Unusual Thermal Hall Effect in a Kitaev Spin Liquid Candidate α-RuCl_{3}

Cobalt-based pyroxenes: A new playground for Kitaev physics

Recent advances in the study of cobaltites have unveiled their potential as a promising platform for realizing Kitaev physics in honeycomb systems and the Ising model in weakly coupled chain materials. In this manuscript, we explore the magnetic properties of pyroxene SrCoGe[Formula: see text]O[Formula: see text] using a combination of neutron scattering, ab initio methods, and linear spin-wave theory. Through careful examination of inelastic neutron scattering powder spectra, we propose a modified Kitaev model to accurately describe the twisted chains of edge-sharing octahedra surrounding Co[Formula: see text] ions. The extended Kitaev-Heisenberg model, including a significant anisotropic bond-dependent exchange term with [Formula: see text], is identified as the key descriptor of the magnetic interactions in SrCoGe[Formula: see text]O[Formula: see text]. Furthermore, our heat capacity measurements reveal an effect of an external magnetic field (approximately 13 T) which shifts the system from a fragile antiferromagnetic ordering with [Formula: see text] K to a field-induced state. We argue that pyroxenes, particularly those modified by substituting Ge with Si and its less extended [Formula: see text] orbitals, emerge as a platform for the Kitaev model. This opens up possibilities for advancing our understanding of Kitaev physics.

Large oscillatory thermal hall effect in kagome metals

The thermal Hall effect recently provided intriguing probes to the ground state of exotic quantum matters. These observations of transverse thermal Hall signals lead to the debate on the fermionic versus bosonic origins of these phenomena. The recent report of quantum oscillations (QOs) in Kitaev spin liquid points to a possible resolution. The Landau level quantization would most likely capture only the fermionic thermal transport effect. However, the QOs in the thermal Hall effect are generally hard to detect. In this work, we report the observation of a large oscillatory thermal Hall effect of correlated Kagome metals. We detect a 180-degree phase change of the oscillation and demonstrate the phase flip as an essential feature for QOs in the thermal transport properties. More importantly, the QOs in the thermal Hall channel are more profound than those in the electrical Hall channel, which strongly violates the Wiedemann-Franz (WF) law for QOs. This result presents the oscillatory thermal Hall effect as a powerful probe to the correlated quantum materials.

Thermal Hall effects due to topological spin fluctuations in YMnO3

The thermal Hall effect in magnetic insulators has been considered a powerful method for examining the topological nature of charge-neutral quasiparticles such as magnons. Yet, unlike the kagome system, the triangular lattice has received less attention for studying the thermal Hall effect because the scalar spin chirality cancels out between adjacent triangles. However, such cancellation cannot be perfect if the triangular lattice is distorted. Here, we report that the trimerized triangular lattice of multiferroic hexagonal manganite YMnO3 produces a highly unusual thermal Hall effect under an applied magnetic field. Our theoretical calculations demonstrate that the thermal Hall conductivity is related to the splitting of the otherwise degenerate two chiralities of its 120˚ magnetic structure. Our result is one of the most unusual cases of topological physics due to this broken Z2 symmetry of the chirality in the supposedly paramagnetic state of YMnO3, due to strong topological spin fluctuations with the additional intricacy of a Dzyaloshinskii-Moriya interaction.

Possible intermediate quantum spin liquid phase in α-RuCl3 under high magnetic fields up to 100 T

Pursuing the exotic quantum spin liquid (QSL) state in the Kitaev material α-RuCl3 has intrigued great research interest recently. A fascinating question is on the possible existence of a field-induced QSL phase in this compound. Here we perform high-field magnetization measurements of α-RuCl3 up to 102 T employing the non-destructive and destructive pulsed magnets. Under the out-of-plane field along the c* axis (i.e., perpendicular to the honeycomb plane), two quantum phase transitions are uncovered at respectively 35 T and about 83 T, between which lies an intermediate phase as the predicted QSL. This is in sharp contrast to the case with in-plane fields, where a single transition is found at around 7 T and the intermediate QSL phase is absent instead. By measuring the magnetization data with fields tilted from the c* axis up to 90° (i.e., in-plane direction), we obtain the field-angle phase diagram that contains the zigzag, paramagnetic, and QSL phases. Based on the K-J-Γ-[Formula: see text] model for α-RuCl3 with a large Kitaev term we perform density matrix renormalization group simulations and reproduce the quantum phase diagram in excellent agreement with experiments.

Identifying and Constructing Complex Magnon Band Topology

Magnetically ordered materials tend to support bands of coherent propagating spin wave, or magnon, excitations. Topologically protected surface states of magnons offer a new path toward coherent spin transport for spintronics applications. In this work we explore the variety of topological magnon band structures and provide insight into how to efficiently identify topological magnon bands in materials. We do this by adapting the topological quantum chemistry approach that has used constraints imposed by time reversal and crystalline symmetries to enumerate a large class of topological electronic bands. We show how to identify physically relevant models of gapped magnon band topology by using so-called decomposable elementary band representations, and in turn discuss how to use symmetry data to infer the presence of exotic symmetry enforced nodal topology.

Phonon drag thermal Hall effect in metallic strontium titanate

SrTiO₃, a quantum paralectric, displays a detectable phonon thermal Hall effect (THE). Here, we show that the amplitude of the THE is extremely sensitive to stoichiometry. It drastically decreases upon substitution of a tiny fraction of Sr atoms with Ca, which stabilizes the ferroelectric order. It drastically increases by an even lower density of oxygen vacancies, which turn the system to a dilute metal. The enhancement in the metallic state exceeds by far the sum of the electronic and the phononic contributions. We explain this observation as an outcome of three features: 1) Heat is mostly transported by phonons; 2) the electronic Hall angle is extremely large; and 3) there is substantial momentum exchange between electrons and phonons. Starting from Herring's picture of phonon drag, we arrive to a quantitative account of the enhanced THE. Thus, phonon drag, hitherto detected as an amplifier of thermoelectric coefficients, can generate a purely thermal transverse response in a dilute metal with a large Hall angle. Our results reveal a hitherto-unknown consequence of momentum-conserving collisions between electrons and phonons.

Large phonon thermal Hall conductivity in the antiferromagnetic insulator Cu3TeO6

Phonons are known to generate a thermal Hall effect in certain insulators, including oxides with rare-earth impurities, quantum paraelectrics, multiferroic materials, and cuprate Mott insulators. In each case, a special feature of the material is presumed relevant for the underlying mechanism that confers chirality to phonons in a magnetic field. A fundamental question is whether a phonon Hall effect is an unusual occurrence-linked to special characteristics such as skew scattering off rare-earth impurities, structural domains, ferroelectricity, or ferromagnetism-or a much more common property of insulators than hitherto believed. To help answer this question, we have turned to a material with none of the previously encountered special features: the cubic antiferromagnet Cu3TeO6. We find that its thermal Hall conductivity [Formula: see text] is among the largest of any insulator so far. We show that this record-high [Formula: see text] signal is due to phonons, and it does not require the presence of magnetic order, as it persists above the ordering temperature. We conclude that the phonon Hall effect is likely to be a fairly common property of solids.

Direct observation of the Mottness and p-d orbital hybridization in the epitaxial monolayer α-RuCl3

α-RuCl₃, a promising material to accomplish the Kitaev honeycomb model, has attracted enormous interest recently. Mottness and p-d bonds play vital roles in generating Kitaev interactions and underpinning the potential exotic states of quantum magnets, and the van der Waals monolayer is considered to be a better platform to approach a two-dimensional Kitaev model than the bulk. Here, we worked out the growth art of an α-RuCl₃ monolayer on a graphite substrate and studied its electronic structure, particularly the delicate orbital occupations, through scanning tunneling microscopy and spectroscopy. An in-plane lattice expansion of 2.67 ± 0.83% is observed and the pronounced t_2g-p_π and e_g-p_σ hybridization are visualized. The Mott nature is unveiled by an ∼0.6 eV full gap at the Fermi level located inside the t_2g-p_π manifold which is further verified by the density functional theory calculations. The monolayer phase of α-RuCl₃ fulfills the a priori criteria of recent theoretical predictions of tuning the relevant properties in this material and provides a novel platform to explore the Kitaev physics.

Phonon thermal Hall effect in a metallic spin ice

It has become common knowledge that phonons can generate thermal Hall effect in a wide variety of materials, although the underlying mechanism is still controversial. We study longitudinal κxx and transverse κxy thermal conductivity in Pr2Ir2O7, which is a metallic analog of spin ice. Despite the presence of mobile charge carriers, we find that both κxx and κxy are dominated by phonons. A T/H scaling of κxx unambiguously reveals that longitudinal heat current is substantially impeded by resonant scattering of phonons on paramagnetic spins. Upon cooling, the resonant scattering is strongly affected by a development of spin ice correlation and κxx deviates from the scaling in an anisotropic way with respect to field directions. Strikingly, a set of the κxx and κxy data clearly shows that κxy correlates with κxx in its response to magnetic field including a success of the T/H scaling and its failure at low temperature. This remarkable correlation provides solid evidence that an indispensable role is played by spin-phonon scattering not only for hindering the longitudinal heat conduction, but also for generating the transverse response.

Disorder, Low-Energy Excitations, and Topology in the Kitaev Spin Liquid

The Kitaev model is a fascinating example of an exactly solvable model displaying a spin-liquid ground state in two dimensions. However, deviations from the original Kitaev model are expected to appear in real materials. In this Letter, we investigate the fate of Kitaev's spin liquid in the presence of disorder-bond defects or vacancies-for an extended version of the model. Considering static flux backgrounds, we observe a power-law divergence in the low-energy limit of the density of states with a nonuniversal exponent. We link this power-law distribution of energy scales to weakly coupled droplets inside the bulk, in an uncanny similarity to the Griffiths phase often present in the vicinity of disordered quantum phase transitions. If time-reversal symmetry is broken, we find that power-law singularities are tied to the destruction of the topological phase of the Kitaev model in the presence of bond disorder alone. However, there is a transition from this topologically trivial phase with power-law singularities to a topologically nontrivial one for weak to moderate site dilution. Therefore, diluted Kitaev materials are potential candidates to host Kitaev's chiral spin-liquid phase.

Dynamical Anyon Generation in Kitaev Honeycomb Non-Abelian Spin Liquids

Relativistic Mott insulators known as "Kitaev materials" potentially realize spin liquids hosting non-Abelian anyons. Motivated by fault-tolerant quantum-computing applications in this setting, we introduce a dynamical anyon-generation protocol that exploits universal edge physics. The setup features holes in the spin liquid, which define energetically cheap locations for non-Abelian anyons, connected by a narrow bridge that can be tuned between spin liquid and topologically trivial phases. We show that modulating the bridge from trivial to spin liquid over intermediate time scales-quantified by analytics and extensive simulations-deposits non-Abelian anyons into the holes with O(1) probability. The required bridge manipulations can be implemented by integrating the Kitaev material into magnetic tunnel junction arrays that engender locally tunable exchange fields. Combined with existing readout strategies, our protocol reveals a path to topological qubit experiments in Kitaev materials at zero applied magnetic field.

Fluctuations in Heat Current and Scaling Dimension

In this work, we theoretically study the heat flow between two 1+1D chiral gapless systems connected by a point contact. With a small temperature gradient between the two, we find that the ratio between fluctuations of the heat current and the heat current itself is proportional to the scaling dimension-a universal number that characterizes the distribution of the particles tunneling through the point contact. We adopt two different approaches, scattering theory and conformal field theory, to calculate this ratio and see that their results agree. Our findings are useful for probing not only fractional charge excitations in fractional quantum Hall states but also neutral ones.

Thermal Hall Effect of Magnons in Collinear Antiferromagnetic Insulators: Signatures of Magnetic and Topological Phase Transitions

We demonstrate theoretically that the thermal Hall effect of magnons in collinear antiferromagnetic insulators is an indicator of magnetic and topological phase transitions in the magnon spectrum. The transversal heat current of magnons caused by a thermal gradient is calculated for an antiferromagnet on a honeycomb lattice. An applied magnetic field drives the system from the antiferromagnetic phase via a spin-flop phase into the field-polarized phase. In addition to these magnetic phase transitions, we find topological phase transitions within the spin-flop phase. Both types of transitions manifest themselves in prominent and distinguishing features in the thermal conductivity, which changes by several orders of magnitude. The variation of temperature provides a tool to discern experimentally the two types of phase transitions. We include numerical results for the van der Waals magnet MnPS_{3}.

Honeycomb-Structure RuI3 , A New Quantum Material Related to α-RuCl3

The layered honeycomb lattice material α-RuCl₃ has emerged as a prime candidate for displaying the Kitaev quantum spin liquid state, and as such has attracted much research interest. Here a new layered honeycomb lattice polymorph of RuI₃ , a material that is strongly chemically and structurally related to α-RuCl₃ is described_. The material is synthesized at moderately elevated pressures and is stable under ambient conditions. Preliminary characterization reveals that it is a metallic conductor, with the absence of long-range magnetic order down to 0.35 K and an unusually large T-linear contribution to the heat capacity. It is proposed that this phase, with a layered honeycomb lattice and strong spin-orbit coupling, provides a new route for the characterization of quantum materials.

Degeneracy-Projected Polarization Formulas for Hall-Type Conductivities

Kubo formulas for Hall, transverse thermoelectric, and thermal Hall conductivities are simplified into on-shell commutators of degeneracy projected polarizations. The new expressions are computationally economical, and apply to general Hamiltonians without a gap restriction. We show that Hall currents in open boundaries are carried by gapless chiral excitations. Extrapolation of finite lattice calculations to the dc-thermodynamic limit is demonstrated for a disordered metal.

Identification of a Kitaev quantum spin liquid by magnetic field angle dependence

Quantum spin liquids realize massive entanglement and fractional quasiparticles from localized spins, proposed as an avenue for quantum science and technology. In particular, topological quantum computations are suggested in the non-abelian phase of Kitaev quantum spin liquid with Majorana fermions, and detection of Majorana fermions is one of the most outstanding problems in modern condensed matter physics. Here, we propose a concrete way to identify the non-abelian Kitaev quantum spin liquid by magnetic field angle dependence. Topologically protected critical lines exist on a plane of magnetic field angles, and their shapes are determined by microscopic spin interactions. A chirality operator plays a key role in demonstrating microscopic dependences of the critical lines. We also show that the chirality operator can be used to evaluate topological properties of the non-abelian Kitaev quantum spin liquid without relying on Majorana fermion descriptions. Experimental criteria for the non-abelian spin liquid state are provided for future experiments.

Non-Abelian phase of Kitaev quantum spin liquid is promising for topological quantum computation. Here, the authors propose a way to identify the non-abelian Kitaev quantum spin liquid by magnetic field angle dependence, providing criteria for such a state for future experiments.

Half-integer quantized anomalous thermal Hall effect in the Kitaev material candidate α-RuCl3

Half-integer thermal quantum Hall conductance has recently been reported for the two-dimensional honeycomb material α-RuCl₃ We found that the half-integer thermal Hall plateau appears even for a magnetic field with no out-of-plane components. The measured field-angular variation of the quantized thermal Hall conductance has the same sign structure as the topological Chern number of the pure Kitaev spin liquid. This observation suggests that the non-Abelian topological order associated with fractionalization of the local magnetic moments persists even in the presence of non-Kitaev interactions in α-RuCl₃.

Electric Probe for the Toric Code Phase in Kitaev Materials through the Hyperfine Interaction

The Kitaev model is a remarkable spin model with gapped and gapless spin liquid phases, which are potentially realized in iridates and α-RuCl_{3}. In the recent experiment of α-RuCl_{3}, the signature of a nematic transition to the gapped toric code phase, which breaks the C_{3} symmetry of the system, has been observed through the angle dependence of the heat capacity. We here propose a mechanism by which the nematic transition can be detected electrically. This is seemingly impossible because J_{eff}=1/2 spins do not have an electric quadrupole moment (EQM). However, in the second-order perturbation, the virtual state with a nonzero EQM appears, which makes the nematic order parameter detectable by nuclear magnetic resonance and Mössbauer spectroscopy. The purely magnetic origin of the EQM is different from conventional electronic nematic phases, allowing the direct detection of the realization of Kitaev's toric error-correction code.

Identification of magnetic interactions and high-field quantum spin liquid in α-RuCl3

The frustrated magnet α-RuCl3 constitutes a fascinating quantum material platform that harbors the intriguing Kitaev physics. However, a consensus on its intricate spin interactions and field-induced quantum phases has not been reached yet. Here we exploit multiple state-of-the-art many-body methods and determine the microscopic spin model that quantitatively explains major observations in α-RuCl3, including the zigzag order, double-peak specific heat, magnetic anisotropy, and the characteristic M-star dynamical spin structure, etc. According to our model simulations, the in-plane field drives the system into the polarized phase at about 7 T and a thermal fractionalization occurs at finite temperature, reconciling observations in different experiments. Under out-of-plane fields, the zigzag order is suppressed at 35 T, above which, and below a polarization field of 100 T level, there emerges a field-induced quantum spin liquid. The fractional entropy and algebraic low-temperature specific heat unveil the nature of a gapless spin liquid, which can be explored in high-field measurements on α-RuCl3.

Giant phonon anomalies in the proximate Kitaev quantum spin liquid α-RuCl3

The Kitaev quantum spin liquid epitomizes an entangled topological state, for which two flavors of fractionalized low-energy excitations are predicted: the itinerant Majorana fermion and the Z2 gauge flux. It was proposed recently that fingerprints of fractional excitations are encoded in the phonon spectra of Kitaev quantum spin liquids through a novel fractional-excitation-phonon coupling. Here, we detect anomalous phonon effects in α-RuCl3 using inelastic X-ray scattering with meV resolution. At high temperature, we discover interlaced optical phonons intercepting a transverse acoustic phonon between 3 and 7 meV. Upon decreasing temperature, the optical phonons display a large intensity enhancement near the Kitaev energy, JK~8 meV, that coincides with a giant acoustic phonon softening near the Z2 gauge flux energy scale. These phonon anomalies signify the coupling of phonon and Kitaev magnetic excitations in α-RuCl3 and demonstrates a proof-of-principle method to detect anomalous excitations in topological quantum materials.

Sign Structure of Thermal Hall Conductivity and Topological Magnons for In-Plane Field Polarized Kitaev Magnets

The appearance of half-quantized thermal Hall conductivity in α-RuCl_{3} in the presence of in-plane magnetic fields has been taken as a strong evidence for the Kitaev spin liquid. Apart from the quantization, the observed sign structure of the thermal Hall conductivity is also consistent with predictions from the exact solution of the Kitaev honeycomb model. Namely, the thermal Hall conductivity changes sign when the field direction is reversed with respect to the heat current, which is perpendicular to one of the three nearest neighbor bonds on the honeycomb lattice. On the other hand, the thermal Hall conductivity is almost zero when the field is applied along the bond direction. Here, we theoretically demonstrate that such a peculiar sign structure of the thermal Hall conductivity is a generic property of the polarized state in the presence of in-plane magnetic fields. In this case, the thermal Hall effect arises from topological magnons with finite Chern numbers, and the sign structure follows from the symmetries of the momentum space Berry curvature. Using a realistic spin model with bond-dependent interactions, we show that the thermal Hall conductivity can have a magnitude comparable to that observed in the experiments. Hence, the sign structure alone cannot make a strong case for the Kitaev spin liquid. The quantization at very low temperatures, however, will be a decisive test as the magnon contribution vanishes in the zero temperature limit.

Chemistry of Quantum Spin Liquids

Quantum spin liquids are an exciting playground for exotic physical phenomena and emergent many-body quantum states. The realization and discovery of quantum spin liquid candidate materials and associated phenomena lie at the intersection of solid-state chemistry, condensed matter physics, and materials science and engineering. In this review, we provide the current status of the crystal chemistry, synthetic techniques, physical properties, and research methods in the field of quantum spin liquids. We highlight a number of specific quantum spin liquid candidate materials and their structure-property relationships, elucidating their fascinating behavior and connecting it to the intricacies of their structures. Furthermore, we share our thoughts on defects and their inevitable presence in materials, of which quantum spin liquids are no exception, which can complicate the interpretation of characterization of these materials, and urge the community to extend their attention to materials preparation and data analysis, cognizant of the impact of defects. This review was written with the intention of providing guidance on improving the materials design and growth of quantum spin liquids, and to paint a picture of the beauty of the underlying chemistry of this exciting class of materials.

Honeycomb layered oxides: structure, energy storage, transport, topology and relevant insights

The advent of nanotechnology has hurtled the discovery and development of nanostructured materials with stellar chemical and physical functionalities in a bid to address issues in energy, environment, telecommunications and healthcare. In this quest, a class of two-dimensional layered materials consisting of alkali or coinage metal atoms sandwiched between slabs exclusively made of transition metal and chalcogen (or pnictogen) atoms arranged in a honeycomb fashion have emerged as materials exhibiting fascinatingly rich crystal chemistry, high-voltage electrochemistry, fast cation diffusion besides playing host to varied exotic electromagnetic and topological phenomena. Currently, with a niche application in energy storage as high-voltage materials, this class of honeycomb layered oxides serves as ideal pedagogical exemplars of the innumerable capabilities of nanomaterials drawing immense interest in multiple fields ranging from materials science, solid-state chemistry, electrochemistry and condensed matter physics. In this review, we delineate the relevant chemistry and physics of honeycomb layered oxides, and discuss their functionalities for tunable electrochemistry, superfast ionic conduction, electromagnetism and topology. Moreover, we elucidate the unexplored albeit vastly promising crystal chemistry space whilst outlining effective ways to identify regions within this compositional space, particularly where interesting electromagnetic and topological properties could be lurking within the aforementioned alkali and coinage-metal honeycomb layered oxide structures. We conclude by pointing towards possible future research directions, particularly the prospective realisation of Kitaev-Heisenberg-Dzyaloshinskii-Moriya interactions with single crystals and Floquet theory in closely-related honeycomb layered oxide materials.

Sizable Suppression of Thermal Hall Effect upon Isotopic Substitution in SrTiO_{3}

We report measurements of the thermal Hall effect in single crystals of both pristine and isotopically substituted strontium titanate. We discovered a 2 orders of magnitude difference in the thermal Hall conductivity between SrTi^{16}O_{3} and ^{18}O-enriched SrTi^{18}O_{3} samples. In most temperature ranges, the magnitude of thermal Hall conductivity (κ_{xy}) in SrTi^{18}O_{3} is proportional to the magnitude of the longitudinal thermal conductivity (κ_{xx}), which suggests a phonon-mediated thermal Hall effect. However, they deviate in the temperature of their maxima, and the thermal Hall angle ratio (|κ_{xy}/κ_{xx}|) shows anomalously decreasing behavior below the ferroelectric Curie temperature T_{c}∼25  K. This observation suggests a new underlying mechanism, as the conventional scenario cannot explain such differences within the slight change in phonon spectrum. Notably, the difference in magnitude of thermal Hall conductivity and rapidly decreasing thermal Hall angle ratio in SrTi^{18}O_{3} is correlated with the strength of quantum critical fluctuations in this displacive ferroelectric. This relation points to a link between the quantum critical physics of strontium titanate and its thermal Hall effect, a possible clue to explain this example of an exotic phenomenon in nonmagnetic insulating systems.

Thermal Hall conductivity in the cuprate Mott insulators Nd2CuO4 and Sr2CuO2Cl2

The heat carriers responsible for the unexpectedly large thermal Hall conductivity of the cuprate Mott insulator La₂CuO₄ were recently shown to be phonons. However, the mechanism by which phonons in cuprates acquire chirality in a magnetic field is still unknown. Here, we report a similar thermal Hall conductivity in two cuprate Mott insulators with significantly different crystal structures and magnetic orders – Nd₂CuO₄ and Sr₂CuO₂Cl₂ – and show that two potential mechanisms can be excluded – the scattering of phonons by rare-earth impurities and by structural domains. Our comparative study further reveals that orthorhombicity, apical oxygens, the tilting of oxygen octahedra and the canting of spins out of the CuO₂ planes are not essential to the mechanism of chirality. Our findings point to a chiral mechanism coming from a coupling of acoustic phonons to the intrinsic excitations of the CuO₂ planes.

What makes the phonons in cuprates become chiral, as measured by their thermal Hall effect, is an unresolved question. Here, the authors rule out two extrinsic mechanisms and argue that chirality comes from a coupling of acoustic phonons to the intrinsic excitations of the CuO₂ planes.

Universal Behavior of the Thermal Hall Conductivity

We report theoretical and experimental analyses of the thermal Hall conductivity in correlated systems. For both fermionic and bosonic excitations with nontrivial topology, we show that at "intermediate" temperatures, the thermal Hall conductivity exhibits an unexpected universal scaling with a simple exponential form. At low temperatures, it behaves differently and reflects the spectral properties of underlying excitations. Our predictions are examined as examples in two prototype compounds, the quantum paraelectric SrTiO_{3} and the spin-liquid compound RuCl_{3}. The experimental data can be largely covered by our proposed minimal phenomenological model independent of microscopic details, revealing dominant bosonic contributions in SrTiO_{3} and gapped fermionic excitations in RuCl_{3}. Our work establishes a phenomenological link between microscopic models and experimental data and provides a unified basis for analyzing the thermal Hall conductivity in correlated systems over a wide temperature region.

Phonon Thermal Hall Effect in Strontium Titanate

It has been known for more than a decade that phonons can produce an off-diagonal thermal conductivity in the presence of a magnetic field. Recent studies of thermal Hall conductivity, κ_{xy}, in a variety of contexts, however, have assumed a negligibly small phonon contribution. We present a study of κ_{xy} in quantum paraelectric SrTiO_{3}, which is a nonmagnetic insulator and find that its peak value exceeds what has been reported in any other insulator, including those in which the signal has been qualified as "giant." Remarkably, κ_{xy}(T) and κ(T) peak at the same temperature and the former decreases faster than the latter at both sides of the peak. Interestingly, in the case of La_{2}CuO_{4} and α-RuCl_{3}, κ_{xy}(T) and κ(T) peak also at the same temperature. We also studied KTaO_{3} and found a small signal, indicating that a sizable κ_{xy}(T) is not a generic feature of quantum paraelectrics. Combined to other observations, this points to a crucial role played by antiferrodistortive domains in generating κ_{xy} of this solid.

Magnon Spin Relaxation and Spin Hall Effect Due to the Dipolar Interaction in Antiferromagnetic Insulators

In the absence of external magnetic field and Dzyaloshinskii-Moriya interaction, the magnon excitations in a uniaxial antiferromagnet insulator are usually described by two degenerate magnon modes with the same dispersion but opposite polarizations. In this Letter, we show that these two modes are actually coupled intrinsically through an effective spin-orbit coupling due to the dipolar interaction. The magnon spin dynamics and transport thus display various electronlike spin-orbit phenomena, such as the D'yakonov-Perel'-type spin relaxation and an intrinsic (inverse) spin Hall effect. Our work may potentially broaden the applications of antiferromagnetic insulators in spintronic devices.

Thermal-transport studies of kagomé antiferromagnets

Searching for the ground state of a kagomé Heisenberg antiferromagnet (KHA) has been one of the central issues of condensed-matter physics, because the KHA is expected to host spin-liquid phases with exotic elementary excitations. Here, we show our longitudinal ([Formula: see text]) and transverse ([Formula: see text]) thermal conductivities measurements of the two kagomé materials, volborthite and Ca kapellasite. Although magnetic orders appear at temperatures much lower than the antiferromagnetic energy scale in both materials, the nature of spin liquids can be captured above the transition temperatures. The temperature and field dependence of [Formula: see text] is analyzed by spin and phonon contributions, and large sample variations of the spin contribution are found in volborthite. Clear changes in [Formula: see text] are observed at the multiple magnetic transitions in volborthite, showing different magnetic thermal conduction in different magnetic structures. These magnetic contributions are not clearly observed in low-[Formula: see text] crystals of volborthite, and are almost absent in Ca kapellasite, showing the high sensitivity of the magnetic excitation in [Formula: see text] to the defects in crystals. On the other hand, a clear thermal Hall signal has been observed in the lowest-[Formula: see text] crystal of volborthite and in Ca kapellasite. Remarkably, both the temperature dependence and the magnitude of [Formula: see text] of volborthite are found to be very similar to those of Ca kapellasite, despite of about an order of magnitude difference in [Formula: see text] We find that [Formula: see text] of both compounds is well reproduced, both qualitatively and quantitatively, by spin excitations described by the Schwinger-boson mean-field theory applied to KHA with the Dzyaloshinskii-Moriya interaction. This excellent agreement demonstrates not only that the thermal Hall effect in these kagomé antiferromagnets is caused by spins in the spin liquid phase, but also that the elementary excitations of this spin liquid phase are well described by the bosonic spin excitations.

Specific heat of 2D interacting Majorana fermions from holography

Majorana fermions are a fascinating medium for discovering new phases of matter. However, the standard analytical tools are very limited in probing the non-perturbative aspects of interacting Majoranas in more than one dimensions. Here, we employ the holographic correspondence to determine the specific heat of a two-dimensional interacting gapless Majorana system. To perform our analysis we first describe the interactions in terms of a pseudo-scalar torsion field. We then allow fluctuations in the background curvature thus identifying our model with a (2 + 1)-dimensional Anti-de Sitter (AdS) geometry with torsion. By employing the AdS/CFT correspondence, we show that the interacting model is dual to a (1 + 1)-dimensional conformal field theory (CFT) with central charge that depends on the interaction coupling. This non-perturbative result enables us to determine the effect interactions have in the specific heat of the system at the zero temperature limit.

Heisenberg-Kitaev physics in magnetic fields

Magnetic insulators in the regime of strong spin-orbit coupling exhibit intriguing behaviors in external magnetic fields, reflecting the frustrated nature of their effective interactions. We review the recent advances in understanding the field responses of materials that are described by models with strongly bond-dependent spin exchange interactions, such as Kitaev's celebrated honeycomb model and its extensions. We discuss the field-induced phases and the complex magnetization processes found in these theories and compare with experimental results in the layered Mott insulators [Formula: see text]-RuCl₃ and Na₂IrO₃, which are believed to realize this fascinating physics.

Vestiges of Topological Phase Transitions in Kitaev Quantum Spin Liquids

We investigate signatures of topological quantum phase transitions (TQPTs) between the Z_{2} quantum spin liquids (QSLs). In two spatial dimensions, Z_{2} QSLs and their TQPTs are only well defined at zero temperature (T=0), and it is imperative to clarify their observable signatures under nonzero temperatures. Here, we present the vestiges of TQPTs between Z_{2} QSLs with Majorana fermions in terms of thermal Hall conductivity κ_{xy} at nonzero temperatures. The κ_{xy}/T shows characteristic temperature dependences around TQPTs. We argue that an exponential upturn near T=0 and the peak of κ_{xy}/T around massive excitation energy are observable smoking-gun signals of the TQPTs. Quantum critical fan-shape temperature dependences are uncovered across TQPTs. We also perform the parton mean-field analysis on a modified Kitaev model with next-nearest neighbor interactions finding TQPTs between the phases with different Chern numbers and their vestiges self-consistently. We discuss the implication of our results to the recent experiments in α-RuCl_{3}.

Emergence of a field-driven U(1) spin liquid in the Kitaev honeycomb model

In the field of quantum magnetism, the exactly solvable Kitaev honeycomb model serves as a paradigm for the fractionalization of spin degrees of freedom and the formation of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Bbb Z}_2$$\end{document}Z2 quantum spin liquids. An intense experimental search has led to the discovery of a number of spin-orbit entangled Mott insulators that realize its characteristic bond-directional interactions and, in the presence of magnetic fields, exhibit no indications of long-range order. Here, we map out the complete phase diagram of the Kitaev model in tilted magnetic fields and report the emergence of a distinct gapless quantum spin liquid at intermediate field strengths. Analyzing a number of static, dynamical, and finite temperature quantities using numerical exact diagonalization techniques, we find strong evidence that this phase exhibits gapless fermions coupled to a massless U(1) gauge field. We discuss its stability in the presence of perturbations that naturally arise in spin-orbit entangled candidate materials.

The Kitaev model is intensively studied as an exactly-solvable starting point for theoretical studies of quantum spin liquid states. Hickey and Trebst show that magnetic fields can destabilize the well-known gapped Kitaev spin liquid and induce a new gapless spin liquid, with a distinct gauge structure and neutral Fermi surface.

Interplay of Spin and Spatial Anisotropy in Low-Dimensional Quantum Magnets with Spin 1/2

Quantum Heisenberg chain and square lattices are important paradigms of a low-dimensional magnetism. Their ground states are determined by the strength of quantum fluctuations. Correspondingly, the ground state of a rectangular lattice interpolates between the spin liquid and the ordered collinear Néel state with the partially reduced order parameter. The diversity of additional exchange interactions offers variety of quantum models derived from the aforementioned paradigms. Besides the spatial anisotropy of the exchange coupling, controlling the lattice dimensionality and ground-state properties, the spin anisotropy (intrinsic or induced by the magnetic field) represents another important effect disturbing a rotational symmetry of the spin system. The S = 1/2 easy-axis and easy-plane XXZ models on the square lattice even for extremely weak spin anisotropies undergo Heisenberg-Ising and Heisenberg-XY crossovers, respectively, acting as precursors to the onset of the finite-temperature phase transitions within the two-dimensional Ising universality class (for the easy axis anisotropy) and a topological Berezinskii–Kosterlitz–Thouless phase transition (for the easy-plane anisotropy). Experimental realizations of the S = 1/2 two-dimensional XXZ models in bulk quantum magnets appeared only recently. Partial solutions of the problems associated with their experimental identifications are discussed and some possibilities of future investigations in quantum magnets on the square and rectangular lattice are outlined.

A cascade of phase transitions in an orbitally mixed half-filled Landau level

Half-filled Landau levels host an emergent Fermi liquid that displays instability toward pairing, culminating in a gapped even-denominator fractional quantum Hall ground state. While this pairing may be probed by tuning the polarization of carriers in competing orbital and spin degrees of freedom, sufficiently high quality platforms offering such tunability remain few. We explore the ground states at filling factor ν = 5/2 in ZnO-based two-dimensional electron systems through a forced intersection of opposing spin branches of Landau levels taking quantum numbers N = 1 and 0. We reveal a cascade of phases with distinct magnetotransport features including a gapped phase polarized in the N = 1 level and a compressible phase in N = 0, along with an unexpected Fermi liquid, a second gapped, and a strongly anisotropic nematic-like phase at intermediate polarizations when the levels are near degeneracy. The phase diagram is produced by analyzing the proximity of the intersecting levels and highlights the excellent reproducibility and controllability that ZnO offers for exploring exotic fractionalized electronic phases.

Spin Thermal Hall Conductivity of a Kagome Antiferromagnet

A clear thermal Hall signal (κ_{xy}) was observed in the spin-liquid phase of the S=1/2 kagome antiferromagnet Ca kapellasite [CaCu_{3}(OH)_{6}Cl_{2}·0.6H_{2}O]. We found that κ_{xy} is well reproduced, both qualitatively and quantitatively, using the Schwinger-boson mean-field theory with the Dzyaloshinskii-Moriya interaction of D/J∼0.1. In particular, κ_{xy} values of Ca kapellasite and those of another kagome antiferromagnet, volborthite, converge to one single curve in simulations modeled using Schwinger bosons, indicating a common temperature dependence of κ_{xy} for the spins of a kagome antiferromagnet.