The Saga of $\alpha$-RuCl${}_3$: Parameters, Models, and Phase Diagrams

Abstract

RuCl${}_3$ was likely the first ever deliberately synthesized ruthenium compound, following the discovery of the ${}_{44}$Ru element in 1844. For a long time it was known as an oxidation catalyst, with its physical properties being discrepant and confusing, until a decade ago when its allotropic form $\alpha$-RuCl${}_3$ rose to exceptional prominence. This "re-discovery" of $\alpha$-RuCl${}_3$ has not only reshaped the hunt for a material manifestation of the Kitaev spin liquid, but it has opened the floodgates of theoretical and experimental research in the many unusual phases and excitations that the anisotropic-exchange magnets as a class of compounds have to offer. Given its importance for the field of Kitaev materials, it is astonishing that the low-energy spin model that describes this compound and its possible proximity to the much-desired spin-liquid state is still a subject of significant debate ten years later. In the present study, we argue that the existing key phenomenological observations put strong natural constraints on the effective microscopic spin model of $\alpha$-RuCl${}_3$, and specifically on its spin-orbit-induced anisotropic-exchange parameters that are responsible for the non-trivial physical properties of this material. These constraints allow one to focus on the relevant region of the multi-dimensional phase diagram of the $\alpha$-RuCl${}_3$ model, suggest an intuitive description of it via a different parametrization of the exchange matrix, offer a unifying view on the earlier assessments of its parameters, and bring closer together several approaches to the derivation of anisotropic-exchange models. We explore extended phase diagrams relevant to the $\alpha$-RuCl${}_3$ parameter space using quasi-classical, Luttinger-Tisza, exact diagonalization, and density-matrix renormalization group methods, demonstrating a remarkably c... (arxiv cutoff; for the rest, see the paper)

arXiv comment39 pages, 28 Figures. Text of immense pedagogical power. Published under different title. Winner of the PRB beauty award (Editor's Suggestion)

References in corpus (120)

• The electronic properties of graphene
• Anyons in an exactly solved model and beyond
• Correlated Electrons in High Temperature Superconductors
• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• Quantum Spin Liquids
• Quantum Spin Liquid States
• Kitaev-Heisenberg Model on Honeycomb Lattice: Possible Exotic Phases in Iridium Oxides $A_2$IrO${}_3$
• The ITensor Software Library for Tensor Network Calculations
• Majorana quantization and half-integer thermal quantum Hall effect in a Kitaev spin liquid
• Proximate Kitaev Quantum Spin Liquid Behaviour in α-RuCl${}_3$
• Kitaev quantum spin liquid - concept and materialization
• $\alpha$-RuCl3: a Spin-Orbit Assisted Mott Insulator on a Honeycomb Lattice
• Spin-Orbit Physics Giving Rise to Novel Phases in Correlated Systems: Iridates and Related Materials
• Neutron tomography of magnetic Majorana fermions in a proximate quantum spin liquid
• Generic spin model for the honeycomb iridates beyond the Kitaev limit
• Models and Materials for Generalized Kitaev Magnetism
• Herbertsmithite and the Search for the Quantum Spin Liquid
• Challenges in Design of Kitaev Materials: Magnetic Interactions from Competing Energy Scales
• The monoclinic crystal structure of $\alpha$-RuCl${}_3$ and the zigzag antiferromagnetic ground state
• 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
• Crystal and Magnetic Structures in Layered, Transition Metal Dihalides and Trihalides
• Physics of the Kitaev model: fractionalization, dynamical correlations, and material connections
• Continuous excitations of the triangular-lattice quantum spin liquid YbMgGaO4
• Quantum Excitations in Quantum Spin Ice
• Low-temperature crystal and magnetic structure of $\alpha$-RuCl3
• Neel order in square and triangular lattice Heisenberg models
• Excitations in the field-induced quantum spin liquid state of alpha-RuCl3
• Fractional spinon excitations in the quantum Heisenberg antiferromagnetic chain
• 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
• Half-integer quantized anomalous thermal Hall effect in the Kitaev material $\alpha$-RuCl${}_3$
• Fermionic response from fractionalization in an insulating two-dimensional magnet
• Spin liquid phase of the $S=\frac{1}{2}$ $J_1-J_2$ Heisenberg model on the triangular lattice
• Spin-orbit excitation energies, anisotropic exchange, and magnetic phases of honeycomb RuCl3
• Disorder-Induced Mimicry of a Spin Liquid in YbMgGaO${}_4$
• Breakdown of Magnons in a Strongly Spin-Orbital Coupled Magnet
• Hunting Majorana Fermions in Kitaev Magnets
• Crystal structure and magnetism in $\alpha$-RuCl3: an ab-initio study
• Phase Diagram of $\alpha$-RuCl${}_3$ in an in-plane Magnetic Field
• Spin-wave excitations evidencing the Kitaev interaction in single crystalline $\alpha$-RuCl${}_3$
• Direct Measurement of the Spin Hamiltonian and Observation of Condensation of Magnons in the 2D Frustrated Quantum Magnet Cs2CuCl4
• Unusual thermal Hall effect in a Kitaev spin liquid candidate $\alpha$-RuCl${}_3$
• Hidden symmetries of the extended Kitaev-Heisenberg model: Implications for honeycomb lattice iridates A2IrO3
• Robustness of the thermal Hall effect close to half-quantization in a field-induced spin liquid state
• An anisotropic spin model of strong spin-orbit-coupled triangular antiferromagnets
• Incommensurate Counterrotating Magnetic Order Stabilized by Kitaev Interactions in the Layered Honeycomb $\alpha$-Li${}_2$IrO${}_3$
• Magnetization processes of zigzag states on the honeycomb lattice: Identifying spin models for $\alpha$-RuCl${}_3$ and Na${}_2$IrO${}_3$
• Non-coplanar and counter-rotating incommensurate magnetic order stabilized by Kitaev interactions in $\gamma$-Li2IrO3
• Topography of Spin Liquids on a Triangular Lattice
• Unconventional magnetic order on the hyperhoneycomb Kitaev lattice in $\beta$-Li2IrO3: full solution via magnetic resonant x-ray diffraction
• Kitaev-Heisenberg models for iridates on the triangular, hyperkagome, kagome, fcc, and pyrochlore lattices
• Probing $\alpha$-RuCl${}_3$ Beyond Magnetic Order: Effects of Temperature and Magnetic Field
• Ferromagnetic Kitaev interaction and the origin of large magnetic anisotropy in $\alpha$-RuCl${}_3$
• Magnetic anisotropy in the Kitaev model systems Na2IrO3 and RuCl3
• Theoretical investigation of the magnetic dynamics in $\alpha$-RuCl${}_3$
• Ground State Phase Diagram of the $t$-$t^{\prime }$-$J$ model
• Dynamical structure factor of triangular-lattice antiferromagnet
• Quantization of the thermal Hall conductivity at small Hall angles
• Finite field regime for a quantum spin liquid in $\alpha$-RuCl${}_3$
• Frustration and anisotropic exchange in ytterbium magnets with edge-shared octahedra
• Anisotropic-Exchange Magnets on a Triangular Lattice: Spin Waves, Accidental Degeneracies, and Dual Spin Liquids
• Rethinking $\alpha$-RuCl${}_3$
• Approximately quantized thermal Hall effect of chiral liquids coupled to phonons
• Weak plaquette valence bond order in the $S=1/2$ honeycomb $J_1-J_2$ Heisenberg model
• Spin-orbit physics of j=1/2 Mott insulators on the triangular lattice
• Quasiparticle Breakdown and Spin Hamiltonian of the Frustrated Quantum Pyrochlore Yb${}_2$Ti${}_2$O${}_7$ in Magnetic Field
• Evidence of a Phonon Hall Effect in the Kitaev Spin Liquid Candidate $\alpha$-RuCl${}_3$
• Phase Diagram and Quantum Order by Disorder in the Kitaev $K_1$-$K_2$ Honeycomb Magnet
• Anisotropic susceptibilities in the honeycomb Kitaev system $\alpha$-RuCl${}_3$
• Proximate ferromagnetic state in the Kitaev model material $\alpha$-RuCl${}_3$
• Unconventional spin dynamics in the honeycomb-lattice material $\alpha$-RuCl${}_3$: high-field ESR studies
• Dynamical and thermal magnetic properties of the Kitaev spin liquid candidate $\alpha$-RuCl${}_3$
• Spin Wave Analysis of Low-Temperature Thermal Hall Effect in the Candidate Kitaev Spin Liquid $\alpha$-RuCl${}_3$
• Field-induced intermediate ordered phase and anisotropic interlayer interactions in $\alpha$-RuCl${}_3$
• Unified theory of spiral magnetism in the harmonic-honeycomb iridates α, β, γ Li2IrO3
• Geometrical frustration versus Kitaev interactions in BaCo${}_2$(AsO${}_4$)${}_2$
• Spin liquids in geometrically perfect triangular antiferromagnets
• High-Field Quantum Disordered State in $\alpha$-RuCl3: Spin Flips, Bound States, and a Multi-Particle Continuum
• Unveiling Magnetic Interactions of Ruthenium Trichloride via Constraining Direction of Orbital moments: Potential Routes to Realize Quantum Spin Liquid
• Beyond Kitaev physics in strong spin-orbit coupled magnets
• Identification of Magnetic Interactions and High-field Quantum Spin Liquid in $\alpha$-RuCl${}_3$
• Field evolution of magnons in $\alpha$-RuCl${}_3$ by high-resolution polarized terahertz spectroscopy
• Order-by-disorder and spin-orbital liquids in a distorted Heisenberg-Kitaev model
• Ground-state phase diagram of an anisotropic spin-$1/2$ model on the triangular lattice
• Magnetic Couplings in Edge-Sharing High-Spin $d^7$ Compounds
• Symmetry Reduction in the Quantum Kagome Antiferromagnet Herbertsmithite
• Nature of Magnetic Excitations in the High-Field Phase of $\alpha$-RuCl${}_3$
• Heisenberg-Kitaev model in a magnetic field: $1/S$ expansion
• Deriving models for the Kitaev spin-liquid candidate material $\alpha$-RuCl${}_3$ from first principles
• Semiclassical ground-state phase diagram and multi-Q phase of a spin-orbit coupled model on triangular lattice
• Magnetoelastic coupling and effects of uniaxial strain in $\alpha$-RuCl${}_3$ from first principles
• Magnon damping in the zigzag phase of the Kitaev-Heisenberg-$\Gamma$ model on a honeycomb lattice
• Unexpected z-Direction Ising Antiferromagnetic Order in a frustrated Spin-1/2 $J_1-J_2$ XY Model on the Honeycomb Lattice
• Kitaev honeycomb models in magnetic fields: Dynamical response and hidden symmetries
• Effective model with strong Kitaev interactions for $\alpha$-$\mathrm{RuC}{\mathrm{l}}_3$
• Classical spiral spin liquids as a possible route to quantum spin liquids
• Where is the Quantum Spin Nematic?
• Origin of oscillatory structures in the magnetothermal conductivity of the putative Kitaev magnet $\alpha$-RuCl${}_3$
• Oscillations in the magnetothermal conductivity of $\mathbf{\alpha }$-RuCl${}_3$: Evidence of transition anomalies
• Magnon dispersion and dynamic spin response in three-dimensional spin models for $\alpha$-RuCl${}_3$
• Magnon interactions in the frustrated pyrochlore ferromagnet Yb${}_2$Ti${}_2$O${}_7$
• "Quasi-particle breakdown" in the quasi-one-dimensional Ising ferromagnet CoNb${}_2$O${}_6$
• Phonon Thermal Hall Conductivity from Scattering with Collective Fluctuations
• Magnetic field-dependent low-energy magnon dynamics in $\alpha$-RuCl3
• Extraction of the interaction parameters for $\alpha -$RuCl${}_3$ from neutron data using machine learning
• Planar thermal Hall effect from phonons in a Kitaev candidate material
• Easy-plane anisotropic-exchange magnets on a honeycomb lattice: quantum effects and dealing with them
• Quantum Phases in the Honeycomb-Lattice $J_1$--$J_3$ Ferro-Antiferromagnetic Model
• Susceptibility anisotropy and its disorder evolution in models for Kitaev materials
• Quantum Spin Dynamics Due to Strong Kitaev Interactions in the Triangular-Lattice Antiferromagnet CsCeSe${}_2$
• Exchange interactions in $d^5$ Kitaev materials: From Na${}_2$IrO${}_3$ to $\alpha$-RuCl${}_3$
• Thermal Hall Effect in the Kitaev-Heisenberg System with Spin-Phonon Coupling
• Machine-Learned Phase Diagrams of Generalized Kitaev Honeycomb Magnets
• Proximate Dirac spin liquid in honeycomb lattice $J_1$-$J_3$ XXZ model: Numerical study and application to cobaltates
• Tuning the confinement potential between spinons in the Ising chain CoNb2O6 using longitudinal fields and quantitative determination of the microscopic Hamiltonian
• Evidence for magnetic fractional excitations in a Kitaev quantum-spin-liquid candidate $\alpha$-RuCl${}_3$
• Magnon interactions in the quantum paramagnetic phase of CoNb${}_2$O${}_6$
• Spin dynamics of counterrotating Kitaev spirals via duality
• Pulling order back from the brink of disorder: Observation of a nodal line spin liquid and fluctuation stabilized order in K${}_2$IrCl${}_6$

Cited by in corpus (8)

• Ferrimagnetism from quantum fluctuations in Kitaev materials
• Topological Majorana flat bands in the Kitaev model on a Bishamon-kikko lattice
• Magnetostriction in the $J$-$K$-$\Gamma$ model: Application of the numerical linked cluster expansion
• Magnetic excitations in the Kitaev material Na${}_2$IrO${}_3$ studied by neutron scattering
• An integrated theoretical and numerical approach to understand modern experiments on quantum magnetism
• Spin sensitive transport in RuCl_3/Pt heterostructures: revealing a field-transverse spin anisotropy in a spin liquid candidate
• Dynamical Response of the Kitaev Spin Liquid under Third-Nearest-Neighbor Heisenberg Interaction
• Thermal and quantum fluctuations in extended Kitaev-Yao-Lee spin-orbital model