Kitaev Magnets Research Articles

One-third magnetization plateau in Quantum Kagome antiferromagnet

The emergence of nontrivial quantum states from competing interactions is a central issue in quantum magnetism. In particular, for the realization of the quantum spin-liquid state, extensive studies have been conducted on frustrated systems, such as kagome antiferromagnets and Kitaev magnets. Novel quantum states in magnetic fields have remained elusive despite the prediction of rich physics. This can be attributed to material scarcity and the difficulty of precise measurements under ultra-high magnetic fields. Here, in this study, we develop the Kapellasite-type compound InCu3(OH)6Cl3, whose exchange interactions are in appropriate energy scale to comprehensively elucidate the magnetic properties of the frustrated S = 1/2 kagome antiferromagnet. The one-third magnetization plateau was clearly observed. Moreover, the large temperature-linear term in the heat capacity was observed in the magnetic fields, indicating the excitation of gapless quasiparticles in the vicinity of the plateau. These results shed light on the critical behaviors between quantum spin-liquid and -solid in kagome antiferromagnets under high magnetic fields.

Anisotropy of the zigzag order in the Kitaev honeycomb magnet α−RuBr3

Kitaev materials often order magnetically at low temperatures due to the presence of non-Kitaev interactions. Torque magnetometry is a very sensitive technique for probing the magnetic anisotropy, which is critical in understanding the magnetic ground state. In this paper, we report detailed single-crystal torque measurements in the proposed Kitaev candidate honeycomb magnet α−RuBr3, which displays zigzag order below 34 K. Based on angular-dependent torque studies in magnetic fields up to 16 T rotated in the plane normal to the honeycomb layers, we find an easy-plane anisotropy with a temperature dependence of the torque amplitude following closely the behavior of the powder magnetic susceptibility. The torque for the field rotated in the honeycomb plane has a clear sixfold periodicity with a sawtooth shape, reflecting the threefold symmetry of the crystal structure and stabilization of different zigzag domains depending on the field orientation, with a torque amplitude that follows an order parameter form inside the zigzag phase. By comparing experimental data with theoretical calculations we highlight the importance of relevant anisotropic interactions and the role of the competition between different zigzag domains in this candidate Kitaev magnet. Published by the American Physical Society 2024

Spin-orbit entangled moments and magnetic exchange interactions in cobalt-based honeycomb magnets BaCo2(XO4)2 (X = P, As, Sb)

Co-based honeycomb magnets have been actively studied recently for the potential realization of emergent quantum magnetism therein such as the Kitaev spin liquid. Here we employ density functional and dynamical mean-field theory methods to examine a family of the Kitaev magnet candidates BaCo2(XO4)2 (X = P, As, Sb), where the compound with X = Sb being not synthesized yet. Our study confirms the formation of Mott insulating phase and the Jeff = 1/2 spin moments at Co2+ sites despite the presence of a sizable amount of trigonal crystal field in all three compounds. The pnictogen substitution from phosphorus to antimony significantly changes the in-plane lattice parameters and direct overlap integral between the neighboring Co ions, leading to the suppression of the Heisenberg interaction. More interestingly, the marginal antiferromagnetic nearest-neighbor Kitaev term changes sign into a ferromagnetic one and becomes sizable at the X = Sb limit. Our study suggests that the pnictogen substitution can be a viable route to continuously tune magnetic exchange interactions and to promote magnetic frustration for the realization of potential spin liquid phases in BaCo2(XO4)2.

Anisotropic magnetic interactions in a candidate Kitaev spin liquid close to a metal-insulator transition

In the Kitaev honeycomb model, spins coupled by strongly-frustrated anisotropic interactions do not order at low temperature but instead form a quantum spin liquid with spin fractionalisation into Majorana fermions and static fluxes. The realization of such a model in crystalline materials could lead to major breakthroughs in understanding entangled quantum states, however achieving this in practice is a very challenging task. The recently synthesized honeycomb material RuI3 shows no long-range magnetic order down to the lowest probed temperatures and has been theoretically proposed as a quantum spin liquid candidate material on the verge of an insulator to metal transition. Here we report a comprehensive study of the magnetic anisotropy in un-twinned single crystals via torque magnetometry and detect clear signatures of strongly anisotropic and frustrated magnetic interactions. We attribute the development of sawtooth and six-fold torque signal to strongly anisotropic, bond-dependent magnetic interactions by comparing to theoretical calculations. As a function of magnetic field strength at low temperatures, torque shows an unusual non-parabolic dependence suggestive of a proximity to a field-induced transition. Thus, RuI3, without signatures of long-range magnetic order, displays key hallmarks of an exciting candidate for extended Kitaev magnetism with enhanced quantum fluctuations.

Response functions for electric field induced two-dimensional nonlinear spectroscopy in a Kitaev magnet

We study the dynamical response functions relevant for electric field induced two-dimensional (2D) coherent nonlinear optical spectroscopy in a Kitaev magnet at finite temperature. We show that these response functions are susceptible to both types of fractional quasiparticles of this quantum spin-liquid, i.e. fermions and flux visons. Focusing on the second order response, we find a strong antidiagonal feature in the 2D frequency plane, related to the galvanoelectric effect of the fractional fermions. Perpendicular to the antidiagonal, the width of this feature is set by quasiparticle relaxation rates beyond the bare Kitaev magnet, thereby providing access to single-particle characteristics within a multi-particle continuum. While the 2D spectrum of the response is set by the fermionic quasiparticles and displays Fermi blocking versus temperature, the emergent bond randomness which arises due to thermally populated visons strongly modifies the fermionic spectrum. Therefore also the presence of gauge excitations is manifest in the 2D nonlinear response as the temperature is increased beyond the flux proliferation crossover.

Probing Majorana Wave Functions in Kitaev Honeycomb Spin Liquids with Second-Order Two-Dimensional Spectroscopy.

Two-dimensional coherent terahertz spectroscopy (2DCS) emerges as a valuable tool to probe the nature, couplings, and lifetimes of excitations in quantum materials. It thus promises to identify unique signatures of spin liquid states in quantum magnets by directly probing properties of their exotic fractionalized excitations. Here, we calculate the second-order 2DCS of the Kitaev honeycomb model and demonstrate that distinct spin liquid fingerprints appear already in this lowest-order nonlinear response χ_{yzx}^{(2)}(ω_{1},ω_{2}) when using crossed light polarizations. We further relate the off-diagonal 2DCS peaks to the localized nature of the matter Majorana excitations trapped by Z_{2} flux excitations and show that 2DCS thus directly probes the inverse participation ratio of Majorana wave functions. By providing experimentally observable features of spin liquid states in the 2D spectrum, our Letter can guide future 2DCS experiments on Kitaev magnets.

Exploring rare-earth Kitaev magnets by massive-scale computational analysis

The Kitaev honeycomb model plays a pivotal role in the quest for quantum spin liquids, in which fractional quasiparticles would provide applications in decoherence-free topological quantum computing. The key ingredient is the bond-dependent Ising-type interactions, dubbed the Kitaev interactions, which require strong entanglement between spin and orbital degrees of freedom. Here we investigate the identification and design of rare-earth materials displaying robust Kitaev interactions. We scrutinize all possible 4f electron configurations, which require up to 6+ million intermediate states in the perturbation processes, by developing a parallel computational program designed for massive-scale calculations. Our analysis reveals a predominant interplay between the isotropic Heisenberg J and anisotropic Kitaev K interactions across all realizations of the Kramers doublets. Remarkably, instances featuring 4f3 and 4f11 configurations showcase the prevalence of K over J, presenting unexpected prospects for exploring the Kitaev quantum spin liquids in compounds, including Nd3+ and Er3+, respectively.

Magnetocaloric effect of topological excitations in Kitaev magnets

Traditional magnetic sub-Kelvin cooling relies on the nearly free local moments in hydrate paramagnetic salts, whose utility is hampered by the dilute magnetic ions and low thermal conductivity. Here we propose to use instead fractional excitations inherent to quantum spin liquids (QSLs) as an alternative, which are sensitive to external fields and can induce a very distinctive magnetocaloric effect. With state-of-the-art tensor-network approach, we compute low-temperature properties of Kitaev honeycomb model. For the ferromagnetic case, strong demagnetization cooling effect is observed due to the nearly free Z2 vortices via spin fractionalization, described by a paramagnetic equation of state with a renormalized Curie constant. For the antiferromagnetic Kitaev case, we uncover an intermediate-field gapless QSL phase with very large spin entropy, possibly due to the emergence of spinon Fermi surface and gauge field. Potential realization of topological excitation magnetocalorics in Kitaev materials is also discussed, which may offer a promising pathway to circumvent existing limitations in the paramagnetic hydrates.

Eight-color chiral spin liquid in the S=1 bilinear-biquadratic model with Kitaev interactions

Multipolar spin systems provide a rich ground for the emergence of unexpected states of matter due to their enlarged spin degree of freedom. In this study, with a specific emphasis on S=1 magnets, we explore the interplay between spin nematic states and spin liquids. Based on the foundations laid in the prior work [R. Pohle , ], we investigate the S=1 Kitaev model with bilinear-biquadratic interactions, which stabilizes, next to Kitaev spin liquid, spin nematic and triple-q phases, also an exotic chiral spin liquid. Through a systematic reduction of the spin degree of freedom—from CP2 to CP1 and ultimately to a discrete eight-color model—we provide an intuitive understanding of the nature and origin of this chiral spin liquid. We find that the chiral spin liquid is characterized by an extensive ground-state degeneracy, bound by a residual entropy, extremely short-ranged correlations, a nonzero scalar spin chirality marked by Z2 flux order, and a gapped continuum of excitations. Our work contributes not only to the specific exploration of S=1 Kitaev magnets but also to the broader understanding of the importance of multipolar spin degree of freedom on the ground state and excitation properties in quantum magnets. Published by the American Physical Society 2024

Topological phase diagrams of in-plane field polarized Kitaev magnets

While the existence of a magnetic field induced quantum spin liquid in Kitaev magnets remains under debate, its topological properties often extend to proximal phases where they can lead to unusual behaviors of both fundamental and applied interests. Subjecting a generic nearest-neighbor spin model of Kitaev magnets to a sufficiently strong in-plane magnetic field, we study the resulting polarized phase and the associated magnon excitations. In contrast to the case of an out-of-plane magnetic field where the magnon band topology is enforced by symmetry, we find that it is possible for topologically trivial and nontrivial parameter regimes to coexist under in-plane magnetic fields. We map out the topological phase diagrams of the magnon bands, revealing a rich pattern of variation of the Chern number over the parameter space and the field angle. We further compute the magnon thermal Hall conductivity as a weighted summation of Berry curvatures, and discuss experimental implications of our results to planar thermal Hall effects in Kitaev magnets. Published by the American Physical Society 2024

Chiral excitations and the intermediate-field regime in the Kitaev magnet α−RuCl3

In the Kitaev magnet α-RuCl3, the existence of a magnetic-field-induced quantum spin-liquid phase and of anyonic excitations is controversially discussed. We address this elusive, exotic phase via helicity-dependent Raman scattering and analyze the Raman optical activity of excitations as a function of magnetic field and temperature. The hotly debated field regime between 7.5 and 10.5T is characterized by clear spectroscopic signatures such as a plateau of the Raman optical activity of the dominant, chiral spin-flip excitation. This provides direct evidence for the existence of a distinct intermediate-field regime with an intriguing ground state featuring chiral excitations. Published by the American Physical Society 2024

Electronic Structures of Kitaev Magnet Candidates RuCl3 and RuI3.

Layered honeycomb magnets with strong atomic spin-orbit coupling at transition metal sites have been intensively studied for the search of Kitaev magnetism and the resulting non-Abelian braiding statistics. α-RuCl3 has been the most promising candidate, and there have been several reports on the realization of sibling compounds α-RuBr3 and α-RuI3 with the same crystal structure. Here, we investigate correlated electronic structures of α-RuCl3 and α-RuI3 by employing first-principles dynamical mean-field theory. Our result provides a valuable insight into the discrepancy between experimental and theoretical reports on transport properties of α-RuI3, and suggests a potential realization of correlated flat bands with strong spin-orbit coupling and a quantum spin-Hall insulating phase in α-RuI3.

Resonating holes vs molecular spin-orbit coupled states in group-5 lacunar spinels

The valence electronic structure of magnetic centers is one of the factors that determines the characteristics of a magnet. This may refer to orbital degeneracy, as for jeff = 1/2 Kitaev magnets, or near-degeneracy, e.g., involving the third and fourth shells in cuprate superconductors. Here we explore the inner structure of magnetic moments in group-5 lacunar spinels, fascinating materials featuring multisite magnetic units in the form of tetrahedral tetramers. Our quantum chemical analysis reveals a very colorful landscape, much richer than the single-electron, single-configuration description applied so far to all group-5 GaM4X8 chalcogenides, and clarifies the basic multiorbital correlations on M4 tetrahedral clusters: while for V strong correlations yield a wave-function that can be well described in terms of four V4+V3+V3+V3+ resonant valence structures, for Nb and Ta a picture of dressed molecular-orbital jeff = 3/2 entities is more appropriate. These internal degrees of freedom likely shape vibronic couplings, phase transitions, and the magneto-electric properties in each of these systems.

Finite-temperature second harmonic generation in Kitaev magnets

Finite-temperature second harmonic generation in Kitaev magnets

Differentiable programming tensor networks for Kitaev magnets

Differentiable programming tensor networks for Kitaev magnets

Spin excitation continuum to topological magnon crossover and thermal Hall conductivity in Kitaev magnets

There has been great interest in identifying a Kitaev quantum spin liquid state in frustrated magnets with bond-dependent interactions. In particular, the experimental report of a half-quantized thermal Hall conductivity in $\alpha$-RuCl$_3$ in the presence of a magnetic field has generated excitement as it could be strong evidence for a field-induced chiral spin liquid. More recent experiments, however, provide a conflicting interpretation advocating for topological magnons in the field-polarized state as the origin of the non-quantized thermal Hall conductivity observed in their experiments. An inherent difficulty in distinguishing between the two scenarios is the phase transition between a putative two-dimensional spin liquid and the field-polarized state exists only at zero temperature, while the behaviour at finite temperature is mostly crossover phenomena. In this work, we provide insights into the finite temperature crossover behavior between the spin excitation continuum in a quantum spin liquid and topological magnons in the field-polarized state in three different theoretical models with large Kitaev interactions. These models allow for a field-induced phase transition from a spin liquid (or an intermediate field-induced spin liquid) to the field-polarized state in the quantum model. We obtain the dynamical spin structure factor as a function of magnetic field using molecular dynamics simulations and compute thermal Hall conductivity in the field-polarized regime. We demonstrate the gradual evolution of the dynamical spin structure factor exhibiting crossover behaviour near magnetic fields where zero-temperature phase transitions occur in the quantum model. We also examine nonlinear effects on topological magnons and the validity of thermal Hall conductivity computed using linear spin wave theory. We discuss the implications of our results to existing and future experiments.

High-field quantum spin liquid transitions and angle-field phase diagram of the Kitaev magnet α−RuCl3

The pursuit of quantum spin liquid (QSL) in the Kitaev honeycomb magnets has drawn intensive attention recently. In particular, $\alpha$-RuCl$_3$ has been widely recognized as a promising candidate for the Kitaev QSL. Although the compound exhibits an antiferromagnetic order under zero field, it is believed to be endowed with fractionalized excitations, and can be driven to the QSL phase by magnetic fields. Here, based on a realistic $K$-$J$-$\Gamma$-$\Gamma'$ model for $\alpha$-RuCl$_3$ [1], we exploit the exponential tensor renormalization group approach to explore the phase diagram of the compound under magnetic fields. We calculate the thermodynamic quantities, including the specific heat, Gr\"uneisen parameter, magnetic torque, and the magnetotropic susceptibility, etc, under a magnetic field with a tilting angle $\theta$ to the $c^*$-axis perpendicular to the honeycomb plane. We find an extended QSL in the angle-field phase diagram determined with thermodynamic responses. The gapless nature of such field-induced QSL is identified from the specific heat and entropy data computed down to very low temperatures. The present study provides guidance for future high-field experiments for the QSL in $\alpha$-RuCl$_3$ and other candidate Kitaev magnets.

Thermal interferometry of anyons

Anyonic interferometry probes the braiding phases of excitations in topologically ordered matter. This technique is well established for charged quasiparticles in the fractional quantum Hall effect. We propose to extend it to neutral anyons, such as Ising anyons in Kitaev magnets and quasiparticles in other neutral spin liquids. We find that the thermal current through an interferometer is sensitive to the statistics of tunneling quasiparticles. We present a systematic investigation of signatures of various Abelian and non-Abelian topological orders in Fabry-P\'erot and Mach-Zehnder interferometers. The heat current through a Fabry-P\'erot device is different for different topological orders and depends on the topological charge inside the interferometer. A Mach-Zehnder device shows interference in topologically trivial systems only. For a non-trivial statistics, the heat current reduces to the sum of the contributions from two constrictions in the interferometer. Furthermore, we identify another probe of topological order that involves the scaling of the thermal current through a single tunneling contact at low temperatures. The current shows a universal temperature dependence, sensitive to the topological order in the system.

Triple-meron crystal in high-spin Kitaev magnets

Skyrmions hold great promise in future spintronics applications since they are robust against local deformations. The meron, due to its topological equivalence to a half skyrmion, has been widely found to appear in pairs. Motivated by recent progresses in high-spin Kitaev magnets, here we investigate numerically a classical Kitaev-Γ model with a single-ion anisotropy. An exotic spin texture consisting of three merons is discovered. Such a state features a peculiar property with an odd number of merons in one magnetic unit cell. Therefore, these merons cannot be dissociated from skyrmions as reported in the literature and their origin is briefly discussed. Moreover, we find that these three merons contribute a finite topological number and thus it can induce the topological Hall effect (THE). Experimentally this spin texture can be observed by the Lorentz transmission electron microscopy and the THE can be used to identify the finite topological number. Our work demonstrates that high-spin Kitaev magnets can host robust unconventional spin textures and thus they offer a versatile platform for exploring exotic spin textures as well as their applications in spintronics.

Topological Magnons in Kitaev Magnets with Finite Dzyaloshinskii-Moriya Interaction at High Field

There have been intensive studies on Kitaev materials for the sake of realization of exotic states such as quantum spin liquid and topological orders. In realistic materials, the Kitaev interaction may coexist with the Dzyaloshinskii–Moriya interaction, and it is of challenge to distinguish their magnitudes separately. Here, we study the topological magnon excitations and related thermal Hall conductivity of kagome magnet exhibiting Heisenberg, Kitaev and Dzyaloshinskii–Moriya interactions exposed to a magnetic field. In a strong magnetic field perpendicular to the plane of the lattice ([111] direction) that brings the system into a fully polarized paramagnetic phase, we find that the magnon bands carry nontrivial Chern numbers in the full region of the phase diagram. Furthermore, there are phase transitions related to two topological phases with opposite Chern numbers, which lead to the sign changes of the thermal Hall conductivity. In the phase with negative thermal conductivity, the Kitaev interaction is relatively large and the width of the phase increases with the strength of Dzyaloshinskii–Moriya interaction. Hence, the present study will contribute to the understanding of related compounds.