This thesis presents research of two novel magnetic materials, LiHoF4 and Tb2Ti2O7. Experiments were performed at low temperatures and in an applied magnetic field to study thermal expansion and magnetostriction using a capacitive dilatometer designed during this project. This thesis presents 3 distinct topics. This manuscript begins with a thermodynamic description of thermal expansion and magnetostriction. The design of a capacitive dilatometer suitable for use at ultra-low temperatures and in high magnetic fields is presented. The thermal expansion of oxygen free high conductivity copper is used as a test of the absolute accuracy of the dilatometer. The first material studied using this dilatometer was LiHoF4. Pure LiHoF4 is a dipolar coupled Ising ferromagnet and in an applied transverse magnetic field is a good representation of the transverse field Ising model. An ongoing discrepancy between theoretical and experimental work motivates further study of this textbook material. Presented here are thermal expansion and magnetostriction measurements of LiHoF4 in an applied transverse field. We find good agreement with existing experimental work. This suggests that there is some aspect of LiHoF4 or the effect of quantum mechanical fluctuations at finite temperatures which is not well understood. The second material studied is the spin liquid Tb2Ti2O7. Despite theoretical predictions that Tb2Ti2O7 will order at finite temperature, a large body of experimental evidence demonstrates that spins within Tb2Ti2O7 remain dynamic to the lowest temperatures studied. In addition Tb2Ti2O7 also exhibits anomalous thermal expansion below 20K, giant magnetostriction, and orders in an applied magnetic field. Thermal expansion and magnetostriction measurements of Tb2Ti2O7 are presented in applied longitudinal and transverse fields. Zero-field thermal expansion measurements do not repeat the previously observed anomalous thermal expansion. A large feature is observed in thermal expansion at 100mK, in rough agreement with existing experimental work. Longitudinal and transverse magnetic fields were applied to Tb2Ti2O7. Longitudinal magnetostriction measurements show qualitatively di erent behavior than previous observations. These measurements were taken along di erent crystal axes so direct comparison cannot be made. Thermal expansion measurements in an applied transverse field show evolution with the strength of the applied field. This evolution may relate to an ordering transition, however difficulties in repeatability in a transverse field require that these results be repeated in an improved setup.

Spin systems with low dimensionality and geometrical frustration have attracted interest because of the possible emergence of novel magnetic phases at low temperatures by suppressing conventional magnetic order, and allow for a novel spin-disordered ground state, such as quantum spin liquid and glass without any apparent structural disorder. In this thesis, we have discussed magnetic and dielectric measurements on the quasi-two-dimensional triangular antiferromagnet NiGa2S3.85, in order to investigate its magnetic state and dielectric property at low temperatures. In the measurement of susceptibility In the measurement of susceptibility £q(T), we found that the freezing temperature is near 6 K. This suggests that the sample with the sulfur deficiency should be close to the stoichiometric NiGa2S3.85. Under 7 T magnetic filed ZFC(zero-field-cooling) and FC(field-cooling) still bifurcate indicating more magnetic order state than spin-liquid. Temperature-dependent dielectric measurement shows an interesting colossal enhancement of dielectric constant with frequency dispersion and is ascribed to the interfacial polarization (termed as Maxwell-Wagner relaxation) at the interface between adjacent layers. Temperature-dependent dielectric measurement under applied magnetic field (up to 9 T) shows negligible magnetodielectric behavior because of the sample is not magneto resistive.

In this thesis we present results from quantum Monte Carlo for the fully-frustrated honeycomb lattice. The XXZ model is of interest in the classical limit, as there is a mapping between the classical fully-frustrated honeycomb Ising model groundstates and the classical hard-core dimer model groundstate. The aim of this work is to explore the effect of quantum fluctuations on the fully-frustrated honeycomb model to see what sort of interesting physics arises. One might expect unusual physics due to the quantum hard-core dimer model, where interesting physics are known to exist. This is because there is a duality mapping between the classical dimer model and the classical fully-frustrated honeycomb Ising model. Indeed, by studying the fully-frustrated honeycomb XXZ model we find that in some cases the system orders into crystal-like structures, a case of order-by-disorder. The most interesting case, when the frustrating bonds are chosen randomly, reveals to us a novel state without any discernible order while at the same time avoiding the freezing one would expect of a glass. This state is a featureless system lacking low temperature magnetic susceptibility---a candidate ``quantum spin liquid''. Future work that might more easily measure quantum spin liquid criteria is suggested.

This thesis presents research of two novel magnetic materials, LiHoF4 and Tb2Ti2O7. Experiments were performed at low temperatures and in an applied magnetic field to study thermal expansion and magnetostriction using a capacitive dilatometer designed during this project. This thesis presents 3 distinct topics. This manuscript begins with a thermodynamic description of thermal expansion and magnetostriction. The design of a capacitive dilatometer suitable for use at ultra-low temperatures and in high magnetic fields is presented. The thermal expansion of oxygen free high conductivity copper is used as a test of the absolute accuracy of the dilatometer. The first material studied using this dilatometer was LiHoF4. Pure LiHoF4 is a dipolar coupled Ising ferromagnet and in an applied transverse magnetic field is a good representation of the transverse field Ising model. An ongoing discrepancy between theoretical and experimental work motivates further study of this textbook material. Presented here are thermal expansion and magnetostriction measurements of LiHoF4 in an applied transverse field. We find good agreement with existing experimental work. This suggests that there is some aspect of LiHoF4 or the effect of quantum mechanical fluctuations at finite temperatures which is not well understood. The second material studied is the spin liquid Tb2Ti2O7. Despite theoretical predictions that Tb2Ti2O7 will order at finite temperature, a large body of experimental evidence demonstrates that spins within Tb2Ti2O7 remain dynamic to the lowest temperatures studied. In addition Tb2Ti2O7 also exhibits anomalous thermal expansion below 20K, giant magnetostriction, and orders in an applied magnetic field. Thermal expansion and magnetostriction measurements of Tb2Ti2O7 are presented in applied longitudinal and transverse fields. Zero-field thermal expansion measurements do not repeat the previously observed anomalous thermal expansion. A large feature is observed in thermal expansion at 100mK, in rough agreement with existing experimental work. Longitudinal and transverse magnetic fields were applied to Tb2Ti2O7. Longitudinal magnetostriction measurements show qualitatively di erent behavior than previous observations. These measurements were taken along di erent crystal axes so direct comparison cannot be made. Thermal expansion measurements in an applied transverse field show evolution with the strength of the applied field. This evolution may relate to an ordering transition, however difficulties in repeatability in a transverse field require that these results be repeated in an improved setup.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第22685号 / 理博第4626号 / 新制||理||1665(附属図書館) / 京都大学大学院理学研究科化学専攻 / (主査)准教授 前里 光彦, 教授 吉村 一良, 教授 有賀 哲也 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM

L’étude de l’état fondamental liquide de spins est un des domaines très actif de la recherche en matière condensée. Le réseau le plus à même de stabiliser un tel état fondamental semble être, à deux dimensions, le réseau kagomé de spins antiferromagnétiques 1/2. Il y a à présent un consensus théorique sur le fait que ce modèle stabilise un état fondamental liquide de spin. Cependant, la nature de cet état est encore inconnue, notamment la nature des corrélations. Nous ne savons toujours pas si ces dernières sont à courte portée avec un gap dans le spectre d’excitations, ou si elles sont à plus longue portée avec un spectre d’excitations sans gap. D’un point de vue expérimental il n’existe que très peu de matériaux et seul l’Herbertsmithite présente un réseau kagomé de spins 1/2 géométriquement parfait. Les différentes études réalisées sur ce composé pointent toutes vers un état liquide de spin sans gap mais révèlent aussi des déviations à l’hamiltonien de Heisenberg qui pourraient être responsables de la fermeture de ce gap.Cette thèse traite de l’étude expérimentale principalement par RMN et µSR de nouveaux composés kagomé à base de vanadium faisant partie d’une famille récemment synthétisée, les vanadates fluorés à géométrie kagomé. Le matériau que nous avons le plus étudié est un composé à réseau kagomé de spins 1/2 à base de V4+, (NH4)2[C7H14N][V7O6F18] (DQVOF). Le modèle magnétique de ce composé peut être décomposé en deux sous systèmes presque indépendants, des plans kagomé trimérisés isolés et des ions V3+ quasi paramagnétiques. Les études de µSR démontrent une absence de gel magnétique jusqu’à 20 mK donc un état liquide de spins dans DQVOF. Les études de chaleur spécifique et de RMN dévoilent un comportement liquide de spin sans gap malgré la trimérisation du réseau et la faible valeur supposée de l’interaction Dzyaloshinskii Moriya. Nos résultats montrent finalement que l’absence de gap, intrinsèque ou due à des déviations à l’hamiltonien idéal, est une caractéristique robuste des matériaux kagomé. Nous avons de plus étudié un second matériau de cette famille, (NH4)2[C2H8N][V3F12] (DDVF), dont le réseau magnétique est formé par des plans kagomé découplés entre eux à base de V3+ (S = 1). Ce réseau présente de fortes distorsions par rapport au réseau idéal et les expériences thermodynamiques et de µSR mettent en évidence une transition magnétique vers un état gelé à 10 K avec une mise en ordre à longue distance qui s’effectue à 6 K uniquement. / The search for quantum liquid state is a very active field in condensed matter research. In two dimensions, the antiferromagnetic spin 1/2 kagome lattice seems to be the most able to stabilize such a ground state. Indeed, from recent theoretical investigations, we are now quite sure that this model has a quantum spin liquid ground state. However, we still do not know its nature, in particular the nature of its correlations. They could be short ranged with a gap in the excitation spectrum, or long ranged with a gapless excitation spectrum. On the experimental side, only few materials exist and only one possesses a geometrically perfect lattice, the Herbertsmithite. All the experiments that have been done on this compound reveal a gapless spin liquid state along with deviations to the spin 1/2 Heisenberg hamiltonian which could be responsible of the gap closure.This thesis deals with the experimental study, mainly by NMR and µSR, of new vanadium based kagomé compounds which are part of a newly synthesized family, the kagome fluoride vanadates. The material that we studied the most is a spin 1/2 kagomé compound based on V4+, (NH4)2[C7H14N][V7O6F18] (DQVOF). The magnetic model of this compound can be decomposed in two rather independent parts, trimerized kagome planes and quasi paramagnetic V3+ ions. The µSR studies, showing the absence of frozen moment down to 20 mK, reveal a spin liquid ground state in DQVOF. The heat capacity and the NMR experiments point out a gapless behavior despite trimerization and likely weak Dzyaloshinskii Moriya interactions. Our results demonstrate that the gapless ground state, whether intrinsic or due to deviation to the ideal hamiltonian, is a rather robust characteristic of kagome materials.Furthermore, we studied another compound of this family, (NH4)2[C2H8N][V3F12] (DDVF), which magnetic lattice is made of uncoupled kagomé planes based on V3+ (S = 1). The lattice shows large deviations to the ideal kagomé and the thermodynamic experiments and the µSR studies reveal a magnetic transition to a frozen state at 10 K with a long distance order which is effective only below 6 K.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第21548号 / 理博第4455号 / 新制||理||1640(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 川上 則雄, 教授 田中 耕一郎, 教授 前野 悦輝 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

This thesis, comprising three publications, explores the efficacy of novel generalization of the fidelity susceptibility and their numerical application to the study of frustrated quantum phase transitions in two and one dimensions. Specifically, they will be used in exact diagonalization studies of the various limiting cases of the anisotropic next-nearest neighbour triangular lattice Heisenberg model (ANNTLHM). These generalized susceptibilities are related to the order parameter susceptibilities and spin stiffness and are believed to exhibit similar behaviour although with greater sensitivity. This makes them ideal for numerical studies on small systems. Additionally, the utility of the excited-state fidelity and twist boundary conditions will be explored. All studies are done through numerical exact diagonalization. In the limit of interchain couplings going to zero the ANNTLHM reduces to the well studied $J_1-J_2$ chain with a known, difficult to identify, BKT-type transition. In the first publication of this work the generalized fidelity susceptibilities introduced therein are shown to be able to identify this transition as well as characterize the already understood phases it straddles. The second publication of this work then seeks to apply these generalized fidelity susceptibilities, as well as the excited-state fidelity, to the study of the general phase diagram of the ANNTLHM. It is shown that the regular and excited-state fidelities are useful quantities for the mapping of novel phase diagrams and that the generalized fidelity susceptibilities can provide valuable information as to the nature of the phases within the mapped phase regions. The final paper sees the application of twisted boundary conditions to the anisotropic triangular model (next-nearest neighbour interactions are zero). It is demonstrated that these boundary conditions greatly enhance the ability to numerically explore incommensurate physics in small systems. / Thesis / Doctor of Science (PhD)

Thesis advisor: Fazel Tafti / The search for an ideal quantum spin-liquid (QSL) material which can host a QSL ground state as well as exotic excitations has been one of the leading research topics in condensed matter physics over the past few decades. Out of all the proposals to realize the physics of a QSL, the Kitaev model is the most promising proposal with a QSL ground state. The Kitaev Hamiltonian is exactly solvable via fractionalization of its spin degrees of freedom into Majorana excitations, and it can be engineered in real materials. Among all the proposed Kitaev candidates, α-Li2IrO3, Na2IrO3, Li2RhO3, and α-RuCl3 are the most promising candidates. During my Ph.D. research I explored new physics related to Kitaev materials via modification of the symmetry and structural properties of these known Kitaev candidates. First, I studied how modification of the inter-layer chemistry can alter the thermodynamic properties of Kitaev candidate α-Li2IrO3 via an enhancement of the spin-orbit coupling (SOC) effect. The light, octahedrally-coordinated inter-layer Li atoms are replaced with heavier, linearly-coordinated Ag atoms to synthesize Ag3LiIr2O6. In addition to these structural modifications to the parent compound α-Li2IrO3, having heavier elements between the honeycomb layers in the Ag compound increased the effect of SOC in the honeycomb layers and led to a decrease in the long-range ordering temperature in Ag3LiIr2O6 compared to its parent compound. Second, I studied the effect of local crystal distortion in the presence of a weak SOC effect to explore a new spin-orbital state different from the Jeff=1/2 state. Based on theoretical predictions, the ground states of Kitaev materials can be tuned to other exotic spin-orbital states such as an Ising spin-1/2 state. To provide the proper conditions for a competition between the trigonal crystal distortion and the SOC effect, I modified the crystal environment around the magnetic elements in the parent compound Li2RhO3 via a topo-chemical method and synthesized Ag3LiRh2O6. An increase in the strength of trigonal distortion in Ag3LiRh2O6, in the presence of weak SOC, led to a transition from the Jeff=1/2 ground state (Kitaev limit) in the parent compound to an Ising spin-1/2 ground state (Ising limit) in the product. This change in spin-orbital state resulted in a dramatic change in magnetic behavior. Whereas Li2RhO3 shows a spin-freezing transition at 6 K, Ag3LiRh2O6 reveals a robust long-range antiferromagnetic transition at 94 K. This is the first realization of a change of ground state between the Kitaev and Ising limits in the same structural family. Lastly, I studied how the crystal symmetry can be an important factor in the physics of Kitaev materials. Honeycomb layered materials can be crystallized in space groups C2/m, C2/c, and P6_322. However, the crystal symmetry of most Kitaev candidates is described by the C2/m space group. We successfully synthesized a polymorph of a 3d Kitaev candidate, hexagonal Na2Co2TeO6 (P6_322 space group) in space group C2/m. The change in crystal symmetry of this cobalt tellurate replaced three anti-ferromagnetic (AFM) orders at 27, 15, 7 K in the hexagonal polymorph by a single AFM peak at 9.6 K in the monoclinic Na2Co2TeO6. / Thesis (PhD) — Boston College, 2023. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Physics.

The experimental quest for a quantum spin-liquid state (QSL) in frustrated magnetic systems addresses fundamental scientific interests, as this intriguing quantum phase provides excellent grounds for discovering exotic collective phenomena. ZnCu3(OH)6Cl2 (herbertsmithite), an S=1/2 kagomé-lattice Heisenberg antiferromagnet, is the most promising candidate for experimentally realizing a QSL. However, despite years of intense research, the nature of its paramagnetic ground state remains highly debated. The root cause of the controversy lies in the difficulty in distinguishing the effects of defects from the intrinsic properties of the kagomé lattice. In this thesis, we present 17-O nuclear magnetic resonance (NMR) measurements of an isotope-enriched ZnCu3(OH)6Cl2 single crystal. We succeeded in distinguishing the intrinsic magnetic behavior of the kagomé lattice from the defect-induced phenomena down to T~0.01J, where J~200K is the Cu-Cu super-exchange interaction. We identify NMR signals arising from the nearest-neighbor 17-O sites of Cu2+ defects occupying the Zn2+ interlayer sites. From the 17-O Knight shift measurements, we show that these Cu2+ defects induce a large Curie-Weiss contribution to the bulk-averaged susceptibility at low temperatures. Moreover, our 17-O single-crystal lineshapes show no signature of nonmagnetic Zn2+ defects within the kagomé lattice, and therefore, we rule out “anti-site disorder” as a cause of the paramagnetic ground state in ZnCu3(OH)6Cl2. Most importantly, we demonstrate that the intrinsic spin susceptibility of the kagome lattice asymptotically tends to zero below T~0.03J, indicating the presence of a finite gap Δ = 0.03~ 0.07J in the spin excitation spectrum; this gap is completely suppressed under the application of a high magnetic field of ~ 9T. The behavior of low-energy spin fluctuations probed by the 17-O nuclear spin-lattice relaxation rate is consistent with the gap signature observed for the 17-O Knight shift. In short, our 17-O NMR results provide the first experimental evidence for a gapped QSL realized in ZnCu3(OH)6Cl2. / Thesis / Doctor of Philosophy (PhD)