Kitaev Quantum Spin Research Articles

Imaging Quantum Interference in a Monolayer Kitaev Quantum Spin Liquid Candidate

Single atomic defects are prominent windows to look into host quantum states because collective responses from the host states emerge as localized states around the defects. Friedel oscillations and Kondo clouds in Fermi liquids are quintessential examples. However, the situation is quite different for quantum spin liquid (QSL), an exotic state of matter with fractionalized quasiparticles and topological order arising from a profound impact of quantum entanglement. Elucidating the underlying local electronic property has been challenging due to the charge neutrality of fractionalized quasiparticles and the insulating nature of QSLs. Here, using spectroscopic-imaging scanning tunneling microscopy, we report atomically resolved images of monolayer α−RuCl3, the most promising Kitaev QSL candidate, on metallic substrates. We find quantum interference in the insulator manifesting as incommensurate and decaying spatial oscillations of the local density of states around defects with a characteristic bias dependence. The oscillation differs from any known spatial structures in its nature and does not exist in other Mott insulators, implying it is an exotic oscillation involved with excitations unique to α−RuCl3. Numerical simulations suggest that the observed oscillation can be reproduced by assuming that itinerant Majorana fermions of Kitaev QSL are scattered across the Majorana Fermi surface. The oscillation provides a new approach to exploring Kitaev QSLs through the local response against defects like Friedel oscillations in metals. Published by the American Physical Society 2024

Nature of Topological Phase Transition of Kitaev Quantum Spin Liquids.

We investigate the nature of the topological quantum phase transition between the gapless and gapped Kitaev quantum spin liquid phases away from the exactly solvable point. The transition is driven by anisotropy of the Kitaev couplings. At the critical point, the two Dirac points of the gapless Majorana modes merge, resulting in the formation of a semi-Dirac point with quadratic and linear band touching directions. We derive an effective Gross-Neveu-Yukawa-type field theory that describes the topological phase transition in the presence of additional magnetic interactions. We obtain the infrared scaling form of the propagator of the dynamical Ising order parameter field and perform a renormalization-group analysis. The universality of the transition is found to be different from that of symmetry-breaking phase transitions of semi-Dirac electrons. However, as in the electronic case, the Majorana fermions acquire an anomalous dimension, indicative of the breakdown of the fractionalized quasiparticle description.

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.

Pressure-tuning of α-RuCl3 towards a quantum spin liquid

The layered material α-RuCl3 is a promising candidate to realize the Kitaev quantum spin liquid (QSL) state. However, at ambient pressure, deviations from the perfect Kitaev geometry prevent the existence of the QSL state at low temperatures. Here we present the discovery of a pressure-induced high-symmetry phase in α-RuCl3, which creates close to ideal conditions for the emergence of a QSL. Employing a novel approach based on Bragg and diffuse scattering of synchrotron radiation, we reveal a pressure-induced reorganization of the RuCl3-layers. Most importantly, this reorganization affects the structure of the layers themselves, which acquire a high trigonal symmetry. For this trigonal phase the largest ratio between the Kitaev (K) and the Heisenberg exchange (J) ever encountered is found: K/J = 124. Additionally, we demonstrate that this phase can also be stabilized by a slight biaxial pressure. This not only resolves the conflicting reports of low-temperature structures in the literature, but also facilitates the investigation of the high-symmetry phase and its potential QSL using a range of experimental techniques.

Incommensurate charge super-modulation and hidden dipole order in layered kitaev material α-RuCl3

The magnetism of Kitaev materials has been widely studied, but their charge properties and the coupling to other degrees of freedom are less known. Here we investigate the charge states of α-RuCl3, a promising Kitaev quantum spin liquid candidate, in proximity to graphite. We discover that few-layered α-RuCl3 experiences a clear modulation of charge states, where a Mott-insulator to weak charge-transfer-insulator transition in the 2D limit occurs by means of heterointerfacial polarization. More notably, distinct signals of incommensurate charge and lattice super-modulations, regarded as an unconventional charge order, accompanied in the insulator. Our theoretical calculations have reproduced the incommensurate charge order by taking into account the antiferroelectricity of α-RuCl3 that is driven by dipole order in the internal electric fields. The findings imply that there is strong coupling between the charge, spin, and lattice degrees of freedom in layered α-RuCl3 in the heterostructure, which offers an opportunity to electrically access and tune its magnetic interactions inside the Kitaev compounds.

Suppression of antiferromagnetic order by strain-enhanced frustration in honeycomb cobaltate.

Layered honeycomb cobaltates are predicted as promising for realizing the Kitaev quantum spin liquid, a many-body quantum entangled ground state characterized by fractional excitations. However, they exhibit antiferromagnetic ordering at low temperatures, hindering the expected quantum state. We demonstrate that controlling the trigonal distortion of CoO6 octahedra is crucial to suppress antiferromagnetic order through enhancing frustration in layered honeycomb cobaltates. Using heterostructure engineering on Cu3Co2SbO6 thin films, we adjust the trigonal distortion of CoO6 octahedra and the resulting trigonal crystal field. The original Néel temperature of 16 kelvin in bulk Cu3Co2SbO6 decreases (increases) to 7.8 kelvin (22.7 kelvin) in strained Cu3Co2SbO6 films by decreasing (increasing) the magnitude of the trigonal crystal fields. The first-principles calculation suggests the enhancement of geometrical frustration as the origin of the suppression of antiferromagnetism. This finding supports the potential of layered honeycomb cobaltate heterostructures and strain engineering in realizing extremely elusive quantum phases of matter.

A quantum critical Bose gas of magnons in the quasi-two-dimensional antiferromagnet YbCl3 under magnetic fields

Bose–Einstein condensation (BEC) is a quantum phenomenon in which a macroscopic number of bosons occupy the lowest energy state and acquire coherence at low temperatures. In three-dimensional antiferromagnets, a magnetic-field-induced transition has been successfully described as a magnon BEC. For a strictly two-dimensional (2D) system, it is known that BEC cannot take place due to the presence of a finite density of states at zero energy. However, in a realistic quasi-2D magnet consisting of stacked magnetic layers, a small but finite interlayer coupling stabilizes marginal BEC but such that 2D physics is still expected to dominate. This 2D-limit BEC behaviour has been reported in a few materials but only at very high magnetic fields that are difficult to access. The honeycomb S = 1/2 Heisenberg antiferromagnet YbCl3 exhibits a transition to a fully polarized state at a relatively low in-plane magnetic field. Here, we demonstrate the formation of a quantum critical 2D Bose gas at the transition field, which, with lowering the field, experiences a BEC marginally stabilized by an extremely small interlayer coupling. Our observations establish YbCl3, previously a Kitaev quantum spin liquid material, as a realization of a quantum critical BEC in the 2D limit.

Manipulating topological quantum phase transitions of Kitaev's quantum spin liquids with electric fields

Manipulating topological quantum phase transitions of Kitaev's quantum spin liquids with electric fields

Majorana-fermion mean field theories of Kitaev quantum spin liquids

We determine the phase diagrams of anisotropic Kitaev-Heisenberg models on the honeycomb lattice using parton mean-field theories based on different Majorana fermion representations of the S=1/2 spin operators. First, we use a two-dimensional Jordan-Wigner transformation (JWT) involving a semi-infinite snake string operator. To ensure that the fermionized Hamiltonian remains local, we consider the limit of extreme Ising exchange anisotropy in the Heisenberg sector. Second, we use the conventional Kitaev representation in terms of four Majorana fermions subject to local constraints, which we enforce through Lagrange multipliers. For both representations, we self-consistently decouple the interaction terms in the bond and magnetization channels and determine the phase diagrams as a function of the anisotropy of the Kitaev couplings and the relative strength of the Ising exchange. While both mean-field theories produce identical phase boundaries for the topological phase transition between the gapless and gapped Kitaev quantum spin liquids, the JWT fails to correctly describe the magnetic instability and finite-temperature behavior. Our results show that the magnetic phase transition is first order at low temperatures but becomes continuous above a certain temperature. At this energy scale, we also observe a finite-temperature crossover on the quantum-spin-liquid side, from a fractionalized paramagnet at low temperatures, in which gapped flux excitations are frozen out, to a conventional paramagnet at high temperatures. Published by the American Physical Society 2024

Evidence for field induced quantum spin liquid behavior in a spin-1/2 honeycomb magnet

<p>One of the most important issues in modern condensed matter physics is the realization of fractionalized excitations, such as the Majorana excitations in the Kitaev quantum spin liquid. To this aim, the 3<i>d</i>-based Kitaev material Na<sub>2</sub>Co<sub>2</sub>TeO<sub>6</sub> is a promising candidate whose magnetic phase diagram of <b>B</b> // <b>a*</b> contains a field-induced intermediate magnetically disordered phase within 7.5 T < |B| < 10 T. The experimental observations, including the restoration of the crystalline point group symmetry in the angle-dependent torque and the coexisting magnon excitations and spinon-continuum in the inelastic neutron scattering spectrum, provide strong evidence that this disordered phase is a field induced quantum spin liquid with partially polarized spins. Our variational Monte Carlo simulation with the effective K-J<sub>1</sub>-Γ-Γ'-J<sub>3</sub> model reproduces the experimental data and further supports this conclusion.</p>

Controlling the magnetic state of the proximate quantum spin liquid α-RuCl3 with an optical cavity

Harnessing the enhanced light-matter coupling and quantum vacuum fluctuations resulting from mode volume compression in optical cavities is a promising route towards functionalizing quantum materials and realizing exotic states of matter. Here, we extend cavity quantum electrodynamical materials engineering to correlated magnetic systems, by demonstrating that a Fabry-Pérot cavity can be used to control the magnetic state of the proximate quantum spin liquid α-RuCl3. Depending on specific cavity properties such as the mode frequency, photon occupation, and strength of the light-matter coupling, any of the magnetic phases supported by the extended Kitaev model can be stabilized. In particular, in the THz regime, we show that the cavity vacuum fluctuations alone are sufficient to bring α-RuCl3 from a zigzag antiferromagnetic to a ferromagnetic state. By external pumping of the cavity in the few photon limit, it is further possible to push the system into the antiferromagnetic Kitaev quantum spin liquid state.

Interedge spin resonance in the Kitaev quantum spin liquid

Interedge spin resonance in the Kitaev quantum spin liquid

Momentum-independent magnetic excitation continuum in the honeycomb iridate H3LiIr2O6

Understanding the interplay between the inherent disorder and the correlated fluctuating-spin ground state is a key element in the search for quantum spin liquids. H3LiIr2O6 is considered to be a spin liquid that is proximate to the Kitaev-limit quantum spin liquid. Its ground state shows no magnetic order or spin freezing as expected for the spin liquid state. However, hydrogen zero-point motion and stacking faults are known to be present. The resulting bond disorder has been invoked to explain the existence of unexpected low-energy spin excitations, although data interpretation remains challenging. Here, we use resonant X-ray spectroscopies to map the collective excitations in H3LiIr2O6 and characterize its magnetic state. In the low-temperature correlated state, we reveal a broad bandwidth of magnetic excitations. The central energy and the high-energy tail of the continuum are consistent with expectations for dominant ferromagnetic Kitaev interactions between dynamically fluctuating spins. Furthermore, the absence of a momentum dependence to these excitations are consistent with disorder-induced broken translational invariance. Our low-energy data and the energy and width of the crystal field excitations support an interpretation of H3LiIr2O6 as a disordered topological spin liquid in close proximity to bond-disordered versions of the Kitaev quantum spin liquid.

Ba9RE2(SiO4)6 (RE = Ho-Yb): A Family of Rare-Earth-Based Honeycomb-Lattice Magnets.

Rare-earth (RE)-based honeycomb-lattice materials with strong spin-orbit coupled Jeff = 1/2 moments have attracted great interest as a platform to realize the Kitaev quantum spin liquid (QSL) state. Herein, we report the discovery of a family of RE-based honeycomb-lattice magnets Ba9RE2(SiO4)6 (RE = Ho-Yb), which crystallize into the rhombohedral structure with the space group R3̅. In these serial compounds, magnetic RE3+ ions are arranged on a perfect honeycomb lattice within the ab-plane and stacked in the "ABCABC"-type fashion along the c-axis. All synthesized Ba9RE2(SiO4)6 (RE = Ho-Yb) polycrystals exhibit the dominant antiferromagnetic interaction and absence of magnetic order down to 2 K. In combination with the magnetization and electron spin resonance results, magnetic behaviors are discussed for the compounds with different RE ions. Moreover, the as-grown Ba9Yb2(SiO4)6 single crystals show large magnetic frustration with frustration index f = θCW/TN > 8 and no long-range magnetic ordering down to 0.15 K, being a possible QSL candidate material. These series of compounds are attractive for exploring the exotic magnetic phases of Kitaev materials with 4f electrons.

Disorder-Enriched Magnetic Excitations in a Heisenberg-Kitaev Quantum Magnet Na_{2}Co_{2}TeO_{6}.

Using optical magnetospectroscopy, we investigate the magnetic excitations of Na_{2}Co_{2}TeO_{6} in a broad magnetic field range (0 T≤B≤17.5 T) at low temperature. Our measurements reveal rich spectra of in-plane magnetic excitations with a surprisingly large number of modes, even in the high-field spin-polarized state. Theoretical calculations find that the Na-occupation disorder in Na_{2}Co_{2}TeO_{6} plays a crucial role in generating these modes. Our Letter demonstrates the necessity to consider disorder in the spin environment in the search for Kitaev quantum spin liquid states in practicable materials.

Emergent orbital magnetization in Kitaev quantum magnets

Unambiguous identification of the Kitaev quantum spin liquid (QSL) in materials remains a huge challenge despite many encouraging signs from various measurements. To facilitate the experimental detection of the Kiteav QSL, here we propose to use remnant charge response in Mott insulators hosting QSL to identify the key signatures of QSL. We predict an emergent orbital magnetization in a Kitaev system in an external magnetic field. The direction of the orbital magnetization can be flipped by rotating the external magnetic field in the honeycomb plane. The orbital magnetization is demonstrated explicitly through a detailed microscopic analysis of the multiorbital Hubbard-Kanamori Hamiltonian and also supported by a phenomenological picture. We first derive the localized electrical loop current operator in terms of the spin degrees of freedom. Thereafter, utilizing the Majorana representation, we estimate the loop currents in the ground state of the chiral Kitaev QSL state, and obtain the consequent current textures, which are responsible for the emergent orbital magnetization. Finally, we discuss the possible experimental techniques to visualize the orbital magnetization which can be considered as the signatures of the underlying excitations.

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.

Tunneling spectroscopic signatures of charge doping and associated Mott transition in α−RuCl3 in proximity to graphite

The layered Mott insulator $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{RuC}{\mathrm{l}}_{3}$ has been extensively studied as a potential Kitaev quantum spin liquid candidate. Here, by constructing heterostructures with graphite, we employed electron tunneling measurements on few-layer $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{RuC}{\mathrm{l}}_{3}$ using scanning tunneling microscopy/spectroscopy. Characteristic tunneling spectra were detected on $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{RuC}{\mathrm{l}}_{3}$ layers in proximity to graphite. In the single-layer $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{RuC}{\mathrm{l}}_{3}$ in direct contact with graphite, distinct states in the Mott gap regime were observed. The in-gap states are demonstrated to be closely related to the electron orbitals in $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{RuC}{\mathrm{l}}_{3}$ and graphite, and to be sensitive to interfacial coupling, where a hybridization at the heterointerface is hypothesized. The in-gap states are also thought of as a charge reservoir for weakly doping the $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{RuC}{\mathrm{l}}_{3}$ upper layers. It demonstrated that the weak doping effect causes a considerable decrease in the Mott gap within the upper layers, suggesting that an unconventional Mott transition is occurring in these layers. The results show that the heterostructure comprising $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{RuC}{\mathrm{l}}_{3}$ and graphite is a good platform for investigating the doping physics in $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{RuC}{\mathrm{l}}_{3}$. Therefore, tunneling into such a doped system is a useful probe for studying otherwise insulating spin liquid candidates.

Signatures of a gapless quantum spin liquid in the Kitaev material Na3Co2−xZnxSbO6

The honeycomb-lattice cobaltate Na$_3$Co$_2$SbO$_6$ has recently been proposed to be a proximate Kitaev quantum spin liquid~(QSL) candidate. However, non-Kitaev terms in the Hamiltonian lead to a zigzag-type antiferromagnetic~(AFM) order at low temperatures. Here, we partially substitute magnetic Co$^{2+}$ with nonmagnetic Zn$^{2+}$ and investigate the chemical doping effect in tuning the magnetic ground states of Na$_3$Co$_{2-x}$Zn$_x$SbO$_6$. X-ray diffraction characterizations reveal no structural transition but quite tiny changes on the lattice parameters over our substitution range $0\leq x\leq0.4$. Magnetic susceptibility and specific heat results both show that AFM transition temperature is continuously suppressed with increasing Zn content $x$ and neither long-range magnetic order nor spin freezing is observed when $x\geq0.2$. More importantly, a linear term of the specific heat representing fermionic excitations is captured below 5~K in the magnetically disordered regime, as opposed to the $C_{\rm m}\propto T^3$ behavior expected for bosonic excitations in the AFM state. Based on the data above, we establish a magnetic phase diagram of Na$_3$Co$_{2-x}$Zn$_x$SbO$_6$. Our results indicate the presence of gapless fractional excitations in the samples with no magnetic order, evidencing a potential QSL state induced by doping in a Kitaev system.

Pressure tuning of structure, magnetic frustration, and carrier conduction in the Kitaev spin liquid candidate Cu2IrO3

The layered honeycomb lattice iridate Cu$_2$IrO$_3$ is the closest realization of the Kitaev quantum spin liquid, primarily due to the enhanced interlayer separation and nearly ideal honeycomb lattice. We report pressure-induced structural evolution of Cu$_2$IrO$_3$ by powder x-ray diffraction (PXRD) up to $\sim$17 GPa and Raman scattering measurements up to $\sim$25 GPa. A structural phase transition (monoclinic $C2/c \: \rightarrow$ triclinic $P\bar{1}$) is observed with a broad mixed phase pressure range ($\sim$4 to 15 GPa). The triclinic phase consists of heavily distorted honeycomb lattice with Ir-Ir dimer formation and a collapsed interlayer separation. In the stability range of the low-pressure monoclinic phase, structural evolution maintains the Kitaev configuration up to 4 GPa. This is supported by the observed enhanced magnetic frustration in dc susceptibility without emergence of any magnetic ordering and an enhanced dynamic Raman susceptibility. High-pressure resistance measurements up to 25 GPa in the temperature range 1.4--300 K show resilient non-metallic $R$($T$) behaviour with significantly reduced resistivity in the high-pressure phase. The Mott 3D variable-range-hopping conduction with much reduced characteristic energy scale $T_0$ suggests that the high-pressure phase is at the boundary of localized-itinerant crossover. Using first-principles density functional theoretical (DFT) calculations, we find that at ambient pressure $\rm Cu_2IrO_3$ exists in monoclinic $P2_1/c$ phase which is energetically lower than $C2/c$ phase (both the structures are consistent with experimental XRD pattern). DFT reveals structural transition from $P2_1/c$ to $P\bar{1}$ structure at 7 GPa (involving dimerization of Ir-Ir bonds) in agreement with experimentally observed transition pressure.