Heisenberg-Kitaev physics in magnetic fields

Abstract

Magnetic insulators in the regime of strong spin-orbit coupling exhibit intriguing behaviors in external magnetic fields, reflecting the frustrated nature of their effective interactions. We review the recent advances in understanding the field responses of materials that are described by models with strongly bond-dependent spin exchange interactions, such as Kitaev's celebrated honeycomb model and its extensions. We discuss the field-induced phases and the complex magnetization processes found in these theories and compare with experimental results in the layered Mott insulators $\alpha$-RuCl${}_3$ and Na${}_2$IrO${}_3$, which are believed to realize this fascinating physics.

21 pages, 17 figures, 1 table; invited Topical Review for J. Phys.: Condens. Matter; v2: additional comments and references; v3: published version

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• Majorana quantization and half-integer thermal quantum Hall effect in a Kitaev spin liquid
• 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
• Hyper-honeycomb iridate $\beta$-Li2IrO3 as a platform for Kitaev magnetism
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• Anisotropic Ru3+ 4d5 magnetism in the alpha-RuCl3 honeycomb system: susceptibility, specific heat and Zero field NMR
• 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
• 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${}_3$
• Emergence of a Field-Driven U(1) Spin Liquid in the Kitaev Honeycomb Model
• Non-coplanar and counter-rotating incommensurate magnetic order stabilized by Kitaev interactions in $\gamma$-Li2IrO3
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• Topological Magnons in Kitaev Magnets at High Fields
• Honeycomb-lattice Heisenberg-Kitaev model in a magnetic field: Spin canting, metamagnetism, and vortex crystals
• Spin-orbit effects in Na${}_4$Ir${}_3$O${}_8$, a hyper-kagomé lattice antiferromagnet
• 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${}_3$
• Theory of the field-revealed Kitaev spin liquid
• Quantization of the thermal Hall conductivity at small Hall angles
• Robust non-Abelian spin liquid and possible intermediate phase in antiferromagnetic Kitaev model with magnetic field
• Dynamical and Topological Properties of the Kitaev Model in a [111] Magnetic Field
• Approximately quantized thermal Hall effect of chiral liquids coupled to phonons
• Topological excitations in the ferromagnetic Kitaev-Heisenberg model
• Spin-orbit physics of j=1/2 Mott insulators on the triangular lattice
• Anisotropic susceptibilities in the honeycomb Kitaev system $\alpha$-RuCl${}_3$
• Large Thermal Hall Effect in $\alpha$-RuCl${}_3$: Evidence for Heat Transport by Kitaev-Heisenberg Paramagnons
• Ultralow-temperature thermal conductivity of the Kitaev honeycomb magnet $\alpha$-RuCl${}_3$ across the field-induced phase transition
• Unconventional spin dynamics in the honeycomb-lattice material $\alpha$-RuCl${}_3$: high-field ESR studies
• Two-dimensional spin liquid behaviour in the triangular-honeycomb antiferromagnet TbInO${}_3$
• Theory of Magnetic Phase Diagrams in Hyperhoneycomb and Harmonic-honeycomb Iridates
• Unified theory of spiral magnetism in the harmonic-honeycomb iridates α, β, γ Li2IrO3
• Successive Majorana Topological Transitions Driven by a Magnetic Field in the Kitaev Model
• Probing the stability of the spin liquid phases in the Kitaev-Heisenberg model using tensor network algorithms
• Dirac and Chiral Quantum Spin Liquids on the Honeycomb Lattice in a Magnetic Field
• Signatures of low-energy fractionalized excitations in $\alpha$-RuCl${}_3$ from field-dependent microwave absorption
• Strong effect of hydrogen order on magnetic Kitaev interactions in H${}_3$LiIr${}_2$O${}_6$
• Intermediate gapless phase and topological phase transition of Kitaev model in a uniform magnetic field
• Role of Hydrogen in the spin-orbital-entangled quantum liquid candidate H${}_3$LiIr${}_2$O${}_6$
• Electronic and phonon excitations in α-RuCl${}_3$
• Magnetic structure and excitation spectrum of the hyperhoneycomb Kitaev magnet $\beta$-Li${}_2$IrO${}_3$
• Spin dynamics and field-induced magnetic phase transition in the honeycomb Kitaev magnet $\alpha$-Li${}_2$IrO${}_3$
• Magnetic field-induced evolution of intertwined orders in the Kitaev magnet $\beta$-Li${}_2$IrO${}_3$
• Quantum spin liquid ground states of the Heisenberg-Kitaev model on the triangular lattice

Cited by in corpus (49)

• Hunting Majorana Fermions in Kitaev Magnets
• Microscopic models for Kitaev's sixteenfold way of anyon theories
• Sign structure of thermal Hall conductivity for in-plane-field polarized Kitaev magnets
• Field-induced intermediate ordered phase and anisotropic interlayer interactions in $\alpha$-RuCl${}_3$
• Geometrical frustration versus Kitaev interactions in BaCo${}_2$(AsO${}_4$)${}_2$
• Topological magnons for thermal Hall transport in frustrated magnets with bond-dependent interactions
• Magnetic ground state of the Kitaev Na${}_2$Co${}_2$TeO${}_6$ spin liquid candidate
• Unusual heat transport of the Kitaev material Na${}_2$Co${}_2$TeO${}_6$: putative quantum spin liquid and low-energy spin excitations
• A Néel-type antiferromagnetic order in the spin 1/2 rare-earth honeycomb YbCl${}_3$
• Heisenberg-Kitaev model in a magnetic field: $1/S$ expansion
• Fractionalized fermionic quantum criticality in spin-orbital Mott insulators
• Electrical probes of the non-Abelian spin liquid in Kitaev materials
• The Heart of Entanglement: Chiral, Nematic, and Incommensurate Phases in the Kitaev-Gamma Ladder in a Field
• 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
• Magnetic Field Induced Spin Liquids in S=1 Kitaev Honeycomb Model
• Kitaev honeycomb models in magnetic fields: Dynamical response and hidden symmetries
• Field-induced phase transitions of the Kitaev material $\alpha$-RuCl${}_3$ probed by thermal expansion and magnetostriction
• Characterizing spin-one Kitaev quantum spin liquids
• Flux crystals, Majorana metals, and flat bands in exactly solvable spin-orbital liquids
• Spin Nematics Meet Spin Liquids: Exotic Quantum Phases in the Spin-$1$ Bilinear-Biquadratic Model with Kitaev Interactions
• Identification of a Kitaev Quantum Spin Liquid by Magnetic Field Angle Dependence
• Magnon dispersion and dynamic spin response in three-dimensional spin models for $\alpha$-RuCl${}_3$
• Revealing the Phase Diagram of Kitaev Materials by Machine Learning: Cooperation and Competition between Spin Liquids
• Kitaev magnetism through the prism of lithium iridate
• Possible Intermediate Quantum Spin Liquid Phase in $\alpha$-RuCl${}_3$ under High Magnetic Fields up to 100 T
• A $j_{\mathrm{eff}}=1/2$ Kitaev material on the triangular lattice: The case of NaRuO${}_2$
• Field-angle dependence of thermal Hall conductivity in magnetically ordered Kitaev-Heisenberg system
• Identification of hidden order and emergent constraints in frustrated magnets using tensorial kernel methods
• Exchange interactions in $d^5$ Kitaev materials: From Na${}_2$IrO${}_3$ to $\alpha$-RuCl${}_3$
• Determining Kitaev interaction in spin-$S$ honeycomb Mott insulators
• Noncoplanar magnetic orders and gapless chiral spin liquid on the kagome lattice with staggered scalar spin chirality
• Machine-Learned Phase Diagrams of Generalized Kitaev Honeycomb Magnets
• Dynamical anyon generation in Kitaev honeycomb non-Abelian spin liquids
• Field evolution of magnetic phases and spin dynamics in the honeycomb lattice magnet Na2Co2TeO6: 23Na NMR study
• Field stability of Majorana spin liquids in antiferromagnetic Kitaev models
• Heisenberg-Kitaev Models on Hyperhoneycomb and Stripyhoneycomb Lattices: 3D-2D Equivalence of Ordered States and Phase Diagrams
• Electric-field control of magnetic anisotropies: applications to Kitaev spin liquids and topological spin textures
• Reentrant incommensurate order and anomalous magnetic torque in the Kitaev magnet $\beta$-${\text{Li}}_2{\text{IrO}}_3$
• Role of Majorana fermions in spin transport of anisotropic Kitaev model
• Spinless fermions in a ${\mathbb{Z}}_2$ gauge theory on the triangular ladder
• Quantum-classical crossover in the spin-1/2 Heisenberg-Kitaev kagome magnet
• Quantized thermal Hall conductance from edge current calculations in lattice models
• Inferring Hidden Symmetries of Exotic Magnets from Detecting Explicit Order Parameters
• Emergent Hyper-Magic Manifold in Twisted Kitaev Bilayers
• High-field quantum spin liquid transitions and angle-field phase diagram of Kitaev magnet $\alpha$-RuCl${}_3$
• Renormalization group analysis of weakly interacting van der Waals Fermi system
• Quantum spin liquids bootstrapped from Ising criticality in Rydberg arrays
• Disorder, Low-Energy Excitations, and Topology in the Kitaev Spin Liquid