Ferromagnetic Kitaev interaction and the origin of large magnetic anisotropy in $\alpha$-RuCl${}_3$

Abstract

$\alpha$-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 $\Gamma$ term) is another contentious question. Here, we present resonant elastic x-ray scattering data that provides unambiguous experimental constraints to the two leading terms in the magnetic interaction Hamiltonian. We show that the Kitaev interaction ($K$) is ferromagnetic, and that the $\Gamma$ term is antiferromagnetic and comparable in size to the Kitaev interaction. Our findings also provide a natural explanation for the large anisotropy of the magnetic susceptibility in $\alpha$-RuCl${}_3$ as arising from the large $\Gamma$ term. We therefore provide a crucial foundation for understanding the interactions underpinning the exotic magnetic behaviours observed in $\alpha$-RuCl${}_3$.

5 pages, two-column, 3 figures

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Cited by in corpus (74)

• Half-integer quantized anomalous thermal Hall effect in the Kitaev material $\alpha$-RuCl${}_3$
• Triaxial magnetic anisotropy in the two-dimensional ferromagnetic semiconductor CrSBr
• Rethinking $\alpha$-RuCl${}_3$
• Antiferromagnetic Kitaev interaction in $J_\rm{eff}=1/2$ cobalt honeycomb materials Na${}_3$Co${}_2$SbO${}_6$ and Na${}_2$Co${}_2$TeO${}_6$
• Proximate ferromagnetic state in the Kitaev model material $\alpha$-RuCl${}_3$
• Sign structure of thermal Hall conductivity for in-plane-field polarized Kitaev magnets
• Geometrical frustration versus Kitaev interactions in BaCo${}_2$(AsO${}_4$)${}_2$
• Topological magnons for thermal Hall transport in frustrated magnets with bond-dependent interactions
• Dominant Kitaev interactions in the honeycomb materials Na${}_3$Co${}_2$SbO${}_6$ and Na${}_2$Co${}_2$TeO${}_6$
• A magnetic continuum observed by terahertz spectroscopy in a quantum spin liquid candidate BaCo${}_2$(AsO${}_4$)${}_2$
• Identification of Magnetic Interactions and High-field Quantum Spin Liquid in $\alpha$-RuCl${}_3$
• Dynamics of visons and thermal Hall effect in perturbed Kitaev models
• Triple-q order in Na${}_2$Co${}_2$TeO${}_6$ from proximity to hidden-SU(2)-symmetric point
• Emergence of a nematic paramagnet via quantum order-by-disorder and pseudo-Goldstone modes in Kitaev magnets
• Magnetism of Kitaev spin-liquid candidate material RuBr${}_3$
• Electronic and magnetic properties of the RuX${}_3$ (X=Cl, Br, I) family: Two siblings -- and a cousin?
• Towards Kitaev Spin Liquid in 3d Transition Metal Compounds
• Functional renormalization group study of the Kitaev-$\Gamma$ model on the honeycomb lattice and emergent incommensurate magnetic correlations
• Significant thermal Hall effect in the 3$d$ cobalt Kitaev system $N{a}_{2}C{o}_{2}Te{O}_6$
• Rare-earth chalcohalides: A family of van der Waals layered Kitaev spin liquid candidates
• Kitaev Quantum Spin Liquids
• Revealing the Phase Diagram of Kitaev Materials by Machine Learning: Cooperation and Competition between Spin Liquids
• Quantum Many-Body Scars in Spin-1 Kitaev Chains
• Universal Thermodynamics in the Kitaev Fractional Liquid
• Light-Induced Control of Magnetic Phases in Kitaev Quantum Magnets
• Magnetic Anisotropy in Two-dimensional van der Waals Magnetic Materials and Their Heterostructures: Importance, Mechanisms, and Opportunities
• Possible Intermediate Quantum Spin Liquid Phase in $\alpha$-RuCl${}_3$ under High Magnetic Fields up to 100 T
• Easy-plane anisotropic-exchange magnets on a honeycomb lattice: quantum effects and dealing with them
• Nature of visons in the perturbed ferromagnetic and antiferromagnetic Kitaev honeycomb models
• Exchange interactions in $d^5$ Kitaev materials: From Na${}_2$IrO${}_3$ to $\alpha$-RuCl${}_3$
• Magnon-magnon interaction and magnon relaxation time in ferromagnetic Cr2Ge2Te6 monolayer
• Machine-Learned Phase Diagrams of Generalized Kitaev Honeycomb Magnets
• Dynamical anyon generation in Kitaev honeycomb non-Abelian spin liquids
• Evidence for magnetic fractional excitations in a Kitaev quantum-spin-liquid candidate $\alpha$-RuCl${}_3$
• Spin vestigial orders in extended Heisenberg-Kitaev models near hidden SU(2) points: Application to Na${}_2$Co${}_2$TeO${}_6$
• Field stability of Majorana spin liquids in antiferromagnetic Kitaev models
• The Saga of $\alpha$-RuCl${}_3$: Parameters, Models, and Phase Diagrams
• Magnetic vortex liquid and anomalous thermal Hall conductivity in frustrated magnets with bond-dependent interactions
• Field-induced phase transitions and quantum criticality in a honeycomb antiferromagnet Na3Co2SbO6
• Proximate Kitaev system for an intermediate magnetic phase in in-plane magnetic fields
• Learning Effective Spin Hamiltonian of Quantum Magnet
• Neutron spectroscopy evidence for a possible magnetic-field-induced gapless quantum-spin-liquid phase in a Kitaev material $\alpha$-RuCl${}_3$
• Single-crystal study of the honeycomb XXZ magnet BaCo${}_2$(PO${}_4$)${}_2$ in magnetic fields
• Optical magnons with dominant bond-directional exchange interactions in a honeycomb lattice iridate $\alpha$-Li${}_2$IrO${}_3$
• Magnetic anisotropy energies and metal-insulator transitions in monolayers of $\alpha$-RuCl${}_3$ and OsCl${}_3$ on graphene
• Ground State Magnetic Structure and Magnetic Field Effects in the Layered Honeycomb Antiferromagnet YbOCl
• First demonstration of tuning between the Kitaev and Ising limits in a honeycomb lattice
• $J=1/2$ Pseudospins and $d$-$p$ Hybridization in the Kitaev Spin Liquid Candidates Ru$X_3$ ($X$ = Cl, Br, I)
• Quantum many-body scars in spin-1 Kitaev chain with uniaxial single-ion anisotropy
• Topological phase diagrams of in-plane field polarized Kitaev magnets
• Magnetic properties of a spin-orbit entangled Jeff = 1/2 honeycomb lattice
• Interplay of magnetic field and trigonal distortion in the honeycomb $\Gamma$ model: Occurrence of a spin-flop phase
• Polarization-dependent magnetic properties of periodically driven $\alpha$-RuCl${}_3$
• Multinode quantum spin liquids in extended Kitaev honeycomb models: the view from variational Monte Carlo
• Interplay between multi-spin and chiral spin interactions on triangular lattice
• Exploration of the two-dimensional Ising magnetic materials in the triangular prismatic crystal field
• Static and fluctuating zigzag order, and possible signatures of Kitaev physics, in torque measurements of $\alpha$-RuCl${}_3$
• Nonequilibrium dynamics of $\alpha$-RuCl${}_3$ -- a time-resolved magneto-optical spectroscopy study
• Giant anisotropic magnetoresistance in few-layer α-RuCl3 tunnel junctions
• Unraveling the magnetic ground-state in alkali-metal lanthanide oxide Na${}_2$PrO${}_3$
• Non-local features of the spin-orbit exciton in Kitaev materials
• High-field quantum spin liquid transitions and angle-field phase diagram of Kitaev magnet $\alpha$-RuCl${}_3$
• Coexistence of anomalous spin dynamics and weak magnetic order in a chiral trillium lattice K2FeSn(PO4)3
• Intermediate phases in $\alpha$-RuCl${}_3$ under in-plane magnetic field via interlayer spin interactions
• Electronic transport mechanisms in a thin crystal of the Kitaev candidate $\alpha$-RuCl${}_3$ probed through guarded high impedance measurements
• Direct evidence for anisotropic magnetic interaction in $\alpha$-RuCl${}_3$ from polarized inelastic neutron scattering
• Signatures of polarized chiral spin disproportionation in rare earth nickelates
• Spin-phonon coupling and thermal Hall effect in the Kitaev model
• Long-range magnetic order with disordered spin orientations in a high-entropy antiferromagnet
• Raman spectroscopy of anyons in generic Kitaev spin liquids
• First-principles study of bulk stacking, $J_{\mathrm{eff}}$ picture, magnetic Hamiltonian, $g$ factors, and structural distortions of $\alpha$-RuCl${}_3$
• Angular-Dependent Thermal Hall Effect in a Honeycomb Magnet: Disentangling Kitaev and Dzyaloshinskii-Moriya Interactions
• Nesting instability of gapless U(1) spin liquids with spinon Fermi pockets in two dimensions
• The field-angle anisotropy of proximate Kitaev systems under an in-plane magnetic field