Kitaev-like honeycomb magnets: Global phase behavior and emergent effective models

Abstract

Compounds of transition metal ions with strong spin-orbit coupling recently attracted attention due to the possibility to host frustrated bond-dependent anisotropic magnetic interactions. In general, such interactions lead to complex phase diagrams that may include exotic phases, e.g. the Kitaev spin liquid. Here we report on our comprehensive analysis of the global phase diagram of the extended Kitaev-Heisenberg model relevant to honeycomb lattice compounds Na2IrO3 and alpha-RuCl3. We have utilized recently developed method based on spin coherent states that enabled us to resolve arbitrary spin patterns in the cluster ground states obtained by exact diagonalization. Global trends in the phase diagram are understood in combination with the analytical mappings of the Hamiltonian that uncover peculiar links to known models - Heisenberg, Ising, Kitaev, or compass models on the honeycomb lattice - or reveal entire manifolds of exact fluctuation-free ground states. Finally, our study can serve as a methodological example that can be applied to other spin models with complex bond-dependent non-Heisenberg interactions.

18 pages, 10 figures

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• Magnetic ground state of the Kitaev Na${}_2$Co${}_2$TeO${}_6$ spin liquid candidate
• Ab initio guided minimal model for the "Kitaev" material BaCo${}_2$(AsO${}_4$)${}_2$: Importance of direct hopping, third-neighbor exchange and quantum fluctuations
• Giant magnetic in-plane anisotropy and competing instabilities in Na3Co2SbO6
• Magnetism of Kitaev spin-liquid candidate material RuBr${}_3$
• Giant Phonon Anomalies in the Proximate Kitaev Quantum Spin Liquid $\alpha$-RuCl${}_3$
• Electronic and magnetic properties of the RuX${}_3$ (X=Cl, Br, I) family: Two siblings -- and a cousin?
• Majorana-mediated spin transport without spin polarization in Kitaev quantum spin liquids
• Towards Kitaev Spin Liquid in 3d Transition Metal Compounds
• Identification of a Kitaev Quantum Spin Liquid by Magnetic Field Angle Dependence
• Floquet engineering of Mott insulators with strong spin-orbit coupling
• Computational design of $f$-electron Kitaev magnets: honeycomb and hyperhoneycomb compounds $A_2$PrO${}_3$ ($A=$ alkali metals)
• Kitaev Quantum Spin Liquids
• Revealing the Phase Diagram of Kitaev Materials by Machine Learning: Cooperation and Competition between Spin Liquids
• Universal Thermodynamics in the Kitaev Fractional Liquid
• Easy-plane anisotropic-exchange magnets on a honeycomb lattice: quantum effects and dealing with them
• Stripe-yz magnetic order in the triangular-lattice antiferromagnet KCeS2
• Exchange interactions in $d^5$ Kitaev materials: From Na${}_2$IrO${}_3$ to $\alpha$-RuCl${}_3$
• Topological phase transition to Abelian anyon phases due to off-diagonal exchange interaction in the Kitaev spin liquid state
• Machine-Learned Phase Diagrams of Generalized Kitaev Honeycomb Magnets
• Electronic and magnetic properties of iridium ilmenites $A$IrO${}_3$ ($A=$ Mg, Zn, and Mn)
• Quantum phase transitions in the spin-1 Kitaev-Heisenberg chain
• Extent of frustration in the classical Kitaev-$\Gamma$ model via bond anisotropy
• Ground-state properties of the $K-\Gamma$ model on a honeycomb lattice
• Dissipationless Spin Current Generation in Kitaev's Chiral Spin Liquid
• Topological Nematic Phase Transition in Kitaev Magnets Under Applied Magnetic Fields
• First demonstration of tuning between the Kitaev and Ising limits in a honeycomb lattice
• Quantum-classical crossover in the spin-1/2 Heisenberg-Kitaev kagome magnet
• Exploring rare-earth Kitaev magnets by massive-scale computational analysis
• Polarization-dependent magnetic properties of periodically driven $\alpha$-RuCl${}_3$
• Inferring Hidden Symmetries of Exotic Magnets from Detecting Explicit Order Parameters
• Evolution of Spin-Orbital Entanglement with Increasing Ising Spin-Orbit Coupling
• Exchange Interactions in Rare-earth Magnets $A_2$PrO${}_3$ ($A$= alkali metals): Revisited
• Vortex creation and control in the Kitaev spin liquid by local bond modulations
• Ligand-SOC enhanced $4f^5$ Kitaev antiferromagnet: Application to ${\mathrm{SmI}}_3$