lattice with the lattice parameter of a: 1d2= h2+k2+l2a2, whilefor a more complicated case of a monoclinic system with lattice parametersa, b, c and β it is given by:1d2monoclinic=h2a2sin2β+k2b2+l2c2sin2β(2.10)+2hlcosβacsin2βThe most frequently used type of XRD measurement is a 2θ−ω scan inwhich the 2θ axis is moved twice the rate of the ω axis. In a 2θ − ω scan,the intensity of the diffracted beam is recorded and plotted as a function of2θ. ω is the angle between the incident beam and the sample surface, and2θ is the angle between the incident beam and the diffracted beam. Theresulting spectrum consists of a set of peaks at some specific angles. Thesepeaks correspond to the above constructive Bragg reflections. Thus, withhaving the incident angles (θ), and the wavelength (λ), d and subsequentlythe sample’s lattice parameters can be found.Lattice ParametersAfter performing an XPS measurement to find the chemical composition ofthe crystals and a preliminary Laue diffraction test, we studied the crystal’sstructure in more detail using single crystal X-Ray Diffraction (XRD) tech-nique. These measurements were performed at the X-Ray Crystallographyfacility of the UBC Chemistry department using Bruker APEX DUO singlecrystal diffractometer, equipped with a TRIUMPH monochromatic Mo Kαradiation (λ = 0.71073A˚ ). The cell was indexed using four scan sets eachconsisting of 24 images (96 in total).As shown in table 2.3, the crystal’s lattice parameters were measured attwo different temperatures. The crystal was found to be of monoclinic P2/m342.3. CharacterizationMonoclinic P2/m (T=90K)a = 6.1728A˚ b = 6.1452A˚ c = 8.6926A˚α = 90.000◦ β = 90.0357◦ γ = 90.000◦Monoclinic I2/m (T=210K)a = 6.1597A˚ b = 6.1537A˚ c = 8.6985A˚α = 90.000◦ β = 90.1333◦ γ = 90.000◦Table 2.3: BaBiO3 single crystal lattice parameters measured at tempera-tures 90 K and 210 K.and monoclinic I2/m structure at T = 90 K and T = 210 K, respectively.These results are in agreement with the previously published reports [2].TwinningAs described in chapter 1, BaBiO3 undergoes multiple structural transitionswith temperature [2]. Therefore, in growing the crystal by cooling downthe BaBiO3 melt at 1085◦ C to room temperature, it has to go throughcubic to rhombohedral to monoclinic transitions. Studies show these typesof structural transitions can cause multi-domain microstructures resultingin a twinned crystal [7, 45]. Therefore, we decided to study the crystal’sstructure in more detail to find out whether the crystal is twinned and if so,to what extent.These measurements were done at AMPEL, UBC using Philips X’pertX-ray diffractometer with a Cu Kα source (λ = 1.54059A˚). These measure-ments (and the following resistivity measurements) were lead and mainlycarried out by Oleksandr Foyevtsov from our group. We started with aθ − 2θ scan on a single crystal. The XRD spectrum and the correspond-ing Bragg reflections are shown in Fig. 2.16. The reflection coordinatesare given in monoclinic notation and as expected from the previous Laueindexing measurement (Fig. 2.11) the main phase is the (110) family inmonoclinic or (100) in cubic notation.However, in a more detailed measurement it was seen that there are somecontributions from another orientation of (001) monoclinic family. As shownin Appendix A these reflections are very close to the other ones; thus, it isdifficult to distinguish and quantify their contributions in a θ− 2θ scan. To352.3. Characterizationachieve that, we performed high-resolution Reciprocal Scan Mapping (RSM)method around each Bragg reflection. 0 10000 20000 30000 40000 50000 60000 10 20 30 40 50 60 70 80 90 100(110)(220)(330)(440)Intensity (a. u.)2Theta (degree)Figure 2.16: X-Ray Diffraction pattern on a grown BaBiO3 single crystalwith the “as grown” surface facing.The Bragg diffraction condition (Eq. 2.9) can alternatively be expressedin the reciprocal space or Laue formulation. Reciprocal lattice representsthe Fourier transform of the lattice in the real space. The axis vectors of areciprocal lattice, b1, b2, b3, are related to the axis vectors of its real spacelattice, a1, a2, a3, via:b1 = 2pia2 × a3a1 · (a2 × a3) (2.11)b2 = 2pia3 × a1a2 · (a3 × a1) (2.12)b3 = 2pia1 × a2a3 · (a1 × a2) (2.13)Then it can be shown that the Bragg condition is equivalent to:362.3. CharacterizationQ = ∆q = G (2.14)whereQ = ∆q = q′−q is the scattering vector and G = k1b1 + k2b2 + k3b3is a reciprocal lattice vector. Each point in a reciprocal space correspondsto a set of planes in its real space. In a reciprocal space x-ray diffractionmeasurement, intensity is plotted against the scattering vector.In a coplanar diffraction geometry, the sample surface normal and theincident and the exit wave vectors all exist in the same plane. Most com-mercially available x-ray diffraction instruments perform in this geometry.In this case of geometry, two angular variables are sufficient to scan the ac-cessible scattering vector plane Qx−Qy.The relevant angles in this geometryare depicted in Fig. 2.19. The components of scattering vector Q and theexperimental angles are related to each other by [64]:Qx =2piλ(cosαf − cosαi) (2.15)Qy =2piλ(sinαf + sinαi) (2.16)Or alternatively in terms of the scattering angles 2θ and φ which isrelated to ω via ω = αi + φ.Qx = −|Q|sinφ = −2piλ.2sin(2θ2)sinφ (2.17)Qy = |Q|cosφ = 2piλ.2sin(2θ2)cosφ (2.18)372.3. CharacterizationFigure 2.17: Schematic illustration of the coplanar diffraction geometry. nis the normal to the sample surface and nφ is the normal to the diffractinglattice planes. αi and αf are the angles of incident and exit. ω is the anglebetween the incident beam and the diffracting lattice planes, ω = αi + φ.It is also relatively straightforward to do the inverse operation and findthe diffractometer angles needed for a given scattering vector. Although,most modern diffractometers give the reciprocal space maps directly in theQ-space.Our reciprocal space maps around each Bragg reflection are shown in Fig.2.19. As can be seen, we have two main sets of constructive Bragg reflectionscorresponding to (110) and (001) families giving evidence to the existence oftwo crystal domains. Now in order to quantify this observation, the ratiosof the two integrated intensities for each two reflections from experiment,r1, have been compared to the corresponding calculated intensity ratio fora powder x-ray diffraction pattern, r2, or with the assumption that thereis an equal amount of both phases in the crystal. The parameter R is alsodefined as the ratio of these two parameters (Eq. 2.19). In table 2.4 thesetwo are compared.382.3. Characterizationr1 =Iexp(110)Iexp(002); (2.19)r2 =Icalc(110)Icalc(002);R(110)/(002) =r1r2If R is equal to one, it means the crystal is 50/50 twinned or there is anequal amount of the both mentioned phases.In table 2.4 these ratios are given for each map. As shown the meanvalue of R is found to be 0.130, which means the 2× 2× 1 mm3 crystal was13% twinned with a standard deviation of 0.020.392.3. CharacterizationFigure 2.18: Reciprocal space maps of crystal BaBiO3 top: around (110)and (002) and bottom: around (220) and (004) Bragg diffractions. The axesare in reciprocal lattice unit (r.l.u) which is λ2dhkl where λ = 1.54059A˚. 402.3. CharacterizationFigure 2.19: Reciprocal space maps of crystal BaBiO3 top: around (330)and (006) and bottom: around (440) and (008) Bragg diffractions. The axesare in reciprocal lattice unit (r.l.u) which is λ2dhkl where λ = 1.54059A˚. 412.3. CharacterizationBragg Reflection Pair Measured/Simulated Intensity Ratio (R)(110)/(002) 0.154(220)/(004) 0.143(330)/(006) 0.125(440)/(008) 0.100Mean Value 0.130Standard Deviation 0.020Table 2.4: The R value for different Bragg reflection pairs. R is definedin Eq. 2.19 and is indicative of contribution from different crystal domains.This result implies that the given crystal was 13% twinned.2.3.3 ResistivityWe also performed temperature dependent resistivity measurements on se-lected single crystals of BaBiO3 using a lock-in technique in a four-probeconfiguration. The schematic representation of the experimental set up isshown in Fig. 2.20. The measurement was done as a function of tempera-ture from 10 K to room temperature. Both direct wire bonding of Si-dopedAl wire and the same wire attached with colloidal silver paste were used tomake contacts. Both methods gave consistent results. The result is shownin Fig. 2.21.The temperature dependence of resistivity is explained by the Arrheniusequation as:ρ ∝ eEakBT (2.20)where Ea is known as the activation energy. Therefore, one can find theactivation energy by finding the slope of the logρ versus 1/T plot (Fig. 2.21).As shown, an abrupt change in the activation energy happens at temperatureabout Tc = 230 K from Ea = 207 meV below Tc to Ea = 143 meV above.This result is consistent with the earlier published results [7, 37, 65].422.3. CharacterizationFigure 2.20: Schematic representation of the 4-probe resistivity measure-ment using a lock-in amplifier. 1 10 100 1000 10000 0.003 0.0035 0.004 0.0045 0.005 0.0055 0.006Ea= 143 meVEa= 207 meVT= 233 Kρ (Ω.m)1/T (K-1)Figure 2.21: Resistivity measurement of BaBiO3 crystal. An abrupt changein slope, i.e. activation energy (Ea), happens at T = 233 K.432.4. Conclusion2.4 ConclusionWe developed a routine to grow high-quality single crystals of BaBiO3 withsizes up to 2 × 2 × 1 mm3. It includes a two-step high-temperature solidstate reaction followed by a congruent melting procedure. Using a two-stepsolid state reaction before the melt growth and also using a wide crucible(> 25 mm outer diameter) during the melt growth were found to be crucialin order to get reasonably big single crystals. Otherwise, the crystal wouldonly form as very thin plates on the surface of the melt.The crystals were characterized using XRD, XPS and found to be sto-ichiometric and monoclinic within the accuracy of these techniques. Thecrystal was found to be of monoclinic P2/m and monoclinic I2/m structureat T = 90 K and T = 210 K, respectively. The lattice parameters at thosetemperatures were also found. Twinning was also studied on a given crystalby a detailed reciprocal space diffraction analysis and the crystal was foundto be 13% twinned with two main domains. The temperature dependentelectronic transport measurement was also performed on the crystal andtwo activation energies were found with a transition at T = 233 K. Theseresults are in agreement with the previously published reports.44Chapter 3X-ray Absorption andResonant X-ray EmissionSpectroscopyIn this chapter, we use x-ray absorption and resonant x-ray emission spec-troscopy techniques to study the electronic structure of the single crystalBaBiO3. The measured crystal was grown as explained in chapter 2. Thex-ray experiments are performed at the Canadian Light Source (CLS), andthe results are compared to the prediction from density functional theory.3.1 IntroductionAfter the discovery of x-rays by Rontgen [66, 67] in 1895, it took abouttwo decades before the first x-ray absorption spectrum was observed by deBroglie in 1913 [68]. The core-level x-ray spectroscopy techniques such asx-ray absorption and x-ray emission have come a long way since then by theremarkable progress made in both experimental and analytical capabilities.Resonant x-ray emission is often used as a powerful complementary tech-nique to x-ray absorption to investigate together the low energy scale valenceand conduction bands of the material. The first theory of x-ray absorptionfine structure was published in 1931 by Ralph Kronig which contained someof the basic concepts of its modern interpretation [69]. The other ground-breaking progress happened in 1971 when Sayers, Stern, and Lytle appliedFourier analysis to the theory of x-ray absorption where they managed toquantitatively determine structural parameters, such as bond distance andcoordination number [70, 71].Arguably, the main experimental development that allowed XAS+RXESto become a reliable and routine analytical tool was the availability of broad-band synchrotron radiation sources starting modestly in the 1970s. Sincethen, these synchrotron radiation laboratories have grown enormously bothin number and in capability. Synchrotron radiation offers significant benefits453.1. Introductionin intensity/flux and experimental quality, along with the ability to select aspecific light wavelength and polarization.XAS involves exciting electrons from a core state to an empty state abovethe Fermi level induced by incident photons. It gives spectra of the x-rayabsorption versus x-ray energy. At some specific energies, mainly dependingon the atomic number of the absorbing atom, the absorption probabilityabruptly increases which is called an “edge”. Each edge represents a dif-ferent core electron binding energy and is named according to the principalquantum number of the excited electron: K for n = 1, L for n = 2, M forn = 3, etc. Since the core level is at a rather sharp and well-defined en-ergy characteristic of the element and its immediate surroundings, scanningthrough the x-ray energy provides information of these unoccupied states inthe material.Absorption near and immediately above an edge is due to the excitationof core electrons into bound states, in the region often called the Near EdgeX-ray Absorption Fine Structure (NEXAFS) or X-ray Absorption Near EdgeStructure (XANES). NEXAFS is rich in information about the electronicand magnetic structure of the absorbing atom as well as its surroundingsymmetry and geometry. The bound states in this region are a result of thestrong Coulomb interaction between the core-hole and the valence electron.They happen if this interaction is much larger than the bandwidth of thevalence electrons due to the interatomic hoping. This is often the case intransition metal compounds as well as rare earth compounds. These boundor “excitonic” states represent the excited states of the atom or ion and thefine structure seen in these bound states together with the dipole selectionrules in XAS provides direct information of the ground state occupation ofthe valence states [71].Further above the edge, the core electron has sufficient energy to reachcontinuum states. This region shows a slow decay in the absorption rateversus energy, with superimposed oscillating structures due to scattering ofthe excited electron off neighbouring atoms. Studying this wide region of thespectra is known as Extended X-ray Absorption Fine Structure (EXAFS).On the other hand, in an x-ray emission process, a core electron is excitedby incident x-ray photons, and then an electron decays from an occupiedvalence band into the unoccupied core state emitting a photon. When thecore electron is excited to the continuum, it is called Normal X-ray EmissionSpectroscopy (NXES), and when the incident x-ray energy is tuned to res-onate with the excitation edge of the core electron, it is called resonant x-rayemission(RXES). For this work, we use the oxygen K-edge NEXAFS+RXESto study our material of interest, BaBiO3.463.1. IntroductionFigure 3.1: The three main regions of an x-ray absorption spectrum [11].3.1.1 TheoryXAS involves exciting electrons by incident photons from a core state to anunoccupied state above the Fermi level. Therefore, it probes the unoccupiedstates and provides valuable information about the electronic structure ofthe material. Due to the localized character of the photon-induced excitationand the specific binding energy of the core electron, XAS is a site-selectivetechnique.In this section, we describe the interaction of x-rays with matter in asimple single-particle picture. The interaction is, in fact, much more com-plicated, but this simplified approach works well in giving insight to theunderlying physics and derivation of the key dipole selection rules.The Hamiltonian for electrons in an electromagnetic field can be ex-pressed as :H =12m(~p+ec~A)2 + V (r) (3.1)where ~A is the vector field of the photons. Here we can use the Coulombgauge for which ~p · ~A = h¯i ~∇· ~A = 0→ p ·A+A ·p = 2p ·A. The Hamiltonianthen becomesH ≈ p22m+emc~A · ~p+ V (r) = H◦ +H1, (3.2)473.1. Introductionwhere H◦ = p22m + V (r) is the Hamiltonian of the system without theincident light, and H1 = emc~A · ~p is the perturbing potential.On the other hand, the decay rate of an initial state ψi into some par-ticular final state ψf is given by Fermi’s golden rule (derived from time-dependant perturbation theory) as:Ri→f =∑i→f2pih¯|〈ψf |H1|ψi〉|2δ(Ef − Ei − h¯ω). (3.3)A is the radiation field operator which can be described using the fol-lowing equations:A = A◦ˆ[ei(~k.~r−ωt) + e−i(~k.~r−ωt)] (3.4)where ˆ gives the direction (or polarization) of the vector potential. Onthe other hand, energy inside a volume V is:EnergyV = Nh¯ω =ω22pic2V |A◦|2, (3.5)Therefore,→ |〈ψf |H1|ψi〉| = |〈f | emc~A · ~p|i〉| = emc(2pi2ωV)12 |〈ψf |e−i~k.~r ˆ.~p|ψi〉| (3.6)For soft x-ray absorption spectra (i.e h¯ω < 1 KeV), the wavelength ismuch larger than the radial extend of the core level wave functions so wecan make the following approximation which is called the electric dipoleapproximation:e−i~k·~r ≈ 1− i~k · ~r + ... ≈ 1 (3.7)Furthermore, if H = p22m + V (~r), then [V (~r), ~r] = 0 and[H,~r] =h¯ipm→ ~p = imh¯[H,~r]→ 〈ψf |e−i~k.~r ˆ.~p|ψi〉 ' ˆ.〈ψf |~p|ψi〉=imˆh¯.〈ψf |[H,~r]|ψi〉 = im(Ef − Ei)h¯.〈ψf |ˆ.~r|ψi〉(3.8)From Eq. 3.3 and 3.8 the absorption rate of dipole excitations is foundto be:483.1. IntroductionRi→f ∝∑i→f2pih¯|〈ψf |ˆ.~r|ψi〉|2δ(Ef − Ei − h¯ω) (3.9)Then, we can write the ˆ.rˆ term in terms of spherical harmonics:ˆ.rˆ = xsinφ+ ysinφ+ zcosθ=√4pi3[zY10 − (x + iy)√2Y11 +(x + iy)√2Yl−1](3.10)〈ψf |ˆ.~r|ψi〉 =√4pi3∫ ∞0r3drR?nf lfRnili∫dΩY ?lfmf (zY10 +−x + iy√2Y11 +x + iy√2Y1−1)Ylimi(3.11)After some additional calculational steps using the Clebsch-Gordan co-efficients, the final result for the matrix elements is found to be:〈ψf |ˆ.~r|ψi〉 =√2(li + 1)2(lf + 1)〈lf0|li100〉∫ ∞0r3drR?nf lfRnili(z〈lfmf |li1mi0〉+ −x + iy√2〈lfmf |li1mi1〉+ x + iy√2〈lfmf |li1mi − 1〉)(3.12)The above Clebsch-Gordan coefficients will be non-zero only if ∆` =0,±1. On the other hand, since Y1m terms are odd parity, if the other twospherical harmonics are the same the integral will be zero; thus, ∆` 6= 0otherwise the transition is forbidden. Consequently, the z components ofthe angular momentum , ml, have to be either 0 or ±1: ∆ml = 0,±1.Note, there are no operators to change the spin, therefore ∆s = 0. Theserestrictions are called Dipole Selection Rules.The more general dipole selection rules for multi-electron atoms areshown below with uppercase symbols. It also shows the restrictions on thetotal angular momentum number J = L+ S, and its projection along the zaxis , MJ . These quantum numbers are important mainly if the spin-orbitcoupling is of importance in which case the spin and orbital parts cannotbe treated separately. Because when the spin-orbit interaction term (L.S)is included in the Hamiltonian, the spin (S) and orbit (L) operators do notcommute with the Hamiltonian anymore.493.1. Introduction∆L = 0,±1, L = 0 6→ L = 0∆MJ = 0,±1∆J = 0,±1∆S = 0(3.13)Note that the above selection rules are valid only for the electric dipoleapproximation which is valid in the soft x-ray absorption process. There isalso one absolute selection rule that comes from angular momentum conser-vation. Since a photon has a spin of 1, no j = 0→ j = 0 transition is allowedin any order of approximation [12, 72, 73]. These selections rules play animportant role in the theory of core-level x-ray spectroscopy techniques.In perovskite compounds, the K edge XAS of the ligands is of particularinterest where a lot can be learned about the electronic structure of thematerial especially the role of ligands. Having the above dipole selectionrules of ∆` = ±1, implies that if we are exciting a core 1s electron withl = 0 (K-edge excitation), the electron can only go to unoccupied states ofp character (l = 1 ). Thus, the K edge NEXAFS spectra provide a goodapproximation to the ligand 2p unoccupied Density Of States (DOS)[11].The intensity of the XAS spectra can, in principle, be given by the Eq.3.9; however, this equation is applicable when the final state has an infinitelifetime. For a finite lifetime in the final state, the δ function has to bereplaced by a Lorentzian profile as:I ∝ Rfi ∝∑i→f|〈ψf |ˆ.~r|ψi〉|2 Γf(Ei − Ef + ω)2 + Γ2f, (3.14)where Γf is the Full Width at Half Maximum (FWHM) of the finalstate’s lifetime-induced Lorentzian broadening [11, 12, 74, 75].On the other hand, XES is a second order process meaning that aftera core electron is excited by incident x-rays, an electron decays from anoccupied valence band into the empty core state emitting a photon, whichis being detected. In a resonant x-ray emission, the incident x-ray energy istuned to resonate with the excitation edge of the core electron. Therefore,the intermediate state in the RXES is the same as the final state in theXAS. The schematic representation of these core-level excitations is shownin Fig. 3.2.Specifically, oxygen K-edge RXES happens when the incident x-ray en-ergy is the same as the energy to excite an oxygen 1s core electron to anunoccupied p state where then an electron decays from an occupied p− like503.1. Introductionstate into the empty core s emitting a photon (due to the dipole selectionrule). Thus, the oxygen K-edge XAS and RXES techniques make a power-ful complementary tool for probing the unoccupied and occupied p partialdensity of states.However, one must remember XAS+RXES does not precisely probe theoxygen-p DOS. That is because through these measurements a core electronis removed and a core hole is created. Thus, these techniques, in fact, probethe states in the presence of a core hole potential. Thankfully, it is foundthat for many materials this core hole potential does not affect the DOSstrongly if it is small compared to the bandwidth of the valence states andwe can still use these techniques for probing the DOS reliably[76].As discussed above, XES is a second order process where the probabilityof emission of photons of energy h¯ω′k in the solid angle dΩk′ is given by theKramers-Heisenberg formula for second order processes[74, 77]:d2σdΩk′d(h¯ω′k)=ω′kωk∑|f〉∣∣∣∣∣∣∑|n〉〈f |T †|n〉〈n|T |i〉Ei − En + h¯ωk + iΓn2∣∣∣∣∣∣2δ(Ei − Ef + h¯ωk − h¯ω′k)(3.15)where Ei, En, Ef are the initial, intermediate and final states of the sys-tem through the process, respectively. h¯ωk is the energy of the incidentphoton, and Γn is the intrinsic broadening of the intermediate state.3.1.2 Detection TechniquesThe x-ray absorption rate or the attenuation of light is related to the samplethickness and its properties via the Beer-Lambert law:I(ω) = I0(ω)eµ(ω)D ⇒ µ(ω) = − 1DlnI(ω)I0(ω)(3.16)where I and I0 are the transmitted and incident beam intensities re-spectively. ω is the energy of the x-rays. D is the sample thickness, andµ is called the “total linear absorption coefficient” or the “attenuation co-efficient”. This coefficient is related to the absorption cross-section anddepends on the material’s properties [71]. Experimentally, one can obtainthe absorption cross section by measuring the incident and transmitted lightthrough the sample namely in the transmission mode.However, there can be a serious issue with the above transmission prob-ing technique. First, it requires an energy-dependent optimization of thick-ness and density for each sample. Second, if µ(ω)D >> 1 photons cannot513.1. IntroductionFigure 3.2: The schematic representation of x-ray photoemis-sion/absorption, normal and resonant emission processes.[12]pass through the sample then one will detect no signal. Even if the at-tenuation is not big enough to stop the incident photons at all energies, itcan still cause artificial suppression of the absorption peaks and affect theanalysis [11]. An alternative indirect approach to avoid this issue uses theyields techniques.In XAS, after the incident photons are absorbed, the sample is left in anexcited state which quickly decays by emitting electrons or photons. It isoften found in practice that the number of transmitted photons (absorptionsignal) is proportional to the number of these emitted photons or electrons.If one detects these emitted electrons as a function of incident photon energy,the technique is called Total Electron Yield or TEY. Since the mean free pathof the electrons is very short, TEY is quite surface sensitive with a probingdepth of several nm[71]. On the other hand, if one records and detects theemitted photons as a way to measure XAS, it is called Total FluorescenceYield (TFY) technique. TFY has a larger probing depth than TEY becausethe soft x-ray photons have larger penetration depths of about ≈ 100nm[11].These techniques are depicted in Fig. 3.3 schematically.523.1. IntroductionTransmission TEY TFY Figure 3.3: Some standard XAS detection techniques. The blue regionsqualitatively represent the detection depths of each technique. [11]3.1.3 REIXS Beam-line at CLSOur XAS and RXES experiments were carried out at the Resonant Elasticand Inelastic X-ray Spectroscopy (REIXS) beam-line at the Canadian LightSource (CLS), a third-generation synchrotron facility. The REIXS beam-lineis a cutting-edge soft x-ray scattering facility located at the 10ID-2 straightsection, Canadian Light Source, Saskatoon, Saskatchewan, Canada[13].Generally, in a synchrotron, the magnets are placed at regular positionson the circumference of a circle. Relativistic electrons moving in the hori-zontal plane are accelerated radially when they pass through the verticallyoriented magnetic fields. By strategic placements of the magnets, the elec-trons can be kept in a stable circulating orbit consisting of straight sectionsinterrupted by the bending magnets. If charged particles are acceleratedthey emit electromagnetic radiation which is in the x-ray range for stronglyrelativistic electrons travelling in strong enough magnetic fields. So x-raysare emitted at each of the positions of the bending magnets which then canbe used after some focusing and monochromatization[78]. The radiationhas a substantial energy spread, so x-ray monochromators are used to selectthe energy which can be scanned through the energy range of interest. Inthe higher generation facilities, the above mentioned straight sections arereplaced by a periodic array of permanent magnets with alternating up and533.1. Introductiondown magnetic fields causing an oscillating motion of the electrons and muchmore intense and directed x radiation.The CLS beam-line, as a third generation synchrotron, allows for variousphoton-in and photon-out experiments with full polarization control, highflux and high resolution and at different temperatures. At the REIXS beam-line station the following techniques are allowed:• X-ray Absorption Spectroscopy (XAS):– Total electron yield (TEY)– Total fluorescence yield (TFY)• Resonant Inelastic X-ray Scattering (RIXS)• Resonant X-Ray Scattering (RXS)• X-ray Absorption Fine Structure (XAFS)• X-ray Emission Spectroscopy (XES)• X-ray Magnetic Linear Dichroism (XMLD)• Surface Science Facility End-station:– Molecular Beam Epitaxy (MBE) with RHEED/LEED– X-ray Photoelectron Spectroscopy (XPS)– ...At this end-station, the Variable-Line-Spacing Plane Grating Monochro-mator (VLS-PGM) is used to optimize the beam flux and to select the pho-ton energy. VLS-PGM has a combination of different mirror coatings (Ni,Si, C, and Au) and gratings to help to suppress the higher order harmon-ics. Some other specifications of the incident beam such as the flux, energyrange, spot size, etc. are presented in table. 3.5. Our XPS measurementsin chapter 4 were also performed in the Surface Science Facility end-stationof the same beam-line.543.2. Oxygen K-edge XAS ResultsFigure 3.4: XAS machine at the REIXS end-station at CLS [13].Figure 3.5: Some specifications of the REIXS beam-line end-station at CLS[14].3.2 Oxygen K-edge XAS ResultsThe oxygen K-edge XAS measurements were carried out on a single crystalof BaBiO3 at temperatures between 20 K and 400 K in 15 K intervals andwith polarizations perpendicular and parallel to the sample surface plane.As shown in Fig. 3.6, no significant change in the overall structure of thespectrum is found with changing temperature or the polarization except for553.2. Oxygen K-edge XAS Resultsan expected slight broadening at the higher temperatures. The spectra arenormalized with respect to the pre-edge and above-edge intensities (at 520and 570 eV, respectively). The most significant feature of the spectrum isthe sharp pre-peak at about 529 eV. It suggests a high oxygen p hole densityin the ground state. The structure of the spectrum will be discussed more inthe next sections when it is compared to the unoccupied oxygen p projectedDOS from DFT (LDA).During the experiment, both bulk sensitive TFY and the more surfacesensitive TEY signals were recorded simultaneously. However, as shownin Fig. 3.7 and was also reported earlier [79], the reproducibility of TFYsignal is better than that of TEY. This is most probably due to the sample’ssurface contamination and TFY known lower surface sensitivity. Therefore,the TFY signals are presented and studied in this work.563.2. Oxygen K-edge XAS Results 0 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004 0.0045 520 530 540 550 560 570Intensity (arb. units)Energy (eV)T=400KT=25K 0 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004 520 530 540 550 560 570Intensity (arb. units)Energy (eV)Vertical incident lightHorizontal incident lightFigure 3.6: Oxygen K-edge XAS of single-crystal BaBiO3 top: measured at20 K and 400 K with vertical polarization. bottom: with polarizations per-pendicular (vertical) and parallel (horizontal) to the sample surface plane atroom temperature. No significant temperature or polarization dependenceis observed.573.2. Oxygen K-edge XAS Results 0 0.0001 0.0002 0.0003 0.0004 0.0005 0.0006 0.0007 520 530 540 550 560 570Intensity (arb.units)Energy (eV)TEY-at t= 24hTEY-at t= 0h 0 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004 0.0045 520 530 540 550 560 570Intensity (arb.units)Energy (eV)TFY-at t= 24hTFY-at t= 0hFigure 3.7: The reproducibility of the top: TEY and bottom: TFY signalsare tested for the oxygen K-edge XAS of single-crystal BaBiO3. The mea-surements are repeated after 24 hours while sample was kept in vacuum.The TFY is found reproducible over time unlike the TEY. 583.3. Oxygen K-edge RXES Results3.3 Oxygen K-edge RXES ResultsThe oxygen K-edge resonant x-ray emission measurements were performedat different resonant x-ray incident energies taken from the correspondingXAS spectrum. The result is presented in Fig. 3.8. The peak at the highestenergy is called the “elastic line” or the “zero-loss” peak. Through thisRXES process, a core 1s electron is excited to a conduction band, andthen another valence electron decays back emitting a photon. However, ifthe same excited electron decays back, it gives rise to a peak at the sameincident energy, namely the “zero-loss” peak. These peaks usually are notrich with information and only used to calibrate the energy. The moresignificant features observed in the spectra are; a peak at about 527 eV, astrong asymmetric peak about 2 eV away (at 525 eV), and another bump atabout 9 eV further down (at 518 eV). The spectrum will be studied furtherin the next section when it is compared to the occupied oxygen p projecteddensity of states from DFT (LDA).No significant change is observed in the overall shape of the spectrumfor the three different resonant energies except for a slight broadening andshift towards the elastic line for the higher incident energies. Observingsome differences is not unexpected as with having different resonant incidentenergies, the excited electron occupies the conduction band at a differentenergy. Thus, its potential can affect the final transitions differently. Infact, studying this effect in detail for a few different resonant energies canpotentially give useful information about the material’s conduction band;however, it is not part of this work.593.4. Theoretical Interpretation of The Experiment 0 0.2 0.4 0.6 0.8 1 510 515 520 525 530 535 540 545Intensity (arb. units)Energy (eV)RXES with RIE= 528.4 eV= 529 eV= 530 eV 530 535 540 545IntensityEnergy (eV)XASFigure 3.8: Main: oxygen K-edge resonant x-ray emission spectra on a singlecrystal of BaBiO3 at three different Resonant Incident Energies (RIE). Inset:oxygen K-edge XAS spectrum. The red dots show the resonant incidentenergies used for the RXES measurement.3.4 Theoretical Interpretation of TheExperimentDensity Functional Theory (DFT) in the Local Density Approximation (LDA)is one of the most powerful and versatile methods in condensed matterphysics. In DFT, the wave-function of a many-electron system is assumedto be described by the Slater determinant of delocalized one-electron Blochstates. Thus, it is in fact a single-particle theory that accounts for corre-lations only in the form of effective single-particle potentials (a mean-field-type approach) [80]. This assumption can be a serious issue for stronglycorrelated systems. For example, when DFT predicts the antiferromagnetic603.4. Theoretical Interpretation of The Experimentinsulator La2CuO4 to be a non-magnetic metal [81]. However, it is quitesuccessful for weakly correlated systems i.e. the systems in which the band-widths are much wider than the Coulomb interactions (W >> U) where itis reasonable to neglect the electron-electron correlations. In such cases, itobtains the correct ground state and magnetic structure and accurate crys-tal structure for a wide range of materials. We use results from DFT tostudy our experimental results.As mentioned earlier, we used XAS+RXES to probe the BaBiO3 p-like density of states and investigate the electronic structure of the lig-and oxygens. We compare the results with the oxygen-p projected DOSfrom DFT(LDA). These calculations were done in our group by KaterynaFoyevtsova et al. The computational settings for these calculations are thesame as their previously published report [4] on the sister compound SrBiO3but using the BaBiO3 structure. This band structure calculation suggeststhat: “the breathing distortion is accompanied by spatial condensation ofhole pairs into local, molecular-like orbitals of the A1g symmetry composedof O-2pσ and Bi-6s atomic orbitals of collapsed BiO6 octahedra. The pri-mary importance of oxygen p states is thus revealed, in contrast to a popularpicture of a purely ionic Bi3+ /Bi5+ charge disproportionation. Octahedratilting is shown to enhance the breathing instability by means of a nonuni-form band narrowing.[4]”The comparison is presented in Fig. 3.9 where the calculated projecteddensity of states is convoluted with a Lorentzian with a Full Width at HalfMaximum of 0.7 eV for comparison to the experiment. The energy axisfor the experiment has also been shifted by -528.5 eV. As shown, we get areasonably good agreement between the experiment and the theory in termsof the energy position of the bands and their relative intensities. RXES evengives the deep Bi 6s states at about −9 eV predicted by the DFT due tothe hybridization between the oxygens and the bismuth states.The measured sharp XAS pre-peak at 0.5 eV(or 529 eV for the XASincident beam energy) gives evidence for a high oxygen p hole density in theBaBiO3 ground state. This, along with the general agreement between theDFT and the experiment, supports the proposed bond disproportionationpicture in which the holes mainly reside on the oxygen anions rather the Bi6s cations as opposed to the conventional purely ionic charge disproportion-ation description.613.4. Theoretical Interpretation of The Experiment 0 2 4 6 8 10 12 14 16 18-10 -5 0 5 10Intensity (arb. units)Energy (eV)Op DOS-DFT(LDA)RXESXASFigure 3.9: Oxygen K-edge RXES and XAS spectra measured on a BaBiO3single crystal and the DFT(LDA) oxygen p projected density of states ofBaBiO3. The energy has been shifted by -528.5 eV for the experimentalaxis to facilitate comparison with the calculation.Nevertheless, some disagreements can still be observed in this compari-son mainly at 5 eV and 7 eV. We also get lower intensity at higher energiesthan expected by DFT as also is shown in Fig. 3.10. This disagreementcan stem from the fact that, as mentioned in previous section, throughXAS+RXES we do not exactly probe the density of states of a charge neu-tral system as is assumed by DFT. Through these processes, we excite acore electron and create a core hole potential. Therefore, what is measuredis the DOS in the presence of such potential. Moreover, on the other hand,DFT as a mean-field single particle theory cannot treat such local poten-tials properly. Mostly for educational purposes, we go on and compare ourexperimental result to some commonly used “modifications” to DOS from623.4. Theoretical Interpretation of The ExperimentDFT.Previously in Fig. 3.9, when the oxygen K-edge XAS+RXES experimen-tal result was compared to the oxygen-p projected DOS from DFT(LDA), itwas assumed that the hole created through the spectroscopy process has noeffect on the final states and, therefore, on the spectrum. As shown before,this assumption works reasonably well for this material but is not perfectespecially for XAS where a core-hole exists in the final state. Through thex-ray emission, the hole exists in the valence state and therefore can be wellscreened and have less effect on the final state. The experimental resolutionis also worse for the XES so not all of the details can be observed, regardless.In this section, we compare and discuss a few other computational ap-proaches that are commonly used to simulate the XAS+RXES results. Forthe first modification, in order to improve the accuracy of the calculation,the XAS spectrum is calculated based on the Fermi’s Golden rule, as wasdescribed previously, using the corresponding transition matrix between theinitial state and the selection rule allowed final states. This calculation isdone using the XSPEC package in the Wien2K program. The result hasbeen compared to the experiment in Fig. 3.10 middle panel. As shown, thismodification does not change the spectrum much compared to the previousversion where it was compared to the oxygen-p projected DOS. However,it helps at the higher energies by giving a lower intensity compared to theprevious version and therefore closer to the experiment. That is perhaps dueto the fact that here the transition probability from a core 1s to p orbitals iscalculated and this probability is less for transitions to higher energies com-pared to the states right above the Fermi which was not taken into accountpreviously.Another commonly used approach to “improve” the DFT DOS corre-spondence to XAS is including the core-hole in the calculation as follows:A supercell is constructed and then one core electron is removed from oneof the atoms in the supercell and one electron is added to the conductionband as a uniform background charge to treat the core-hole potential effecton the XAS result. The result of this approach for a 2 × 2 × 2 supercell isshown in Fig. 3.10 bottom panel.As shown, not only does this step not improve but even worsens theresult. This approach is frequently used by the DFT community to findthe core level spectroscopy result, but this example demonstrates the funda-mental problem with this solution. When in DFT the additional electron isadded to the conduction band it means these unoccupied states are now lessunoccupied. Therefore, when the transition happens from the core state,there is less hole density at the unoccupied band, and therefore the XAS633.4. Theoretical Interpretation of The Experimentpre-peak loses its intensity compared to the real scenario. Thus, this “ap-proximation” treats the oxygen more like fluorine which is not correct.643.4. Theoretical Interpretation of The Experiment 0 0.5 1 1.5 2 2.5 3-5 0 5 10 15 20 25Intensity (arb. units)Energy (eV)Op DOS DFT(LDA)-empty statesoxygen K-edge XAS 0 0.5 1 1.5 2 2.5 3-5 0 5 10 15 20 25Intensity (arb. units)Energy (eV)Op DOS DFT(LDA)-empty states-XSPECoxygen K-edge XAS 0 0.5 1 1.5 2 2.5-5 0 5 10 15 20 25Intensity (arb. units)Energy (eV)Op DOS DFT(LDA)-empty states-XSPEC+core holeoxygen K-edge XASFigure 3.10: Oxygen K-edge XAS compared to oxygen p projected densityof unoccupied states from top: DFT(LDA). middle: DFT(LDA) and theXSPEC package which takes into account the transition probabilities incalculating the intensity. bottom: DFT (LDA) on a 2× 2× 2 supercell witha core-hole.653.5. Conclusion3.5 ConclusionWe used oxygen K-edge XAS and RXES on the BaBiO3 single crystal tostudy the oxygens’ bonding and anti bonding p-bands close to the chemicalpotential. The strong pre-peak found at the XAS suggests a high holeconcentration in the material. The XAS+RXES result was compared to theDFT(LDA) oxygen-p projected density of states and a reasonable agreementwas found. The presence of the mentioned XAS pre-peak and this achievedagreement give evidence for the BaBiO3 bond- disproportionation insulatingmechanism where holes mainly reside on the ligand oxygens rather than thepurely ionic charge- disproportionation picture.We also showed that adding a core-hole potential to the DFT calculationsto simulate the XAS process is not an appropriate approach. It gives a muchlower intensity in the XAS pre-peak because adding an electron (to screenthe core-hole) makes the unoccupied band less empty and lowers its truehole density.66Chapter 4X-ray PhotoemissionIn this chapter, we proceed with the investigation of the electronic struc-ture of the BaBiO3 using oxygen 1s x-ray photoemission technique. Themeasurement is done on a home-grown BaBiO3 single crystal described inchapter 2. The sample is cleaned systematically in order to achieve a re-liable oxygen 1s spectrum. The experiments are performed at CanadianLight Source Surface Science laboratory.4.1 IntroductionX-ray photoemission spectroscopy (XPS) is one of the most widely usedtechniques in studying the composition and the electronic structure of ma-terials. XPS quantification and its fundamental physics can be traced backto Einstein’s photoelectric theory in 1905 [82]. However, its main develop-ment did not happen until the 1950s when Kai Siegbahn and his researchgroup at the University of Uppsala, Sweden contributed significantly to itsdevelopment and improvement as a detection technique. In 1981, Siegbahnreceived a Nobel Prize for his contribution in developing the high-resolutionXPS, which was mostly known as Electron Spectroscopy for Chemical Anal-ysis (ESCA) at the time [83].The XPS process involves ejecting core electrons from the material byincident x-ray photons. The emitted electrons are then detected, and theirkinetic energy is measured. However, this kinetic energy depends on theenergy of the incident x-rays and therefore is not intrinsic to the material.On the other hand, the binding energy of the electron is a characteristicproperty of the excited element. Thankfully, these two energies are relatedto each other with:Eb = Ehν − Ek −W, (4.1)where Eb is the binding energy of the emitted electron, Ehν is the incidentphoton energy, Ek is the measured kinetic energy of the emitted electron,and W is the work function of the material if the binding energy is referenced674.1. IntroductionFigure 4.1: XPS spectrum of lead illustrating schematically how excitingelectrons from each orbital can give rise to a distinct peak in the spectrum [3].Those electrons that are excited and leave the surface without an energy lossproduce the characteristic peaks and those that undergo inelastic scatteringand energy loss processes contribute to the background.to the Fermi energy. All the three quantities on the right hand side of theEq. 4.1 are either known or can be measured. Therefore, the electron’sbinding energy can be found straightforwardly.The XPS spectrum is then obtained by plotting the number of ejectedelectrons per energy interval versus their binding energy. It consists of a se-ries of distinct lines or “peaks” corresponding to the sequence of the occupiedcore levels of the material. An example of such spectrum is shown in Fig.4.1. These binding energies are characteristic of each element, and thereforeXPS spectra can serve to detect the chemical elements of the system understudy.The schematic diagram of the core 1s XPS process is shown in Fig. 4.2where an electron is ejected from the K shell. There are different notationsand formalisms in describing the involved atomic transitions depending onthe excited electrons and their quantum numbers. Two conventional typesof notation are known as the “atomic notation” and the “x-ray notation”.They are presented for the first few atomic levels in Table 4.1.684.1. Introductionvalence bandvacuumFermi levelKL1L2,3ejected 1s electronhvFigure 4.2: Schematic presentation of the core 1s XPS processn l j Atomic Notation(nlj) X-ray Notation1 0 1/2 1s(1/2) K12 0 1/2 2s(1/2) L12 1 1/2 2p(1/2) L22 1 3/2 2p(3/2) L33 0 1/2 3s(1/2) M13 1 1/2 3p(1/2) M23 1 3/2 3p(3/2) M33 2 3/2 3d(3/2) M43 2 5/2 3d(5/2) M5Table 4.1: The relation between quantum numbers, atomic notation andx-ray notation for the first few energy levels [3]. j is the total angularmomentum quantum number which takes |`− s| ≤ j ≤ |`+ s| values wheres = 1/2 for electrons.694.1. Introduction4.1.1 XPS detection techniqueThe probability of interaction with the matter is much smaller for photonsthan for electrons, and that is why the detection depth is much bigger forthe photon-in photon-out techniques (such as XAS and RXES) than for theelectron-out techniques. The detection depth for such photon-out techniquesis of the order of micrometers while it is only of the order of tens of angstromsfor the electron-out ones such as XPS. This makes XPS a very surface sen-sitive technique which means it is crucial to have a clean sample surface toget a reliable spectrum.The detection depth of XPS can be determined by a quantity known asthe attenuation length(λ) of the electrons under study. λ depends on thekinetic energy of the electrons and also the properties of the material [3]:λ =538aAE2A+ 0.41aA(aAEA)0.5, (4.2)where a3A is the volume of the atom in nm3, EA is the energy of theelectron in eV and λ is in nm.Following the Beer-Lambert equation, the intensity of electrons (I) ejectedat an angle θ to the surface normal is given by:I = I0e− dλcosθ (4.3)where I0 is the electron intensity from an infinite and uniform substrate.Further analysis of the above equation gives that 65 percent of the de-tected signals in electron spectroscopy come from a depth less than λ, 85percent from a depth less than 2λ and 95 percent from a depth less than3λ. The angle of the sample to the detector can be varied to change thedetection depth. A sample mounted at an angle normal to the analyzer axisis probed deeper than the one with a more shallow electron take-off angle[3, 15] as demonstrated in Fig. 4.3.4.1.2 TheoryIn this section, we explain the photoionization phenomenon in a simplifiedsingle particle picture [17, 84]. This description can, in fact, be very use-ful in understanding the XPS process especially when there are no strongelectronic correlations. Very similar to what was explained in chapter 3for the x-ray absorption theory, the most general approach of the photoe-mission theory is also based on the Fermi’s Golden rule derived from thetime-dependent perturbation theory. In this approach the XPS current or704.1. IntroductionFigure 4.3: This shows how at a low electron take off angle (grazing) thesurface sensitivity is enhanced and the thin oxide layer on the silicon is moredominant [15].the transition rate from an initial state |ψi > to a final state |ψk,s > is givenby:Ik(hν) =2pih¯∑s| < ψk,s|H1|ψi > |2δ(k − s − hν), (4.4)where the final state |ψk,s > is the state with the photoelectron of mo-mentum k and energy Ek =h¯2k22meand a system with the remaining N − 1electrons.The index s is the set of quantum numbers of all the possible fi-nal states. H1 is also the perturbing potential describing the interaction ofelectrons in an electromagnetic field. As explained in chapter 3, H1 can begiven by:H1 =emec~A.~p (4.5)where ~p is the momentum operator and ~A is the electromagnetic vectorpotential.Now in order to proceed with the calculation, an approximation,namelythe sudden approximation, has to be made. This approximation allows usto decouple the photoelectron from the remaining N − 1-electron system inthe final state. Therefore, in Eq. 4.4 we can substitute the |ψk,s > state714.1. Introductionwith c†k,s|N−1, s > where c†k,s is the creation operator for the photoelectron.With this approximation, Eq. 4.4 becomes:Ik(hν) =2pih¯∑k|∆κk|2A<k (κ − hν) (4.6)where ∆κk = | < ψκ|H1|ψk > | are the photoemission transition proba-bility matrix elements, and A<k (hν) =∑s | < N − 1, s|ck|N > |2δ(hν − s)is known as the single particle spectral function. Eq. 4.6 can also be writtenin terms of the Green’s function as the spectral function A is related to theGreen’s function G as:A(k, ω) =1pi|ImG(k, ω)| (4.7)4.1.3 XPS, core levels and satellitesA key advantage of XPS is its ability to identify the elements based on theirbinding energies and chemical shifts of the photoemission lines. In a simpleK shell XPS process a core 1s electron is excited by an incident photon, andits kinetic energy is measured and thereby its binding energy is found. Atypical result of such measurement is shown in Fig. 4.4 for elements of thesecond row of the periodic table from Li to F. As shown in the figure, theXPS spectra consist of a line at a binding energy that expectedly increaseswith the atomic number.An XPS peak can also exhibit a multiplet splitting in its structure. Thissplitting arises in a 1s XPS peak when the compound contains unpairedelectrons in its valence band. Multiplet structure results from the exchangeinteraction which can only be operative if the electrons in the valence shellare not all paired, i.e., if there is a net local spin moment2. A core holeis created through the photoionization process which can couple with theunpaired valence electron. This can create multiple available final states atdifferent energies resulting in the multiplet splitting of the main peak. Thisis shown in Fig. 4.5 where the oxygen core 1s XPS of H2O is compared tothe O2 gas. Diamagnetic H2O has a closed-shell configuration with all itselectrons paired and a total spin of zero. Therefore, the coupling between2Multiplet structure can also occur for systems with all paired electrons but a notcompletely filled valence shell and with very small bandwidths so that the valence shellelectrons on the atom with the core hole are bound to the core hole. Now, one has two openshells, and this causes multiplet structure not only because of the exchange interaction butdue to the higher multiple Coulomb interactions between the core hole and the valenceelectrons.724.2. XPS ResultsFigure 4.4: Core 1s XPS spectra of elements with the atomic numbers of3 to 9. The binding energy increases with increasing the atomic number[16, 17].the spin up and spin down core hole to the valence electrons gives degeneratestates with the same energy. Thus, its XPS spectrum consists of a singlepeak. However, O2 is paramagnetic with two unpaired electrons in its pi?2porbitals. The core-hole (or the remaining single electron) created throughthe XPS, can be either parallel or antiparallel to the valence electrons re-sulting in two different non-degenerate final states with an energy differenceof ∆E = 1.1 eV. This type of splitting is called multiplet splitting. They cangive additional rich information regarding the fine structure of the atomsand their chemical environment [17, 18].Shake-up satellites are another possible source of additional lines in anXPS spectrum. These can occur when the ejected photoelectron interactswith a valence electron and gives some of its kinetic energy to excite thecompound to a higher energy state. This will be detected as an additionalline at a lower kinetic energy or a higher binding energy than the main peakand is called a “shake up” peak or satellite.4.2 XPS ResultsWe employed XPS as one of the most powerful spectroscopy techniques tostudy our material of interest BaBiO3. As mentioned before, we are partic-ularly interested in investigating the role of ligand oxygens in the electronic734.2. XPS ResultsFigure 4.5: Oxygen 1s XPS of O2 and H2O in their gas phase. O2 isparamagnetic with two unpaired electrons in its valence shell. The core-holecreated through the XPS process can interact with these and gives two non-degenerate states observed as the two XPS lines. H2O is diamagnetic with allits valence electrons paired; therefore, it gives one single XPS peak.[17, 18]744.2. XPS Resultsbehaviour of the material. We achieved this partly by doing oxygen K-edgeXAS and RXES on our single crystal in chapter 3. They confirmed the exis-tence of a high hole density in the oxygens ground state consistent with theband structure calculation results and the proposed bond disproportionationinsulating mechanism.However, this result, in turn, poses the following question: If these core-level experiments give evidence for a high oxygen p hole density, one shouldbe able to see that evidence in an oxygen 1s XPS measurement, too. Withinthis bond-disproportionation picture, there have to be two holes per octa-hedron or 1/3 hole per oxygen on average. Therefore, due to the strongCoulomb interaction between this 1/3 hole and the O 1s core-hole, createdthrough the XPS, one would generally expect to see a main peak and astrong satellite structure in the oxygen 1s XPS spectrum. However, whilemany find such structure, they assign it merely to the surface contamination[28, 31, 34] and avoid explaining the oxygens’ electronic role in the spectrum.Moreover, on the other hand, some assign this structured peak to the dif-ferent oxidation states of the oxygens without perhaps the required diligentcleaning procedure [30].In this work, to address this problem, we start by cleaning our high-quality single crystals systematically by monitoring the carbon peak andthe corresponding oxygen peak simultaneously. we then enhance the clean-ing procedure accordingly. In the following sections, each cleaning stage isexplained, and the corresponding result is shown.First AttemptCleaving a crystal is a well-known solution to expose a clean surface foran XPS experiment. Cleaving often works nicely for “two-dimensional”materials such as cuprates where the layers are bonded only through a weakVan der Waals force. However, since BaBiO3 is a three-dimensional materialafter trying multiple times, we found that the crystal does not cleave butinstead fractures with a very rough surface at best. In most attempts atcleaving, the crystal itself was removed with nothing left on the sampleholder. There does not seem to be a clear cleavage plane consistent with thethree-dimensional crystal structure.Therefore, for our first attempt, we cleaned the single crystal with ace-tone and deionized water in an ultrasonic bath for 10 minutes each. Then wedried the surface using nitrogen flow. Next, the sample was heated (“baked”)in vacuum at 100◦C for 20 minutes in the “transfer chamber”, before beingtransferred to the ultra-high vacuum XPS chamber. These measurements754.2. XPS Results-20020406080100120140160 526 528 530 532 534 536Intensity (arb. units)Binding Energy (eV)oxygen 1s-first attempt-505101520 280 285 290 295 300Intensity (arb. units)Binding Energy (eV)carbon 1s-first attemptFigure 4.6: Oxygen 1s and carbon 1s XPS spectra after our first attempt incleaning the surface of the single crystal BaBiO3.were done at the Surface Science Facility of the REIXS beam-line at theCLS. XPS was collected using a monochromatic x-ray source correspondingto the aluminium Kα emission line at 1486.6 eV with an energy resolutionof 0.4 eV. All of the measurements were done at the normal electron take-offangle for the least surface sensitivity. The specifications of the XPS systemis given in chapter 2.3.1.For each attempt, a wide-range scan, an oxygen 1s, and a carbon 1s scanwere done. The wide-range scans were used to make sure the stoichiometryof the crystal does not change with the cleaning procedure. The oxygen andcarbon 1s spectra after this preliminary cleaning step are shown in Fig. 4.6.As it can be seen, the oxygen spectrum has some significant shoulder at ahigher binding energy, but the carbon peak also indicates the presence ofsome surface contaminations. Therefore, it is not possible to conclude if theoxygens structure is intrinsic or extrinsic since the high binding energy peakin O 1s spectra is well known to be indicative of H2O or CO2 contaminationof the surface.Second AttemptAfter the previous attempt, we noticed under the optical microscope, thatthe acetone damages the surface by leaving some coppery stains on thegolden surface of the crystal. Therefore, we opted for heptane which isknown as a less destructive cleaning solvent. We repeated the previouscleaning steps but with heptane instead of acetone and on a new singlecrystal (but from the same batch). The result is shown in Fig. 4.7 and is764.2. XPS Resultscompared to the previous result. As shown, here we get a different carbon1s spectrum and also a different oxygen 1s peak. This is an indication thatthe oxygen XPS structure is at least partly due to the surface contaminationand we indeed need to take good care of our cleaning steps.Third AttemptHere, as our third modification to the cleaning procedure, we repeated the“second attempt” cleaning steps but we increased the “baking” time from20 minutes to 40 minutes. The result is shown in Fig.4.7 and is comparedto the previous measurements. As it can be seen, the carbon peak has lostits intensity indicating that increasing the baking time helps with removingthe carbon-containing surface contaminations.Fourth AttemptAt this point, we decided to add another step to enhance our cleaning pro-cedure further. For our fourth attempt, after all the steps taken previously,we transferred the crystal to an ultra-high vacuum chamber with the basepressure of less than 1 × 10−10 Torr. There, it was annealed at 200◦ C for1 hour in 1.7 × 10−7 Torr oxygen atmosphere with a strong atomic oxygencomponent using a 55 W power thermal gas cracker. Atomic oxygen is highlyoxidizing and helps oxidizing any carbon-containing molecules physisorbedto the surface. It also protects the sample against oxygen deficiency. Theresult after this procedure is shown in Fig. 4.7. As shown, this step wasquite successful in removing the carbon contribution.Fifth AttemptAfter we found that annealing in the atomic oxygen is very effective inremoving the carbon-containing contaminations, we decided to repeat theprocedure but at a higher temperature of 350◦ C rather than 200◦ C. Theresult is shown in Fig. 4.7. It can be seen that this, in fact, improved thesurface cleaning by removing the carbon contamination even further.Final AttemptWe managed to remove the carbon peak to a large extent so far. We alsofound out the structure of the oxygen peak is affected by the surface con-tamination significantly. However, there are still some carbon-containing774.2. XPS Results-20020406080100120140160 526 528 530 532 534 536Intensity (arb. units)Binding Energy (eV)oxygen 1s-first attempt-505101520 280 285 290 295 300Intensity (arb. units)Binding Energy (eV)carbon 1s-first attempt020406080100120140160 526 528 530 532 534 536Intensity (arb. units)Binding Energy (eV)oxygen 1s-second attempt-505101520 280 285 290 295 300Intensity (arb. units)Binding Energy (eV)carbon 1s-second attempt-20020406080100120140160 526 528 530 532 534 536Intensity (arb. units)Binding Energy (eV)oxygen 1s-third attempt-505101520 280 285 290 295 300Intensity (arb. units)Binding Energy (eV)carbon 1s-third attempt-20020406080100120140160180200 526 528 530 532 534 536Intensity (arb. units)Binding Energy (eV)oxygen 1s-fourth attempt-505101520 280 285 290 295 300Intensity (arb. units)Binding Energy (eV)carbon 1s-fourth attempt-20020406080100120140160180200 526 528 530 532 534 536Intensity (arb. units)Binding Energy (eV)oxygen 1s-fifth attempt-505101520 280 285 290 295 300Intensity (arb. units)Binding Energy (eV)carbon 1s-fifth attempt-20020406080100120140160180200 526 528 530 532 534 536Intensity (arb. units)Binding Energy (eV)oxygen 1s-final attempt-505101520 280 285 290 295 300Intensity (arb. units)Binding Energy (eV)carbon 1s-final attemptFigure 4.7: Oxygen 1s and carbon 1s XPS spectra at different stages of ourcleaning procedure on the single crystal BaBiO3. The removal of the carbonpeak confirms the effectiveness of the procedure.784.2. XPS Results-20020406080100120140160180200 526 528 530 532 534 536Intensity (arb. units)Binding Energy (eV)oxygen 1s-final attempt-505101520 280 285 290 295 300Intensity (arb. units)Binding Energy (eV)carbon 1s-final attemptFigure 4.8: Oxygen 1s and carbon 1s XPS spectra of single crystal BaBiO3after the optimized cleaning procedure described in the text. The oxygenspectrum loses most of its structure with the progression of the cleaning butremains slightly asymmetric.contamination remained that we wish to remove. To achieve that, we re-peated the previous steps but did the atomic oxygen annealing step longerfor two hours rather than one.The result along with the result from the previous attempts are shownin Fig. 4.7. As shown, we finally managed to remove the carbon peak ,i.e.,all the carbon-containing surface contaminations from the surface perfectly.The assumption then is that the non-carbon-containing molecules such asH2O are also desorbed during this whole process.One important observation through this whole process was how thestructure of the oxygen spectrum was affected by removing the carbon.At the end, it lost much of its structure but remained slightly asymmet-ric as shown in Fig .4.8. It confirms its satellite structure was mainly due tothe surface contamination and not intrinsic to the material. This result israther surprising at first given the previous XAS+RXES results indicatinga high hole density on the oxygens. As mentioned before, one would haveexpected to see a strong satellite structure in an oxygen 1s XPS due to thisoxygen hole density. We address this question in the next chapter wherewe calculate the BaBiO3 oxygen 1s XPS using exact diagonalization clustercalculation.794.3. Conclusion4.3 ConclusionWe studied single crystal BaBiO3 using oxygen 1s XPS technique. Weshowed surface contamination could be a serious issue in interpreting thestructure of the oxygen spectrum. We managed to develop a successfulcleaning routine to remove the carbon-containing compounds from the sur-face. Annealing at atomic oxygen atmosphere was found highly effectivein this routine. We showed by removing the surface contamination oxygen1s spectrum also loses much of its structure and its shoulder but remainsslightly asymmetric.80Chapter 5Exact DiagonalizationCluster ModelIn this chapter, we use the cluster calculation method to investigate theelectronic structure of BaBiO3 and also to calculate its oxygen 1s XPS tounderstand the experimental results shown in the previous chapters. Inchapter 3 we discussed how the oxygen K-edge XAS+RXES confirms thepresence of a high oxygen hole density in the material. We then in chapter4 showed the oxygen 1s XPS results on a clean single crystal. Due to thestrong Coulomb interaction between the XPS core-hole and the assumedhole density on the oxygens one would have expected to see a strong satellitestructure in the oxygen 1s XPS. However, we showed the observed shoulderof the main peak is virtually only due to the surface contamination andthe XPS of a clean surface does not have any strong satellite or multipletstructure. Now in this chapter, we use the exact diagonalization clustermodel to address this problem.5.1 IntroductionAs discussed in the previous chapters, in order to calculate various x-rayspectra one needs to have the initial and the final many-body quantumstates of the system(ψi and ψf ). In order to get these states, one has tosolve the Schrdinger equation 5.1 with a given Hamiltonian.Hψ = Eψ (5.1)Solving the Schrodinger equation with the real Hamiltonian of a many-body system is nearly impossible. However, one can make some approxima-tions and construct a more manageable model Hamiltonian and still extractmuch information about the system by solving that. Depending on the com-plexity of the system, the desired result, and the available computationalpower, these model Hamiltonians can vary in their levels of complexity. Be-low we introduce some of these approaches and their model Hamiltonians in815.1. Introductionan increasing order of complexity.5.1.1 Atomic ModelFor a non-relativistic time-independent atomic model, where electrons andthe nucleus are treated as point charges, the Hamiltonian of a system withj electrons and a nucleus with an atomic number of Z looks like:HCoulomb = Te + Ue−n + Ue−e = − h¯22me∑j∇2j −∑jZe2rj+∑j>ke2rjk(5.2)where Te is the kinetic energy of the electrons with the effective mass ofme. Ue−n is the Coulomb interaction between the electrons and the nucleuswhere rj is the distance between the nucleus and the electron j. Ue−e is theCoulomb interaction among the electrons where rjk is the distance betweenthe electron j and the electron k [85]. Here the interaction terms due tothe electronic and nuclear spin are neglected. Although this Hamiltonianmakes major approximations in treating the system, it is still impossible tosolve analytically for molecules with more than a few electrons. However,thanks to the modern computational power, some self-consistent iterativeapproaches can give reasonably accurate answers for single atoms [11, 86].Almost all approaches to solving the Coulomb Hamiltonian are based onthe Born-Oppenheimer (BO) approximation which is based on the assump-tion that the electronic and the nuclear parts of the Hamiltonian can beseparated. Consequently, the wave-function of the total Hamiltonian can bewritten in terms of the nuclear and the electronic wave-functions as:ψtot = ψelectronic × ψnuclear (5.3)One step further in the “atomic model” is considering the interactionbetween the spin and angular motion of the electrons via the spin-orbitcoupling term. This can be written as:Hatomic = HCoulomb +HSO = HCoulomb +∑jξj(rj)(lj .sj) (5.4)where lj and sj are the orbital and spin angular momentum operatorsof the electron j, and ξ is the spin-orbit coupling constant. For an electronmoving in a central potential U(r), ξ can be expressed as ξ = h¯22m2c21rδU(r)δ(r)[85].825.1. IntroductionThe Pauli principle states no two electrons can occupy the same spinorbitals. In other words, all the wave-functions must be anti-symmetricalunder exchange of any two of the electrons ( or more generally fermions).This will result in the wave-functions of the form of a normalized “Slaterdeterminant” which satisfies the antisymmetric properties of a fermionicwave-function:Ψ(x1,x2, . . . ,xN ) =1√N !∣∣∣∣∣∣∣∣∣χ1(x1) χ2(x1) · · · χN (x1)χ1(x2) χ2(x2) · · · χN (x2)....... . ....χ1(xN ) χ2(xN ) · · · χN (xN )∣∣∣∣∣∣∣∣∣ (5.5)where the many-electron wave-function Ψ(x1,x2, . . . ,xN ) is expressedin terms of χi(xi)s which form a complete orthonormal basis set of wave-functions for single electrons.The next step in treating the “atomic model” is writing the electron-electron interaction potential matrix elements with wave-functions of theabove form (< Ψ|∑Nj>k e2rjk |Ψ >). This will lead to the formation of so-called Slater integrals (F k(i, j)) corresponding to the Coulomb and exchangeinteractions between electron pairs. Thus, the Slater integrals are not de-fined according to the total many-body wave function but are the Coulombintegrals describing the average interaction between two electrons in theserespective one-particle wave functions. These energies are the main em-pirical values used in this model [85, 87]. However, one has to rememberthese energies are often strongly screened and reduced in solids due to thepolarization effects [80, 88].In summary, in this model Hamiltonian, we assume that the atomic one-electron wave functions remain unchanged in the solid and that the wavefunction of electrons moving in the solid is a result of a linear combinationof atomic wave functions centred on the atoms of the solid. In quantumchemistry, this is called the linear combination of atomic orbitals method,and in solid state physics, these would result in the so-called tight bindingwave functions describing the band structure of the electrons in the solid.While this model gives valuable insight into the basic physics of a many-electron system, one has to go further to extract truly useful and practicalinformation about a real condensed matter system.835.1. Introduction5.1.2 Crystal Field ModelThe basic idea in the crystal field model is that the atom of interest is sub-jected to an electrostatic field produced by its surrounding ions or ligands.In this model, the ligands are treated as point charges. The key idea of thismodel was discussed by Becquerel in 1929 [89], and was formulated into arigorous theory by Bethe in the same year [85, 90]. Bethe showed how thesymmetry and the strength of this electrostatic potential could affect theenergy levels of an ion. In 1932, Van Vleck successfully demonstrated thecapability of this theory by explaining “why nickel salts are nearly isotropicmagnetically, while those of cobalt exhibit over 25 percent anisotropy eventhough the Ni++ and Co++ ions are both in F states and are adjacent inthe periodic table” [91].In this model, the role of ligands is somewhat limited since their electronscannot hybridize or overlap with each other or the metal ion. Therefore, itsHamiltonian can be easily modelled by adding a perturbing electrostaticpotential V , the potential created by ligands, to the Hamiltonian of the freeion:HCF = Hatomic + V (5.6)Note that V must have the same symmetry as the symmetry group ofthe molecule because the Hamiltonian of the system must remain invariantunder all symmetry operations [85]. This model finds the energy levels ofthe system to be very sensitive to the geometry of the ligands.Neglecting the spin-orbit coupling for the moment, Fig. 5.1 shows howthe crystal field with different symmetries affect the five d orbitals. The rea-son is simply that the d electrons want to avoid the regions with the highestelectron density from the ligands to lower the Coulomb repulsion energy.That is why the d orbitals, which are all degenerate in a spherical potential(SO3), split into two different energy levels in an octahedral symmetry (Oh)namely the eg and t2g orbitals. eg orbitals are the ones pointing directlytowards the vertices of the octahedron where the ligands with their negativecharges reside. Thus, they will have higher energy than the other three or-bitals (t2g) that are located off-axis and therefore have a lower energy [92].The energy difference between these two is usually known as 10Dq. Thespin-orbit coupling can split the energy levels even further.845.1. IntroductionFigure 5.1: d orbitals in various crystal field symmetries. The specific sym-metry of the ligands affect the energy levels of the metal ion [11].855.1. IntroductionHund’s rulesIt was mentioned how a crystal field can split the orbitals’ energy levels andlift the degeneracy. The Hund’s rules, introduced by Friedrich Hund around1925, dictate how these orbitals are filled in the ground state [93]:• The first rule is also known as the “Hund’s rule of maximum multi-plicity” where multiplicity is defined as 2S + 1 where S is the totalspin. This rule implies the total spin S has to be maximized in theground state. In other words, the number of parallel spin pairs has tobe maximized. From the Pauli exclusion principle, this requires elec-trons to be in different spatial orbitals which minimizes the Coulombrepulsion and lowers the energy.• For a given multiplicity, the second rule requires the total orbital an-gular momentum to be maximized for the ground state. This alsoresults in a lower Coulomb repulsion and minimizes the energy.• And finally the third rule says that for the less-than-half filled outershells, the state with the minimum total angular momentum quantumnumber (J = L− S) is the ground state while for the more-than-halffilled shells, the level with the maximum total angular momentumquantum number (J = L+ S) becomes the lowest energy state.The Hund’s ground state energy for a system with n electrons is deter-mined by (neglecting spin orbit coupling) :E(n,Hund) = αI(n)I + α0F (n)F0 + αJ(n)J + αC(n)C (5.7)where I is the one-electron potential, F 0 is the monopole part of theCoulomb integral, C describes the angular part of the multiplet splittingand J is the Hund’s exchange interaction energy. αI = n , α0F (n) =n!2 , andαJ(n) is the number of parallel spin pairs [92, 94, 95] .As an example, the arrangements of d electrons are presented in Table.5.2 in an octahedral complex following the above Hund’s rules [96]. Notethat depending on the Hund’s exchange interaction energy (J) and the on-site energies of the orbitals, states with a low spin can have a lower Hund’sground state energy than the high spin state like the 4 d electrons in a weakcrystal field potential versus in a strong crystal field potential.865.1. IntroductionNumber of d electronsIn weak crystal field NIn strong crystal field N1 0 02 1 13 3 34 6 35 10 46 10 67 11 98 13 139 16 16t2g eg t2g egFigure 5.2: The arrangement of d electrons in the ground state of anoctahedral complex following the Hund’s rules. N is the number of distinctpairs of electrons with parallel spins. The crystal field potential here is theenergy difference between the t2g and the e1g orbitals.875.1. Introduction5.1.3 Ligand Field ModelAs mentioned before, in the crystal field model, ligands are treated only aspoint charges by creating an electrostatic potential. Therefore, it ignoresthe nature of the ligands and hybridization effects completely. To takethe crystal field model one step further, the bonding and covalency amongthe ligands and the metal are explicitly considered in the so-called “ligandfield model” where the charge transfer among the atoms is allowed. Ligandfield theory includes the molecular orbital theory concepts and symmetryconcerns and allows bonding, anti-bonding and non-bonding hybridizationsamong the atomic orbitals.One approach to the ligand field model is to include the central atom andthe nearest neighbour ligands interacting through the configuration interac-tion mixing. The set of atoms included in the model is called a cluster andthe arrangement of the electrons among the atoms is known as a configura-tion. This ligand field model is also known as the configuration interactioncluster model (or cluster calculation for short) where the wave-functions areexpressed as a linear combination of different possible configurations.Typically within cluster calculations, a many-electron basis is definedon which a Hamiltonian matrix is constructed. The Hamiltonian is thendiagonalized, and the ground state energy and wave-functions are foundusing various algorithms such as the Lancsoz routine [97]. By having thewave-functions, the expectation value of different operators such as spin,angular momentum, number operators, etc. can be found. For spectroscopysimulations, a final state basis and the final state Hamiltonian also have tobe defined. Then the spectra can be calculated by using the Greens functionmethod:G(ω) = 〈ψi|T † 1ω −H + iΓ2T |ψi〉, (5.8)where T is the transition operator. For an absorption process the transi-tion operator would be a product of an annihilation and a creation operator,and for photoemission, it is only an annihilation operator [98, 99]. The rela-tion between the photoemission transition probability and a Green functionwas given in section 4.1.2.CovalencyCovalency is a type of interaction among different atoms of a material. Itarises from sharing electrons among atomic orbitals of the atoms. Depending885.1. Introductionon the symmetry of the atomic orbitals and their energies, different types ofcovalency or hybridization can occur. These interactions can be describedas the overlap of the atomic orbitals or 〈ψA|H|ψB〉 where ψA and ψB arethe wave-functions (orbitals) of the atom A and atom B, respectively. De-pending on the phases of the atomic orbitals and their symmetries theseoverlaps or hybridizations can be “constructive (anti-bonding)” or “destruc-tive (bonding)”.In an anti-bonding interaction, for a simple diatomic molecule, the re-sulting molecular orbitals (MO) has a node between the two atoms. It meansthere is a lower electron density between them. An anti-bonding interactionincreases the energy relative to the separated atoms, and a destructive over-lap weakens the bond between them. On the other hand, when the atomicorbitals are added in phase, the overlap is constructive, and the electronsdensity is higher at the middle. This has a lower energy and is more stablethan the two separate atoms. It is called a bonding interaction. When thereis incompatible symmetry between the atomic orbitals, no interaction willhappen. The resulting molecular orbitals are known as non-bonding orbitals.Non-bonding orbitals have the same energy as the separated atoms.The resulting molecular orbitals are often labeled with σ and pi symme-tries. If the bonding MO is symmetrical with respect to the internuclearaxis (axis joining the two nuclear centers), it is called a σ orbital. An anti-bonding MO orbital with a σ symmetry is called a σ? orbital. If the bondingorbital is asymmetrical with respect to the internuclear axis, it is called piorbital. A pi orbital finds an opposite phase by rotation about the inter-nuclear axis. The anti-bonding pi orbital is called pi? orbital. pi bonds areusually weaker than σ bonds. σ and pi bonding and anti-bonding orbitalsare illustrated in Fig. 5.3 for p orbitals.Coulomb and exchange interactionsIn configuration interaction ligand field theory, there can be multiple possi-ble distributions of electrons ,i.e., configurations or multiplets. These mul-tiplets each can be at a different energy level due to their different electron-electron interaction energies. In Hartree-Fock type formalism these many-body electron-electron Coulomb interactions can be expressed in terms ofone- and two-electron integral operators. This is shown below skipping thedetailed mathematical derivation [87, 92].895.1. IntroductionFigure 5.3: A schematic representation of a: σ and b: pi bonding and anti-bonding molecular orbitals of p orbitals. The figure is taken from Ref. [19]and has been modified slightly by adding the signs.Ee−e = 〈Ψ(x1, ..., xN )|He−e|Ψ(x1, ..., xN )〉, (5.9)He−e =N∑i,j>i1rij,Ψ(x1, ..., xN ) ≡ |ψ1( ~x1)ψ2( ~x2)...ψN ( ~xN )|Ee−e =12[N∑m 6=n∫ψ?n( ~x1)ψn( ~x1)1r12ψ?m( ~x2)ψm( ~x2)dx1dx2(5.10)−∫ψ?n( ~x1)ψm( ~x1)1r12ψ?m( ~x2)ψn( ~x2)dx1dx2] = 〈nn|mm〉 − 〈nm|mn〉In Eq. 5.10, the first and the second integrals are generally referredto as the Slater integral (F k) and the exchange integral (Gk), respectively.The ψ?n( ~x1)ψn( ~x1) and the ψ?m( ~x2)ψm( ~x2) terms in the Slater integral arelike the charge density distribution (or the probabilities) of electron 1 inorbital n located at x1 and electron 2 in orbital m located at x2, respec-tively. Therefore this term is similar to the classical Coulomb interactionenergy. However, the exchange term does not have a classical counterpartand is rooted in the “Pauli exclusion principle”. These two integrals canbe expressed as one single integral in the following form where P ′s are theLegendre polynomials, r< = min(r1, r2), and r> = max(r1, r2).905.2. ComputationsRk(ij, kl) =∫ ∫2rk<rk+1>P ?i (r1)P?j (r2)Pk(r1)Pl(r2)dr1dr2 (5.11)where the Slater integral F k(i, j) = Rk(ij, ij), and the exchange integralGk(i, j) = Rk(ij, ji). F 0 and F 2 integrals are often known as the monopoleand dipole Slater or Coulomb integrals, respectively.5.2 ComputationsIn this work, we used the exact diagonalization cluster calculation method toinvestigate the electronic structure of BaBiO3. These calculations were donein quanty-“a quantum many-body script language”. The code is developedby Maurits W. Haverkort and coworkers [100, 101] in the Lua programminglanguage. It has several pre-defined operators in second quantization thatallows the user to focus on the model and its physical aspects without worry-ing too much about the mathematics. In this section, we explain the modeland present its results [1].5.2.1 ClusterIn our model, the cluster is an octahedron of six oxygens at the corners anda bismuth atom at the centre. There are three p (px, py, and pz) orbitalsand a core 1s orbital for each oxygen, and a 6s orbital for the bismuth.All the oxygen core 1s orbitals are full, and a hole will be created on onethrough the XPS process for the XPS spectra simulation part. There are 36electrons in total in the oxygen 2p and bismuth 6s orbitals ,i.e., two holesin the octahedron. The octahedron is depicted in Fig. 5.4.5.2.2 Model HamiltonianOur model Hamiltonian includes the following terms:Htotal = HhoppingOp +HUOp +HF 2Op +HQOsp+HG1Osp (5.12)+HhoppingBi6s−OA1g +HCF +Honsites.Each term will be explained below.915.2. ComputationsO5 O2O3O4O1O6BixzyFigure 5.4: The model single cluster of BaBiO3 with six oxygens at thecorners and a bismuth atom at the center.Hybridization terms: HhoppingOp and HhoppingBi6s−OA1gIn this model, we allow hybridization among the oxygens p orbitals(HhoppingOp ),and also hopping between the bismuth and the oxygens (HhoppingBi6s−OA1g ).• HhoppingOp includes the hybridization terms among all oxygens’ 2p or-bitals. These are constructed in accordance with the Slater-Kosterhopping matrix elements for an octahedral complex in terms of thetppσ and tpppi hopping integrals[102].tpx,px = l2tppσ + (1− l2)tpppi (5.13)tpx,py = lmtppσ − lmtpppitpx,pz = lntppσ − lntpppiwhere l, m, and n are the direction cosines to the neighbouring oxy-gens. The hopping energies are expressed in terms of tppσ and tpppi en-ergies. These energies are taken as tppσ = 0.63 eV and tpppi = −0.04 eVfrom tight-binding model parameterization of the band-structure[103].Ref. [4] finds the very similar values of tppσ = 0.64 eV and tpppi = −0.03eV for the sister compound SrBiO3.925.2. Computations• HhoppingBi6s−OA1g is the hybridization term between the bismuth 6s orbitalat the centre of the octahedron and the A1g combination of the six O2p orbitals around. This combination is the only allowed symmetrycombination with which an s orbital can hybridize. Note that as shownbelow the effective Bi-O hopping energy is equal to√6tspσ where tspσ isthe single bond hopping integral as schematically shown in Fig. 5.5-a:|ψA1g >=1√6(|ψ2p1 > +|ψ2p2 > +|ψ2p3 > (5.14)+|ψ2p4 > +|ψ2p5 > +|ψ2p6 >),tOp−Bi6s =< ψA1g |H|ψ6s >=6√6< ψ2p1 |H|ψ6s >=√6tspσ.The same tight-binding model parameterization of the band-structure[103]gives tspσ = 2.1 eV for BaBiO3 structure. Ref. [4] finds tspσ = 2.3 eVfor SrBiO3.935.2. Computations-tpp tppπ-tpp -tʹpptsp𝛔 tpp𝛔126534acbdFigure 5.5: A schematic presentation of the involved hybridization termsin our model Hamiltonian. There are bismuth s orbital at the centre andoxygen p orbitals at the corners of the octahedron. a: tOp−Bi6s =√6tspσ.b: σ and pi oxygen p hopping terms. c (and a): tpp = 1/2(tppσ − tpppi). d:t′pp = 1/2(tppσ + tpppi)[1].Coulomb and Exchange Terms :HUOp, HF 2Op, HQOsp, and HG1Osp• HUOp : The monopole on-site Coulomb interaction between the electronson the oxygen p’s.• HF 2Op : The higher multipole on-site Hund’s rule interaction betweenthe electrons on the oxygen p’s.• HQOsp : The monopole Coulomb interaction between the O 1s core holeand the O valence 2p electrons.• HG1Osp : The exchange interaction between the O 1s core hole and theO valence 2p electrons.Note that the Coulomb interaction between the two s electrons on Bi areneglected in our model Hamiltonian because of the very large radial extendof the 6s orbital with its 5 radial nodes.945.2. ComputationsCrystal Field Energy: HCFDue to the crystal field potential produced by the bismuth’s electrons, elec-trons in the p orbitals pointing towards the cation (pσ) have a higher energythan the electrons in the orbitals perpendicular to it (ppi)[104]. This is takeninto account in the Hamiltonian with the term: σ − pi = ECF .On-site Energies: HonsitesThe on-site energies for the oxygen 1s, 2p and bismuth 6s orbitals are ex-pressed in terms of the charge transfer energy (∆), monopole Coulomb re-pulsion U , and the core-hole potential Q as shown below.We define the charge transfer energy as the energy difference betweenthe following two configurations.E(|ψ12O1s >, |ψ2Bi6s >, |ψ34O2p >) = 0, (5.15)E(|ψ12O1s >, |ψ1Bi6s >, |ψ35O2p >) = ∆.where the superscripts are the number of electrons i.e |ψ34O2p > meansthere are 34 electrons (or 2 holes) in O 2p orbitals. According to DFT thismaterial is a negative charge transfer material with ∆ = −4 eV[4].The energies of the above configurations can be written in terms of ∆,U and Q to find the on-site energies:121s + 26s + 342p + [4×(62)+ 2×(52)]× U + 2× [4× 6 + 2× 5]Q = ∆121s + 16s + 352p + [5×(62)+ 1×(52)]× U + 2× [5× 6 + 1× 5]Q = 0Now we set the 1s ≡ 0 and solve for the other on-site energies to yield:e1s ≡ 0, (5.16)e2p =−∆− 45U − 36Q18,e6s =17∆ + 45U18.The values of the the core-hole potential Q, monopole Coulomb energyU , and the crystal field potential ECF are taken as 3.6 eV, 3 eV and 1 eV,955.3. Ground-State Spin Calculationrespectively. These values do not deviate from the well-established rangesover the past decades [12, 85, 104–106]. The dipole Coulomb and exchangeterms (F 2 and G1, respectively) are also taken from atomic oxygen calcu-lated values as G1sp = 3.04 eV and F2pp = 7.25 eV.5.3 Ground-State Spin CalculationWe begin the calculation by first examining the spin state of the groundstate for various values of the crystal field energy (ECF ), and the oxygen-bismuth hybridization energy (tspσ). We know BaBiO3 is a diamagneticmaterial with the total spin of zero in its ground state [4, 7]. On the otherhand, tight-binding calculation for an octahedron of only six oxygens at thecorners with two holes gives a triplet ground state with wave function ofmainly (eg)2 configuration when U > 0[104]. However, when the bismuthcation is added to the system and allowed to hybridize with the oxygens,the ground state has to change to the expected singlet state with an A1gsymmetry where the two holes in the ground state have to be antiparallelwith the total spin of zero (low-spin) due to the Pauli exclusion principle.We examine the above statement by finding the total spin of the groundstate for various values of the crystal field energy (ECF ), and the oxygen-bismuth hybridization energy (tspσ). As shown in Fig. 5.6, starting fromECF=0, and tspσ=0, first we need to turn on the ECF , so that for tspσ=0we get the correct triplet ground state. When tspσ=0 the system is basicallywithout the bismuth cation and consists of only the six oxygens. Then wehave to increase the tspσ energy so that we achieve the expected low spinground state when the bismuth is present. These minimum or thresholdECF and tspσ energies are small enough that for any reasonable value weachieve the correct ground state in our calculation. Remember that ourexpected values of tspσ and ECF are respectively 2.1 eV and 1 eV fromprevious tight-binding calculations[103, 104]. Therefore, the ground statewill always stay in the low spin blue region above this graph as expected.965.4. Hole Distribution CalculationFigure 5.6: The total spin of the ground state as a function of crystal fieldenergy (ECF ) and oxygen-bismuth hybridization energy (tspσ) for U = 3eV. The first arrow indicates that we need to turn on the ECF , so that fortspσ=0 we get the correct triplet ground state for a bismuthless octahedronwith two holes. The second arrow shows we have to increase the tspσ energyso that we achieve the expected low spin ground state when the bismuth ispresent.5.4 Hole Distribution CalculationNow we continue the calculation by finding the hole distribution betweenthe ligand oxygens and the bismuth cation in the octahedron. As describedin chapter 1 the insulating mechanism of BaBiO3 is often explained in termsof charge disproportion of Bi4++Bi4+ into Bi3+ and Bi5+. In this picture,it is assumed the oxygen anions are full, and holes reside on the bismuthcation. However, many experimental studies [28–30] as well as band struc-ture calculations [4, 26] find relatively small charge differences between thebismuth sites.We also showed in chapter 3 that core-level spectroscopy measurementssuch as XAS give evidence for having holes on the oxygens whereas the XPS975.4. Hole Distribution Calculationresult in chapter 4 might not support that. Here, we address this questionby calculating the average number of holes on the oxygen anions versus thebismuth cation for a wide range of ∆ and tspσ. As shown in Fig. 5.7, fora wide range of these energies, holes indeed mainly reside on the ligandoxygens.985.4. Hole Distribution Calculation 0 0.5 1 1.5 2 0 0.5 1 1.5 2 2.5 3 3.5 4∆ = -4 eVNumber of Holestspσ (eV)aOxygen 2pBismuth 6s 0 0.5 1 1.5 2-6 -5 -4 -3 -2 -1 0tspσ = 2.1 eVNumber of Holes∆ (eV)bOxygen 2pBismuth 6sFigure 5.7: The average number of holes as a function of a: Bi 6s/O phybridization energy (tspσ) for ∆ = −4 eV. and b: the charge transfer energy∆ for tspσ = 2.1 eV. For a large range of parameters, holes reside primarilyon the ligand oxygens.995.5. XPS calculation5.5 XPS calculationIn the previous chapter, we presented the oxygen 1s x-ray photoemissionmeasurements on BaBiO3 single crystal. We showed how the spectrum losesmost of its structure through the progression of the surface cleaning proce-dure and becomes almost structureless but remains slightly asymmetric.We discussed how one would expect a different result due to the discussedhigh hole density on the oxygens in chapter 3. In the previous section, wecalculated that indeed there is a high hole density on the ligand oxygens.Therefore, the question still remains regarding the shape of the oxygen 1sXPS structure. To address this problem, in this section we calculate theoxygen 1s XPS spectra of BaBiO3 for varying parameters.We begin by setting the O-O and O-Bi hybridization to zero. We thencalculate the O 1s XPS for different core hole potentials (Q) while preservingthe QU = 1.2 ratio [107]. Because the O-Bi hybridization is zero and wehave a negative charge transfer energy, the two holes reside entirely on theoxygen sites. Further, since we have no O-O hybridization, we have a setof degenerate ground states where the two holes are distributed among thesix oxygen sites (though with no double occupancy when there is a finiteCoulomb interaction U). Averaging over the degenerate states, each oxygensite has a 13 probability of hosting one of the two holes.As can be seen from Fig. 5.8, for the case of Q = 0 only a single peakis present in the XPS. The energy of this peak is 0 eV, as we set the onsiteenergy of the core 1s level to zero for simplicity here. For a finite Q, twopeaks are present in the XPS. The more intense peak originates from thecase where the core hole is created on a site where there is no valence 2p hole.The weaker peak at +Q higher in energy originates from the case where thecore hole is created on a site having a valence 2p hole. The 2 : 1 intensityratio between the two peaks is to be expected: there is a 13 probability thata valence hole is on the core hole site and a 23 probability that there is novalence hole. This example shows how one might expect to see the effect ofthe self-doped oxygen holes in the oxygen XPS through the appearance ofa satellite peak.Now to examine the effect of the bismuth atom at the centre and oxygens’p−p hybridization, we turn on the p−p hopping terms and then increase theBi-O hopping, tspσ, from 0 to 2 eV. As shown in Fig. 5.9, we get a relativelystrong satellite structure with turning on the hybridization among the porbitals due to the holes distributed among the ligand oxygens. However,when we allow the hybridization between the Bi 6s and the oxygens, theirintensities are suppressed dramatically. This is due to the strong dilution1005.5. XPS calculation 0 5 10 15 20 25 30-30 -25 -20 -15 -10 -5 0 55Q6QIntensity (arb. units)Energy (eV)4 eV3 eV2 eV 1 eVQ = 0 eVFigure 5.8: Calculated oxygen 1s XPS spectra with all the hybridizationterms set to zero for different core-hole potential (Q) values. The curves areshifted along the “Intensity” axis.1015.5. XPS calculation 0 50 100 150 200-1 0 1 2 3 4 5 6 7Intensity (arb. units)Energy (eV)2.1 eV 1.5 eV1 eV0.5 eVtspσ= 0 eVFigure 5.9: Calculated oxygen 1s XPS spectra for different Bi 6s/O p hy-bridization energies (tspσ), for tpppi = −0.04eV, tppσ = 0.63 eV, U = 3 eV,Q = 3.6 eV, and ECF = 1 eV. Multiplets lose their intensities significantlywith turning on the bismuth-oxygen hybridization. The curves are shiftedalong the “Intensity” axis.of the influence of the oxygen 1s core hole which has negligible interactionwith the Bi 6s hole.This result explains the relatively sharp but slightly asymmetric O 1speak of the XPS experiment even in the presence of a substantial oxygen 2phole concentration. This analysis provides direct evidence for the dominantinfluence of the oxygen 2p- bismuth 6s hybridization. This study providesfurther insight into the importance of self-doped ligand oxygen 2p states inthis high Tc family of oxides. It shows that the O 2p states should play anessential role in the description of what happens with the hole or electrondoping of the bismuthates and therefore, in the description of the origin ofsuperconductivity in the doped materials.1025.6. Conclusion5.6 ConclusionWe employed exact diagonalization cluster calculation on an octahedron ofsix oxygens around and a bismuth at the center with two holes in total.We found that for a wide range of charge transfer energies and O 2p-Bi6s hybridization energies, holes mainly reside on the ligand oxygens ratherthan the conventionally accepted purely ionic picture that assigns holes tothe bismuth cation.We also used this model, to simulate the oxygen 1s XPS spectrum forvarying values of core-hole potential and O 2p-Bi 6s hybridization. From thisanalysis along with the XPS experimental results of chapter 4, we concludethat the O 2p-Bi 6s hybridization energy is the dominant energy scale inthis problem which determines the low energy scale electronic structure.103Chapter 6Summary and Future Work6.1 SummaryIn chapter 1, we reviewed the main properties of the material, BaBiO3, in-cluding its general electronic and crystal structure and its superconductingphase. We also discussed the importance of studying the roles of oxygen an-ions in this material by comparing its properties to nickelates and cuprates.In chapter 2, we presented our congruent melting technique to grow sin-gle crystals of BaBiO3 with sizes up to 2×2×1 mm3. We then characterizedthe grown crystals by XPS chemical composition measurement, XRD andresistivity measurements. They all confirmed the growth of high-quality sin-gle crystals. We showed that using a two-step solid state reaction before themelt growth and also using a wide crucible during the growth are crucial inorder to get reasonably big single crystalsIn chapter 3, we used oxygen K-edge XAS and RXES to study theoxygens’ bonding and antibonding p-bands close to the chemical potential.The result was then compared to the DFT(LDA) oxygen-p projected den-sity of states. These gave evidence for a high hole concentration in theoxygens’ states in contrast to the generally assumed purely ionic charge-disproportionation picture where holes are believed to reside mainly on thebismuth cations.In chapter 4, we proceeded with the investigation of the oxygens’ rolesin the electronic structure of the BaBiO3 using detailed oxygen 1s XPS.We showed surface contamination can be a serious issue in interpreting thestructure of the oxygen spectrum. We presented our cleaning routine whichwas successful in removing the carbon-containing compounds from the sur-face to achieve a reliable oxygen 1s spectrum. We showed by removing thesurface contamination, oxygen 1s spectrum also loses much of its structureand its shoulder but remains slightly asymmetric. We were later able toexplain this result by performing exact diagonalization cluster calculationsin chapter 5.Finally, in chapter 5, we did exact diagonalization model calculation onan octahedron of six oxygens at the corners and a bismuth at the centre to1046.2. Future Worksfind the hole distribution between the oxygens and the bismuth, and alsoto simulate the oxygen 1s XPS spectrum for different electronic energies.We demonstrated that for a wide range of charge transfer and hybridizationenergies, holes mainly reside on the ligand oxygens in agreement with theresults from chapter 3. The XPS calculation and its comparison with theexperimental spectrum from chapter 4 also suggested that the O 2p-Bi 6shybridization energy has to be the dominant energy scale in this problemwhich determines the low energy scale electronic structure.6.2 Future Works6.2.1 Further Characterization of the Single CrystalsIn chapter 2, we characterized the crystal structure of the grown BaBiO3crystal by XRD and found its chemical composition by XPS and also per-formed temperature dependent electronic transport measurements. How-ever, the crystals are still being characterized in more detail by measur-ing their magnetic susceptibility, the Young modulus of elasticity and alsostudying the surface by the Atomic Force Microscopy technique and carefuloptical photography.6.2.2 Electron Doped MaterialTo this date, there has been no significant success in making an electron-doped BaBiO3 compound. Finding such a compound in a crystalline formis unlikely due to the ionic radii of the candidate dopants. Lanthanum isusually proposed to substitute the barium to add electrons to the system.However, considering the ionic radii of the involved ions, most probably theLanthanum 3+ will take the Bi 3+ sites rather than the Ba 2+ sites [38]:• Ionic radius of Ba2+ with the coordination number of 12: 1.61 A˚• Ionic radius of Bi3+ with the coordination number of 6: 1.03 A˚• Ionic radius of La3+ with the coordination number of 12: 1.36 A˚• Ionic radius of La3+ with the coordination number of 6: 1.032A˚It can be seen that La3+ and Bi3+ with six coordination numbers havevery close ionic radii, while the La3+ and Ba2+ with 12 coordination numbershave quite different ionic radii. Remember in the ABO3 perovskite structure,1056.2. Future WorksA and B atoms have coordination numbers of 12 and six, respectively. Thisproblem exists for the other proposed dopants such as yttrium, too.However, electron doping the BaBiO3 film might be possible by using anelectron donor like caesium atoms placed on top of the surface. Of course,this would only create electron doping close to the surface but would be away to get electrons into the system, regardless. It has also been suggestedby our group that one could use an alternation of a polar material withSrBiO3 in heterostructure in which SrBiO3 would be electron or hole dopedin order to compensate for the polar divergence of the potential in the polarmaterials [108]. Growing and studying such a martial, which can very wellbe superconducting, will be very interesting and also give valuable insightsregarding these systems.6.2.3 Resonant Photoemission MeasurementsA detailed resonant x-ray photoemission measurement looking at bismuthp → s transition can be an effective way to gather further information onthe amount of s and p character in the density of states of the material. InRPES, the photoemission signal is recorded while varying the photon energyacross an x-ray absorption edge or a resonance energy where the incidentphoton excites an electron from the resonating core state into an empty stateabove the chemical potential. From the band structure calculation [4], wewould expect to see about 50% bismuth 6s character just below the Fermienergy, but also some at a much deeper energy.The momentum resolved band structure of single crystal BaBiO3 canalso be measured by Angular Resolved PES technique. 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Experimental and theoretical study of the electronic structure of single-crystal BaBiO₃
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