Beyond Kitaev physics in strong spin-orbit coupled magnets

Abstract

We review the recent advances and current challenges in the field of strong spin-orbit coupled Kitaev materials, with a particular emphasis on the physics beyond the exactly-solvable Kitaev spin liquid point. To that end, we give a comprehensive overview of the most relevant exchange interactions in $d^5$ and $d^7$ iridates and similar compounds, an exposition of their microscopic origin, and a systematic attempt to map out the most interesting correlated regimes of the multi-dimensional parameter space, guided by powerful symmetry and duality transformations as well as by insights from wide-ranging analytical and numerical studies. We also survey recent exciting results on quasi-1D models and discuss their relevance to higher-dimensional models. Finally, we highlight some of the key questions in the field as well as future directions.

fixed typos

References in corpus (56)

• 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
• Models and Materials for Generalized Kitaev Magnetism
• On the Origin of Zigzag Magnetic Order in Iridium Oxide Na2IrO3
• 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
• Topological characterization of quantum phase transitions in a S=1/2 spin model
• Hyper-honeycomb iridate $\beta$-Li2IrO3 as a platform for Kitaev magnetism
• Long range magnetic ordering in Na${}_2$IrO${}_3$
• 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
• Pseudospin exchange interactions in d^7 cobalt compounds: Possible realization of the Kitaev model
• Experimental identification of quantum spin liquids
• Kitaev-Heisenberg Hamiltonian for High-Spin $d^7$ Mott Insulators
• Possible proximity of the Mott insulating Iridate Na2IrO3 to a topological phase: Phase diagram of the Heisenberg-Kitaev model in a magnetic field
• Exact results on the Kitaev model on a hexagonal lattice: spin states, string and brane correlators, and anyonic excitations
• Anisotropic Ru3+ 4d5 magnetism in the alpha-RuCl3 honeycomb system: susceptibility, specific heat and Zero field NMR
• Hidden symmetries of the extended Kitaev-Heisenberg model: Implications for honeycomb lattice iridates A2IrO3
• Non-coplanar and counter-rotating incommensurate magnetic order stabilized by Kitaev interactions in $\gamma$-Li2IrO3
• Possible Kitaev Quantum Spin Liquid State in 2D Materials with S=3/2
• Unconventional magnetic order on the hyperhoneycomb Kitaev lattice in $\beta$-Li2IrO3: full solution via magnetic resonant x-ray diffraction
• Microscopic mechanism for higher-spin Kitaev model
• Honeycomb-lattice Heisenberg-Kitaev model in a magnetic field: Spin canting, metamagnetism, and vortex crystals
• Kitaev interactions in the Co honeycomb antiferromagnets Na${}_3$Co${}_2$SbO${}_6$ and Na${}_2$Co${}_2$TeO${}_6$
• Spin-S Kitaev model: Classical Ground States, Order by Disorder and Exact Correlation Functions
• Interplay of quantum and thermal fluctuations in a frustrated magnet
• Magnetic anisotropy in the Kitaev model systems Na2IrO3 and RuCl3
• Weak-field induced nonmagnetic state in a Co-based honeycomb
• Importance of anisotropic exchange interactions in honeycomb iridates. Minimal model for zigzag antiferromagnetic order in Na${}_2$IrO${}_3$
• Theory of the field-revealed Kitaev spin liquid
• Ground-state phase diagram of a spin-1/2 frustrated ferromagnetic XXZ chain: Haldane dimer phase and gapped/gapless chiral phases
• Weyl spin liquids
• Magnetic field effect on topological spin excitations in CrI${}_3$
• Quantum Selection of Order in an $XXZ$ Antiferromagnet on a Kagomé Lattice
• Magnetic order in single crystals of Na3Co2SbO6 with a honeycomb arrangement of 3d${}^7$ Co${}^{2+}$ ions
• Theory of Magnetic Phase Diagrams in Hyperhoneycomb and Harmonic-honeycomb Iridates
• Thermodynamic Evidence of Proximity to a Kitaev Spin-Liquid in Ag${}_3$LiIr${}_2$O${}_6$
• Phase diagram and spin correlations of the Kitaev-Heisenberg model: Importance of quantum effects
• Order-by-disorder and spin-orbital liquids in a distorted Heisenberg-Kitaev model
• Probing the stability of the spin liquid phases in the Kitaev-Heisenberg model using tensor network algorithms
• Magnon damping in the zigzag phase of the Kitaev-Heisenberg-$\Gamma$ model on a honeycomb lattice
• Ground state and low-energy excitations of the Kitaev-Heisenberg ladder
• Exchange interactions, Jahn-Teller coupling, and multipole orders in pseudospin one-half $5{\mathbf{d}}^2$ Mott insulators
• Density-Matrix Renormalization Group Study of Extended Kitaev-Heisenberg Model
• Thermodynamic classification of three-dimensional Kitaev spin liquids
• Quantum Fluctuations of Chirality in One-Dimensional Spin-1/2 Multiferroics: Gapless Dielectric Response from Phasons and Chiral Solitons
• Magnetic excitations of the field induced states in BaCo2(AsO4)2 probed by time-domain terahertz spectroscopy
• Significant thermal Hall effect in the 3$d$ cobalt Kitaev system $N{a}_{2}C{o}_{2}Te{O}_6$
• Classical Heisenberg spins on a hexagonal lattice with Kitaev couplings
• Oscillations in the magnetothermal conductivity of $\mathbf{\alpha }$-RuCl${}_3$: Evidence of transition anomalies
• Effect of structural disorder on the Kitaev magnet Ag${}_3$LiIr${}_2$O${}_6$
• High-resolution resonant inelastic x-ray scattering study of the electron-phonon coupling in honeycomb $\alpha$-Li${}_2$IrO${}_3$
• Electronic and magnetic properties of iridium ilmenites $A$IrO${}_3$ ($A=$ Mg, Zn, and Mn)
• Extent of frustration in the classical Kitaev-$\Gamma$ model via bond anisotropy
• Unconventional magnetic field response of the hyperhoneycomb Kitaev magnet $\beta -{\text{Li}}_2{\text{IrO}}_3$
• Twice Hidden String Order and Competing Phases in the Spin-1/2 Kitaev-Gamma Ladder

Cited by in corpus (46)

• Kitaev Quantum Spin Liquids
• The Saga of $\alpha$-RuCl${}_3$: Parameters, Models, and Phase Diagrams
• Spin-$S$ Kitaev-Heisenberg model on the honeycomb lattice: A high-order treatment via the many-body coupled cluster method
• Ferrimagnetism from triple-q order in Na${}_2$Co${}_2$TeO${}_6$
• Microscopic Roadmap to a Yao-Lee Spin-Orbital Liquid
• Transforming from Kitaev to Disguised Ising Chain: Application to CoNb${}_2$O${}_6$
• Kitaev Interactions Through an Extended Superexchange Pathway in the jeff = 1/2 Ru3+ Honeycomb Magnet, RuP3SiO11
• Pyrochlore NaYbO2: A potential Quantum Spin Liquid Candidate
• Dynamical response theory of interacting Majorana fermions and its application to generic Kitaev quantum spin liquids in a field
• Chiral spin state and nematic ferromagnet in the spin-1 Kitaev-$\Gamma$ model
• Multinode quantum spin liquids in extended Kitaev honeycomb models: the view from variational Monte Carlo
• High Chern numbers and topological flat bands in high-field polarized Kitaev magnets on the star lattice
• Topological phase transitions and thermal Hall effect in a noncollinear spin texture
• Magnetic versus nonmagnetic polymorphs of RuBr${}_3$ under pressure
• Static and fluctuating zigzag order, and possible signatures of Kitaev physics, in torque measurements of $\alpha$-RuCl${}_3$
• Theory of rare-earth Kramers magnets on a Shastry-Sutherland lattice: dimer phases in presence of strong spin-orbit coupling
• Successive topological phase transitions in two distinct spin-flop phases on the honeycomb lattice
• Local spin-flip transitions induced by magnetic quantum impurities in two-dimensional magnets
• Phonon Dynamics in the Chiral Kitaev Spin Liquid
• Quantum subspace expansion approach for simulating dynamical response functions of Kitaev spin liquids
• Interplay of Kitaev Interaction and Off-diagonal Exchanges: Exotic Phases and Quantum Phase Diagrams
• Ferrimagnetism from quantum fluctuations in Kitaev materials
• Intermediate phases in $\alpha$-RuCl${}_3$ under in-plane magnetic field via interlayer spin interactions
• Quantum Spin Liquid phases in Kitaev Materials
• Field-Induced Ordered Phases in Anisotropic Spin-1/2 Kitaev Chains
• Pairing tendencies in the doped Kitaev-Heisenberg model
• Exfoliation and Optical Properties of S=1 Triangular Lattice Antiferromagnet NiGa${}_2$S${}_4$
• Complex orders and chirality in the classical Kitaev-$\Gamma$ model
• Exact Ground States and Phase Diagram of the Quantum Compass Model under an in-plane Field
• Signatures of fractionalization in the optical phonons of hyperhoneycomb Kitaev magnet $\beta$-Li${}_2$IrO${}_3$
• Direct evidence for anisotropic magnetic interaction in $\alpha$-RuCl${}_3$ from polarized inelastic neutron scattering
• Field-induced magnetic phases in the Kitaev candidate Na${}_3$Co${}_2$SbO${}_6$
• Topological Majorana flat bands in the Kitaev model on a Bishamon-kikko lattice
• Eleven Competing Phases in the Heisenberg-Gamma (J$\Gamma$) Ladder
• Ferrichiral skyrmions with sublattice-resolved chirality in extended Kitaev model in triangular lattice
• Pressure-dependent magnetism of the Kitaev candidate Li${}_2$RhO${}_3$
• Field-induced phase transitions in the Kitaev-Heisenberg model: A sign-problem-free quantum Monte Carlo study and possible application to $\alpha$-RuCl3
• Schwinger boson theory for $S=1$ Kitaev quantum spin liquids
• Reviving Majorana zero modes in the spin-1/2 Kitaev ladder model
• 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
• Thermal and quantum fluctuations in extended Kitaev-Yao-Lee spin-orbital model
• Ligand-SOC enhanced $4f^5$ Kitaev antiferromagnet: Application to ${\mathrm{SmI}}_3$
• Constructing Emergent U(1) Symmetries in the Gamma-prime $\left({\mathbf{\Gamma }}^{\prime }\right)$ model
• Real-space chirality from crystalline topological defects in the Kitaev spin liquid
• Dynamical Response of the Kitaev Spin Liquid under Third-Nearest-Neighbor Heisenberg Interaction