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Anisotropic Interactions in Transition Metal Oxides, Quantum Chemistry Study of Strongly Correlated Materials Gutachter: Prof

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Anisotropic Interactions in Transition Metal Oxides, Quantum Chemistry Study of Strongly Correlated Materials Gutachter: Prof European Commission erasmus mundus A NISOTROPICINTERACTIONSINTRANSITION METALOXIDES dissertation zur Erlangung des akademischen Grades Doctor rerum naturalium (Dr. rer. nat.) vorgelegt von nikolay bogdanov geboren am 09.01.1987 in Moskau, Russland Fachrichtung Physik Fakultät für Mathematik und Naturwissenschaften Technische Universität Dresden 2017 Nikolay Bogdanov: Anisotropic interactions in transition metal oxides, Quantum chemistry study of strongly correlated materials gutachter: Prof. Dr. Jeroen van den Brink Prof. Dr. Ria Broer eingereicht am: 29 September 2017 disputation am: 6 April 2018 Моим родителям, Ирине и Александру. To my parents, Irina and Alexander. ACKNOWLEDGEMENTS First of all, I would like to express my deep gratitude to my direct advisor Liviu Hozoi and my supervisor Jeroen van den Brink for the continuous support of my study and research. Liviu, you not only introduced me to quantum chemistry, practi- cal use of quantum mechanics and many other things, but also were the person I looked up to. Thank you for your constant motivation, patience and guidance during my time at IFW and especially when writing this thesis. Jeroen, thank you for the generous encouragement during my stay in Dresden and during the later stages of finishing the thesis. It was my pleasure to talk to you, as you always had a great project to pro- pose, an interesting idea to check, or a smart explanation of results we obtained. I would like to thank Ria Broer for refereeing the thesis, her sug- gestions and comments helped me to improve it a lot. I am grateful to Hermann Stoll for his help in overcoming diffi- culties I had with quantum chemical methods, both conceptual and practical. I would like to express my gratitude to Peter Fulde for insightful discussions that led to better understanding of the electron correla- tion problem on my side. I have greatly benefited from learning and working together with Vamshi Katukuri. Vamshi, thank you for pointing out so many im- portant papers and for sharing your ideas during our numberless discussions. I knew that I could always count on you. Among people I had the opportunity to work with in Dresden, I learned the most from Judit Romhányi, Ioannis Rousochatzakis and Viktor Yushankhai. Judit, thank you for sharing your knowledge on everything, especially on group theory, spin-wave theory and dif- ferent aspects of magnetism. Ioannis, I appreciate your help in un- derstanding the spin Hamiltonian machinery and its connection to macroscopic properties. Viktor, I am grateful to you for your detailed explanations of the spin-orbit coupling in solids, especially in the iri- dates problem and for suggesting great books on crystal-field theory. I had the luck to collaborate with Rémi Maurice during my short visit to Groningen. Rémi, thank you for showing me the chemist view on model Hamiltonian problems and demonstrating me the concept of effective Hamiltonian. Advice and comments given by Ganesh has been a great help in learning lattice models and reciprocal-space properties. v I would like to thank all other fellows at ITF who kindly discussed science with me, Alexander, André, Beom Hyun, Ching-Hao, Dai- Ning, Dmitry, Frank, Jörn, Hsiao-Yu, Katia, Krzysztof, Lei, Liudmila, Pasquale, Sahinur, Satoshi, Stefanos, Stefan-Ludwig and Ravi. I am grateful to Ulrike Nitzsche for the IT support and to Grit Rötzer for her help in solving practical issues. I also acknowledge financial support from the Erasmus Mundus Programme of the European Union. I give my special thanks to Anna Efimenko and Maria Bogdanova, without their assistance I would never find my way to Dresden. Finally, I want to thank my family for their constant support and love. Спасибо всем вам! vi CONTENTS introduction 1 i theoretical foundations 5 1 quantum chemistry approach 7 1.1 Local correlation treatment 9 1.2 Embedding for cluster calculations 14 ii 3d transition-metal compounds 25 2 d-level electronic structure of one-dimensional cuprates 27 2.1 Computational details 28 2.2 Chains of corner-sharing CuO4 plaquettes 29 2.3 Corner-sharing CuF6 octahedra in KCuF3 31 2.4 Chains of edge-sharing CuO4 plaquettes 32 2.5 A ladder cuprate: CaCu2O3 34 2.6 Conclusions 36 3 d–d excitation energies in Ti and V oxychlorides 37 3.1 Structural and computational details 37 3.2 Quasi-one-dimensional titanium oxychloride 39 3.3 Quasi-two-dimensional vanadium oxychloride 41 3.4 Conclusions 43 4 computationofx-ray d-ion spectra in solids 45 4.1 Resonant inelastic X-ray scattering 45 4.2 Electron – field interaction 46 4.3 X-ray absorption cross section 48 4.4 RIXS double differential cross section 49 4.5 Computational scheme for Cu L-edge excitations 50 4.6 Results and discussion 53 4.7 Conclusions 56 iii 5d transition-metal systems 57 5 magnetic properties of pyrochlore Cd2Os2O7 59 5.1 Os d3 electron configuration, single-ion physics 60 5.2 Isotropic and antisymmetric exchange interactions 64 5.3 Conclusions 68 6 anisotropic magnetism in 214 strontium iridate 71 6.1 Model Hamiltonian and ESR measurements 72 6.2 Quantum chemistry calculations of g factors 75 6.3 Anisotropic exchange couplings in Sr2IrO4 78 6.4 Conclusions 84 vii viii contents 7 post perovskite a 1 2 quasi 1d anti CaIrO3 - , jeff ≈ / - - ferromagnet 87 7.1 d–d splittings and magnetic g factors 89 7.2 Intersite exchange interactions 92 7.3 Conclusions 99 summary 101 publications 103 bibliography 105 LISTOFFIGURES Figure 1.1 Exact solution and limiting cases within the CI paradigm 10 Figure 1.2 (a) Construction of configurations using the CAS scheme; (b) The notation for excited determi- nants 12 Figure 2.1 Chains of CuO4 plaquettes in Sr2CuO3 and SrCuO2 29 Figure 2.2 Chains of edge-sharing CuO4 plaquettes in four studied systems 33 Figure 2.3 MRCI crystal-field splittings in 1D Cu d9 com- pounds 36 Figure 3.1 Layered crystal structure of TiOCl and VOCl 38 Figure 3.2 Singly occupied Ti 3d orbitals for the ground and excited states in TiOCl 40 Figure 4.1 Sketch of the scattering geometry in Li2CuO2 52 Figure 4.2 Calculated versus experimental L3-edge dou- ble differential cross section 54 Figure 4.3 Theoretical RIXS plots for Li2CuO2 using the geometrical setup 55 Figure 5.1 Sketch of (a) the cluster used for the ZFS calcu- lations, (b) the compressive trigonal distortion in Cd2Os2O7 60 Figure 5.2 (a) Single-ion anisotropy parameter D and (b) total energy of the cluster ∆Etot, as functions of the trigonal distortion angle ∆θ 64 Figure 5.3 The cluster used for computing the intersite magnetic couplings for Cd2Os2O7 66 Figure 5.4 Network of corner-shared Os4 tetrahedra in Cd2Os2O7 67 Figure 6.1 TM t2g splittings for tetragonal distortions of the oxygen octahedron 72 Figure 6.2 ESR data for Sr2IrO4 73 Figure 6.3 Planar IrO2 network in Sr2IrO4 78 Figure 7.1 Structural details of CaIrO3 88 Figure 7.2 Local coordination and the main AF superex- change path for corner-sharing IrO6 octahedra in CaIrO3 92 Figure 7.3 Sketch of the NN magnetic interactions in CaIrO3 99 ix LISTOFTABLES Table 2.1 d–d excitation energies in Sr2CuO3 and SrCuO2 30 Table 2.2 d–d excitation energies in KCuF3 32 Table 2.3 d–d excitation energies for edge-sharing chain compounds 34 Table 2.4 d–d excitation energies for the ladder system CaCu2O3 35 Table 3.1 d-d excitation energies in TiOCl 39 Table 3.2 d-d excitation energies in VOCl 42 Table 4.1 Relative energies for Cu2+ 3d9 and 2p53d10 states of Li2CuO2 52 5+ 3 Table 5.1 Os 5d multiplet structure of Cd2Os2O7 61 Table 5.2 Single-site effective interaction matrix obtained by MRCI+SOC for Cd2Os2O7 62 Table 5.3 Interaction matrix for the single-ion anisotropy model Hamiltonian and S=3=2 62 Table 5.4 Os5+ 5d3 multiplet structure in a hypothetical Cd2Os2O7 crystal with no trigonal distortions 63 Table 5.5 Energies of the singlet, triplet, quintet, and septet 3 states for two adjacent Os d sites in Cd2Os2O7 65 Table 5.6 Model interaction matrix in the coupled basis tot tot 69 S , MS for two-sites and S1,2 =3=2 Table 5.7 Effective interaction matrix in the coupled ba- tot tot sis S , MS , obtained from two-site MRCI+SOC calculations for Cd2Os2O7 70 Table 6.1 g factors for Sr2IrO4 and Ba2IrO4 77 Table 6.2 Ir t2g splittings and g factors for Sr2IrO4 and Ba2IrO4 as obtained with the orca program 77 Table 6.3 Matrix elements of the ab initio spin-orbit Hamil- tonian for Sr2IrO4 79 Table 6.4 Matrix elements of the model spin Hamilto- nian diagonal in zero field 79 Table 6.5 Notations used to define anisotropic exchange 80 Table 6.6 Matrix form of the model spin Hamiltonian in the ‘uncoupled’ bond basis 81 Table 6.7 Matrix elements of the model spin Hamilto- nian in the coupled basis 82 Table 6.8 Matrix form of the model spin Hamiltonian with J and Γ¯ exchange brought to diagonal form 82 Table 6.9 NN magnetic couplings and g-factors in Sr2IrO4 as obtained from the SO MRCI 84 7 1 5 90 Table . Relative energies of t2g states in CaIrO3 x Table 7.2 Energies of the singlet and triplet states for two adjacent Ir d5 sites along c and a directionsin CaIrO3 93 Table 7.3 Matrix elements of the ab initio SOC Hamil- tonian for NN octahedra along the c bond in CaIrO3 95 Table 7.4 Matrix form of the model Hamiltonian for the c bond in CaIrO3 95 Table 7.5 NN magnetic couplings and g-factors for corner- sharing octahedra in CaIrO3 96 Table 7.6 NN magnetic couplings and g-factors for edge- sharing a-axis octahedra in CaIrO3 96 Table 7.7 Matrix elements of the ab initio spin-orbit Hamil- tonian for a bond in CaIrO3 98 Table 7.8 Matrix form of the model Hamiltonian for a- axis bonds in CaIrO3 98 ACRONYMS 1D one-dimensional
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