Pursuing the exotic quantum spin liquid (QSL) state in the Kitaev material $α$-RuCl$_3$ has intrigued great research interest recently. A fascinating question is on the possible existence of field-induced QSL phase in this compound. Here we perform a high-field measurement of the magnetization process of $α$-RuCl$_3$ 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 36 T and about 83 T, between which there lies an intermediate phase as the predicted QSL. By measuring the magnetization data with fields tilted from the c$^*$ axis up to $90^\circ$ (i.e., in-plane direction), we obtain the field-angle phase diagram that contains the zigzag, paramagnetic, and QSL phases. Based on the accurate $K$-$J$-$Γ$-$Γ^{\prime}$ model of $α$-RuCl$_3$, we perform density matrix renormalization group simulations and reproduce the quantum phase diagram in excellent agreement with experiments.
Recently considerable excitement has arisen due to the experimental observation of a field-induced spin liquid phase in the compound $α$-RuCl$_3$. However, the nature of this putative spin liquid phase and the relevant microscopic model Hamiltonian remain still unclear. In this work, we address these questions by performing large-scale numerical simulations of a generalized Kitaev-Heisenberg model proposed to describe the physics of $α$-RuCl$_3$. While there is no evidence for an intermediate phase for in-plane magnetic fields, our results strongly suggest that a stable intermediate spin liqui…
$α$-RuCl$_3$ is a leading candidate material for theobservation of physics related to the Kitaev quantum spin liquid (QSL). By combined susceptibility, specific-heat, and nuclear-magnetic-resonance measurements, we demonstrate that $α$-RuCl$_3$ undergoes a quantum phase transition to a QSL in a magnetic field of 7.5 T applied in the $ab$ plane. We show further that this high-field QSL phase has gapless spin excitations over a field range up to 16 T. This highly unconventional result, unknown in either Heisenberg or Kitaev magnets, offers insight essential to establishing the physics of $α$-RuC…
Inspired by experiments on the magnetic field induced phases of the spin-orbit coupled $2d$ Mott insulator $α$-RuCl$_3$, we study some general aspects of gapped $Z_2$ Quantum Spin Liquids (QSL) enriched by lattice translation symmetry. We show that there are $12$ distinct such phases with different implementations of translation symmetry. In some of these phases the vison excitations of this QSL may form topological Chern bands. We explore a phenomenological description of a putative $Z_2$ QSL as a candidate ground state at intermediate magnetic fields in $α$-RuCl$_3$. This state has broad con…
Frustrated magnets with strong spin-orbit coupling promise to host topological states of matter, with fractionalized excitations and emergent gauge fields. Kitaev's proposal for a honeycomb-lattice Majorana spin liquid has triggered an intense search for experimental realizations, with bond-dependent Ising interaction being the essential building block. A prime candidate is $α$-RuCl$_3$ whose phase diagram in a magnetic field is, however, not understood to date. Here we present conclusive experimental evidence for a novel field-induced ordered phase in $α$-RuCl$_3$, sandwiched between the zigz…
Motivated by the recent experimental observation of the half-quantized thermal Hall conductivity for the candidate material of the Kitaev spin liquid, $α$-RuCl$_3$[ Y. Kasahara et al., Nature 559, 227 (2018)], we investigate effects of non-Kitaev exchange interactions, which exist in the real material, on the gapped chiral spin liquid state realized in the case with an applied magnetic field. It is found that off-diagonal exchange interactions enhance significantly the mass gap of Majorana fermions. This result provides a possible explanation for robust quantization of the thermal Hall conduct…
We use the constrained random phase approximation (cRPA) to derive from first principles the Ru-$t_{2g}$ Wannier function based model for the Kitaev spin-liquid candidate material $α$-RuCl$_3$. We find the non-local Coulomb repulsion to be sizable compared to the local one. In addition we obtain the contribution to the Hamiltonian from the spin-orbit coupling and find it to also contain non-negligible non-local terms. We invoke strong coupling perturbation theory to investigate the influence of these non-local elements of the Coulomb repulsion and the spin-orbit coupling on the magnetic intera…
Proposed effective Hamiltonians from the literature for the material $α$-RuCl${}_3$ are used to compute the magnon thermal Hall conductivity, $κ_{xy}$, using linear spin wave theory for the magnetically ordered state. No model previously proposed that was tested explains published experimental data. Models with Kitaev interaction $K>0$ are seen to predict $κ_{xy}\gtrsim 0$, which is inconsistent with the data. Fluctuations toward a Kitaev-type spin liquid would have the wrong sign to explain the data. However, a slight variant of a previously proposed model predicts a large $κ_{xy}$, demonstra…
We report a $^{35}$Cl nuclear magnetic resonance study in the honeycomb lattice, $α$-RuCl$_3$, a material that has been suggested to potentially realize a Kitaev quantum spin liquid (QSL) ground state. Our results provide direct evidence that $α$-RuCl$_3$ exhibits a magnetic field-induced QSL. For fields larger than $\sim 10$ T a spin-gap opens up while resonance lines remain sharp, evidencing that spins are quantum disordered and locally fluctuating. The spin gap increases linearly with increasing magnetic field, reaching $\sim50$ K at 15 T, and is nearly isotropic with respect to the field d…
A key characteristic of quantum spin liquids(QSL) is the presence of fractional excitations related to their entanglement properties, yet experimental verification of their statistics is missing. For example, in the potential Kitaev spin liquid, RuCl3 experiments uncovered signs of fractional particles, though not their Fermi statistics. Here we employ Raman scattering to reveal the true nature of the magnetic excitations, using improved experimental methods and analysis to remove the influence of laser heating and thermal fluctuations. Via the energy loss and gain spectra, we extract the ener…
The Kitaev quantum spin liquid displays the fractionalization of quantum spins into Majorana fermions. The emergent Majorana edge current is predicted to manifest itself in the form of a finite thermal Hall effect, a feature commonly discussed in topological superconductors. Here we report on thermal Hall conductivity $κ_{xy}$ measurements in $α$-RuCl$_3$, a candidate Kitaev magnet with the two-dimensional honeycomb lattice. In a spin-liquid (Kitaev paramagnetic) state below the temperature characterized by the Kitaev interaction $J_K/k_B \sim 80$ K, positive $κ_{xy}$ develops gradually upon c…
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. Detection of these excitations remains challenging, because of their fractional quantum numbers and non-locality. 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 uncover this effect in $α$-RuCl3 using inelastic X-ray scattering with meV resolut…
What is the correct low-energy spin Hamiltonian description of $α$-RuCl$_3$? The material is a promising Kitaev spin liquid candidate, but is also known to order magnetically, the description of which necessitates additional interaction terms. The nature of these interactions, their magnitudes and even signs, remain an open question. In this work we systematically investigate dynamical and thermodynamic magnetic properties of proposed effective Hamiltonians. We calculate zero-temperature inelastic neutron scattering (INS) intensities using exact diagonalization, and magnetic specific heat usin…
The Kitaev quantum spin liquid (QSL) on the two-dimensional honeycomb lattice epitomizes an entangled topological state, where the spins fractionalize into Majorana fermions. This state has aroused tremendous interest because it harbors non-Abelian anyon excitations. The half-integer quantized thermal Hall (HIQTH) conductance observed in $α$-RuCl$_3$ is a key signature of these excitations. However, the fate of this topologically nontrivial state at intense fields remains largely elusive. Here, we report the thermal conductivity $κ$ and specific heat $C$ of $α$-RuCl$_3$ with in-plane magnetic …
The material $α$-RuCl$_3$ has been the subject of intense scrutiny as a potential Kitaev quantum spin liquid, predicted to display Majorana fermions as low energy excitations. In practice, $α$-RuCl$_3$ undergoes a transition to a state with antiferromagnetic order below a temperature $T_{\rm N}$ $\approx$ 7 K, but this order can be suppressed by applying an external in-plane magnetic field of $H_\parallel$ = 7 T. Whether a quantum spin liquid phase exists just above that field is still an open question, but the reported observation of a quantized thermal Hall conductivity at $H_\parallel$ $>$ …
Despite extensive investigations, a topological state that hosts Majorana edge modes in the magnetic field-induced quantum disordered state of the Kitaev candidate material $α$-RuCl$_3$ has been hotly debated. To gain more insight into this issue, we measured the thermal Hall conductivity $κ_{xy}$ of various samples grown by the Bridgman method. The results show that the half-integer quantum thermal Hall effect is intimately related to the magnitude of longitudinal thermal conductivity and the Néel temperature at zero field, both of which are sample dependent. Samples exhibiting the half-integ…
Spin liquids may host emergent quasiparticles, collective excitations of the spin degrees of freedom with characteristic features of Majorana fermions, which experimentally are detectable by broad excitation continua due to spin fractionalization. The latter is predicted for the Kitaev spin liquid, an exactly solvable model with bond-dependent interactions on a two-dimensional honeycomb lattice. Here we report on detailed THz experiments in α-RuCl3, identifying these characteristic fingerprints of Majorana fermions. The continuum intensity decreases and finally vanishes on increasing temperatu…
A recent experiment has reported oscillations of the thermal conductivity of $α$-RuCl$_3$ driven by an in-plane magnetic field that are reminiscent of the quantum oscillations in metals. At first glance, these observations are consistent with the presence of the long-sought-after spinon Fermi surface state. Strikingly, however, the experiment also reported vanishing thermal Hall conductivity coexisting with the oscillations of the longitudinal one. Such absence of the thermal Hall effect must originate from crystalline symmetries of $α$-RuCl$_3$. But if the system was a traditional spinon ferm…
We study on transport and magnetic properties of hydrated and lithium-intercalated $α$-RuCl$_3$, Li$_x$RuCl$_3 \cdot y$H$_2$O, for investigating the effect on mobile-carrier doping into candidate materials for a realization of a Kitaev model. From thermogravitometoric and one-dimensional electron map analyses, we find two crystal structures of this system, that is, mono-layer hydrated Li$_x$RuCl$_3 \cdot y$H$_2$O~$(x\approx0.56, y\approx1.3)$ and bi-layer hydrated Li$_x$RuCl$_3 \cdot y$H$_2$O~$(x\approx0.56, y\approx3.9)$. The temperature dependence of the electrical resistivity shows a temper…
In the class of materials called spin liquids, a magnetically ordered state cannot be attained even at milliKelvin temperatures because of conflicting constraints on each spin (for e.g. from geometric or exchange frustration). The resulting quantum spin-liquid (QSL) state is currently of intense interest because it exhibits novel excitations as well as wave-function entanglement. The layered insulator $α$-RuCl$_3$ orders as a zigzag antiferromagnet below $\sim$7 K in zero magnetic field. The zigzag order is destroyed when a magnetic field $\bf H$ is applied parallel to the zigzag axis a. Withi…
The combination of electronic correlation and spin-orbit coupling is thought to precipitate a variety of highly unusual electronic phases in solids, including topological and quantum spin liquid states. We report a Raman scattering study that provides evidence for unconventional excitations in $α$-RuCl$_3$, a spin-orbit coupled Mott insulator on the honeycomb lattice. In particular, our measurements reveal unusual magnetic scattering, typified by a broad continuum. The temperature dependence of this continuum is evident over a large scale compared to the magnetic ordering temperature, suggesti…
Intensive studies of the interplay between spin-orbit coupling (SOC) and electronic correlations in transition metal compounds have recently been undertaken. In particular, $j_{\rm eff}$ = 1/2 bands on a honeycomb lattice provide a pathway to realize Kitaev's exactly solvable spin model. However, since current wisdom requires strong atomic SOC to make $j_{\rm eff}=1/2$ bands, studies have been limited to iridium oxides. Contrary to this expectation, we demonstrate how Kitaev interactions arise in 4$d$-orbital honeycomb $α$-RuCl$_3$, despite having significantly weaker SOC than the iridium oxid…
Topologically ordered states of matter are generically characterized by excitations with quantum number fractionalization. A prime example is the spin liquid realized in Kitaev's honeycomb-lattice compass model where spin-flip excitations fractionalize into Majorana fermions and Ising gauge fluxes. While numerous compounds have been proposed to be proximate to such a spin-liquid phase, clear-cut evidence for fractionalized excitations is lacking. Here we employ microwave absorption measurements to study the low-energy excitations in $α$-RuCl$_3$ over a wide range of frequencies, magnetic field…
An external magnetic field can induce a transition in $α$-RuCl$_3$ from an ordered zigzag state to a disordered state that is possibly related to the Kitaev quantum spin liquid. Here we present new field dependent inelastic neutron scattering and magnetocaloric effect measurements implying the existence of an additional transition out of the quantum spin liquid phase at an upper field limit $B_u$. The neutron scattering shows three distinct regimes of magnetic response. In the low field ordered state the response shows magnon peaks; the intermediate field regime shows only continuum scattering…
We study the extended Kitaev model called the K$Γ$ model, using a perturbative expansion combined with a well-controlled mean-field approximation and a cutting-edge exact diagonalization. In the phase diagram, we discover a nematic Kitaev spin liquid and a Kekulé Kitaev spin liquid. The former potentially explains the high-field nematic state with zero Chern number experimentally observed in $α$-RuCl$_3$, even for sufficiently small values of $Γ/|K|$. The latter has a Majorana zero mode in its $Z_3$ vortex core, which can be potentially controlled by the domain wall motion. This opens a possib…
The frustrated magnet $α$-RuCl$_3$ 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 $α$-RuCl$_3$, 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 fi…
$α$-RuCl$_{3}$ is a major candidate for the realization of the Kitaev quantum spin liquid, but its zigzag antiferromagnetic order at low temperatures indicates deviations from the Kitaev model. We have quantified the spin Hamiltonian of $α$-RuCl$_{3}$ by a resonant inelastic x-ray scattering study at the Ru $L_{3}$ absorption edge. In the paramagnetic state, the quasi-elastic intensity of magnetic excitations has a broad maximum around the zone center without any local maxima at the zigzag magnetic Bragg wavevectors. This finding implies that the zigzag order is fragile and readily destabilize…
The 2D layered insulator $α$-RuCl$_3$ is a candidate material for a quantum spin-liquid state, which may be realized when a magnetic field suppresses the antiferromagnetic order present at low temperature. Oscillations in the field dependence of the thermal conductivity, observed for an in-plane magnetic field $B$ up to a critical field $B^{\star}$, have been attributed to exotic charge-neutral fermions, viewed as evidence of a quantum spin-liquid state between the critical field $B_{c}$ $\simeq 7$ T at which the antiferromagnetic phase ends and $B^{\star}$. Here we report measurements of the …
Intermediate Field Spin(on) Dynamics in $α$-RuCl$_3$
Oak Ridge National Laboratory（橡树岭国家实验室）；Purdue University（普渡大学）；Technical University of Munich（慕尼黑工业大学）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）
The pursuit of quantum spin liquid (QSL) in the Kitaev honeycomb magnets has drawn intensive attention recently. In particular, $α$-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 $K$-$J$-$Γ$-$Γ'$ model for $α$-RuCl$_3$ [1], we exploit the exponential tensor renormalization group approach to explore the phase diagram of the compound under magnet…
The Kitaev model on a honeycomb lattice predicts a paradigmatic quantum spin liquid (QSL) exhibiting Majorana Fermion excitations. The insight that Kitaev physics might be realized in practice has stimulated investigations of candidate materials, recently including alpha-RuCl3. In all the systems studied to date, non-Kitaev interactions induce magnetic order at low temperature. However, in-plane magnetic fields of roughly 8 Tesla suppress the long-range magnetic order in alpha-RuCl3 raising the intriguing possibility of a field-induced QSL exhibiting non-Abelian quasiparticle excitations. Here…
Excitation by light pulses enables the manipulation of phases of quantum condensed matter. Here, we photoexcite high-energy holon-doublon pairs as a way to alter the magnetic free energy landscape of the Kitaev-Heisenberg magnet $α$-RuCl$_3$, with the aim to dynamically stabilize a proximate spin liquid phase. The holon-doublon pair recombination through multimagnon emission is tracked through the time-evolution of the magnetic linear dichroism originating from the competing zigzag spin ordered ground state. A small holon-doublon density suffices to reach a spin disordered state. The phase tra…
Recent experiments reveal that the honeycomb ruthenium trichloride α-RuCl3 is a prime candidate of the Kitaev quantum spin liquid (QSL). However, there is no theoretical model which can properly describe its experimental dynamical response, due to the lack of a full understanding of its magnetic interactions. Here, we propose a general scheme to calculate the magnetic interactions in systems (e.g., α-RuCl3) with non-negligible orbital moments by constraining the directions of orbital moments. With this scheme, we put forward a minimal J1-K1-Γ1-J3-K3 model for α-RuCl3 and find that: (I) The thi…
Using quantum chemistry calculations we shed fresh light on the electronic structure and magnetic properties of RuCl3, a proposed realization of the honeycomb Kitaev spin model. It is found that the nearest-neighbor Kitaev exchange K is weaker than in 5d5 Ir oxides but still larger than other effective spin couplings. The electronic-structure computations also indicate a ferromagnetic K in the halide, which is supported by a detailed analysis of the field-dependent magnetization. From exact-diagonalization calculations for extended Kitaev-Heisenberg Hamiltonians we additionally find that a tra…
The pure Kitaev honeycomb model harbors a quantum spin liquid in zero magnetic fields, while applying finite magnetic fields induces a topological spin liquid with non-Abelian anyonic excitations. This latter phase has been much sought after in Kitaev candidate materials, such as $α$-RuCl$_3$. Currently, two competing scenarios exist for the intermediate field phase of this compound ($B=7-10$ T), based on experimental as well as theoretical results: (i) conventional multiparticle magnetic excitations of integer quantum number vs. (ii) Majorana fermionic excitations of possibly non-Abelian natu…
We report on terahertz spectroscopy of quantum spin dynamics in $α$-RuCl$_3$, a system proximate to the Kitaev honeycomb model, as a function of temperature and magnetic field. An extended magnetic continuum develops below the structural phase transition at $T_{s2}=62$K. With the onset of a long-range magnetic order at $T_N=6.5$K, spectral weight is transferred to a well-defined magnetic excitation at $\hbar ω_1 = 2.48$meV, which is accompanied by a higher-energy band at $\hbar ω_2 = 6.48$meV. Both excitations soften in magnetic field, signaling a quantum phase transition at $B_c=7$T where we …
In $α$-RuCl$_3$, an external magnetic field applied within the honeycomb plane can induce a transition from a magnetically ordered state to a disordered state that is potentially related to the Kitaev quantum spin liquid. In zero field, single crystals with minimal stacking faults display a low-temperature state with in-plane zigzag antiferromagnetic order and a three-layer periodicity in the direction perpendicular to the honeycomb planes. Here, we present angle-dependent magnetization, ac susceptibility, and thermal transport data that demonstrate the presence of an additional intermediate-f…
Emergent low-energy thermodynamics and universal $B/T$ scaling in $α$-RuCl$_3$
Institute of Science and Technology Austria（奥地利科学技术研究院）；Department of Physics, Stockholm University（斯德哥尔摩大学物理系）；Laboratory of Atomic and Solid State Physics, Cornell University（康奈尔大学原子与固态物理实验室）；Canadian Institute for Advanced Research（加拿大高级研究院）；National High Magnetic Field Laboratory, Florida State University（佛罗里达州立大学国家高磁场实验室）；Department of Physics, University of Toronto（多伦多大学物理系）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；Institute for Theoretical Physics, Julius-Maximilians-Universität Würzburg（维尔茨堡大学理论物理研究所）；Würzburg-Dresden Cluster of Excellence ctd.qmat, Julius-Maximilians-Universität Würzburg（维尔茨堡大学维尔茨堡-德累斯顿卓越集群ctd.qmat）
The ruthenium halide $α$-RuCl$_{3}$ is a promising candidate for a Kitaev spin liquid. However, the microscopic model describing $α$-RuCl$_{3}$ is still debated partly because of a lack of analogue materials for $α$-RuCl$_{3}$, which prevents tracking of electronic properties as functions of controlled interaction parameters. Here, we report a successful synthesis of RuBr$_{3}$. The material RuBr$_{3}$~possesses BiI$_3$-type structure (space group: $R\overline{3}$) where Ru$^{3+}$ form an ideal honeycomb lattice. Although RuBr$_{3}$ has a negative Weiss temperature, it undergoes a zigzag antif…
$α$-RuCl$_3$ has been studied extensively because of its proximity to the Kitaev quantum-spin-liquid (QSL) phase and the possibility of approaching it by tuning the competing interactions. Here we present the first polarized inelastic neutron scattering study on $α$-RuCl$_3$ single crystals to explore the scattering continuum around the $Γ$ point at the Brillouin zone center, which was hypothesized to be resulting from the Kitaev QSL state but without concrete evidence. With polarization analyses, we find that while the spin-wave excitations around the M point vanish above the transition tempe…
A quantum spin-liquid might be realized in $α$-RuCl$_{3}$, a honeycomb-lattice magnetic material with substantial spin-orbit coupling. Moreover, $α$-RuCl$_{3}$ is a Mott insulator, which implies the possibility that novel exotic phases occur upon doping. Here, we study the electronic structure of this material when intercalated with potassium by photoemission spectroscopy, electron energy loss spectroscopy, and density functional theory calculations. We obtain a stable stoichiometry at K$_{0.5}$RuCl$_3$. This gives rise to a peculiar charge disproportionation into formally Ru$^{2+}$ (4$d^6$) a…
We report on the unusual behavior of the in-plane thermal conductivity ($κ$) and torque ($τ$) response in the Kitaev-Heisenberg material $α$-RuCl$_3$. $κ$ shows a striking enhancement with linear growth beyond H = 7 T, where magnetic order disappears, while $τ$ for both of the in-plane symmetry directions shows an anomaly at the same field. The temperature- and field-dependence of $κ$ are far more complex than conventional phonon and magnon contributions, and require us to invoke the presence of unconventional spin excitations whose properties are characteristic of a field-induced spin-liquid …
Muon spin rotation measurements have been performed on a powder sample of a-RuCl3, a layered material which previously has been proposed to be a quantum magnet on a honeycomb lattice close to a quantum spin liquid ground state. Our data reveal two distinct phase transitions at 11 K and 14 K which we interpret as originating from the onset of three-dimensional order and in-plane magnetic order, respectively. We identify, with the help of density functional theory calculations, likely muon stopping sites and combine these with dipolar field calculations to show that the two measured muon rotatio…
Heat transport mediated by Majorana edge modes in a magnetic insulator leads to a half-integer thermal quantum Hall conductance, which has recently been reported for the two-dimensional honeycomb material $α$-RuCl$_3$. While the conventional electronic Hall effect requires a perpendicular magnetic field, we find that this is not the case in $α$-RuCl$_3$. Strikingly, the thermal Hall plateau appears even for a magnetic field with no out-of-plane components. The field-angular variation of the quantized thermal Hall conductance has the same sign structure of the topological Chern number, which is…
Magnetization and high-resolution x-ray diffraction measurements of the Kitaev-Heisenberg material alpha-RuCl3 reveal a pressure-induced crystallographic and magnetic phase transition at a hydrostatic pressure of p=0.2 GPa. This structural transition into a triclinic phase is characterized by a very strong dimerization of the Ru-Ru bonds, accompanied by a collapse of the magnetic susceptibility. Ab initio quantum-chemistry calculations disclose a pressure-induced enhancement of the direct 4d-4d bonding on particular Ru-Ru links, causing a sharp increase of the antiferromagnetic exchange intera…
Spin sensitive transport in RuCl_3/Pt heterostructures: revealing a field-transverse spin anisotropy in a spin liquid candidate
WPI Advanced Institute for Materials Research (AIMR) and Center for Science and Innovation in Spintronics (CSIS), Tohoku University（东北大学材料高等研究所（AIMR）与自旋电子学科学与创新中心（CSIS））；Department of Physics and Astronomy and Purdue Quantum Science and Engineering Institute, Purdue University（普渡大学物理与天文学系及普渡量子科学与工程研究所）；Department of Physics, The University of Tokyo（东京大学物理学系）；Institute for Materials Research (IMR), Tohoku University（东北大学材料研究所（IMR））；Materials Science and Technology Division, Oak Ridge National Laboratory（橡树岭国家实验室材料与科技分部）；The Quantum Science Center, Oak Ridge National Laboratory（橡树岭国家实验室量子科学中心）；Computational Sciences and Engineering Division, Oak Ridge National Laboratory（橡树岭国家实验室计算科学与工程分部）；Department of Materials Science and Engineering, University of Tennessee（田纳西大学材料科学与工程系）；Neutron Scattering Division, Oak Ridge National Laboratory（橡树岭国家实验室中子散射分部）；School of Electrical and Computer Engineering and Birck Nanotechnology Center, Purdue University（普渡大学电气与计算机工程学院及Birck纳米技术中心）；Institute of Physics and Astronomy and Villum Centers for Dirac Materials and for Hybrid Quantum Materials and Devices, Aarhus University（奥胡斯大学物理与天文学研究所及Villum狄拉克材料与混合量子材料及器件中心）
As one of the most promising Kitaev quantum-spin-liquid (QSL) candidates, $α$-RuCl$_3$ has received a great amount of attention. However, its ground state exhibits a long-range zigzag magnetic order, which defies the QSL phase. Nevertheless, the magnetic order is fragile and can be completely suppressed by applying an external magnetic field. Here, we explore the evolution of magnetic excitations of $α$-RuCl$_3$ under an in-plane magnetic field, by carrying out inelastic neutron scattering measurements on high-quality single crystals. Under zero field, there exist spin-wave excitations near th…
$α$-RuCl$_3$ is drawing much attention as a promising candidate Kitaev quantum spin liquid. However, despite intensive research efforts, controversy remains about the form of the basic interactions governing the physics of this material. Even the sign of the Kitaev interaction (the bond-dependent anisotropic interaction responsible for Kitaev physics) is still under debate, with conflicting results from theoretical and experimental studies. The significance of the symmetric off-diagonal exchange interaction (referred to as the $Γ$ term) is another contentious question. Here, we present resonan…
