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.

arXiv commentfixed typos

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• 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
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• Effective quantum pseudospin-1/2 model for Yb pyrochlore oxides
• Ground state and low-energy excitations of the Kitaev-Heisenberg ladder
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• Effect of structural disorder on the Kitaev magnet Ag${}_3$LiIr${}_2$O${}_6$
• Robust spin correlations at high magnetic fields in the honeycomb iridates
• Computational design of $f$-electron Kitaev magnets: honeycomb and hyperhoneycomb compounds $A_2$PrO${}_3$ ($A=$ alkali metals)
• Novel chiral quantum spin liquids in Kitaev magnets
• Majorana spin liquids and projective realization of SU(2) spin symmetry
• Unusual excitations and double-peak specific heat in a bond-alternating spin-$1$ $K$-$\Gamma$ chain
• Revealing the Phase Diagram of Kitaev Materials by Machine Learning: Cooperation and Competition between Spin Liquids
• Magnetic Raman continuum in single crystalline H${}_3$LiIr${}_2$O${}_6$
• Strong antiferromagnetic interaction owing to a large trigonal distortion in the spin-orbit-coupled honeycomb lattice iridate CdIrO${}_3$
• Quantum coherence in a compass chain under an alternating magnetic field
• High-resolution resonant inelastic x-ray scattering study of the electron-phonon coupling in honeycomb $\alpha$-Li${}_2$IrO${}_3$
• Quantum and classical behavior of spin-$S$ Kitaev models in an anisotropic limit
• Tensor network simulation of the Kitaev-Heisenberg model at finite temperature
• On the saw-tooth torque in anisotropic $j_{\mathrm{eff}}=1/2$ magnets: Application to $\alpha$-RuCl${}_3$
• ${\mathbb{Z}}_2$ spin liquids in the higher spin-$S$ Kitaev honeycomb model: An exact deconfined ${\mathbb{Z}}_2$ gauge structure in a non-integrable model
• Classical spin order near antiferromagnetic Kitaev point in the spin-1/2 Kitaev-Gamma chain
• Kitaev magnetism through the prism of lithium iridate
• Easy-plane anisotropic-exchange magnets on a honeycomb lattice: quantum effects and dealing with them
• Spin-1 Kitaev model in one dimension
• Plaquette order in classical spin liquid stabilized by strong off-diagonal exchange
• Triple-meron crystal in high-spin Kitaev magnets
• Probing signatures of fractionalization in candidate quantum spin liquid Cu2IrO3 via anomalous Raman scattering
• Determining Kitaev interaction in spin-$S$ honeycomb Mott insulators
• Chiral spin-order in some purported Kitaev spin-liquid compounds
• Anisotropic temperature-field phase diagram of single-crystalline $\beta$-Li${}_2$IrO${}_3$: magnetization, specific heat, and ${}^7$Li NMR study
• Exchange interactions in $d^5$ Kitaev materials: From Na${}_2$IrO${}_3$ to $\alpha$-RuCl${}_3$
• Counter-rotating spiral order in three dimensional iridates: signature of hidden symmetry in Kitaev-$\Gamma$ model
• Antiferromagnetic Kitaev Interactions in Polar Spin-Orbit Mott Insulators
• Instabilities of spin-1 Kitaev spin liquid phase in presence of single-ion anisotropies
• Electronic and magnetic properties of iridium ilmenites $A$IrO${}_3$ ($A=$ Mg, Zn, and Mn)
• Machine-Learned Phase Diagrams of Generalized Kitaev Honeycomb Magnets
• Quantum liquids of the S=3/2 Kitaev honeycomb and related Kugel-Khomskii models
• Unusual spin dynamics in the low-temperature magnetically ordered state of Ag${}_3$LiIr${}_2$O${}_6$
• Magnon-spinon dichotomy in the Kitaev hyperhoneycomb $\beta$-Li${}_2$IrO${}_3$
• Exact zero modes in a quantum compass chain under inhomogeneous transverse fields
• Flux mobility delocalization in the Kitaev spin ladder
• Field stability of Majorana spin liquids in antiferromagnetic Kitaev models
• Extent of frustration in the classical Kitaev-$\Gamma$ model via bond anisotropy
• Field-induced Kitaev multipolar liquid in spin-orbit coupled $d^2$ honeycomb Mott insulators
• Magnetic vortex liquid and anomalous thermal Hall conductivity in frustrated magnets with bond-dependent interactions
• Ground-state properties of the $K-\Gamma$ model on a honeycomb lattice
• Field evolution of low-energy excitations in the hyperhoneycomb magnet $\beta$-Li${}_2$IrO${}_3$
• Field Induced Chiral Soliton Phase in the Kitaev Spin Chain
• Heisenberg-Kitaev Models on Hyperhoneycomb and Stripyhoneycomb Lattices: 3D-2D Equivalence of Ordered States and Phase Diagrams
• Symmetry analysis of bond-alternating Kitaev spin chains and ladders
• Exchange interactions and spin dynamics in the layered honeycomb ferromagnet CrI${}_3$
• Reentrant incommensurate order and anomalous magnetic torque in the Kitaev magnet $\beta$-${\text{Li}}_2{\text{IrO}}_3$
• Magnetic Excitations and Interactions in the Kitaev Hyperhoneycomb Iridate $\beta$-Li${}_2$IrO${}_3$
• Spontaneous Chiral-Spin Ordering in Spin-Orbit Coupled Honeycomb Magnets
• Unconventional magnetic field response of the hyperhoneycomb Kitaev magnet $\beta -{\text{Li}}_2{\text{IrO}}_3$
• Hidden spin-orbital order in the Kitaev hyperhoneycomb $\beta$-Li${}_2$IrO${}_3$
• Phase diagrams of spin-$S$ Kitaev ladders
• Magnon Condensation in Dimerized Antiferromagnets with Spin-Orbit Coupling
• Islands of Chiral Solitons in Integer Spin Kitaev Chains
• Signatures of non-Loudon-Fleury Raman scattering in the Kitaev magnet $\beta$-Li${}_2$IrO${}_3$
• Twice Hidden String Order and Competing Phases in the Spin-1/2 Kitaev-Gamma Ladder
• Confinement transition in a Kitaev-like honeycomb model with bond anisotropy
• Magnetic order and spin excitations in the Kitaev--Heisenberg model on the honeycomb lattice
• Quantum-classical crossover in the spin-1/2 Heisenberg-Kitaev kagome magnet
• Ground-state phase diagram of anisotropically interacting Heisenberg-$\Gamma$ models on a honeycomb lattice
• The free energy of anisotropic quantum spin systems: Functional integral representation

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