Die vorliegende Arbeit befasst sich mit dem Dünnfilmwachstum der ternären Oxide Na2IrO3, Li2IrO3, Y2Ir2O7 und YBiO3. All diesen oxidischen Materialien ist gemein, dass sie Verwirklichungen sogenannter Topologischer Isolatoren oder Spin-Flüssigkeiten sein könnten. Diese neuartigen Materiezustände versprechen eine zukünftige Anwendung in der Quantencomputation, in magnetischen Speichern und in elektrischen Geräten mit geringer Leistungsaufnahme. Die Herstellung der hier gezeigten Dünnfilme ist daher ein erster Schritt zur Umsetzung dieser Anwendungen in der Zukunft. Alle Dünnfilme werden mittels gepulster Laserplasmaabscheidung auf verschiedenen einkristallinen Substraten hergestellt. Die strukturellen, optischen und elektrischen Eigenschaften der Filme werden mittels etablierter experimenteller Verfahren wie Röntgenbeugung, spektroskopischer Ellipsometrie und elektrischenWiderstandsmessungen untersucht. Die strukturellen Eigenschaften von erstmalig in der Masterarbeit des Authors verwirklichten Na2IrO3-Dünnfilmen können durch Abscheidung einer ZnO-Zwischenschicht deutlich verbessert werden. Einkristalline Li2IrO3-Dünnfilme mit einer definierten Kristallausrichtung werden erstmalig hergestellt. Die Messung der dielektrischen Funktion gibt Einblick in elektronische Anregungen, die gut vergleichbar mit Li2IrO3-Einkristallen und verwandten Iridaten sind. Des Weiteren wird aus den Daten eine optische Energielücke von ungefähr 300 meV bestimmt. In Y2Ir2O7-Dünnfilmen wird eine mögliche (111)-Vorzugsorientierung in Wachstumsrichtung gefunden. Im Vergleich mit der chemischen Lösungsabscheidung zeigen die hier mittels gepulster Laserplasmaabscheidung hergestellten YBiO3-Dünnfilme eine definierte, biaxiale Kristallausrichtung in der Wachstumsebene bei einer deutlich höheren Schichtdicke. Über die gemessene dielektrische Funktion können eine direkte und indirekte Bandlücke bestimmt werden. Deren Größe gibt eine notwendige experimentelle Rückmeldung an theoretische Berechnungen der elektronischen Bandstruktur von YBiO3, welche zur Vorhersage der oben erwähnten, neuartigen Materiezuständen verwendet werden. Nach einer Einleitung und Motivation dieser Arbeit gibt das zweite Kapitel einen Überblick über den gegenwärtigen Forschungsstand der hier untersuchten Materialien. Die folgenden zwei Kapitel beschreiben die Probenherstellung und die verwendeten experimentellen Untersuchungsmethoden. Anschließend werden für jedes Material einzeln die experimentellen Ergebnisse dieser Arbeit diskutiert. Die Arbeit schließt mit einer Zusammenfassung und einem Ausblick. / The present thesis reports on the thin film growth of ternary oxides Na2IrO3, Li2IrO3, Y2Ir2O7 and YBiO3. All of these oxides are candidate materials for the so-called topological insulator and spin liquid, respectively. These states of matter promise future application in quantum computation, and in magnetic memory and low-power electronic devices. The realization of the thin films presented here, thus represents a first step towards these future device applications. All thin films are prepared by means of pulsed laser deposition on various single-crystalline substrates. Their structural, optical and electronic properties are investigated with established experimental methods such as X-ray diffraction, spectroscopic ellipsometry and resistivity measurements. The structural properties of Na2IrO3 thin films, that were previously realized in the author’s M. Sc. thesis for the first time, are improved significantly by deposition of an intermediate ZnO layer. Single-crystalline Li2IrO3 thin films are grown for the first time and exhibit a defined crystal orientation. Measurement of the dielectric function gives insight into electronic excitations that compare well with single crystal samples and related iridates. From the data, an optical energy gap of about 300 meV is obtained. For Y2Ir2O7 thin films, a possible (111) out-of-plane preferential crystal orientation is obtained. Compared to chemical solution deposition, the pulsed laser-deposited YBiO3 thin films presented here exhibit a biaxial in-plane crystal orientation up to a significantly larger film thickness. From the measured dielectric function, a direct and indirect band gap energy is determined. Their magnitude provides necessary experimental feedback for theoretical calculations of the electronic structure of YBiO3, which are used in the prediction of the novel states of matter mentioned above. After the introduction and motivation of this thesis, the second chapter reviews the current state of the science of the studied thin film materials. The following two chapters introduce the sample preparation and the employed experimental methods, respectively. Subsequently, the experimental results of this thesis are discussed for each material individually. The thesis concludes with a summary and an outlook.

Die vorliegende Arbeit befasst sich mit dem Dünnfilmwachstum der ternären Oxide Na2IrO3, Li2IrO3, Y2Ir2O7 und YBiO3. All diesen oxidischen Materialien ist gemein, dass sie Verwirklichungen sogenannter Topologischer Isolatoren oder Spin-Flüssigkeiten sein könnten. Diese neuartigen Materiezustände versprechen eine zukünftige Anwendung in der Quantencomputation, in magnetischen Speichern und in elektrischen Geräten mit geringer Leistungsaufnahme. Die Herstellung der hier gezeigten Dünnfilme ist daher ein erster Schritt zur Umsetzung dieser Anwendungen in der Zukunft. Alle Dünnfilme werden mittels gepulster Laserplasmaabscheidung auf verschiedenen einkristallinen Substraten hergestellt. Die strukturellen, optischen und elektrischen Eigenschaften der Filme werden mittels etablierter experimenteller Verfahren wie Röntgenbeugung, spektroskopischer Ellipsometrie und elektrischenWiderstandsmessungen untersucht. Die strukturellen Eigenschaften von erstmalig in der Masterarbeit des Authors verwirklichten Na2IrO3-Dünnfilmen können durch Abscheidung einer ZnO-Zwischenschicht deutlich verbessert werden. Einkristalline Li2IrO3-Dünnfilme mit einer definierten Kristallausrichtung werden erstmalig hergestellt. Die Messung der dielektrischen Funktion gibt Einblick in elektronische Anregungen, die gut vergleichbar mit Li2IrO3-Einkristallen und verwandten Iridaten sind. Des Weiteren wird aus den Daten eine optische Energielücke von ungefähr 300 meV bestimmt. In Y2Ir2O7-Dünnfilmen wird eine mögliche (111)-Vorzugsorientierung in Wachstumsrichtung gefunden. Im Vergleich mit der chemischen Lösungsabscheidung zeigen die hier mittels gepulster Laserplasmaabscheidung hergestellten YBiO3-Dünnfilme eine definierte, biaxiale Kristallausrichtung in der Wachstumsebene bei einer deutlich höheren Schichtdicke. Über die gemessene dielektrische Funktion können eine direkte und indirekte Bandlücke bestimmt werden. Deren Größe gibt eine notwendige experimentelle Rückmeldung an theoretische Berechnungen der elektronischen Bandstruktur von YBiO3, welche zur Vorhersage der oben erwähnten, neuartigen Materiezuständen verwendet werden. Nach einer Einleitung und Motivation dieser Arbeit gibt das zweite Kapitel einen Überblick über den gegenwärtigen Forschungsstand der hier untersuchten Materialien. Die folgenden zwei Kapitel beschreiben die Probenherstellung und die verwendeten experimentellen Untersuchungsmethoden. Anschließend werden für jedes Material einzeln die experimentellen Ergebnisse dieser Arbeit diskutiert. Die Arbeit schließt mit einer Zusammenfassung und einem Ausblick. / The present thesis reports on the thin film growth of ternary oxides Na2IrO3, Li2IrO3, Y2Ir2O7 and YBiO3. All of these oxides are candidate materials for the so-called topological insulator and spin liquid, respectively. These states of matter promise future application in quantum computation, and in magnetic memory and low-power electronic devices. The realization of the thin films presented here, thus represents a first step towards these future device applications. All thin films are prepared by means of pulsed laser deposition on various single-crystalline substrates. Their structural, optical and electronic properties are investigated with established experimental methods such as X-ray diffraction, spectroscopic ellipsometry and resistivity measurements. The structural properties of Na2IrO3 thin films, that were previously realized in the author’s M. Sc. thesis for the first time, are improved significantly by deposition of an intermediate ZnO layer. Single-crystalline Li2IrO3 thin films are grown for the first time and exhibit a defined crystal orientation. Measurement of the dielectric function gives insight into electronic excitations that compare well with single crystal samples and related iridates. From the data, an optical energy gap of about 300 meV is obtained. For Y2Ir2O7 thin films, a possible (111) out-of-plane preferential crystal orientation is obtained. Compared to chemical solution deposition, the pulsed laser-deposited YBiO3 thin films presented here exhibit a biaxial in-plane crystal orientation up to a significantly larger film thickness. From the measured dielectric function, a direct and indirect band gap energy is determined. Their magnitude provides necessary experimental feedback for theoretical calculations of the electronic structure of YBiO3, which are used in the prediction of the novel states of matter mentioned above. After the introduction and motivation of this thesis, the second chapter reviews the current state of the science of the studied thin film materials. The following two chapters introduce the sample preparation and the employed experimental methods, respectively. Subsequently, the experimental results of this thesis are discussed for each material individually. The thesis concludes with a summary and an outlook.

The layered honeycomb lattice iridate Na2IrO3 is a novel candidate material for either a topological insulator or spin liquid. These states of matter are one possible starting point for the future realization of scalable quantum computation, but may also find application in magnetic memory or low-power electronic devices. This thesis reports on the pulsed laser deposition of high-quality heteroepitaxial (001)-oriented Na2IrO3 thin films with well-defined in-plane epitaxial relationship on 5-by-5 and 10-by-10 square millimeter single-crystalline sapphire, YAlO3 and zinc oxide substrates. Three-dimensional Mott variable range hopping is the dominant conduction mechanism between 40 and 300 K. Moreover, a signature of the proposed topological insulator phase is found in magnetoresistance by observation of the weak antilocalization effect that is associated with topological surafce states. Compared to single crystals, a smaller, 200-meV optical gap in Na2IrO3 thin films is found by Fourier-transform infrared transmission spectroscopy.

An exploration of some organic-inorganic hybrid metal fluorides and lanthanide containing metal organic frameworks (Ln-MOFs) has been carried out under ionothermal conditions. In this synthesis technique an ionic liquid (IL) or deep eutectic mixture (DES) is used as the solvent and in many cases as the provider of the organic structure directing agent. A wide range of ILs and DESs have been investigated as the reaction solvent for the synthesis of organically templated vanadium fluorides and oxyfluorides (VOFs), and initially this has proved to be successful with the isolation of 13 phases, including eight new materials. In the VOFs synthesis the IL acts as a solvent, however the DES acts as a solvent and also as a template delivery agent, where the expected template is provided by the partial breakdown of the urea derivative component. Interestingly, it has been shown that the same structure can be accessible via two different ways; either by using IL with an added templating source, or simply through the use of a DES without any other additive; since the template is provided by the in situ breakdown of the DES. The synthesis of VOFs with extended structures was achieved by the use of the hydrophobic IL 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide (EMIM Tf₂N) as the solvent. [HNC₅H₅][V₂O₂F₅] represents the first VOF with a 2D network that contains exclusively V⁴⁺. This material may be considered as arising via condensation of the previously known ladder-like chains. Furthermore, using imidazole as an added template has produced another layer material that has significant similarities to the [HNC₅H₅][V₂O₂F₅] structure, but with some key differences. Within the same system three other phases were also isolated, including two novel materials displaying the known ladder-type building units. Further investigations in the ionothermal synthesis of VOF using EMIM Tf₂N resulted in a successful synthesis of [NH₄]₂[HNC₇H₁₃][V₇O₆F₁₈], a novel material displaying a unique double layered topology featuring a S = ½ kagome type lattice of V⁴⁺ ions (d¹). Two of the V⁴⁺ based kagome sheets are pillared by V³⁺ ions to form a double layered structure templated by both ammonium and quinuclidinium cations. This compound exhibits a high degree of magnetic frustration, with significant antiferromagnetic interactions but no long range ordering was observed above 2 K. This material presents an interesting comparison to the famous Herbertsmithite, ZnCu₃(OH)₆Cl₂, and may provide an excellent candidate for realising a quantum spin liquid (QSL) ground state. Interestingly, in this system the use of EMIM Tf₂2N as a solvent produces mainly V⁴⁺-containing materials, despite the high reaction temperature (170 °C). This characteristic is unprecedented in VOFs synthesis, as rising the reaction temperature above 150 °C in other techniques (i.e. hydrothermal synthesis) would often result in further reduction of V⁴⁺ to V³⁺. Using the ionothermal technique in the synthesis of hybrid iron fluorides resulted in the isolation of three chain-type materials. Again, the IL acts as the solvent and the DES acts as the solvent and also as the template provider where the expected template is released by the partial breakdown of the urea derivative component of the DES. The synthesis of Ln-MOF using a choline chloride/ 1,3-dimethylurea deep eutectic mixture has produced three novel isostructural materials. Usually, in ionothermally prepared materials (i.e. zeolites) the urea portion of the DES is unstable and breaks down in situ to form ammonium or alkylammonium cations. In the ionothermal synthesis of Ln-MOF, 1,3-dimethyurea (DMU) remains intact and is occluded in the final structure. Using a choline chloride/ethylene glycol deep eutectic solvent led to the isolation of a Ln-MOF with interesting structural properties, however none of the DES components appeared in the final structure. These results demonstrate once more the usefulness and applicability of the ionothermal synthesis method and emphasise how this synthesis technique can be further extended and applied in the preparation of important structures with unique properties and functionalities.

Doping nonmagnetic materials is known as an effective way of investigating the properties of frustrated magnets. LiCuSbO4 is one of the simplest quasi-one dimensional spin-1/2 magnets which can be modelled with ferromagnetic(FM) nearest neighbour and antiferromagnetic (AFM) next nearest neighbour interactions. Here, doping with both non-magnetic ions, Zn, Mg, and magnetic ions, Co, is investigated. LiCu1-xMxSbO4 (M=Mg, Zn, Co 0≦x≦0.1) samples were synthesized by a ceramics process. At higher doping levels (x≧0.04), paramagnetic Curie features are observed below 4 K, however the broad peak characteristic of short range ordering at 6 K is retained. Isothermal magnetization indicates that the critical field found at 12 T in LiCuSbO4 was shifted by Zn and Mg doping. While the field is increased as the amount of Mg doping, it was increased as Zn doping in the range of 0≦x≦0.02 but decreased by x≧0.04. The trend in critical field is observed to follow that of the c lattice parameter for both Zn and Mg doping. On doping with Co2+ (S = 3/2), a low temperature Curie feature was observed from x=0.02. The value of the critical field increased on doping from (x=0) 12 T for 13.5 T (x=0.10). As for non-magnetic doping the trend in Hc has the same behaviour as the lattice parameter. The effect of doping on the pyrochlore spin ice A2B2O7 is also explored. The effect of oxygen vacancies induced by the aliovalent substitution on the B site on the crystal electric field was explored in the ceramic solid solutions. The effect of aliovalent doping on the pyrochlore A2Sn2(1-x)Sc2xO7-x (A=Ho and Dy 0≦x≦0.10) Tb2B2(1-x)Sc2xO7-x (B=Sn and Ti 0≦x≦0.05) were studied. While no dramatic changes of the saturation value of isothermal magnetization and heat capacities was observed in Dy2Sn2O7 by Sc doping in the range of 0≦x≦0.1, the saturation value of isothermal magnetization and magnetic entropy in Ho2Sn2O7 was clearly increased by Sc doping more than x=0.05, This difference could be from the difference of Kramer’s and non-Kramer’s spins between Dy and Ho, as while Dy is a Kramer’s ion and its ground state is protected, Ho is a non-Kramer’s ion and its ground state could be split. While Tb2Sn2O7 is known as quantum spin ice, Tb2Ti2O7 is known as spin liquid. A peak at 6 K of heat capacity, which is assigned as being due to a crystal electric field excitation to an excited doublet in Tb2Sn2O7 and Tb2Ti2O7 was observed in the Tb2Sn2(1-x)Sc2xO7-x sample. However in Tb2Ti2(1-x)Sc2xO7-x it was not observed. This indicates that the increased strain in the ceramic solid solution has a larger impact on the crystal electric field.

Submitted by Automa??o e Estat?stica (sst@bczm.ufrn.br) on 2017-07-17T13:08:15Z No. of bitstreams: 1 CarlenePaulaSilvaDeFarias_TESE.pdf: 2687014 bytes, checksum: a677490ff19b9514e32959228d355d32 (MD5) / Approved for entry into archive by Arlan Eloi Leite Silva (eloihistoriador@yahoo.com.br) on 2017-07-18T14:15:39Z (GMT) No. of bitstreams: 1 CarlenePaulaSilvaDeFarias_TESE.pdf: 2687014 bytes, checksum: a677490ff19b9514e32959228d355d32 (MD5) / Made available in DSpace on 2017-07-18T14:15:39Z (GMT). No. of bitstreams: 1 CarlenePaulaSilvaDeFarias_TESE.pdf: 2687014 bytes, checksum: a677490ff19b9514e32959228d355d32 (MD5) Previous issue date: 2017-04-10 / The main objective of this thesis is to investigate the competing ordered phases in the metallic heavy fermion compound URu2Si2, which displays a bodycentered tetragonal lattice. We first provide a study case of the competition between antiferromagnetic (AF) and spin liquid phases. The antiferromagnetic state is study with spin-wave theory. Whereas the spin liquid analysis has been carried out in an algebraic spin liquid representation. In the second part, we describe an effective theory for Raman scattering experiments at these particular phases. We provide insight about the hidden order phase displayed by the heavy fermion compound URu2Si2. / L?objectif central de cette th?se est d??tudier des phases ordonn?es en comp?tition dans des mat?riaux magn?tiques pr?sentant une structure cristalline t?tragonale centr?e. Ce travail est divis? en deux parties principales. Dans la premi?re, nous pr?sentons les r?sultats de notre ?tude de la comp?tition entre des ?tats ordonn?s antiferromagn?tiques et des phases liquides de spin. Nous montrons comment ces derni?res peuvent ?tre stabilis?es par la frustration g?om?trique et par une g?n?ralisation de la sym?trie de spin au groupe SU(n). Les ?tats antiferromagn?tiques sont d?crits par une th?orie d?onde de spin et l?analyse de liquide de spin est effectu?e par une repr?sentation fermionique des op?rateurs de spin. Dans la deuxi?me partie, nous d?crivons une th?orie effective pour d?rcrire des exp?riences de diffusion Raman. Nous fournissons un aper?u de la phase d?ordre cach? affich?e par le compos? de fermions lourds URu2Si2.

A very important step in the art of cooking up models for the study of natural phenomena is the identification of the relevant ingredients. Taking into account too many details will lead to an overly complicated model, not at all useful to work with, but neglecting some crucial elements will lead to an equally useless model. So it is often the case that the actual experimental situation presents unavoidable sources of local randomness, whilst the analysed phenomenon does not really rely on presence/absence of such imperfections. For some other set of phenomena, however, disorder can play a crucial role, and must be carefully taken into account. Such is for example the case in certain phases of matter, the spin-glass phase, or the many-body localised phase. In this thesis we explore disorder in both of these situations and also as a theoretical means of testing the regime of liquidity in certain two-dimensional highly frustrated magnetic models. The focus here is placed on classical Heisenberg models defined on lattices consisting of clusters all sites of which interact mutually pairwise. This natural way to introduce frustration has been known in the literature to lead to so-called Coulomb spin-liquids, the single class of classical spin-liquids acknowledged to exist so far in Heisenberg models. Here we show that in fact two different classes of classical spin-liquids can be obtained from similarly defined frustrated models. In one of these, algebraic correlations exist at $T=0$, similar to the Coulomb phase, but the system exhibits a rather different low$-T$ effective action from the Coulomb phase. In the other class, the spin-liquid has spin correlations that decay exponentially with distance, with a correlation length smaller than a lattice spacing even at $T=0$. One special effect of disorder in these models, considered in the form of dilution by non-magnetic impurities, is to nucleate local degrees of freedom, so-called orphans, which express the concomitant spin-liquid phase through their non-trivial fractionalisation. When the associated spin-liquid exhibit algebraic correlations, it is also possible to find new effective spin-glass models as an effective $T=0$ description for interactions between the orphans, leading to so-called `random Coulomb magnets'. One part of this thesis is devoted to the first study of these new models. This investigation consists mainly of Monte Carlo simulations and numerical solution of the relevant large$-n$ equations ($n$ being the number of spin components). A clear spin-glass transition for infinitely large coupling strength is determined for the case of spins with an infinite number of components. The results presented on the situation for a finite number of spin components are more of an exploratory character, and large-scale simulations with further optimization schemes to ensure equilibration are still required to locate the transition. The final investigation treated in this thesis deals with the dynamics in a quantum model with disorder displaying the many-body localized phase, where in addition a periodic drive is applied. For a certain range of driving frequencies and amplitudes, it was found recently that the many-body localized phase is robust. These pioneering studies restricted themselves to an analysis of the stability of such a phase in the long time limit, while very little was known about the dynamics towards the asymptotic fate. Our study focuses on this aspect, and analyses the different dynamical behaviors as one varies the driving parameters, so that the many-body localized phase survives or is destroyed by the driving. We discover that on the border between these two asymptotic fates, a new dynamical behavior emerges, where the system heats up at a very slow, logarithmic in time, rate. / Die Bestimmung der wichtigsten Bestandteile stellt einen sehr wichtigen Schritt in der Kunst des Erstellens von Modellen dar. Die Annahme von zu vielen Details ergibt ein sehr kompliziertes, zu nichts zu gebrauchendes Modell, doch die Vernachlässigung von bedeutenden Zusammenhängen führt ebenfalls zu einem unbrauchbaren Ergebnis. Es ist so z.B. häufig der Fall, dass ein Experiment unter dem Einfluss von unvermeindlichen lokalen Zufälligkeiten steht, die allerdings kaum einen Einfluss auf ein beobachtetes Phänomen haben. Für gewisse Phänomene spielt Unordnung jedoch eine wesentliche Rolle und sie muss sehr genau in Betracht gezogen werden. Das ist für bestimmte Phasen, wie beispielsweise Spinglas oder die Vielteilchen-Lokalisation, der Fall. In dieser Dissertation untersuchen wir ungeordnete Systeme, die solche Phasen aufweisen. Außerdem verwenden wir Unordnung als ein theoretisches Werkzeug für die Analyse von bestimmten `Spinflüssigkeiten' in zweidimensionalen Spinmodellen. Der Fokus liegt hierbei auf klassischen Heisenberg Modellen definiert auf Gittern, die aus einer Anordnung von Clustern bestehen, sodass jede einzelne paarweise Heisenberg-Wechselwirkung innerhalb eines Clusters stattfindet. Dadurch weist das System geometrische Frustration auf und in mehreren Fällen tritt eine sogennante Coulomb Spinflüssigkeit ---die bislang einzig bekannte Klasse von klassischen Spinflüssigkeit in Heisenberg Modellen--- auf. Wir zeigen, dass mindestens zwei weitere Arten von klassischen Spinflüssigkeiten in solchen Modellen zu finden sind. Für die eine Klasse sind Spinkorrelationen zu erwarten, die algebraisch mit der Entfernung bei $T=0$ abnehmen, ähnlich wie für eine Coulomb Phase. Diese neu entdeckte Spinflüssigkeit lässt sich jedoch von der Coulomb Phase durch eine neue effektive Tieftemperatur-Theorie unterscheiden. Für die andere Klasse von Spinflüssigkeiten sind die Spinkorrelationen kurzreichweitig, und selbst bei $T=0$ nehmen sie exponentiell ab, mit einer Korrelationslänge, die kleiner als ein Gitterabstand ist. Unordnung, in der Form von nicht-magnetischen Störstellen, kann lokale Freiheitsgrade entstehen lassen (diese werden in der Literatur auch als `Orphans', Waisen, bezeichnet). Die Orphans verweisen durch ihre `Fraktionierung' eindeutig auf die nicht trivialen Korrelationen der spinflüssigen Phase. Falls die Spinflüssigkeit algebraische Korrelationen aufweist, findet man auch langreichweitige Wechselwirkungen zwischen den Orphans bei $T=0$. Dies führt zu neuen Spinglasmodellen, sogenannten `Random Coulomb Magnets'. Ein Teil dieser Dissertation ist der Untersuchung solcher Modelle gewidmet. Diese Untersuchung besteht hauptsächlich aus Monte Carlo Simulationen und numerischer Lösung der relevanten Large-$n$ Gleichungen (wobei $n$ hier auf die Anzahl an Spinkomponenten hinweist). In dem Fall von Spins mit unendlich vielen Spinkomponenten können wir einen eindeutigen Spinglas Phasenübergang für eine unendlich große Kopplungsstärke bestimmen. Die entsprechenden Ergebnisse für den Fall von Spins mit einer endlichen Anzahl an Spinkomponenten sind von einem exploratorischen Charakter. Zusätzliche Simulationen, die möglicherweise weitere Optimierungsschema verwenden um Äquilibrium zu gewährleisten, sind noch von nöten um eine eindeutige Aussage über den Übergang in solchen Fällen zu treffen. Der letzte Teil dieser Dissertation widmet sich der Untersuchung der Dynamik eines ungeordneten Quantenmodells. Das ausgewählte Modell weist die sogennante Vielteilchen-lokalisierte Phase auf, und wir untersuchen insbesondere den Effekt eines periodischen Antriebs auf die Dynamik des Systems. Für eine bestimmte Auswahl der Antriebs-frequenz und -amplitude, wurde es bereits vor kurzem bewiesen, dass die Vielteilchen-lokalisierte Phase diese Störung übersteht. Unsere Studie ist darauf ausgelegt, wie sich die Dynamik des Systems durch Variation der Antriebsparameter ändert, so dass die Vielteilchen-lokalisierte Phase für lange Zeit entweder den Antrieb übersteht oder von ihm zerstört wird. Wir konnten dadurch entdecken, dass an der Grenze zwischen diesen beiden Fällen ein neues dynamisches Verhalten entsteht, bei der das System eine sehr langsame, logarithmisch mit der Zeit, Erwärmung aufweist.

In the search for novel magnetic materials, systems with strong spin-orbit coupling are a focus. 5d Ir-oxides and 4d Ru-halide, in particular, are associated in this context with a flurry of new theoretical concepts, models, and predictions, and more recently to various exotic topological states. In this thesis, we use computational quantum-chemistry methods to determine nearest-neighbor (NN) magnetic interactions in such systems. We also explore different routes to tune NN exchange couplings and provide guidelines for material design. In the first chapter, an introduction to concepts of electron correlations, spin-orbit coupling and magnetic interactions is provided. Many-body quantum chemistry methods used to determine electronic and magnetic properties of the transition metal systems in this work are outlined in the second chapter. In chapter 3, we determine multiplet-structure, magnetic g factors as well as NN magnetic interaction for the edge-shared 4d5 honeycomb lattice-based system, i.e., α-RuCl3. We find that the the magnetic anisotropy shows up in the form of bond-dependent Kitaev couplings, which defines the largest superexchange energy scale in this system. Magnetic couplings obtained by mapping the ab initio data onto an effective spin Hamiltonian are then used in the the subsequent exact diagonalization calculation to retrieve the magnetic phase diagram as a function of second and third NN coupling. Further, in chapter 4, we investigate the effects of uniform pressure and strain on the magnetic interactions in honeycomb and related lattice-based systems. We find that the Heisenberg and Kitaev terms are affected differently: for strain, in particular, the Heisenberg component decreases more rapidly than the Kitaev counterpart. This suggests a scenario where strain can stabilize a spin liquid state in such materials. In chapter 5, we discuss another factor that allows to modify magnetic couplings, i.e., the electrostatics between layered stackings with different metallic species. We examine magnetic interactions between Ir moments in H3LiIr2O6, a recently proposed Kitaev spin liquid candidate, and clarify the effect of interlayer electrostatics on the anisotropic Kitaev exchange . We show that the precise position of H+ cations between magnetically active [LiIr2O6]3− honeycomb-like layers has a strong impact on the magnitude of Kitaev interactions. In the last chapter, we examine Ir-oxides on the pyrochlore lattice. In these corner-sharing systems the NN anisotropic exchange occurs in the form of antisymmetric exchange, also known as Dzyaloshinskii-Moriya (DM) coupling. Our calculations predict that a highly unusual regime can be realized in such systems due to the vanishing NN Heisenberg interaction, making the antisymmetric DM exchange to be the dominant interaction in the oxides where the Ir-O-Ir links show bond-angles less than 125◦. We also confirm the accuracy of the employed quantum-chemistry methods by reproducing experimental data for Sm2Ir2O7.:Table of contents 1 Introduction 1 1.1 Electronic correlations 2 1.2 Crystal fields and d-level splitting 5 1.3 Spin-orbit Coupling 8 1.4 Magnetic interactions 10 1.5 Conclusions 13 2 Quantum Chemistry Methods 15 2.1 Introduction 15 2.2 Motivation for using quantum chemical approach 17 2.3 The Hartree-Fock approach 19 2.4 Multiconfigurational approach 22 2.5 Multireference configuration interaction 26 2.5.1 Recent developments towards performing FCI 27 2.6 Embedded cluster approach 28 2.7 Conclusions 30 3 Anisotropic spin interactions in α-RuCl3 31 3.1 Introduction 31 3.2 Spin-orbit ground state and excitations 33 3.2.1 Structural details .34 3.2.2 Computational details 37 3.2.3 Results and Discussions 40 3.3 Intersite exchange interactions for j=1/2 moments 44 3.3.1 Kitaev-Heisenberg model and symmetric anisotropies 45 3.3.2 Computational details 49 3.3.3 Results and Discussion 53 3.4 Conclusions 61 x Table of contents 4 Strain and pressure tuned magnetic interactions in Kitaev materials 63 4.1 Introduction 64 4.2 Qualitative analysis: Kitaev-Heisenberg model 65 4.3 Quantitative analysis: ab initio results 66 4.3.1 Computational approach 69 4.3.2 Results and discussion 70 4.4 Experimental results for pressurized α-RuCl3 74 4.4.1 Pressure induced dimerization 75 4.4.2 Ab initio calculations 76 4.5 Conclusions 78 5 Impact of inter-layer species on in-plane magnetism in H3LiIr2O6 79 5.1 Introduction 79 5.2 Structural details 81 5.3 Computational approach 82 5.4 Results and discussion 85 5.4.1 Magnetic couplings 85 5.4.2 Phase diagram and longer-range interactions 86 5.4.3 Position of H cations and effect on in-plane interactions 88 5.4.4 Angle dependence, the Kitaev limit 91 5.5 Conclusions 92 6 Anisotropic spin interactions in pyrochlore iridates 95 6.1 Introduction 95 6.2 Structural details 97 6.3 Computational details 98 6.3.1 Embedded cluster and basis sets 98 6.3.2 Quantum chemistry calculations 99 6.3.3 Effective spin model Hamiltonian 99 6.4 Results and Discussion 101 6.4.1 Magnetic couplings 101 6.4.2 Spin Dynamics 103 6.4.3 Magnetic ground state 105 6.5 Conclusions 109 Summary 111

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The study of topological phases in condensed matter physics has seen remarkable advancements, primarily focusing on systems with a well-defined bulk and boundary. However, the emergence of topological phenomena on self-similar systems, characterized by the absence of a clear distinction between bulk and boundary, presents a fascinating challenge. This thesis focuses on the topological phases on self-similar systems, shedding light on their unique properties through the lens of adiabatic charge pumping. We observe that the spectral flow in these systems exhibits striking qualitative distinctions from that of translationally invariant non-interacting systems subjected to a perpendicular magnetic field. We show that the instantaneous eigenspectra can be used to understand the quantization of the charge pumped over a cycle, and hence to understand the topological character of the system. Furthermore, we establish a correspondence between the local contributions to the Hall conductivity and the spectral flow of edge-like states. We also find that the edge-like states can be approximated as eigenstates of the discrete angular-momentum operator, with their chiral characteristics stemming from this unique perspective. We also investigate the effect of local structure on the topological phases on self-similar structures embedded in two dimensions. We study a geometry dependent model on two self-similar structures having different coordination numbers, constructed from the Sierpinski gasket. For different non-spatial symmetries present in the system, we numerically study and compare the phases on both structures. We characterize these phases by the localization properties of the single-particle states, their robustness to disorder, and by using a real-space topological index. We find that both structures host topologically nontrivial phases and the phase diagrams are different on the two structures, emphasizing the interplay between non-spatial symmetries and the local structure of the self-similar unit in determining topological phases. Furthermore, we demonstrate the presence of topologically ordered chiral spin liquid on fractals by extending the Kitaev model to the Sierpinski Gasket. We show a way to perform the Jordan-Wigner transformation to make this model exactly solvable on the Sierpinski Gasket. This system exhibits a fractal density of states for Majorana modes and showcases a transition from a gapped to a gapless phase. Notably, the gapped phase features symmetry-protected Majorana corner modes, while the gapless phase harbors robust zero-energy and low-energy self-similar Majorana edge-like modes. We also study the vortex excitations, characterized by remarkable localization properties even in small fractal generations. These localized excitations exhibit anyonic behavior, with preliminary calculations hinting at their fundamental differences from Ising anyons observed in the Kitaev model on a honeycomb lattice.