Context: Slivan (2002) determined spin state of ten asteroids in the Koronis family. Surprisingly, all four asteroids with prograde sense of rotation were shown to have spin axes nearly parallel in the inertial space. All asteroids with retrograde sense of rotation had large obliquities and rotation periods either short or long. It was shown that Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effect can explain all these peculiar facts. In particular, it drives spin axes of the prograde rotators to be captured in a secular spin-orbital resonance known as Cassini state 2. Vokrouhlický et al. (2002) dubbed these configurations "Slivan states". Aims: A question arises whether Slivan states could exist also in other regions of the main asteroid belt, in particular its inner part, where observations are most easily obtained. Here, however, dynamical difficulties arise due to convergence of the proper frequency s and the planetary frequency s6. We investigate possibilities of a long-term stable capture in the Slivan state in the inner part of the main belt. Method: We used SWIFT integrator to determine orbital evolution of selected asteroids in the inner part of the main belt. In the case of 20 Massalia, we observed the asteroid in 2011, and used these new data to help better solve the rotation state using the...

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Ce mémoire est une partie d’un programme de recherche qui étudie la superintégrabilité des systèmes avec spin. Plus particulièrement, nous nous intéressons à un hamiltonien avec interaction spin-orbite en trois dimensions admettant une intégrale du mouvement qui est un polynôme matriciel d’ordre deux dans l’impulsion. Puisque nous considérons un hamiltonien invariant sous rotation et sous parité, nous classifions les intégrales du mouvement selon des multiplets irréductibles de O(3). Nous calculons le commutateur entre l’hamiltonien et un opérateur général d’ordre deux dans l’impulsion scalaire, pseudoscalaire, vecteur et pseudovecteur. Nous donnons la classification complète des systèmes admettant des intégrales du mouvement scalaire et vectorielle. Nous trouvons une condition nécessaire à remplir pour le potentiel sous forme d’une équation différentielle pour les cas pseudo-scalaire et pseudo-vectoriel. Nous utilisons la réduction par symétrie pour obtenir des solutions particulières de ces équations. / This thesis is part of a research program studying superintegrable systems with spin. In particular, we consider a Hamiltonian with a spin-orbital interaction in three dimensions admitting an integral of motion that is a matrix polynomial second order in the momenta. Since we are considering a Hamiltonian which is invariant under rotation and parity, we classify the integrals of motion into irreducible O(3) multiplets. We obtain the commutator of the Hamiltonian with the scalar, pseudoscalar, vector and axial vector operators. We provide a complete classification for the scalar and vector cases. We find the necessary condition for superintegrability on the potential as a differential equation. We use symmetry reduction methods to obtain particular solutions of this equation.

This thesis presents details of x-ray and neutron scattering experiments used to probe quantum magnets with strong spin-orbit interaction. The first of these systems are the three-dimensional iridate compounds, in which the three-fold co-ordination of IrO₆ octahedra has been theoretically hypothesized to stabilize anisotropic exchange between Ir⁴⁺ ions. This novel interaction between these spin-orbital entangled, J_eff=1/2 moments is described by a Hamiltonian first proposed by Kitaev, and would be the first physical realization of this Hamiltonian in a condensed matter system. This thesis details the determination of the structure of a new polytype within these compounds, the 'stripyhoneycomb' &gamma;-Li₂IrO₃. Furthermore, through resonant magnetic x-ray diffraction experiments on single crystals of &beta;-Li₂IrO₃ and &gamma;-Li₂IrO₃, an incommensurate, non-coplanar structure with counter-rotating moments is found. The counter-rotating moment structure is a rather counter-intuitive result, as it is not stabilizied by Heisenberg exchange between magnetic sites, however, the Kitaev exchange naturally accounts for this feature. As such, these experiments reveal, for the first time, systems which exhibit dominant Kitaev interactions. The ordering wavevector of both &beta;- and &gamma;-Li₂IrO₃ polytypes are found to be identical, suggesting that the same magnetic interactions are responsible for stabilizing magnetic order in both materials, despite their different lattice topologies. Following this, the spinel FeSc₂S₄ is considered. Here, despite the presence of strong exchange between Fe<sup>2+,/sup>, and the fact that these ions sit in a Jahn-Teller active environment, the system does not order in the spin or orbital degrees of freedom. A 'spin-orbital singlet' has been theoretically proposed to describe the groundstate of this system, and here inelastic neutron scattering (INS) is used to probe the resulting triplon excitations. This allows determination of microscopic parameters in the single ion and exchange Hamiltonians, and moreover experiments in external magnetic field reveal the true spin-and-orbital nature of these triplon excitations. Finally, Ba₃CoSb₂O₉, a physical realization of the canonical triangular antiferromagnet model is explored with INS and the high energy excitations from the 120 degree magnetic structure are found to display significant differences from those calculated by linear spin wave theory, suggesting the presence of quantum dynamics not captured in the 1/S linear spin wave expansion.

It has been found that non-magnetic organic semiconductors can show some magnetic responses in low magnetic field (<100 >mT). When applying magnetic field, the electroluminescence, electrical current, photocurrent, and photoluminescence could change with magnetic field, which are called magnetic field effects. Magnetic field effects are generated through spin-dependent process affected by the internal magnetic interaction. In nonmagnetic materials, hyperfine interaction has been supposed to dominantly affect the spin-dependent process recently. But the conclusion was made in weak spin-orbital coupling organic semiconductor. The hyperfine interaction might not be the main reason responsible for magnetic field effects in strong spin-orbital coupling materials. Therefore, the study of magnetic field effects in strong spin-orbital coupling organic semiconductor is important to get a whole view of the origin of the magnetic field effects in nonmagnetic organic semiconductors. This dissertation will clarify the generation mechanism of magnetic field effect in nonmagnetic organic semiconductors and further explore how the strong spin-orbital coupling affecting the magnetic field effect. It has been found the intermolecular excited states are important inter-median for magnetic field effects. The change of intersystem crossing at intermolecular excited states will change the singlet/triplet ratio and further generate magnetic field effects through different recombination and dissociation properties of singlet and triplet intermolecular excited states. Both the energy transfer effect coupled spin orbital coupling and energy transfer effect free spin orbital-coupling are discussed in the dissertation. The tuning of the magnetic field effect by adjusting the spin-orbital coupling is also established through distance effect and interface effect. It has been found that changing inter-molecular spin-orbital coupling is a critical factor to generate magnetic field effects in organic semiconductors. And the sensitivity of different magnetic field effects to strong spin-orbital coupling strength is depending on the final product. The internal magnetic interaction can be hyperfine interaction, spin orbital coupling and spin-spin interaction between electrons. The hyperfine interaction and spin orbital coupling are important in nonmagnetic organic semiconductors. But the electron spin-spin interaction is important in magnetic organic semiconductors. The magnetocurrent for magnetic and nonmagnetic organic semiconductors at different temperature has been compared.

Ce mémoire est une partie d’un programme de recherche qui étudie la superintégrabilité des systèmes avec spin. Plus particulièrement, nous nous intéressons à un hamiltonien avec interaction spin-orbite en trois dimensions admettant une intégrale du mouvement qui est un polynôme matriciel d’ordre deux dans l’impulsion. Puisque nous considérons un hamiltonien invariant sous rotation et sous parité, nous classifions les intégrales du mouvement selon des multiplets irréductibles de O(3). Nous calculons le commutateur entre l’hamiltonien et un opérateur général d’ordre deux dans l’impulsion scalaire, pseudoscalaire, vecteur et pseudovecteur. Nous donnons la classification complète des systèmes admettant des intégrales du mouvement scalaire et vectorielle. Nous trouvons une condition nécessaire à remplir pour le potentiel sous forme d’une équation différentielle pour les cas pseudo-scalaire et pseudo-vectoriel. Nous utilisons la réduction par symétrie pour obtenir des solutions particulières de ces équations. / This thesis is part of a research program studying superintegrable systems with spin. In particular, we consider a Hamiltonian with a spin-orbital interaction in three dimensions admitting an integral of motion that is a matrix polynomial second order in the momenta. Since we are considering a Hamiltonian which is invariant under rotation and parity, we classify the integrals of motion into irreducible O(3) multiplets. We obtain the commutator of the Hamiltonian with the scalar, pseudoscalar, vector and axial vector operators. We provide a complete classification for the scalar and vector cases. We find the necessary condition for superintegrability on the potential as a differential equation. We use symmetry reduction methods to obtain particular solutions of this equation.

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.