Thesis advisor: Ziqiang Wang / The discovery of high-Tc superconductivity in cuprates, quantum Hall effect greatly challenge the single-electron understanding of condensed matter physics. In contrast to phonon-mediated BCS mechanism, the unconventional high-Tc superconductivity is widely believed to come from strongly electronic correlation. Strong electron-electron repulsion leads to the interplay among spin, charge, orbital and lattice degrees of freedom, resulting in high-temperature superconductivity, charge or spin density wave, Mott insulator, orbital order, nematicity etc. On the other hand, quantum Hall effect brings us the realization of the mathematical concept of topology in condensed matter. Topology has been widely explored in the topological insulator, topological superconductors, symmetry protected topological order etc. In this dissertation, we study theoretically the physics of electronic correlation and topology in various systems, including superconductivity in single layer CuO₂, electronic nematicity in FeSe, chiral spin density wave in honeycomb lattice and antiferromagnetic Chern insulator in 2D non-centrosymmetric systems. / Thesis (PhD) — Boston College, 2018. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Physics.

Nous présentons une étude par Résonance Magnétique Nucléaire (RMN) de l'azurite, Cu3(CO3)2(OH)2, un système de spins quantiques. Ce composé peut être modélisé comme une chaine quasi-unidimensionnelle, frustrée, ‘de type diamant', de spins électroniques S=1/2 portés par les ions de cuivre Cu2+. Il présente dans sa courbe de l'aimantation en fonction du champ magnétique, entre 11 et 30 T et à très basse température, un plateau à 1/3 de l'aimantation à saturation. Nous avons effectué des mesures RMN du cuivre dans l'azurite à T=1.5 K afin de déterminer sa structure magnétique microscopique. Les résultats obtenus dans le plateau démontrent que le ‘dimère' des deux spins qui sont plus fortement couplés est approximativement dans l'état singulet, tandis que le troisième spin (le ‘monomère') est presque complètement polarisé. Cela confirme que la configuration électronique du plateau à 1/3 est un nouvel état quantique qui n'a pas d'équivalent classique [F. Aimo et al., Phys. Rev. Lett. 102 127205, (2009)]. Par RMN du proton à très haut champ magnétique, entre 31 et 34 T à T=0.6 K, nous avons aussi étudié le passage depuis le plateau à 1/3 vers la polarisation complète du système, afin de confirmer ou infirmer l'existence éventuelle d'un plateau à 2/3. Ce plateau est attendu dans le cas exceptionnel où les corrélations longitudinales de spins sont dominantes et stabilisent un ordre incommensurable longitudinal. L'analyse détaillée du dédoublement très symétrique des spectres RMN nous amène à conclure que c'est un ordre antiferromagnétique transverse et non longitudinal qui est établi, ce qui est incompatible avec l'existence du plateau à 2/3. / We present a Nuclear Magnetic Resonance (NMR) study of azurite, Cu3(CO3)2(OH)2, a quantum spin system. This compound has been recognised as a model system for a quasi-1D, frustrated, ‘diamond' chain of S=1/2 spins beared by Cu2+ ions. In the magnetisation curve as a function of magnetic field it presents, between 11 and 30 T and at very low temperatures, a plateau at 1/3 of the saturation magnetisation. We performed Cu NMR measurements in azurite at T=1.5 K in order to determine its microscopic magnetic structure. The obtained results show that the ‘dimer' of two more strongly coupled spins is approximately in a singlet state while the third spin (the ‘monomer') is almost fully polarised. This confirms that the electronic configuration of the 1/3 plateau is a new quantum state without classical analogue [F. Aimo et al., Phys. Rev. Lett. 102, 127205, (2009)]. By very high magnetic field proton NMR, between 31 and 34 T and at T=0.6 K, we have also studied the transition region between the 1/3 plateau and the full polarisation of the system in order to test for the possible existence of a 2/3 plateau. This plateau is expected in rather exceptional case when longitudinal spin correlations are dominant and stabilise an incommensurable longitudinal order. However, our analysis showed that the symmetric splitting of NMR spectra corresponds to an antiferromagnetic transverse and not longitudinal order, which is incompatible with the existence of a 2/3 plateau.

Quantum magnetic materials provide pathways to exotic spin-disordered phases. We study two broad classes of quantum spin systems and their ground states. The first class is that of spin-dimer systems, which form valence-bond-solid states. In such systems, competition between interactions among the dimers can lead to interesting magnetization behaviour. We explain the magnetization of Ba3Cr2O8 as a Bose-Einstein condensate of spin-carrying excitations. Furthermore, we investigate possible dimerized and nearby magnetically ordered states in the Shastry-Sutherland compound (CuCl)LaNb2O7. The second class of spin systems feature geometric frustration, which may stabilize spin-liquid states without any order or particular dimerization. We argue the proximity of the face-centred-cubic double perovskite La2LiMoO6 to such a phase, to explain its lack of long-range order. We argue for the coexistence of such a state, along with spiral magnetic order, to explain the anomalous thermodynamic measurements in the spin-density-wave phase of powder samples of Volborthite, a distorted kagome-lattice spin system. Finally, we study spin liquid phases that have spin correlations consistent with those found from inelastic neutron scattering of the disordered kagome-lattice material Herbertsmithite. We predict electron spin resonance absorption lineshapes associated with these phases.

Quantum magnetic materials provide pathways to exotic spin-disordered phases. We study two broad classes of quantum spin systems and their ground states. The first class is that of spin-dimer systems, which form valence-bond-solid states. In such systems, competition between interactions among the dimers can lead to interesting magnetization behaviour. We explain the magnetization of Ba3Cr2O8 as a Bose-Einstein condensate of spin-carrying excitations. Furthermore, we investigate possible dimerized and nearby magnetically ordered states in the Shastry-Sutherland compound (CuCl)LaNb2O7. The second class of spin systems feature geometric frustration, which may stabilize spin-liquid states without any order or particular dimerization. We argue the proximity of the face-centred-cubic double perovskite La2LiMoO6 to such a phase, to explain its lack of long-range order. We argue for the coexistence of such a state, along with spiral magnetic order, to explain the anomalous thermodynamic measurements in the spin-density-wave phase of powder samples of Volborthite, a distorted kagome-lattice spin system. Finally, we study spin liquid phases that have spin correlations consistent with those found from inelastic neutron scattering of the disordered kagome-lattice material Herbertsmithite. We predict electron spin resonance absorption lineshapes associated with these phases.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第20892号 / 理博第4344号 / 新制||理||1624(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 高橋 義朗, 教授 川上 則雄, 教授 田中 耕一郎 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

Dans les systèmes de spins quantiques, la frustration et la basse dimensionnalité génèrent des fluctuations quantiques et donnent lieu à des phases exotiques. Cette thèse étudie un modèle d'échelle de spins avec des couplages frustrants le long des montants, motivé par les expériences sur le cuprate BiCu$_2$PO$_6$. Dans un premier temps, on présente une méthode variationnelle originale pour décrire les excitations de basse énergie d'une seule chaîne frustrée. Le diagramme de phase de deux chaînes couplées est ensuite établi à l'aide de méthodes numériques. Le modèle exhibe une transition de phase quantique entre une phase dimérisée est une phase à liens de valence résonnants (RVB). La physique de la phase RVB et en particulier l'apparition de l'incommensurabilité sont étudiées numériquement et par un traitement en champ moyen. On étudie ensuite les effets d'impuretés non-magnétiques sur la courbe d'aimantation et la loi de Curie à basse température. Ces propriétés magnétiques sont tout d'abord discutées à température nulle à partir d'arguments probabilistes. Puis un modèle effectif de basse énergie est dérivé dans la théorie de la réponse linéaire et permet de rendre compte des propriétés magnétiques à température finie. Enfin, on étudie l'effet d'un désordre dans les liens, sur une seule chaîne frustrée. La méthode variationnelle, introduite dans le cas non-désordonné, donne une image à faible désordre de l'instabilité de la phase dimérisée, qui consiste en la formation de domaines d'Imry-Ma délimités par des spinons localisés. Ce résultat est finalement discuté à la lumière de la renormalisation dans l'espace réel à fort désordre. / In quantum spins systems, frustration and low-dimensionality generate quantum fluctuations and give rise to exotic quantum phases. This thesis studies a spin ladder model with frustrating couplings along the legs, motivated by experiments on cuprate BiCu$_2$PO$_6$. First, we present an original variational method to describe the low-energy excitations of a single frustrated chain. Then, the phase diagram of two coupled chains is computed with numerical methods. The model exhibits a quantum phase transition between a dimerized phase and resonating valence bound (RVB) phase. The physics of the RVB phase and in particular the onset of incommensurability are studied numerically and by a mean-field treatment. Afterwards, we study the effects of non-magnetic impurities on the magnetization curve and the Curie law at low temperature. These magnetic properties are first discussed at zero temperature with probability arguments. Then a low-energy effective model is derived within the linear response theory and is used to explain the magnetic properties at finite temperature. Eventually, we study the effect of bonds disorder, on a single frustrated chain. The variational method introduced in the non-disordered case gives a low disorder picture of the dimerized phase instability, which consists in the formation of Imry-Ma domains delimited by localized spinons. This result is finally discussed in the light of the strong disorder real space renormalization.

Propriedades dinâmicas de sistemas quânticos de muitos corpos é um tópico de grande interesse em física da matéria condensada. Estas propriedades nos dão informação sobre a propagação de excitações elementares e de mecanismos de relaxação em sistemas interagentes. Neste contexto, as funções de correlação tem se tornado ainda mais relevantes devido a experimentos em sistemas de átomos frios e íons armadilhados que medem diretamente no domínio temporal os comportamentos assintóticos no tempo. No entanto, até o momento a maioria dos estudos em cadeias de spin quânticas focaram-se em correlações de um único spin. Utilizando a cadeia de spin XX unidimensional, nós estudamos métodos exatos para calcular as funções de correlação das componentes do tensor de dois spins, Tabi,j = SaiSbj. Estes operadores aparecem, por exemplo, como a resposta da seção de choque de espalhamento inelástico de raios X. Baseados no teorema de Wick, nós mostramos que algumas funções de correlação das componentes locais do tensor de dois operadores de spins de sítios vizinhos, na representação de férmions, podem ser escritas como uma combinação de funções de Green de uma única partícula. Utilizamos diagramas de Feynman para organizar esta combinação e calcular as funções de correlação. Em seguida, considerando esses propagadores para tempos longos e grandes distâncias ao longo do cone de luz, encontramos o comportamento dessas funções de correlação como leis de potência oscilatórias que decaem com o tempo e distância. Uma aplicação direta das funções de correlação é para o estudo de quantidades conservadas e não conservadas, uma análise sobre algumas dessas quantidades foi feita. Discutimos também as funções de correlação das componentes do tensor que não são locais na representação fermiônica. Nesse caso os cálculos foram mais desafiadores, mas usamos o fato que funções de correlação dependente do tempo podem ser expressadas em termos dos determinantes de Fredholm. / Dynamical properties of quantum many body systems is a major topic of interest in condensed matter physics. These properties tell us about the propagation of elementary excitation and mechanisms of relaxation in interacting systems. In this context correlation functions have became even more relevant due the experiments in systems of cold atoms and trapped ions that measure real time dependence directly out to relatively long times. However, most studies in quantum spins chains so far have focused on correlations of single spins. Using the one dimensional XX spin chain, we study exact methods to calculate the correlation functions of the components of the tensor operator involving two spins, Tabi,j = SaiSbj. This operator appear, for example, as a response of inelastic x-ray scattering cross section. Based on Wick\'s theorem, we show that some correlation functions of local components of the tensor operator of two pairs of neighbor sites, in the fermion space, can be written as a combination of Greens functions of a single particle. We have used Feynman diagrams to organize this combination and calculate the correlation functions. Then, considering these propagators for long times and large distances along the light cone, we found the behavior of these correlation functions as a oscillatory and power law decay on time. A direct application of correlation functions is to study conserved and non-conserved quantities, and such analysis has been made. We also considered other two-spin operators which are not local in the fermionic representation. In this case the calculation is more challenging, but the time-dependent correlation functions can be expressed in terms of Fredholm determinants.

Dans ce mémoire nous présentons plusieurs études expérimentales des propriétés magnétiques d’un condensat de Bose-Einstein de Chrome chargé dans un réseau 3D, en nous focalisant sur les effets associés aux interactions dipolaires. Nous montrons que dans un réseau 3D, la relaxation dipolaire est un processus résonant du fait de la réduction de la densité d’états orbitaux accessibles. Les résonances sont observées à des champs magnétiques Bres tels que l’énergie Zeeman relâchée soit égale à l’énergie nécessaire à exciter les atomes dans une bande d’énergie supérieure du réseau. Nous pouvons inhiber ce processus en appliquant un champ différent de Bres. L’analyse des résonances a permis de sonder la structure de bande 3D du réseau, ainsi que la mise en évidence de l’effet des interactions entre atomes. Nous avons étudié la dynamique d’échange de spin dans un réseau 3D. Nous présentons en particulier la première observation d’échange de spin entre atomes localisés dans des sites séparés. Ces études permettent une exploration nouvelle du magnétisme en réseau. En variant la profondeur du réseau, nous étudions ces effets dans le régime superfluide, bien décrit par une théorie de champ moyen, et dans le régime fortement corrélé, dont la description théorique est difficile. Enfin, nous étudions l’évolution de deux spins géants interagissant par interaction dipolaire. Le condensat initialement divisé en deux, les atomes des deux nuages sont préparés dans des états de spin opposés formant ainsi deux spins géants ±3xN. Nous montrons que toute dynamique de spin est énergétiquement inhibée pour de grands spins ce qui est bien reproduit par une théorie classique. / This Thesis reports on several experimental studies of magnetic properties of a Chromium Bose-Einsteincondensate loaded into a 3D optical lattice, focusing on the effects induced by dipolar interactions.We show that in a 3D lattice dipolar relaxation is a resonant process due to the reduction of the density ofaccessible orbital states. These resonances are observed for magnetic fields Bres such that the Zeeman energyreleased matches an excitation towards higher-energy bands of the lattice. We can thus inhibit those processes byapplying a field different from Bres. Analyses of the resonances allowed us to probe the lattice 3D band structureas well as to demonstrate the effects of local interactions between atoms.We study spin exchange dynamics in a 3D lattice. We especially observed for the first time spin exchangebetween atoms localized in different lattice sites mediated by dipolar interactions. These studies are the firststep toward a new exploration of magnetism in lattice. Varying the depth of the lattice we study these effects inthe superfluid regime, well described by mean filed theories, as well as in the strongly correlated regime, whosetheoretical description is still challenging.Finally, we study the evolution dynamics of two giant spins interacting through dipolar interactions. Thecondensate being initially splitted in half, atoms from the two clouds are prepared in opposite spin states thusproducing two giant spins ±3×N. We show that any spin dynamics is energetically inhibited for large spinswhich is well accounted for by a classical theory

Low-dimensional magnetic systems are of interest due to several new effects and modifications that occur at sizes below the average domain grain boundary within the bulk material. Molecule-like magnetite (Fe3O4) nanoparticles, with sizes ranging from one to two nm were synthesized and characterized in order to investigate new properties arising from quantum size effects. These small systems will provide opportunities to investigate magnetism of zero-dimension systems. A zero-dimensional object is usually called a quantum dot or artificial atom because its electronic states are few and sharply separated in energy, resembling those within an atom. Since the surface to volume ratio is the highest for zero-dimensional systems, most of the changes to magnetic behavior will be observed in ultra-fine magnetic particles. Chemically functional magnetic nanoparticles, comprised of a Fe3O4 magnetite core encased in a thin aliphatic carboxylate, have been prepared by sequential high temperature decomposition of organometallic compounds in a coordinating solvent. In this work, aliphatic carboxylic acid chain length, reaction temperature and duration were varied to produce small core diameters. In order to correlate size effects with changes in particle formation, it is important to have a through understanding of the structural components. This includes studies of the core size, surface effects, decomposition, electronic properties and magnetic behavior. Quantum size effects were observed in the (Fe3O4)X(carboxylate)Y monolayer protected clusters (MPCs) when the average core diameter was ≤ 2.0 nm, evidenced by a blue shifted absorbance band maxima, suggesting the onset of quantum confinement. These (Fe3O4)X(carboxylate)Y MPCs also posses a complex interplay between surface and finite size effects, which govern the magnetic properties of these zero-dimensional systems. These MPCs are all superparamagnetic above their blocking temperatures with total magnetic anisotropy values greater than the bulk value due to an increase in surface and magnetocrystalline anisotropy. A non-linear decrease in saturation magnetization (MS) [Bohr Magneton] per cluster) as a function of the reciprocal of core radius have been attributed to surface effects such as a magnetically inactive layer or an increase in spin disorder as core diameter decreases. The reduced core dimensions of these MPCs make them ideal candidates for further investigation of quantum magnetic systems.

Propriedades dinâmicas de sistemas quânticos de muitos corpos é um tópico de grande interesse em física da matéria condensada. Estas propriedades nos dão informação sobre a propagação de excitações elementares e de mecanismos de relaxação em sistemas interagentes. Neste contexto, as funções de correlação tem se tornado ainda mais relevantes devido a experimentos em sistemas de átomos frios e íons armadilhados que medem diretamente no domínio temporal os comportamentos assintóticos no tempo. No entanto, até o momento a maioria dos estudos em cadeias de spin quânticas focaram-se em correlações de um único spin. Utilizando a cadeia de spin XX unidimensional, nós estudamos métodos exatos para calcular as funções de correlação das componentes do tensor de dois spins, Tabi,j = SaiSbj. Estes operadores aparecem, por exemplo, como a resposta da seção de choque de espalhamento inelástico de raios X. Baseados no teorema de Wick, nós mostramos que algumas funções de correlação das componentes locais do tensor de dois operadores de spins de sítios vizinhos, na representação de férmions, podem ser escritas como uma combinação de funções de Green de uma única partícula. Utilizamos diagramas de Feynman para organizar esta combinação e calcular as funções de correlação. Em seguida, considerando esses propagadores para tempos longos e grandes distâncias ao longo do cone de luz, encontramos o comportamento dessas funções de correlação como leis de potência oscilatórias que decaem com o tempo e distância. Uma aplicação direta das funções de correlação é para o estudo de quantidades conservadas e não conservadas, uma análise sobre algumas dessas quantidades foi feita. Discutimos também as funções de correlação das componentes do tensor que não são locais na representação fermiônica. Nesse caso os cálculos foram mais desafiadores, mas usamos o fato que funções de correlação dependente do tempo podem ser expressadas em termos dos determinantes de Fredholm. / Dynamical properties of quantum many body systems is a major topic of interest in condensed matter physics. These properties tell us about the propagation of elementary excitation and mechanisms of relaxation in interacting systems. In this context correlation functions have became even more relevant due the experiments in systems of cold atoms and trapped ions that measure real time dependence directly out to relatively long times. However, most studies in quantum spins chains so far have focused on correlations of single spins. Using the one dimensional XX spin chain, we study exact methods to calculate the correlation functions of the components of the tensor operator involving two spins, Tabi,j = SaiSbj. This operator appear, for example, as a response of inelastic x-ray scattering cross section. Based on Wick\'s theorem, we show that some correlation functions of local components of the tensor operator of two pairs of neighbor sites, in the fermion space, can be written as a combination of Greens functions of a single particle. We have used Feynman diagrams to organize this combination and calculate the correlation functions. Then, considering these propagators for long times and large distances along the light cone, we found the behavior of these correlation functions as a oscillatory and power law decay on time. A direct application of correlation functions is to study conserved and non-conserved quantities, and such analysis has been made. We also considered other two-spin operators which are not local in the fermionic representation. In this case the calculation is more challenging, but the time-dependent correlation functions can be expressed in terms of Fredholm determinants.