<p>We report low temperature specific heat and positive muon spin rotation measurements of both polycrystal and single crystal Yb2Ti2O7. Our zero field (ZF) measurements show little spin relaxation temperature dependence in the polycrystal Yb2Ti2O7, contrast to previously reported results. We observe no collinear ferromagnetic order, rather a hidden order ground state where spin fluctuations remain dynamic down to 16 mK. Single crystal Yb2Ti2O7 zero field measurements with the crystallographic [111] direction parallel to the initial muon polarization show small but measurable temperature dependence. In addition, our transverse field measurements show the spin susceptibility undergoes a distinct change at temperatures corresponding to the magnetic transition measured in the specific heat.</p> / Master of Science (MSc)

Current proposals for large-scale quantum technologies rely on the integration of distinct quantum systems within a heterogeneous architecture. Such hybrid composition requires the design and development of interfaces to facilitate the seamless transfer of quantum information. While multiple physical interfaces have been explored based on photons and phonons, interaction mechanisms based on magnetically ordered spin textures are comparatively unexplored. The emerging field of quantum magnonics addresses this research gap by studying the interaction of quantum systems with magnons - the quanta of collective spin excitations. Most of the research progress in this field has been reported for hybrid systems composed of spin qubits in Nitrogen-vacancy centers in diamond and magnons in yttrium-iron-garnet (YIG), with both materials presenting fabrication challenges for wafer-scale integration. In this thesis, I take a departure from this commonly used hybrid composition and explore hybrid magnetic-quantum systems using more technologically mature material systems. Specifically, I explore silicon vacancy defects in silicon carbide and NiFe (permalloy) microstructures as the components of a hybrid quantum system. I start by describing each subsystem separately, discussing their theoretical basis and experimental methods, before addressing their interactive regimes. Two interaction schemes can be distinguished: one where the magnetic element is 'passive', merely representing a static influence to the spin defects, and another one where it is more 'active', inducing dipole-allowed transitions in the spin states of the vacancy. Remarkably, this 'active' scheme is enabled by magnon nonlinearities in a vortex-state disc, opening up the way towards studying the convergence of quantum systems with the rich nonlinear physics of magnons. I envision the results included in this thesis as a stepping stone for further exploration of magnon nonlinearities to enhance quantum functionalities.

In the study of strongly interacting condensed-matter systems controlled microscopic theories hold a key position. Spin-wave theory, large-N expansion, and $epsilon$-expansion are some of the few successful cornerstones. In this doctoral thesis work, we have developed a novel large-$d$ expansion method, $d$ being the spatial dimension, to study model Hamiltonians hosting a quantum phase transition between a paramagnet and a magnetically ordered phase. A highlight of this technique is that it can consistently describe the entire phase diagram of the above mentioned models, including the quantum critical point. Note that most analytical techniques either efficiently describe only one of the phases or suffer from divergences near the critical point. The idea of large-$d$ formalism is that in this limit, non-local fluctuations become unimportant and that a suitable product state delivers exact expectation values for local observables, with corrections being suppressed in powers of $1/d$. It turns out that, due to momentum summation properties of the interaction structure factor, all diagrams are suppressed in powers of $1/d$ leading to an analytic expansion. We have demonstrated this method in two important systems namely, the coupled-dimer magnets and the transverse-field Ising model. Coupled-dimer magnets are Heisenberg spin systems with two spins, coupled by intra-dimer antiferromagnetic interaction, per crystallographic unit cell (dimer). In turn, spins from neighboring dimers interact via some inter-dimer interaction. A quantum paramagnet is realized for a dominant intra-dimer interaction, while a magnetically ordered phase exists for a dominant (or of the same order as intra-dimer interaction) inter-dimer interaction. These two phases are connected by a quantum phase transition, which is in the Heisenberg O(3) universality class. Microscopic analytical theories to study such systems have been restricted to either only one of the phases or involve uncontrolled approximations. Using a non-linear bond-operator theory for spins with S=$1/2$, we have calculated the $1/d$ expansion of static and dynamic observables for coupled dimers on a hypercubic lattice at zero temperature. Analyticity of the $1/d$ expansion, even at the critical point, is ensured by correctly identifying suitable observables using the mean-field critical exponents. This method yields gapless excitation modes in the continuous symmetry broken phase, as required by Goldstone\'s theorem. In appropriate limits, our results match with perturbation expansion in small ratio of inter-dimer and intra-dimer coupling, performed using continuous unitary transformations, as well as the spin-wave theory for spin-$1/2$ in arbitrary dimensions. We also discuss the Brueckner approach, which relies on small quasiparticle density, and derive the same $1/d$ expansion for the dispersion relation in the disordered phase. Another success of our work is in describing the amplitude (Higgs) mode in coupled-dimer magnets. Our novel method establishes the popular bond-operator theory as a controlled approach. In $d=2$, the results from our calculations are in qualitative agreement with the quantum Monte Carlo study of the square-lattice bilayer Heisenberg AF spin-$1/2$ model. In particular, our results are useful to identify the amplitude (Higgs) mode in the QMC data. The ideas of large-$d$ are also successfully applied to the transverse-field Ising model on a hypercubic lattice. Similar to bond operators, we have introduced auxiliary Bosonsic operators to set up our method in this case. We have also discussed briefly the bilayer Kitaev model, constructed by antiferromagnetically coupling two layers of the Kitaev model on a honeycomb lattice. In this case, we investigate the dimer quantum paramagnetic phase, realized in the strong inter-layer coupling limit. Using bond-operator theory, we calculate the mode dispersion in this phase, within the harmonic approximation. We also conjecture a zero-temperature phase diagram for this model.

An exploration of some organic-inorganic hybrid metal fluorides and lanthanide containing metal organic frameworks (Ln-MOFs) has been carried out under ionothermal conditions. In this synthesis technique an ionic liquid (IL) or deep eutectic mixture (DES) is used as the solvent and in many cases as the provider of the organic structure directing agent. A wide range of ILs and DESs have been investigated as the reaction solvent for the synthesis of organically templated vanadium fluorides and oxyfluorides (VOFs), and initially this has proved to be successful with the isolation of 13 phases, including eight new materials. In the VOFs synthesis the IL acts as a solvent, however the DES acts as a solvent and also as a template delivery agent, where the expected template is provided by the partial breakdown of the urea derivative component. Interestingly, it has been shown that the same structure can be accessible via two different ways; either by using IL with an added templating source, or simply through the use of a DES without any other additive; since the template is provided by the in situ breakdown of the DES. The synthesis of VOFs with extended structures was achieved by the use of the hydrophobic IL 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide (EMIM Tf₂N) as the solvent. [HNC₅H₅][V₂O₂F₅] represents the first VOF with a 2D network that contains exclusively V⁴⁺. This material may be considered as arising via condensation of the previously known ladder-like chains. Furthermore, using imidazole as an added template has produced another layer material that has significant similarities to the [HNC₅H₅][V₂O₂F₅] structure, but with some key differences. Within the same system three other phases were also isolated, including two novel materials displaying the known ladder-type building units. Further investigations in the ionothermal synthesis of VOF using EMIM Tf₂N resulted in a successful synthesis of [NH₄]₂[HNC₇H₁₃][V₇O₆F₁₈], a novel material displaying a unique double layered topology featuring a S = ½ kagome type lattice of V⁴⁺ ions (d¹). Two of the V⁴⁺ based kagome sheets are pillared by V³⁺ ions to form a double layered structure templated by both ammonium and quinuclidinium cations. This compound exhibits a high degree of magnetic frustration, with significant antiferromagnetic interactions but no long range ordering was observed above 2 K. This material presents an interesting comparison to the famous Herbertsmithite, ZnCu₃(OH)₆Cl₂, and may provide an excellent candidate for realising a quantum spin liquid (QSL) ground state. Interestingly, in this system the use of EMIM Tf₂2N as a solvent produces mainly V⁴⁺-containing materials, despite the high reaction temperature (170 °C). This characteristic is unprecedented in VOFs synthesis, as rising the reaction temperature above 150 °C in other techniques (i.e. hydrothermal synthesis) would often result in further reduction of V⁴⁺ to V³⁺. Using the ionothermal technique in the synthesis of hybrid iron fluorides resulted in the isolation of three chain-type materials. Again, the IL acts as the solvent and the DES acts as the solvent and also as the template provider where the expected template is released by the partial breakdown of the urea derivative component of the DES. The synthesis of Ln-MOF using a choline chloride/ 1,3-dimethylurea deep eutectic mixture has produced three novel isostructural materials. Usually, in ionothermally prepared materials (i.e. zeolites) the urea portion of the DES is unstable and breaks down in situ to form ammonium or alkylammonium cations. In the ionothermal synthesis of Ln-MOF, 1,3-dimethyurea (DMU) remains intact and is occluded in the final structure. Using a choline chloride/ethylene glycol deep eutectic solvent led to the isolation of a Ln-MOF with interesting structural properties, however none of the DES components appeared in the final structure. These results demonstrate once more the usefulness and applicability of the ionothermal synthesis method and emphasise how this synthesis technique can be further extended and applied in the preparation of important structures with unique properties and functionalities.

This PhD thesis presents a study of structure-composition correlations of bioactive glasses (BGs) by employing solid-state Nuclear Magnetic Resonance (NMR) spectroscopy. Silicate-based Na2O−CaO−SiO2−P2O5 BGs are utilized clinically and are extensively investigated for bone regeneration purposes. Once implanted in the human body, they facilitate bone regeneration by partially dissolving in the body fluids, followed by the formation of a biomimetic surface-layer of calcium hydroxy-carbonate apatite (HCA). Eventually, the implanted BG totally integrates with the bone. The bioactivity of melt-prepared BGs depends on their composition and structure, primarily on the phosphorus content and the average silicate-network connectivity (NC). We explored these composition-structure relationships for a set of BGs for which the NC and phosphorus contents were varied independently. The short-range structural features of the glasses were explored using 29Si and 31P magic-angle-spinning (MAS) NMR spectroscopy. 31P MAS NMR revealed that the orthophosphate content is directly proportional to the total P content of the glass, with a linear correlation observed between the orthophosphate content and the silicate network connectivity. The bearings of the results for future BG design are discussed. By using multiple-quantum coherence-based 31P NMR experiments, the spatial distribution of orthophosphate groups was probed in the melt prepared BGs, as well as in two mesoporous bioactive glasses prepared by an evaporation-induced self-assembly technique. The results evidence randomly distributed orthophosphate groups in the melt-prepared BGs, whereas the pore-walls of the mesoporous bioactive glasses constitute nanometer-sized clusters of calcium phosphate. The distribution of Na+ ions among the phosphate/silicate groups were studied by heteronuclear dipolar-based 23Na−31P NMR experiments, verifying that sodium is dispersed nearly randomly in the glasses. The phosphorus and proton environments in biomimetically grown HCA were investigated by using 1H and 31P MAS NMR experiments. Our studies revealed that the biomimetic HCA shared many local structural features with synthetic and well-ordered hydroxy-apatite. / <p>At the time of the doctoral defense, the following paper was unpublished and had a status as follows: Paper 4: Accepted.</p>

The recent discoveries of topological insulators (TI) has opened a new realm for study¬ing topological systems and exploring the exotic properties they offer. The in-built topological protection against direct backscattering and absence of localization makes two-dimensional (2D) surface states of bismuth chalcogenide-based strong TI a promising platform for studying interesting phenomena in condensed matter physics like dissipation-less transport, quantum anomalous hall effect, topological magnetoelectric effect, majo¬rana fermions etc. and also makes this system very suitable for applications in the fields of electronics and spintronics. However, realization of these novel states can be difficult because of scattering of surface states from different types of disorders (intrinsic or ex¬trinsic) or the presence of parallel channels in the bulk of the sample which can dominate over surface transport. The main goal of this thesis is to evaluate the performance of TI as an electronic element and look into elastic and inelastic scattering processes and kinetics of these scatterers. In most part of this work we concentrate on the magnitude and origin of low-frequency flicker noise or the 1/f-noise, a key performance marker in electronics, to characterize the electrical transport in TI. In this work we have studied 1/f-noise in both mechanically exfoliated TI-flakes and epitaxially grown TI films by varying chemical potential and temperature. Our study of exfoliated TI-flakes with a wide range of thickness (10 nm to 80 μm) suggests that whereas at thinner (<100 nm) samples and at low temperature (<70 K), the electrical transport happens entirely at the surface, resistance fluctuations in the surface states are mainly caused by potential fluctuations caused by generation-recombination processes in the bulk of TI. Study of 1/f-noise in MBE-grown magnetically doped TI reveals signature of hopping transport through localized bulk mid gap states. These states can either be Cr-impurity band or disorder-induced mobility edge states of bulk valence band. Our study of quantum transport in exfoliated TI-devices indicate presence of a de-coherence mechanism which saturates phase-coherence length and temperature below T< 3 K and results from a unique scattering mechanism caused by localized magnetic moments in these systems

Cette thèse est une étude par diffusion neutronique des pyrochlores Tb2Ti2O7 et Pr2Zr2O7. Ces composés, pour lesquels les ions magnétiques sont des ions Non-Kramers (NK), sont présentés comme de potentielles glaces de spin quantiques. Dans Pr2Zr2O7, l'étude des réponses élastique et inélastique et des structures induites sous champ nous amènent à conclure que l'état fondamental serait une recombinaison du doublet fondamental de champ cristallin (CEF) du fait de l'existence de termes multipolaires dans l'Hamiltonien. Ces termes seraient dus à un couplage magnéto-cristallin. Dans l'approximation de champ moyen, un modèle local de distorsion structurale semble en effet reproduire nos résultats. Dans Tb2Ti2O7, malgré de notables différences avec Pr2Zr2O7, nos mesures indiquent qu'un mécanisme semblable de mélange des fonctions d'onde du doublet fondamental de CEF a lieu. Ce mélange impliquerait des termes multipolaires également dus au couplage magnéto-cristallin et nous avons pu observer une signature directe de ce couplage. Les mécanismes en jeu dans ces systèmes ne seraient pas ceux proposés pour les glaces de spin quantiques mais dus à la sensibilité des ions NK à leur environnement. L'étude de composés non-st¿chiométriques montre la réactivité du magnétisme aux perturbations. / This work is the neutron scattering study of the pyrochlores Tb2Ti2O7 and Pr2Zr2O7. These compounds where magnetic ions are Non-Kramers ions are expected to be quantum spin ices. In Pr2Zr2O7, the study of the elastic and inelastic response together with the study of the magnetic structures in applied magnetic field lead to the conclusion that the magnetic ground state is a mixing of the wave functions of the crystal-field ground state doublet because of quadrupolar terms in the Hamiltonian. These terms would originate from a coupling to the lattice. Using the mean-field approximation, a model based on a local structural distortion reproduces quite well our measurements. Despite strong differences with Pr2Zr2O7, our measurements provide evidence for a similar mechanism in Tb2Ti2O7. Again, this would be caused by multipolar terms in the Hamiltonian reflecting a strong coupling of the magnetic moments to the lattice. Then, these pyrochlores would not be quantum spin ices. Instead, the extreme sensibility to the environment characteristic of the Non-Kramers ions would lead to these fluctuations. Our measurements of samples slightly off-stoichiometry emphases the strong reactivity of the magnetic behavior of these compounds.

Dans cette thèse sont principalement étudiés des systèmes quantiques intégrables critiques avec l’ansatz de Bethe qui ont la propriété particulière d’être non-unitaires ou non-compacts. Ceci concerne des modèles de physique statistique non-locaux tels que la percolation, mais aussi par exemple les systèmes désordonnés. Ce manuscrit présente à la fois des études détaillées de la limite continue de modèles intégrables sur réseau, et développe de nouvelles techniques pour étudier cette correspondance. Dans une première partie nous étudions en détail la limite continue de chaînes de superspins non-unitaires (et parfois non-compactes) qui ont une symétrie orthosymplectique. Nous montrons qu’il s’agit de modèles sigma sur supersphère en calculant leur spectre avec la théorie des champs, avec l’ansatz de Bethe, et numériquement. Leur non-unitarité autorise une brisure spontanée de symétrie habituellement interdite par le théorème de Mermin-Wagner. Leur caractère de perturbation marginale d’une théorie conforme des champs logarithmique est particulièrement étudié. Nous établissons également une correspondance précise entre le spectre et des configurations de boucles avec intersections, et obtenons de nouveaux exposants critiques pour les chemins non-recouvrants compacts ainsi que leurs corrections logarithmiques multiplicatives. Cette étude fut par ailleurs l’occasion de développer une nouvelle méthode pour calculer le spectre d’excitation d’une chaîne de spin quantique critique à partir de l’ansatz de Bethe, incluant les corrections logarithmiques, également en présence de racines de Bethe dites ’en chaînes’, et qui évite les méthodes de Wiener-Hopf et les équations intégrales non-linéaires. Dans une deuxième partie nous abordons l’influence d’un champ magnétique sur une chaîne de spin quantique et montrons que des séries convergentes peuvent être obtenues pour plusieurs quantités physiques telles que l’aimantation acquise ou les exposants critiques, dont les coefficients peuvent être calculés efficacement par récurrence. La structure de ces relations de récurrence permet d’étudier génériquement le spectre d’excitation, et elles sont applicables y compris dans certains cas où les racines de Bethe sont sur une courbe dans le plan complexe. Nous espérons que l’étude de la continuation analytique de ces séries puisse être utile pour les chaînes non-compactes. Par ailleurs, nous montrons que les fluctuations à l’intérieur de la courbe arctique du modèle à six vertex avec conditions aux bords de type mur sont décrites par un champ Gaussien libre avec une constante de couplage dépendant de la position, qui peut être calculée à partir de l’énergie libre de la chaîne XXZ avec une torsion imaginaire dans un champ magnétique. / This thesis mainly deals with integrable quantum critical systems that exhibit peculiar features such as non-unitarity or non-compactness, through the technology of Bethe ansatz. These features arise in non-local statistical physics models such as percolation, but also in disordered systems for example. The manuscript both presents detailed studies of the continuum limit of finite-size lattice integrable models, and develops new techniques to study this correspondence. In a first part we study in great detail the continuum limit of non-unitary (and sometimes non-compact) super spin chains with orthosymplectic symmetry which is shown to be supersphere sigma models, by computing their spectrum from field theory, from the Bethe ansatz, and numerically. The non-unitarity allows for a spontaneous symmetry breaking usually forbidden by the Mermin-Wagner theorem. The fact that they are marginal perturbations of a Logarithmic Conformal Field Theory is particularly investigated. We also establish a precise correspondence between the spectrum and intersecting loops configurations, and derive new critical exponents for fully-packed trails, as well as their multiplicative logarithmic corrections. During this study we developed a new method to compute the excitation spectrum of a critical quantum spin chain from the Bethe ansatz, together with their logarithmic corrections, that is also applicable in presence of so-called ’strings’, and that avoids Wiener-Hopf and Non-Linear Integral Equations. In a second part we address the problem of the behavior of a spin chain in a magnetic field, and show that one can derive convergent series for several physical quantities such as the acquired magnetization or the critical exponents, whose coefficients can be efficiently and explicitely computed recursively using only algebraic manipulations. The structure of the recurrence relations permits to study generically the excitation spectrum content – moreover they are applicable even to some cases where the Bethe roots lie on a curve in the complex plane. It is our hope that the analytic continuation of such series might be helpful the study non-compact spin chains, for which we give some flavour. Besides, we show that the fluctuations within the arctic curve of the six-vertex model with domain-wall boundary conditions are captured by a Gaussian free field with space-dependent coupling constant that can be computed from the free energy of the periodic XXZ spin chain with an imaginary twist and in a magnetic field.

No description available.

The study of topological phases in condensed matter physics has seen remarkable advancements, primarily focusing on systems with a well-defined bulk and boundary. However, the emergence of topological phenomena on self-similar systems, characterized by the absence of a clear distinction between bulk and boundary, presents a fascinating challenge. This thesis focuses on the topological phases on self-similar systems, shedding light on their unique properties through the lens of adiabatic charge pumping. We observe that the spectral flow in these systems exhibits striking qualitative distinctions from that of translationally invariant non-interacting systems subjected to a perpendicular magnetic field. We show that the instantaneous eigenspectra can be used to understand the quantization of the charge pumped over a cycle, and hence to understand the topological character of the system. Furthermore, we establish a correspondence between the local contributions to the Hall conductivity and the spectral flow of edge-like states. We also find that the edge-like states can be approximated as eigenstates of the discrete angular-momentum operator, with their chiral characteristics stemming from this unique perspective. We also investigate the effect of local structure on the topological phases on self-similar structures embedded in two dimensions. We study a geometry dependent model on two self-similar structures having different coordination numbers, constructed from the Sierpinski gasket. For different non-spatial symmetries present in the system, we numerically study and compare the phases on both structures. We characterize these phases by the localization properties of the single-particle states, their robustness to disorder, and by using a real-space topological index. We find that both structures host topologically nontrivial phases and the phase diagrams are different on the two structures, emphasizing the interplay between non-spatial symmetries and the local structure of the self-similar unit in determining topological phases. Furthermore, we demonstrate the presence of topologically ordered chiral spin liquid on fractals by extending the Kitaev model to the Sierpinski Gasket. We show a way to perform the Jordan-Wigner transformation to make this model exactly solvable on the Sierpinski Gasket. This system exhibits a fractal density of states for Majorana modes and showcases a transition from a gapped to a gapless phase. Notably, the gapped phase features symmetry-protected Majorana corner modes, while the gapless phase harbors robust zero-energy and low-energy self-similar Majorana edge-like modes. We also study the vortex excitations, characterized by remarkable localization properties even in small fractal generations. These localized excitations exhibit anyonic behavior, with preliminary calculations hinting at their fundamental differences from Ising anyons observed in the Kitaev model on a honeycomb lattice.