<p>Lithium ion insertion into electrode materials is commonly used in rechargeable battery technology. The insertion implies changes in both the crystal structure and the electronic structure of the electrode material. Side-reactions may occur on the surface of the electrode, which is exposed to the electrolyte and form a solid electrolyte interface (SEI). The understanding of these processes is of great importance for improving battery performance. The chemical and physical properties of water and alcohols are complicated by the presence of strong hydrogen bonding. Various experimental techniques have been used to study geometrical structures and different models have been proposed to view the details of how these liquids are geometrically organized by hydrogen bonding. However, very little is known about the electronic structure of these liquids, mainly due to the lack of suitable experimental tools.</p><p>This thesis addresses the electronic structure of liquids and lithium battery materials using resonant inelastic X-ray scattering (RIXS) at high brightness synchrotron radiation sources. The electronic structure of battery electrodes has been probed, before and after lithiation, studying the doping of electrons into the host material. The chemical composition of the SEI on cycled graphite electrodes was determined. The local electronic structure of water, methanol and mixtures of the two have been examined using a special liquid cell. Results from the study of liquid water showed a strong influence on the 3a₁ molecular orbital and orbital mixing between molecules upon hydrogen bonding. The study of methanol showed the existence of ring and chain formations in the liquid phase and the dominating structures are formed of 6 and 8 molecules. Upon mixing of the two liquids, a segregation at the molecular level was found and the formation of new structures, which could explain the unexpected low increase of the entropy.</p>

This thesis addresses the electronic structure of vanadium and copper oxides using soft X-ray absorption (SXA) spectroscopy and resonant inelastic X-ray scattering (RIXS) at high brightness synchrotron radiation sources. In RIXS incident photons, tuned to the energy of specific absorption resonances, are inelastically scattered leaving behind a low energy valence excitation in the system studied. Effects of electron localization are reflected by the occurrence of low-energy excitations in form of dd- and charge-transfer excitations that are modelled by cluster calculations. Band-like states are dominating when the intermediate core excited state is delocalized. RIXS at V 2p and O 1s resonances has been used to study the electronic structure of the monovalent vanadium oxides VO2 and V2O3, and of the mixed valence compounds, NaV2O5 and V6O13. For NaV2O5 and V6O13 significant contributions from localized low-energy excitations reflect the partly localized character of their valence band electronic structure, whereas VO2 and V2O3 appear mostly as band-like. Effects of carrier doping are addressed for the case of Mo doping into VO2 and reveal a quasi-rigid band behavior. In the cases of VO2 and V6O13 the temperature dependent metal-insulator transition could be monitored by following the spectral evolution of bands originating from V 3d and V 3d - O2p hybridized states. For Na2V3O7 nanotubes it was possible to selectively probe states from the apical and the basal oxygen sites of VO5 pyramids that constitute these nanotubes. Furthermore, the RIXS technique has been demonstrated to be highly valuable in characterizing the charge transfer processes that accompany lithium insertion into vanadium oxide battery cathodes. Finally, for insulating cuprates RIXS at O 1s, Cu 3p and Cu 3s resonances has been recorded at high-resolution for the detailed investigation of crystal field excitations.

Lithium ion insertion into electrode materials is commonly used in rechargeable battery technology. The insertion implies changes in both the crystal structure and the electronic structure of the electrode material. Side-reactions may occur on the surface of the electrode, which is exposed to the electrolyte and form a solid electrolyte interface (SEI). The understanding of these processes is of great importance for improving battery performance. The chemical and physical properties of water and alcohols are complicated by the presence of strong hydrogen bonding. Various experimental techniques have been used to study geometrical structures and different models have been proposed to view the details of how these liquids are geometrically organized by hydrogen bonding. However, very little is known about the electronic structure of these liquids, mainly due to the lack of suitable experimental tools. This thesis addresses the electronic structure of liquids and lithium battery materials using resonant inelastic X-ray scattering (RIXS) at high brightness synchrotron radiation sources. The electronic structure of battery electrodes has been probed, before and after lithiation, studying the doping of electrons into the host material. The chemical composition of the SEI on cycled graphite electrodes was determined. The local electronic structure of water, methanol and mixtures of the two have been examined using a special liquid cell. Results from the study of liquid water showed a strong influence on the 3a1 molecular orbital and orbital mixing between molecules upon hydrogen bonding. The study of methanol showed the existence of ring and chain formations in the liquid phase and the dominating structures are formed of 6 and 8 molecules. Upon mixing of the two liquids, a segregation at the molecular level was found and the formation of new structures, which could explain the unexpected low increase of the entropy.

Les oxydes d’iridium (iridates) ont attiré particulière attention au cours de la dernière décennie grâce à l’identification d’un état isolant de Mott induit par l’action conjointe du champ cristallin, de la corrélation électronique et du couplage spin-orbite. Cet état a été intensément investigué et des phases et excitations nouvelles ont été prédites théoriquement et aussi individuées expérimentalement. Sans doute, la diffusion inélastique résonante de rayons X (RIXS) est l’une des techniques les plus adoptée pour mesurer les excitations à basse énergie des iridates. En effet, la section efficace relativement large de la spectroscopie RIXS au seuil L3 de l’iridium et la bonne résolution en énergie ont encouragé l’emploi de cette technique. Cette thèse se pose un double objectif : concevoir des développements instrumentaux ayant pour but d’améliorer les possibilités offertes par la spectroscopie RIXS, et appliquer le RIXS afin d’étudier la physique à basse énergie de certains iridates.Le principal projet de développement instrumental est un nouveau spectromètre RIXS avec résolution en polarisation. L’analyse de la polarisation des rayons X diffusés permet d’obtenir des informations sur la symétrie et donc la nature des excitations. Cependant, elle est peu employée à cause de problèmes techniques qui naissent quand l’on veut préserver aussi la résolution en énergie et l’efficience du spectromètre. Même si le polarimètre RIXS projeté n’est pas encore disponible, le schéma optique a été vérifié et validé. Le polarimètre aura une résolution en énergie et une efficience équivalentes à celles des spectromètres RIXS courants. Le second développement technique comprend l’équipement permettant de réaliser des mesures RIXS à basse température et haute pression. Ces équipements ont permis d’investiguer l’évolution en pression des excitations magnétique du composé Sr3Ir2O7 en dessous de la température de Néel et jusqu’au 12 GPa. Les mesures peuvent aider l’affinage des modèles magnétiques courants pour ce système. Ces mesures démontrent que les excitations magnétiques peuvent être acquises en haute pression par la spectroscopie RIXS, démontrant ainsi la possible utilisation de cette technique dans ce nouveau domaine.Cette thèse comprend aussi des ultérieurs travails expérimentaux. Le premier considère le composé CaIrO3, dont la structure cristalline est constituée par des octaèdres partageant un sommet et une arête dans deux directions orthogonales. Du coup, les interactions magnétiques sont très différentes selon la direction cristallographique. Spécifiquement, la suppression du couplage de type Heisenberg dans la direction où les octaèdres partagent une arête produit des interactions magnétiques principalement unidimensionnelles. La caractéristique de ceux-ci est la présence d’un continuum d’excitations avec une dépendance en énergie et quantité de mouvement typique, qui a été révélé par la spectroscopie RIXS. Les excitations électroniques de CaIrO3 ont aussi des caractéristiques propres. Enfin, j’ai étudié les propriétés électroniques du composé Rb2[IrF6]. Des calculs récents proposaient que ce système possède un état d’isolant de Mott similairement aux oxydes d’iridium. Les mesures RIXS ont aidé à éclairer les propriétés électroniques de ce composé. La solidité des propriétés électroniques a été vérifiée par rapport à la substitution du métal alcalin ou de l’halogène, et à l’application de pression.Cette thèse accroit l’importance de l’utilisation de la spectroscopie RIXS dans des domaines qui étaient précédemment inexplorés. L’analyse de la polarisation des rayons X diffusés sera avantageuse dans les cas où la nature des excitations ne peut être établie sans ambiguïté. L’équipement développé pour réaliser les mesures RIXS en conditions extrêmes permet d’étudier la dynamique électronique et magnétique dans des phases de la matière inaccessibles jusqu’à aujourd’hui. / Iridium oxides (iridates) have raised notable attention in the last decade due to the identification of a Mott insulating state realized by the joint action of crystal field, electron correlation, and spin-orbit coupling. Such state has been intensively investigated and novel quantum phases and excitations have been theoretically predicted and experimentally found. Undoubtedly, one of the most employed techniques to elucidate the low-energy physics of iridates is resonant inelastic X-ray scattering (RIXS). At the iridium L3 edge, it benefits from a particularly good energy resolution, which matches the energy scales of the relevant excitations, and from a favorable inelastic cross-section. The aim of the present thesis is twofold: conceive challenging instrumental upgrades that contribute to the advancement of the technique itself, and apply RIXS to inspect the magnetic and electronic properties of selected iridates.The main instrumental development concerns the design of a new RIXS spectrometer with polarization resolution. Polarization analysis of the scattered X-rays provides useful information about the symmetry and thus the nature of an excitation. However, it is rather unexploited because of severe technical challenges when energy resolution and efficiency must be preserved. The designed RIXS spectrometer with polarization analysis capabilities is still under construction, however the optical scheme has been validated by preliminary tests. Full polarization analysis is expected without degradation of energy resolution or efficiency with respect to current state-of-the-art RIXS spectrometers. Additional technical developments include sample-environment equipment to perform RIXS experiments in low-temperature and high-pressure conditions. The equipment has been successfully utilized to investigate the magnetic dynamics of the bilayer-perovskite Sr3Ir2O7 below its Néel temperature and up to 12 GPa. Our measurements provide additional observations that may sharpen the challenge to theoretical understanding of the magnetic dynamics of this material. Moreover, we demonstrate for the first time that RIXS experiments of the magnetic dynamics can be extended to unexplored thermodynamic conditions.Besides instrumental advances, additional experimental work has been carried out in order to study the magnetic and electronic excitations of the post-perovskite CaIrO3. Owing to its peculiar crystal structure, featuring both edge- and corner-sharing octahedra, the magnetic interactions of CaIrO3 are very different along orthogonal directions. In particular, the inhibition of the Heisenberg coupling along the edge-sharing direction induces one-dimensional magnetic behavior with characteristic fractional spinon-like excitations, which have been detected by RIXS. Electronic excitations are also found to have particular properties. Finally, I have focused on the electronic structure of Rb2[IrF6], which was theoretically predicted to realize a Mott insulating state similar to the one of iridium oxides. RIXS measurements helped to elucidate the electronic properties of this compound. The robustness of the electronic state has been tested against substitutions of the alkali metal and halogen, and application of physical pressure.The present work extends the potential of the RIXS technique to domains previously unexplored, i.e. polarization analysis of the scattered X-rays and high-pressure low-temperature experiments. I hope that the instrumental upgrades and applications of RIXS discussed in this thesis will further promote the technique as a powerful and reliable tool to characterize elementary excitations in correlated-electron systems.

Les propriétés physiques intriguantes présentées dans certains oxydes complexes de métaux de transition sont attractives non seulement pour la recherche fondamentale, mais pour les applications, par exemple, la supraconductivité, la magnétorésistance colossale, la multiferroïcité. La forte corrélation électronique est à l'origine de ces comportements.La thèse contribue à la fois à l'effort expérimental de détermination de la structure électronique des systèmes fortement corrélés et à l'analyse critique des modèles théoriques les décrivant. Expérimentalement, le travail a porté sur la diffusion inélastique résonante des rayons X pour déterminer les excitations électroniques de basse énergie de l'état fondamental (excitations d-d, transfert de charge, etc.). Les expériences ont été effectuées sur la ligne de lumière SEXTANTS du synchrotron SOLEIL (France), en utilisant le spectromètre AERHA avec un haut pouvoir résolvant. L'analyse des résulats a été focalisée sur la détermination du champ cristallin des métaux de transition en jeu en utilisant la théorie des multiplets avec champ cristallin.Deux systèmes ont été étudiés: les composés multiferroïques RMnO3 (R = Tb, Dy) et un isolant de Mott ferromagnétique Lu2V2O7. / The intriguing physical properties presented in some complex oxides of transition metals draw attention not only in fundamental research but also in applications, for instance, superconductivity, colossal magnetoresistance, multiferroicity. The strong electronic correlation is at the origin of these behaviours. The thesis is a contribution to both the experimental effort to determine the electronic structure of strongly correlated systems and the critical assesment of the theoretical models describing them. Experimentally, the work of is devoted to the investigations of the low-energy excitations (d-d excitations, charge transfer, …) of the ground state by resonant inelastic x-ray scattering. The experiments have been performed on the SEXTANTS beamline of SOLEIL synchrotron (France) using the high resolving power AERHA spectrometer. The analysis of the data has been focused on the determination of the the crystal field of the transition metal involved using the crystal field multiplets theory.Two systems have been investigated: the multiferroics RMnO3 (R = Tb, Dy) and the ferromagnetic Mott insulator Lu2V2O7.

This thesis explores and expands upon theoretical means of quantifying a number of nonlinear spectroscopies, including two-photon absorption, resonant-inelastic x-ray scattering, Jones birefringence, and magnetic circular dichroism. On top of that, detailed information is given for the derivation and program implementation of damped cubic response functions. Complex-valued cubic response functions have been implemented in the quantum chemistry package DALTON, based on working equations formulated for an approximate-state wave function. An assessment of the implementation, such that for small frequencies the second-order hyperpolarizability should behave according to an analytic function that depends quadratically on the optical frequencies. It is demonstrated how two-photon absorption (TPA) can be described either through second-order transition moments or via the damped cubic response function. A few calculated TPA profiles are produced for a set of smaller molecules, in order to display the capability of the cubic response function in the x-ray frequency region. Resonance-inelastic x-ray scattering (RIXS) is explored in a similar manner as two-photon absorption. It is shown how the second-order hyperpolarizability can represent RIXS in the limit of intermediate-state and final-state resonances. Complications emerging from the complex dispersion of the hyperpolarizability are discussed. Moreover, linear birefringences, with focus on the Jones birefringence, are investigated for noble gases, monosubstituted benzenes, furan homologues, and a pure acetonitrile liquid. A linear relation between the Jones birefringence and the empirical para-Hammett constant as well as the permanent electric dipole moment is presented. Estimations of three linear birefringences --- Kerr, Cotton--Mouton, and Jones ---are obtained by averaging over a set of liquid snapshots. The Jones effect for acetonitrile turns out to be unusually large inmparison to the other two investigated linear birefringences. The final chapter of the thesis investigates magnetically induced circular dichroism (MCD). A question regarding relative stability of the first set of excited states for DNA-related molecular systems is resolved through MCD by exploiting the signed nature of circular dichroisms. Furthermore, to what extent solvent contributions affect MCD spectra is explored. The effect on uracil MCD spectrum due to thionation is studied, for which the degree of redshifting for systems 2-thiouracil and 4-thiouracil can be seen to be addative as compared to the 2,4-dithiouracil system. / <p>QC 20171129</p>

Um neue Halbleiter-Bauelemente zu entwickeln und die Effizienz bereits existierender zu verbessern, müssen neue Materialien erkundet und untersucht werden. Für Anwendungen in Hochleistungselektronik und UV-Optoelektronik ist Ga2O3 mit seiner ultra-weiten Bandlücke von 4.8 eV ein vielversprechender Kandidat. Diese Anwendung haben zu wachsendem Interesse an seinen fundamentalen elektronischen und optischen Eigenschaften geführt. Diese Dissertation präsentiert eine umfassende ab initio-Untersuchung der elektronischen Anregungen in Ga2O3, um zu dem Verständnis dieser fundamentalen Eigenschaften beizutragen. Die Arbeit besteht aus zwei Teilen: Im ersten Teil präsentieren wir eine Vielteilchen-Störungstheorie Methode zur konsistenten Berechnung der neutralen Anregungen von Valenz- und Kernelektronen in kristallinen Halbleitern. Diese ermöglicht die präzise Berechnung von Absorptions- und Streuungsspektren vom optischen bis zum Röntgenbereich. Zusätzlich präsentieren wir einen neuartigen Ausdruck für resonante inelastische Röntgenstreuung (RIXS) innerhalb unseres Vielteilchen-Formalismus, der eine detaillierte Analyse dieser Streuung erlaubt. Mit ausgewählten Beispielen demonstrieren wir das Potential unserer Implementation, die Spektren dieser verschiedenen spektroskopischen Methoden zu berechnen, zu analysieren und zu interpretieren. Im zweiten Teil der Dissertation verwenden wir unsere Methode, um die Anregungen der Valenzelektronen, sowie der Ga 1s-, Ga 2p- und O 1s-Elektronen in Ga2O3 zu berechnen. Wir finden ausgeprägte Unterschiede in den diversen Röntgenabsorptionsspektren von Ga2O3 -Polymorphen, die von der unterschiedlichen lokalen elektronischen Struktur stammen. Wir bestimmen die Zusammensetzung der Valenz- und Kernanregungen und analysieren ihre Signatur in den verschiedenen Absorptions- und Streuungsspektren. Abschließend demonstrieren wir wie RIXS einen zusätzlichen Blickwinkel auf die Valenz- und Kernanregungen und deren Wechselwirkungen ermöglicht. / To develop new semiconductor devices and improve the performance of existing ones, the exploration and understanding of novel materials is required. With an ultra-wide band gap of around 4.8 eV, Ga2O3 is a promising candidate for applications in UV-optoelectronics and power electronics. These applications have led to an increasing interest in its fundamental electronic and optical properties. In this thesis, we present a comprehensive first-principles study of the electronic excitations of Ga2O3 to contribute to the understanding of these fundamental properties. The thesis consists of two parts: In the first part, we present an all-electron many-body perturbation theory (MBPT) approach for consistent calculations of neutral core and valence excitations. It enables accurate calculation of absorption and inelastic scattering spectra in the optical, UV, and x-ray region. While these spectroscopic techniques probe either the valence or core excitations, resonant inelastic x-ray scattering (RIXS) reveals the interplay between the two. We present a novel expression for the RIXS cross section within our all-electron many-body formalism that allows for a detailed analysis of this interplay. We demonstrate the capability of our implementation to compute, analyze, and interpret the different spectroscopic techniques with selected examples of prototypical insulators. In the second part, we apply our approach to study valence excitations, as well as excitations of various core states, i.e. the gallium 1s, gallium 2p, and oxygen 1s states in Ga2O3 . Comparing the core spectra of Ga2O3 polymorphs, we find distinct differences that originate from their local environments. We determine the composition of valence and core excitons, and analyze their signatures in the various absorption and scattering spectra. Finally, we demonstrate how RIXS can be employed to provide a different viewpoint on the core and valence excitations and unravel the interplay between them.

Quantum spin liquids (QSLs) are strongly correlated systems displaying fascinating phenomena like long-range entanglement and fractionalized excitations. The research on these states has since its beginning followed trends generated by the synthesis of new compounds and the construction of new theoretical tools. In coherence with this history, a manifold of new results about QSLs were established during the past decade due to studies on the integrable Kitaev model on the honeycomb lattice. This j = 1/2 model displays bond-dependent and anisotropic exchanges that are essential to stabilize its QSL ground state with Majorana fermion excitations and emergent Z2 gauge field. Even more interestingly, this model is relevant to understand the magnetism of a certain class of 4/5d5 Mott insulators with specific lattice constraints, t2g orbital degeneracy and strong spin-orbit coupling (SOC). This mechanism defining these so-called Kitaev materials can be applied to similar compounds based on transition metal ions in different electronic configurations. In this thesis, I investigate minimal models for two types of 4/5d1 Mott insulators: the ones on the ordered double perovskite structure (ODP) and the ones isostructural to the Kitaev materials. Their effective models generically show bond-dependent and anisotropic interactions involving multipoles of an effective j = 3/2 angular momentum. Such degrees of freedom are conveniently written in terms of pseudospin s and pseudo-orbital &tau; operators resembling spin and orbital operators of Kugel-Khomskii models with twofold orbital degeneracy. Despite their anisotropy, the two realistic models display continuous global symmetries in the limit of vanishing Hund\'s coupling enhancing quantum fluctuations and possibly stabilizing a QSL phase. Parton mean-field theory was used to propose fermionic QSLs that will be called quantum spin-orbital liquids (QSOLs) due their dependence with s and &tau;. On ODPs, I studied a chiral QSOL with Majorana fermion excitations and a gapless spectrum characterized by nodal lines along the edges of the Brillouin zone. These nodal lines are topological defects of a non-Abelian Berry connection and the system exhibits dispersing surface states. Several experimental responses of the chiral QSOL within the mean-field approximation are compared with the experimental data available for the spin liquid candidate Ba2YMoO6. Moreover, based on a symmetry analysis, I discuss the operators involved in resonant inelastic X-ray scattering (RIXS) amplitudes for 4/5d1 Mott insulators and show that the RIXS cross sections allow one to selectively probe pseudospin and pseudo-orbital degrees of freedom. For the chiral spin-orbital liquid in particular, these cross sections provide information about the spectrum for different flavors of Majorana fermions. The model for materials isostructural to the Kitaev materials has an emergent SU(4) symmetry that is made explicit by means of a Klein transformation on pseudospin degrees of freedom. The model is known to stabilize a QSOL on the honeycomb lattice and instigated the investigation of QSOLs on a generalization of this lattice to three dimensions. Parton mean-field theory was used once again to propose the liquid states, and a variational Monte Carlo (VMC) method was used to compute the energies of the projected wave functions. The numerical results show that the lowest-energy QSOL corresponds to a zero-flux state with a Fermi surface of four-color fermionic partons. Further VMC computations also revealed that this state is stable against formation of plaquette ordering (tetramerization). The energy of this QSOL is highly competitive even when Hund\'s coupling induced perturbations are included, as shown by comparison with simple ordered states. Extensions and perspectives for future work are discussed in the end of this thesis. / Líquidos de spin quânticos (QSLs) são sistemas fortemente correlacionados que apresentam fenômenos fascinantes como emaranhamento de longo alcance e excitações fracionárias. A pesquisa a respeito destes estados seguiu tendências geradas pela síntese de novos compostos e construção de novas técnicas teóricas desde seu princípio. Coerentemente com essa história, uma variedade de novos resultados a respeito de líquidos de spin foram estabelecidos na última década graças a estudos feitos sobre o modelo integrável de Kitaev na rede colmeia. Este modelo de spins j = 1/2 apresenta interações de troca anisotrópicas e direcionalmente dependentes que são essenciais para estabilizar um estado fundamental do tipo QSL com férmions de Majorana e campo de gauge Z2 emergente. Ainda mais interessante, este modelo é relevante para se entender o magnetismo de uma certa classe de isolantes de Mott baseados em metais de transição na configuração 4/5d5 em redes específicas, degenerescência orbital t2g e acoplamento spin-órbita forte (SOC). Esse mecanismo que define os chamados materiais do tipo Kitaev podem ser aplicados a compostos baseados em metais de transição em configurações eletrônicas diferentes. Nesta tese, eu investigo modelos mínimos para dois tipos de isolantes de Mott do tipo 4/5d1: os que se apresentam na estrutura perovskita dupla ordenada (ODP) e os isostruturais aos materiais do tipo Kitaev. Seus modelos efetivos genericamente apresentam interações multipolares anisotrópicas e direcionalmente dependentes de um momento angular efetivo j = 3/2. Estes graus de liberdade são convenientemente escritos em termos de operadores de pseudospin s e pseudo-orbital &tau; semelhantes a operadores de spin e orbital de modelos do tipo Kugel-Khomskii com orbitais duplamente degenerados. A despeito da anisotropia, esses dois modelos realísticos apresentam simetrias globais contínuas no limite de acoplamento de Hund nulo que incrementam flutuações quânticas e possivelmente estabilizam uma fase do tipo QSL. A teoria de campo médio com partons foi usada para propor QSLs fermiônicos que serão chamados de líquidos spin-orbitais quânticos (QSOLs) devido à dependência deles com s e &tau;. Em ODPs, eu estudei um líquido de spin quiral com excitações do tipo férmion de Majorana e um espectro sem gap caracterizado por linhas nodais ao longo das arestas da zona de Brillouin. Essas linhas nodais são defeitos topológicos de uma conexão de Berry não-abeliana e o sistema apresenta estados de superfície dispersivos. Várias respostas experimentais foram calculadas para o QSOL quiral dentro da aproximação de campo médio e comparadas com os dados experimentais disponíveis para o candidato a líquido de spin Ba2YMoO6. Além disso, baseado em uma análise de simetria, discuto os operadores envolvidos nas amplitudes de espalhamento de raios-x ressonante para isolantes de Mott na configuração 4/5d1 e mostro que seções de choque de RIXS permitem estudar seletivamente os graus de liberdade de pseudospins e pseudo-orbitais. Para o caso particular do líquido spin-orbital quiral, essas seções de choque nos fornecem informações sobre o espectro de diferentes sabores de férmions de Majorana. Esse modelo possui uma simetria SU(4) emergente que é tornada explícita através de uma transformações de Klein nos graus de liberdade de pseudospin. Sabe-se que este modelo estabiliza um QSOL na rede colmeia, o que instigou uma investigação de QSOLs na generalização desta rede em três dimensões. A teoria de campo médio com partons foi usada novamente para propor estes líquidos quânticos, e o método de Monte Carlo Variacional (VMC) foi usado para calcular as energias das funções de onda projetadas. Os resultados numéricos mostraram que o QSOL de menor energia corresponde a um estado de fluxo-zero com superfície de Fermi envolvendo partons fermiônicos de quatro cores. Cálculos adicionais com VMC também demonstraram que este estado é estável à formação de ordem de plaquetas (tetramerização). A energia deste QSOL é altamente competitiva mesmo quando perturbações induzidas pelo acoplamento de Hund são incluídas, o que é mostrado através da comparação com estados ordenados simples. Extensões e perspectivas para trabalhos futuros são discutidas no final desta tese.

Quantum spin liquids (QSLs) are strongly correlated systems displaying fascinating phenomena like long-range entanglement and fractionalized excitations. The research on these states has since its beginning followed trends generated by the synthesis of new compounds and the construction of new theoretical tools. In coherence with this history, a manifold of new results about QSLs were established during the past decade due to studies on the integrable Kitaev model on the honeycomb lattice. This j = 1/2 model displays bond-dependent and anisotropic exchanges that are essential to stabilize its QSL ground state with Majorana fermion excitations and emergent Z2 gauge field. Even more interestingly, this model is relevant to understand the magnetism of a certain class of 4/5d5 Mott insulators with specific lattice constraints, t2g orbital degeneracy and strong spin-orbit coupling (SOC). This mechanism defining these so-called Kitaev materials can be applied to similar compounds based on transition metal ions in different electronic configurations. In this thesis, I investigate minimal models for two types of 4/5d1 Mott insulators: the ones on the ordered double perovskite structure (ODP) and the ones isostructural to the Kitaev materials. Their effective models generically show bond-dependent and anisotropic interactions involving multipoles of an effective j = 3/2 angular momentum. Such degrees of freedom are conveniently written in terms of pseudospin s and pseudo-orbital &tau; operators resembling spin and orbital operators of Kugel-Khomskii models with twofold orbital degeneracy. Despite their anisotropy, the two realistic models display continuous global symmetries in the limit of vanishing Hund\'s coupling enhancing quantum fluctuations and possibly stabilizing a QSL phase. Parton mean-field theory was used to propose fermionic QSLs that will be called quantum spin-orbital liquids (QSOLs) due their dependence with s and &tau;. On ODPs, I studied a chiral QSOL with Majorana fermion excitations and a gapless spectrum characterized by nodal lines along the edges of the Brillouin zone. These nodal lines are topological defects of a non-Abelian Berry connection and the system exhibits dispersing surface states. Several experimental responses of the chiral QSOL within the mean-field approximation are compared with the experimental data available for the spin liquid candidate Ba2YMoO6. Moreover, based on a symmetry analysis, I discuss the operators involved in resonant inelastic X-ray scattering (RIXS) amplitudes for 4/5d1 Mott insulators and show that the RIXS cross sections allow one to selectively probe pseudospin and pseudo-orbital degrees of freedom. For the chiral spin-orbital liquid in particular, these cross sections provide information about the spectrum for different flavors of Majorana fermions. The model for materials isostructural to the Kitaev materials has an emergent SU(4) symmetry that is made explicit by means of a Klein transformation on pseudospin degrees of freedom. The model is known to stabilize a QSOL on the honeycomb lattice and instigated the investigation of QSOLs on a generalization of this lattice to three dimensions. Parton mean-field theory was used once again to propose the liquid states, and a variational Monte Carlo (VMC) method was used to compute the energies of the projected wave functions. The numerical results show that the lowest-energy QSOL corresponds to a zero-flux state with a Fermi surface of four-color fermionic partons. Further VMC computations also revealed that this state is stable against formation of plaquette ordering (tetramerization). The energy of this QSOL is highly competitive even when Hund\'s coupling induced perturbations are included, as shown by comparison with simple ordered states. Extensions and perspectives for future work are discussed in the end of this thesis. / Líquidos de spin quânticos (QSLs) são sistemas fortemente correlacionados que apresentam fenômenos fascinantes como emaranhamento de longo alcance e excitações fracionárias. A pesquisa a respeito destes estados seguiu tendências geradas pela síntese de novos compostos e construção de novas técnicas teóricas desde seu princípio. Coerentemente com essa história, uma variedade de novos resultados a respeito de líquidos de spin foram estabelecidos na última década graças a estudos feitos sobre o modelo integrável de Kitaev na rede colmeia. Este modelo de spins j = 1/2 apresenta interações de troca anisotrópicas e direcionalmente dependentes que são essenciais para estabilizar um estado fundamental do tipo QSL com férmions de Majorana e campo de gauge Z2 emergente. Ainda mais interessante, este modelo é relevante para se entender o magnetismo de uma certa classe de isolantes de Mott baseados em metais de transição na configuração 4/5d5 em redes específicas, degenerescência orbital t2g e acoplamento spin-órbita forte (SOC). Esse mecanismo que define os chamados materiais do tipo Kitaev podem ser aplicados a compostos baseados em metais de transição em configurações eletrônicas diferentes. Nesta tese, eu investigo modelos mínimos para dois tipos de isolantes de Mott do tipo 4/5d1: os que se apresentam na estrutura perovskita dupla ordenada (ODP) e os isostruturais aos materiais do tipo Kitaev. Seus modelos efetivos genericamente apresentam interações multipolares anisotrópicas e direcionalmente dependentes de um momento angular efetivo j = 3/2. Estes graus de liberdade são convenientemente escritos em termos de operadores de pseudospin s e pseudo-orbital &tau; semelhantes a operadores de spin e orbital de modelos do tipo Kugel-Khomskii com orbitais duplamente degenerados. A despeito da anisotropia, esses dois modelos realísticos apresentam simetrias globais contínuas no limite de acoplamento de Hund nulo que incrementam flutuações quânticas e possivelmente estabilizam uma fase do tipo QSL. A teoria de campo médio com partons foi usada para propor QSLs fermiônicos que serão chamados de líquidos spin-orbitais quânticos (QSOLs) devido à dependência deles com s e &tau;. Em ODPs, eu estudei um líquido de spin quiral com excitações do tipo férmion de Majorana e um espectro sem gap caracterizado por linhas nodais ao longo das arestas da zona de Brillouin. Essas linhas nodais são defeitos topológicos de uma conexão de Berry não-abeliana e o sistema apresenta estados de superfície dispersivos. Várias respostas experimentais foram calculadas para o QSOL quiral dentro da aproximação de campo médio e comparadas com os dados experimentais disponíveis para o candidato a líquido de spin Ba2YMoO6. Além disso, baseado em uma análise de simetria, discuto os operadores envolvidos nas amplitudes de espalhamento de raios-x ressonante para isolantes de Mott na configuração 4/5d1 e mostro que seções de choque de RIXS permitem estudar seletivamente os graus de liberdade de pseudospins e pseudo-orbitais. Para o caso particular do líquido spin-orbital quiral, essas seções de choque nos fornecem informações sobre o espectro de diferentes sabores de férmions de Majorana. Esse modelo possui uma simetria SU(4) emergente que é tornada explícita através de uma transformações de Klein nos graus de liberdade de pseudospin. Sabe-se que este modelo estabiliza um QSOL na rede colmeia, o que instigou uma investigação de QSOLs na generalização desta rede em três dimensões. A teoria de campo médio com partons foi usada novamente para propor estes líquidos quânticos, e o método de Monte Carlo Variacional (VMC) foi usado para calcular as energias das funções de onda projetadas. Os resultados numéricos mostraram que o QSOL de menor energia corresponde a um estado de fluxo-zero com superfície de Fermi envolvendo partons fermiônicos de quatro cores. Cálculos adicionais com VMC também demonstraram que este estado é estável à formação de ordem de plaquetas (tetramerização). A energia deste QSOL é altamente competitiva mesmo quando perturbações induzidas pelo acoplamento de Hund são incluídas, o que é mostrado através da comparação com estados ordenados simples. Extensões e perspectivas para trabalhos futuros são discutidas no final desta tese.