Spin-wave excitations evidencing the Kitaev interaction in single crystalline $\alpha$-RuCl${}_3$

Abstract

Kitaev interactions underlying a quantum spin liquid have been long sought, but experimental data from which their strengths can be determined directly is still lacking. Here, by carrying out inelastic neutron scattering measurements on high-quality single crystals of $\alpha$-RuCl${}_3$, we observe spin-wave spectra with a gap of $\sim$2 meV around the M point of the two-dimensional Brillouin zone. We derive an effective-spin model in the strong-coupling limit based on energy bands obtained from first-principle calculations, and find that the anisotropic Kitaev interaction $K$ term and the isotropic antiferromagentic off-diagonal exchange interaction $\Gamma$ term are significantly larger than the Heisenberg exchange coupling $J$ term. Our experimental data can be well fit using an effective-spin model with $K=-6.8$ meV and $\Gamma =9.5$ meV. These results demonstrate explicitly that Kitaev physics is realized in real materials.

To appear in PRL

References in corpus (16)

• Non-Abelian Anyons and Topological Quantum Computation
• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• $\alpha$-RuCl3: a Spin-Orbit Assisted Mott Insulator on a Honeycomb Lattice
• On the Origin of Zigzag Magnetic Order in Iridium Oxide Na2IrO3
• Scattering Continuum and Possible Fractionalized Excitations in $\alpha$-RuCl${}_3$
• Magnetic order in $\alpha$-RuCl${}_3$: a honeycomb lattice quantum magnet with strong spin-orbit coupling
• Exact results for spin dynamics and fractionization in the Kitaev Model
• Successive magnetic phase transitions in $\mathbf{\alpha }$-RuCl${}_3$: XY-like frustrated magnet on the honeycomb lattice
• Kitaev magnetism in honeycomb RuCl3 with intermediate spin-orbit coupling
• Crystal field splitting and correlation effect on the electronic structure of A2IrO3
• Anisotropic Ru3+ 4d5 magnetism in the alpha-RuCl3 honeycomb system: susceptibility, specific heat and Zero field NMR
• The magnetic and crystal structures of Sr2IrO4: A neutron diffraction study
• Magnetic anisotropy in the Kitaev model systems Na2IrO3 and RuCl3
• Importance of anisotropic exchange interactions in honeycomb iridates. Minimal model for zigzag antiferromagnetic order in Na${}_2$IrO${}_3$
• Neutron scattering study of correlated phase behavior in Sr2IrO4
• $J_{eff}=1/2$ Mott Insulating State in Rh and Ir Fluorides

Cited by in corpus (78)

• Models and Materials for Generalized Kitaev Magnetism
• Experimental identification of quantum spin liquids
• Magnetic Excitations and Continuum of a Field-Induced Quantum Spin Liquid in $\alpha$-RuCl${}_3$
• Magnetization processes of zigzag states on the honeycomb lattice: Identifying spin models for $\alpha$-RuCl${}_3$ and Na${}_2$IrO${}_3$
• Weak-field induced nonmagnetic state in a Co-based honeycomb
• Field-induced magnetic transition and spin fluctuation in quantum spin liquid candidate CsYbSe${}_2$
• Unconventional spin dynamics in the honeycomb-lattice material $\alpha$-RuCl${}_3$: high-field ESR studies
• Topological magnon insulator spin excitations in the two-dimensional ferromagnet CrBr${}_3$
• Identification of Magnetic Interactions and High-field Quantum Spin Liquid in $\alpha$-RuCl${}_3$
• Comprehensive study of the dynamics of a classical Kitaev spin liquid
• Thermodynamic perspective on the field-induced behavior of $\alpha$-RuCl${}_3$
• Kitaev-like honeycomb magnets: Global phase behavior and emergent effective models
• High-pressure magnetization and NMR studies on $\alpha$-RuCl${}_3$
• Magnetic anisotropy reversal driven by structural symmetry-breaking in monolayer α-RuCl3
• Electronic and phonon excitations in α-RuCl${}_3$
• Synthesis, magnetization and heat capacity of triangular lattice materials NaErSe${}_2$ and KErSe${}_2$
• Angle-dependent thermodynamics of $\alpha$-RuCl${}_3$
• Kitaev Quantum Spin Liquids
• Universal Thermodynamics in the Kitaev Fractional Liquid
• Extraction of the interaction parameters for $\alpha -$RuCl${}_3$ from neutron data using machine learning
• Possible Intermediate Quantum Spin Liquid Phase in $\alpha$-RuCl${}_3$ under High Magnetic Fields up to 100 T
• Evolution of magnetic Dirac bosons in a honeycomb lattice
• Susceptibility anisotropy and its disorder evolution in models for Kitaev materials
• Disorder-induced broadening of the spin waves in a triangular-lattice quantum-spin-liquid candidate YbZnGaO${}_4$
• Thermal Hall Effect in the Kitaev-Heisenberg System with Spin-Phonon Coupling
• Topological superconductivity in the extended Kitaev-Heisenberg model
• Evidence for magnetic fractional excitations in a Kitaev quantum-spin-liquid candidate $\alpha$-RuCl${}_3$
• The Saga of $\alpha$-RuCl${}_3$: Parameters, Models, and Phase Diagrams
• Symmetry analysis of bond-alternating Kitaev spin chains and ladders
• Neutron spectroscopy evidence for a possible magnetic-field-induced gapless quantum-spin-liquid phase in a Kitaev material $\alpha$-RuCl${}_3$
• Evidence of Kitaev interaction in the monolayer 1T-CrTe${}_2$
• Phonon Dynamics in the Generalized Kitaev Spin Liquid
• Differentiable programming tensor networks for Kitaev magnets
• Dynamics of fractionalized mean-field theories: consequences for Kitaev materials
• Sign Changes in Heat, Spin, and Orbital Magnon Transport Coefficients in Kitaev Ferromagnets
• Suppression of the antiferromagnetic order by Zn doping in a possible Kitaev material Na${}_2$Co${}_2$TeO${}_6$
• Origin of nonsymmorphic bosonization formulas in generalized antiferromagnetic Kitaev spin-$\frac{1}{2}$ chains from a renormalization-group perspective
• Topological phase diagrams of in-plane field polarized Kitaev magnets
• Quantum phase transition between spin liquid and spin nematics in spin-1 Kitaev honeycomb model
• Field-Angle-Resolved Specific Heat in Na${}_2$Co${}_2$TeO${}_6$: Evidence against Kitaev Quantum Spin Liquid
• Interplay of magnetic field and trigonal distortion in the honeycomb $\Gamma$ model: Occurrence of a spin-flop phase
• Extended Quantum Spin Liquid with Spinon-like Excitations in an Anisotropic Kitaev-Gamma Model
• Engineering the Kitaev spin liquid in a quantum dot system
• Chiral spin state and nematic ferromagnet in the spin-1 Kitaev-$\Gamma$ model
• High Chern numbers and topological flat bands in high-field polarized Kitaev magnets on the star lattice
• Room temperature relaxometry of single nitrogen-vacancy centers in proximity to $\alpha$-RuCl${}_3$ nanoflakes
• Topological phase transitions and thermal Hall effect in a noncollinear spin texture
• Kinetic Ferromagnetism and Topological Magnons of the Hole-Doped Kitaev Spin Liquid
• Interplay between multi-spin and chiral spin interactions on triangular lattice
• Phonon Dynamics in the Chiral Kitaev Spin Liquid
• Nonsymmorphic bosonization in one-dimensional generalized Kitaev spin-1/2 models
• Emergent SU(2)${}_1$ conformal symmetry in the spin-1/2 Kitaev-Gamma chain with a Dzyaloshinskii-Moriya interaction
• Interplay of Kitaev Interaction and Off-diagonal Exchanges: Exotic Phases and Quantum Phase Diagrams
• Signatures of a gapless quantum spin liquid in the Kitaev material Na${}_3$Co${}_{2-x}$Zn${}_x$SbO${}_6$
• Emergent Hyper-Magic Manifold in Twisted Kitaev Bilayers
• High-field quantum spin liquid transitions and angle-field phase diagram of Kitaev magnet $\alpha$-RuCl${}_3$
• Ground state and magnetic transitions of the orthorhombic antiferromagnet CaCo${}_2$TeO${}_6$
• A universal pairing gap measurement proposal by dynamical excitations in 2D doped attractive Fermi-Hubbard model with spin-orbit coupling
• Possible Realization of Kitaev Spin Liquids in van der Waals Heterostructures of $\alpha$-RuCl${}_3$ and Cr$X_3$ ($X$=Cl and I)
• Intermediate phases in $\alpha$-RuCl${}_3$ under in-plane magnetic field via interlayer spin interactions
• Spectrum of the hole excitation in spin-orbit Mott insulator Na${}_2$IrO${}_3$
• Eleven Competing Phases in the Heisenberg-Gamma (J$\Gamma$) Ladder
• Coupled spin-1/2 antiferromagnetic chain Cs${}_2$LiRuCl${}_6$ with partially disordered crystal lattice
• Direct evidence for anisotropic magnetic interaction in $\alpha$-RuCl${}_3$ from polarized inelastic neutron scattering
• Field tuning Kitaev systems for spin fractionalization and topological order
• Magnetostriction in the $J$-$K$-$\Gamma$ model: Application of the numerical linked cluster expansion
• First-principles study of bulk stacking, $J_{\mathrm{eff}}$ picture, magnetic Hamiltonian, $g$ factors, and structural distortions of $\alpha$-RuCl${}_3$
• Understanding the magnetic interactions of the zig-zag honeycomb lattice: Application to $\alpha$-RuCl${}_3$
• Field-induced phase transitions in the Kitaev-Heisenberg model: A sign-problem-free quantum Monte Carlo study and possible application to $\alpha$-RuCl3
• Disorder-induced spin excitation continuum and spin-glass ground state in the inverse spinel CuGa${}_2$O${}_4$
• Dominant Kitaev Interaction and Field-induced Quantum Disordered Phase in the Cobaltate Na${}_2$Co${}_2$TeO${}_6$
• Ligand-SOC enhanced $4f^5$ Kitaev antiferromagnet: Application to ${\mathrm{SmI}}_3$
• Strategy to Extract Kitaev Interaction using Symmetry in Honeycomb Mott Insulators
• Nesting instability of gapless U(1) spin liquids with spinon Fermi pockets in two dimensions
• Sizable Ligand-Mediated Bond-Dependent Interactions in a Spin-1 Triangular Antiferromagnet NiI${}_2$
• Ground state of the staggered Heisenberg-$\Gamma$ honeycomb model in a magnetic field
• The field-angle anisotropy of proximate Kitaev systems under an in-plane magnetic field
• Magnetic excitations in the Kitaev material Na${}_2$IrO${}_3$ studied by neutron scattering