On the Spin-Dynamics of the Quasi-One-Dimensional, Frustrated Quantum Magnet Li2CuO2: Studies by means of Inelastic Neutron Scattering and Thermodynamic Methods

Die magnetischen Eigenschaften von Li2CuO2 sind seit mehr als zwei Jahrzehnten Gegenstand theoretischen und experimentellen Interesses. Über die genaue Natur der magnetischen Wechselwirkungen in diesem Isolator konnte jedoch keine Einigkeit erzielt werden. Während das Material von Seiten theoretischer Untersuchungen als quasi-eindimensionaler Magnet mit starken ferromagnetischen Kopplungen entlang der Kette verstanden wurde, legten experimentelle Studien dominierende dreidimensionale Zwischenkettenkopplungen nahe. Im Rahmen dieser Dissertation werden auf der Grundlage von Untersuchungen des magnetischen Anregungsspektrums mittels inelastischer Neutronenstreuung und dessen Analyse innerhalb eines Spinwellenmodels die führenden magnetischen Wechselwirkungen in Li2CuO2 bestimmt. Es wird zweifelsfrei nachgewiesen, dass das Material eine quasi-eindimensionale Spinkettenverbindung darstellt. Insbesondere kann die Konkurrenz von ferro- und antiferromagnetischen Wechselwirkungen entlang der Ketten nachgewiesen werden. Die Anwendbarkeit einer Spinwellenanalyse dieses niedrigdimensionalen Spin-1=2 Systems wird gezeigt. Das magnetische Phasendiagramm wird mittels Messungen von spezifischer Wärme, thermischer Ausdehnung und Magnetostriktion sowie der Magnetisierung in statischen und gepulsten Magnetfeldern untersucht und im Bezug auf die Austauschwechselwirkungen diskutiert. Aufgrund seiner einfachen kristallographischen und magnetischen Struktur stellt Li2CuO2 ein potentiell wertvolles Modellsystem in der Klasse der Spinkettenverbindungen mit konkurrierenden ferro- und antiferromagnetischen Wechselwirkungen dar.:1. Motivation 9 I. Introduction 13 2. Li2CuO2 15 2.1. ... as a cuprate 15 2.2. ... as a quasi-one dimensional magnet 17 2.3. Literature review on magnetic properties 21 2.3.1. Crystallographic structure 21 2.3.2. Magnetic structure and magnetic properties 21 3. Employed experimental techniques 25 3.1. Thermodynamic studies 25 3.2. Inelastic magnetic neutron scattering 28 4. Sample properties and characterization 33 4.1. A sample for INS 33 4.2. Crystal growth and characterization 36 II. Inelastic neutron scattering studies 41 5. Magnon excitations & spin-wave analysis 43 5.1. Linear spin-wave model 44 5.2. Experimental setup 46 5.3. Magnon dispersion for q || b* 46 5.3.1. Thermal neutrons 46 5.3.2. Cold neutrons 49 5.4. Magnon dispersion for q b* 52 5.5. Magnon dispersion at the zone boundary 55 5.6. Spin-wave analysis 58 5.7. Frustration of inter-chain couplings 64 6. Low energy excitations 69 III. Studies on thermodynamic properties 79 7. The magnetic phase diagram 81 7.1. High temperature short range order 83 7.2. The antiferromagnetic phase 85 7.3. The meta-magnetic transition and intermediate phase 88 7.4. Low temperature anomalies 93 7.4.1. Weak ferromagnetism 94 7.4.2. Anomalous magnetization at low T 100 8. Magnetization studies 105 8.1. Magnetization M(T) 105 8.2. Magnetization M(H) 110 9. Analysis of the magnetic specific heat 117 9.1. Estimate of phononic specific heat 118 9.2. Fluctuations, correlations near TN 120 9.3. Entropy 124 9.4. Specific heat at low temperature 129 10. Magneto-elastic coupling 133 10.1. Remarks on the measurement setup 133 10.2. Uniaxial pressure dependence of TN 135 10.3. Exploration of the easy axis magnetic phase diagram 139 10.3.1. Low temperature magnetostriction 139 10.3.2. Comprehensive survey of thermal expansion and magnetostriction data 141 10.3.3. A phenomenological model 146 10.4. Thermal expansion in magnetic fifields along the hard axes 150 IV. Conclusion 153 11.Summary and Outlook 155 V. Appendix 159 A. Supplementary data 161 A.1. Excitation spectrum in applied magnetic fifield 161 A.2. Low temperature specific heat 163 A.3. Pressure dependence of TN for H||a = 12T 163 A.4. Pressure dependence of magnetization 164 Bibliography 180The magnetic properties of Li2CuO2 have attracted interest since more than two decades, both in theory and experiment. Despite these efforts, the precise nature of the magnetic interactions in this insulator remained an issue of controversial debate. From theoretical studies, the compound was understood as a quasi-one-dimensional magnet with strong ferromagnetic interactions along the chain, while in contrast, experimentally studies suggested dominant three-dimensional inter-chain interactions. In this thesis, the leading magnetic exchange interactions of Li2CuO2 are determined on the basis of a detailed inelastic neutron scattering study of the magnetic excitation spectrum, analyzed within spin-wave theory. It is unequivocally shown, that the material represents a quasi-one-dimensional spin-chain compound. In particular, the competition of ferro- and antiferromagnetic interactions in the chain has been evidenced. The applicability of a spin-wave model for analysis of this low-dimensional spin-1=2 system is shown. The magnetic phase diagram of Li2CuO2 is studied by specific heat, thermal expansion and magnetostriction measurements as well as magnetization measurements in both static and pulsed magnetic fifields. The phase diagram is discussed with respect to the exchange interactions. With its simple crystallographic and magnetic structure, Li2CuO2 may serve as a worthwhile model system in the class of spin-chain compounds with competing ferromagnetic and antiferromagnetic interactions.:1. Motivation 9 I. Introduction 13 2. Li2CuO2 15 2.1. ... as a cuprate 15 2.2. ... as a quasi-one dimensional magnet 17 2.3. Literature review on magnetic properties 21 2.3.1. Crystallographic structure 21 2.3.2. Magnetic structure and magnetic properties 21 3. Employed experimental techniques 25 3.1. Thermodynamic studies 25 3.2. Inelastic magnetic neutron scattering 28 4. Sample properties and characterization 33 4.1. A sample for INS 33 4.2. Crystal growth and characterization 36 II. Inelastic neutron scattering studies 41 5. Magnon excitations & spin-wave analysis 43 5.1. Linear spin-wave model 44 5.2. Experimental setup 46 5.3. Magnon dispersion for q || b* 46 5.3.1. Thermal neutrons 46 5.3.2. Cold neutrons 49 5.4. Magnon dispersion for q b* 52 5.5. Magnon dispersion at the zone boundary 55 5.6. Spin-wave analysis 58 5.7. Frustration of inter-chain couplings 64 6. Low energy excitations 69 III. Studies on thermodynamic properties 79 7. The magnetic phase diagram 81 7.1. High temperature short range order 83 7.2. The antiferromagnetic phase 85 7.3. The meta-magnetic transition and intermediate phase 88 7.4. Low temperature anomalies 93 7.4.1. Weak ferromagnetism 94 7.4.2. Anomalous magnetization at low T 100 8. Magnetization studies 105 8.1. Magnetization M(T) 105 8.2. Magnetization M(H) 110 9. Analysis of the magnetic specific heat 117 9.1. Estimate of phononic specific heat 118 9.2. Fluctuations, correlations near TN 120 9.3. Entropy 124 9.4. Specific heat at low temperature 129 10. Magneto-elastic coupling 133 10.1. Remarks on the measurement setup 133 10.2. Uniaxial pressure dependence of TN 135 10.3. Exploration of the easy axis magnetic phase diagram 139 10.3.1. Low temperature magnetostriction 139 10.3.2. Comprehensive survey of thermal expansion and magnetostriction data 141 10.3.3. A phenomenological model 146 10.4. Thermal expansion in magnetic fifields along the hard axes 150 IV. Conclusion 153 11.Summary and Outlook 155 V. Appendix 159 A. Supplementary data 161 A.1. Excitation spectrum in applied magnetic fifield 161 A.2. Low temperature specific heat 163 A.3. Pressure dependence of TN for H||a = 12T 163 A.4. Pressure dependence of magnetization 164 Bibliography 18

Anisotropic interactions in transition metal oxides: Quantum chemistry study of strongly correlated materials

This thesis covers different problems that arise due to crystal and pseudospin anisotropy present in 3d and 5d transition metal oxides. We demonstrate that the methods of computational quantum chemistry can be fruitfully used for quantitative studies of such problems. In Chapter 2, Chapter 3, and Chapter 7 we show that it is possible to reliably calculate local multiplet splittings fully ab initio, and therefore help to assign peaks in experimental spectra to corresponding electronic states. In a situation of large number of peaks due to low local symmetry such assignment using semi-empirical methods can be very tedious and non-unique. Moreover, in Chapter 4 we present a computational scheme for calculating intensities as observed in the resonant inelastic X-ray scattering and X-ray absorption experiments. In our scheme highly-excited core-hole states are calculated explicitly taking into account corresponding orbital relaxation and electron polarization. Computed Cu L-edge spectra for the Li2CuO2 compound reproduce all features present in experiment. Unbiased ab initio calculations allow us to unravel a delicate interplay between the distortion of the local ligand cage around the transition metal ions and the anisotropic electrostatic interactions due to second and farther coordination shells. As shown in Chapter 5 and Chapter 6 this interplay can lead to the counter intuitive multiplet structure, single-ion anisotropy, and magnetic g factors. The effect is quite general and may occur in compounds with large difference between charges of metal ions that form anisotropic environment around the transition metal, like Ir 4+ in plane versus Sr 2+ out of plane in the case of Sr2IrO4. An important aspect of the presented study is the mapping of the quantum chemistry results onto simpler physical models, namely extended Heisenberg model, providing an ab initio parametrization. In Chapter 5 we employ the effective Hamiltonian technique for extracting parameters of the anisotropic Heisenberg model with single-ion anisotropy in the case of quenched orbital moment and second-order spin-orbit coupling. Calculated strong easy-axis anisotropy of the same order of magnitude as the symmetric exchange is consistent with experimentally-observer all-in/all-out magnetic order. In Chapter 6 we introduce new flavour of the mapping procedure applicable to systems with first-order spin-orbit coupling, such as 5d 5 iridates based on analysis of the wavefunction and interaction with magnetic field. In Chapter 6 and Chapter 7 we use this new procedure to obtain parameters of the pseudospin anisotropic Heisenberg model. We find large antisymmetric exchange leading to the canted antiferromagnetic state in Sr2IrO4 and nearly ideal one-dimensional Heisenberg behaviour of the CaIrO3, both agree very well with experimental findings

Estudio teórico de cupratos de litio como posibles materiales catódicos para baterías

In this work, the projected density of states (DOS-p) and the local softness, s(r), were studied as properties related with the performance of Li2CuO2, LiCuO2, and Li2Cu1−xMxO2 (M = Co, Ni or Ti, x = 0.25 or 0.5) as cathode materials. All calculations were done within the framework of the density functional theory (DFT) using periodic boundary conditions. Through the analysis of the DOS-p of each system, the electronic states involved in the initial charge process of the battery (cathode oxidation) were identified. This information allowed stablishing the oxygen participation in the redox process that has been related to a decrease in the capacity during the charge-discharge process. The use of the s(r) has been proposed instead of DOS-p to analyze the initial redox processes. It was found that it is better to use the s(r) because it shows susceptible sites to lose electrons and allow us to do direct comparisons between the systems in a simpler way than the DOS-p. The obtained results predict that Li2Cu1−xTixO2 systems involve less oxygen redox participation and therefore a better retention of capacity during the charge-discharge process. In addition, the s(r) was used to identify the most susceptible atoms toward oxidation, in iron sulphides of hydrometallurgical importance for Mexico. A good agreement was found between the predicted susceptible atoms to oxidation by s(r) and those determined in experimental studies. Hence, we have demonstrated that the s(r) could be applied to different redox process in solids.En el presente trabajo, la densidad de estados proyectada (DOS-p) y la blandura local, s(r), fueron estudiadas como propiedades relacionadas con el desempeño de Li2CuO2, LiCuO2 y Li2Cu1−xMxO2 (M = Co, Ni o Ti, x = 0.25 o 0.5) como materiales catódicos. Todos los cálculos fueron realizados en el marco de la teoría de los funcionales de la densidad (DFT por sus siglas en inglés) bajo condiciones periódicas. Mediante el análisis de la DOS-p de cada sistema, los estados electrónicos involucrados en el proceso inicial de carga de la batería (oxidación del cátodo) fueron identificados. Esta información permitió establecer la participación del oxígeno en el proceso redox, que ha sido relacionada con una disminución en la capacidad durante el proceso de carga-descarga. La utilización de la s(r) ha sido propuesta en lugar de la DOS-p para analizar los procesos redox iniciales. Se encontró que es mejor usar la s(r), debido a que muestra los sitios susceptibles a perder electrones, permitiendo hacer comparaciones directas entre sistemas, en una forma más simple que la DOS-p. Los resultados obtenidos predicen que los sistemas Li2Cu1−xTixO2 involucran menor participación redox de oxígeno y, por lo tanto, una mejor retención de la capacidad durante el proceso de carga-descarga. Además, se utilizó la s(r) para identificar los átomos más susceptibles a oxidarse, en sulfuros de hierro de importancia hidrometalúrgica para México. Una buena concordancia fue encontrada entre los átomos susceptibles a oxidarse predichos por la s(r) y aquellos determinados en estudios experimentales. Por lo tanto, demostramos que la s(r) puede ser aplicada a diferentes procesos de redox en sólidos