京都大学 / 0048 / 新制・課程博士 / 博士(人間・環境学) / 甲第21876号 / 人博第905号 / 新制||人||216(附属図書館) / 2018||人博||905(吉田南総合図書館) / 京都大学大学院人間・環境学研究科相関環境学専攻 / (主査)教授 内本 喜晴, 教授 田部 勢津久, 教授 吉田 鉄平 / 学位規則第4条第1項該当 / Doctor of Human and Environmental Studies / Kyoto University / DFAM

Classical and quantum spin systems are widely used models in both experimental and theoretical condensed matter physics. In many materials, the electronic interactions can be difficult to model exactly. However, in some insulators (Mott insulators), the magnetic (spin) interactions can be captured well with spin-only models. Several models are studied in this thesis. First, I report the solution of a long-standing issue in a classical frustrated spin model (i.e., where the quantum effects are neglected and the complexity is due to competing interactions): the nature of the thermal phase transition to a stripe state in the two dimensional (2D) J1-J2 model. Here J1 and J2 are nearest- and next-nearest-neighbor couplings. Monte Carlo simulations with single-spin updates are used for the calculations, and an extended-ensemble method, a generalization of the Wang-Landau algorithm, is also developed and tested. I focus on the study of "weak universality" behavior (continuously varying critical exponents, with one of the exponents staying fixed), for which I show a correspondence with a known class of conformal field theories with charge c = 1. Next, moving to quantum spins, to shed light on magnetic systems studied experimentally and to investigate new types of quantum states of interest in developing theories of quantum magnetism, I study the S = 1/2 Heisenberg model on the 2D square lattice with added six-spin interactions (the so-called J-Q3 model) as well as a set of 3D quantum antiferromagnets on dimerized lattices. Here I use the stochastic series expansion quantum Monte Carlo method. In the study of the J-Q3 model, I report on a similar weak-universality behavior as in the classical J1-J2 model, but with a mapping to a different known class of c = 1 conformal field theories. The critical behavior of the system again shows continuously changing exponents, in a way which corresponds to a gradual weakening of Z4 symmetry-breaking to an emergent U(1) symmetry. In the study of dimerized antiferromagnets, I report on a universal behavior of the Néel temperature TN, which can be related to ground state parameters independently of the microscopic interaction details in several different models.

Les matériaux multiferroïques magnétoélectriques (ME) présentant simultanément des propriétés couplées de ferromagnétisme et de ferroélectricité suscitent beaucoup d’attention, non seulement pour leurs applications (comme la RAM magnétique de nouvelle génération), mais aussi pour la compréhension de la physique relative à ce couplage. Le but de cette thèse était de découvrir et de caractériser de nouveaux composés potentiellement multiferroïques, d’où le choix des trirutiles inverses. Ce manuscrit présente l'étude détaillée du trirutile inverse Mn2TeO6 et quelques résultats sur la série substituée au chrome Mn2-xCrxTeO6. Les composés Mn2TeO6 et substitués sont préparés par réaction à l'état solide à relativement basse température (<700°C). De nombreuses expériences de diffraction de neutrons et de rayons-X ont été réalisées pour étudier les structures cristallines et magnétiques en fonction de la température (de 700°C à 1.5K), ces données ont été analysées en lien avec les caractérisations des propriétés magnétiques et électriques. Mn2TeO6 s’est révélé un matériau complexe et riche en transitions en fonction de la température. En température décroissante, Mn2TeO6 présente d’abord une transition d’une structure tétragonale (P42/mnm) à une double maille monoclinique (P21/c) vers 400°C due à l'effet Jahn-Teller. Une seconde transition très hystérétique apparait à plus basse température, avec la coexistence de deux phases monocliniques entre 45 et 100K. Des transitions magnétiques sont également observées par des mesures de susceptibilité magnétique et de diffraction neutronique. La structure cristalline à température ambiante met en évidence un ordre orbitalaire, dû au manganèse trivalent, complexe et inédit avec une alternance d’octaèdres MnO6 allongés et aplatis décrivant des chevrons. L’impact de l’effet Jahn-Teller induit par le manganèse trivalent est confirmé dans les composés substitués au Cr (avec x ≥ 0,15) qui conservent la structure quadratique sur toute la gamme de température. / Magnetoelectric (ME) multiferroic materials, which present simultaneously two coupled properties between ferromagnetism and ferroelectricity, have attracted much attention recently, not only owing to their application perspectives, e.g., next-generation magnetic RAM, but also for the rich physics associated with the understanding of this coupling. Inverse trirutiles are of particular interest here since ME properties have been reported in this family of compounds. This manuscript presents the study of inverse trirutile Mn2TeO6 and its Cr-substitution series Mn2-xCrxTeO6. Mn2TeO6 and Cr-substituted series were prepared by solid state reaction at relatively low-temperature (< 700°C). Thanks to an extensive use of different techniques performed in a large temperature range (1.5K to 700°C), encompassing synchrotron, neutron and electron diffraction experiments combined with physical properties measurements, the very complex behaviour of Mn2TeO6 was revealed. A structural transition at 400°C from tetragonal (P42/mnm) to monoclinic (P21/c) is observed first, and related to a cooperative Jahn-Teller effect. Further cooling the sample, a hysteretic structural transition is observed spanning more than 50K, which leads to the coexistence of two monoclinic phases. A series of magnetic transitions are also observed between 48K and 22K, with magnetization, heat capacity measurement and neutron diffraction. Cr-substituted (x ≥ 0.15) samples crystallize in the tetragonal phase, implying the suppression of the cooperative Jahn-Teller effect, and involving a simpler, though short–range, magnetic order.

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京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第18999号 / 工博第4041号 / 新制||工||1622(附属図書館) / 31950 / 京都大学大学院工学研究科物質エネルギー化学専攻 / (主査)教授 作花 哲夫, 教授 安部 武志, 教授 邑瀬 邦明 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第20551号 / 理博第4309号 / 新制||理||1619(附属図書館) / 京都大学大学院理学研究科化学専攻 / (主査)教授 北川 宏, 教授 竹腰 清乃理, 教授 吉村 一良 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM

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Phase transitions are critical in understanding the properties of different phases of matter, and their identification is an essential research focus in condensed matter physics. However, defining phase transitions for topological systems is more complex than for common mesoscale materials. This complexity is further compounded when disorders are present in the system. In this thesis work, we provide a comprehensive review of machine learning, topological insulators, and the conventional approach to classifying different topological phases. We focus on the Benalcazar, Bernevig, and Hughes (BBH) model, a higher-order topological insulator model, and investigate the challenges of identifying phase transitions in topological systems, particularly in the presence of disorders. To overcome these challenges, we implement the diffusion maps method, which accurately predicts the same transition points as traditional numerical calculations for both clean and disordered systems. Moreover, we demonstrate the efficacy of the diffusion maps method in predicting the transition point for the topological Anderson insulator. Our findings suggest that this approach has the potential to be generalized and applied to a broader range of disordered systems. Overall, this thesis work provides a novel method for identifying phase transition points in topological systems, which could have significant implications for the design and development of future topological materials.

In this thesis we study the scaling properties of unconventional metals that arise at quantum critical points using low-energy effective field theories. Due to high rate of scatterings between electrons and critical fluctuations of the order parameter associated with spontaneous symmetry breaking, Landau’s Fermi liquid theory breaks down at the critical points. The theories that describe these critical points generally flow into strong coupling regimes at low energy in two space dimensions. Here we develop and utilize renormalization group methods that are suitable for the interacting non-Fermi liquids. We focus on the critical points arising at excitonic, and commensurate spin and charge density wave transitions. By controlled analyses we find stable non-Fermi liquid and marginal Fermi liquid states, and extract the scaling behaviour. The field theories for the non-Fermi liquids are characterized by symmetry groups, local curvature of the Fermi surface, the dispersion of the order parameter fluctuations, and dimensions of space and Fermi surface. / Thesis / Doctor of Philosophy (PhD)

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