Kitaev-Heisenberg Hamiltonian for High-Spin $d^7$ Mott Insulators

Abstract

In the search for quantum spin liquids, candidate materials for the Kitaev model and its extensions have been intensively explored during the past decade, as the models realize the exact quantum spin liquids in the ground state. Thus far, insulating magnets in the low-spin $d^5$ electron configuration under the strong spin-orbit coupling have been studied for realizing the Kitaev-type bond-dependent anisotropic interactions between the spin-orbital entangled Kramers doublets. To extend the candidates, here we investigate the systems in a high-spin $d^7$ electron configuration, whose ground state is described by the spin-orbital entangled Kramers doublet. By the second- order perturbation in terms of the $t_{2g}$-$t_{2g}$ and $t_{2g}$-$e_g$ hoppings, we show that the effective spin model possesses the anisotropic Kitaev interactions as well as the isotropic Heisenberg ones. While the Kitaev interaction is always ferromagnetic, the Heisenberg interaction can become either ferromagnetic or antiferromagnetic depending on the Coulomb interactions and the crystalline electric fields. We also derive the effective model for the low-spin $d^5$ electron configuration within the same perturbation scheme, in which the Kitaev interaction becomes both ferromagnetic and antiferromagnetic, while the Heisenberg one always ferromagnetic. Referring to the previous study for the Kitaev-Heisenberg model, we find that the quantum spin liquid phase exists in the reasonable parameter region in both $d^7$ and $d^5$ cases, while the former has a richer structure of the phase diagram. We discuss the advantages of the $d^7$ case in comparison with the $d^5$ case. Our results indicate that the high-spin $d^7$ state provides another platform for the Kitaev-type quantum spin liquid.

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Cited by in corpus (116)

• Pseudospin exchange interactions in d^7 cobalt compounds: Possible realization of the Kitaev model
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• Weak-field induced nonmagnetic state in a Co-based honeycomb
• Magnetic order in single crystals of Na3Co2SbO6 with a honeycomb arrangement of 3d${}^7$ Co${}^{2+}$ ions
• Geometrical frustration versus Kitaev interactions in BaCo${}_2$(AsO${}_4$)${}_2$
• Excitations in the ordered and paramagnetic states of honeycomb magnet Na2Co2TeO6
• Dominant Kitaev interactions in the honeycomb materials Na${}_3$Co${}_2$SbO${}_6$ and Na${}_2$Co${}_2$TeO${}_6$
• Beyond Kitaev physics in strong spin-orbit coupled magnets
• Magnetic ground state of the Kitaev Na${}_2$Co${}_2$TeO${}_6$ spin liquid candidate
• Magnetic Couplings in Edge-Sharing High-Spin $d^7$ Compounds
• Thermal Hall effects in quantum magnets
• Kitaev-like honeycomb magnets: Global phase behavior and emergent effective models
• Giant magnetic in-plane anisotropy and competing instabilities in Na3Co2SbO6
• Non-Kitaev vs. Kitaev Honeycomb Cobaltates
• Triple-q order in Na${}_2$Co${}_2$TeO${}_6$ from proximity to hidden-SU(2)-symmetric point
• Bond-dependent anisotropy and magnon decay in cobalt-based Kitaev triangular antiferromagnet
• Planar Thermal Hall Effects in Kitaev Spin Liquid Candidate Na2Co2TeO6
• 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 $N{a}_{2}C{o}_{2}Te{O}_6$
• Thermal Transport of Fractionalized Antiferromagnetic and Field Induced States in the Kitaev Material Na${}_2$Co${}_2$TeO${}_6$
• Ground-state phase diagram of spin-$S$ Kitaev-Heisenberg models
• Kitaev Quantum Spin Liquids
• Multiflavor Mott insulators in quantum materials and ultracold atoms
• Quantum Many-Body Scars in Spin-1 Kitaev Chains
• Easy-plane multi-$\mathbf{q}$ magnetic ground state of Na${}_3$Co${}_2$SbO${}_6$
• Magnetic phase diagram and possible Kitaev-like behavior of honeycomb-lattice antimonate Na3Co2SbO6
• Planar thermal Hall effect from phonons in a Kitaev candidate material
• Highly frustrated magnetism in relativistic ${\mathbf{d}}^4$ Mott insulators: Bosonic analog of Kitaev honeycomb model
• Easy-plane anisotropic-exchange magnets on a honeycomb lattice: quantum effects and dealing with them
• Intrinsic transverse field in frustrated quantum Ising magnets: its physical origin and quantum effects
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• Quantum Spin Supersolid as a precursory Dirac Spin Liquid in a Triangular Lattice Antiferromagnet
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• Quantum liquids of the S=3/2 Kitaev honeycomb and related Kugel-Khomskii models
• Field evolution of magnetic phases and spin dynamics in the honeycomb lattice magnet Na2Co2TeO6: 23Na NMR study
• Phononic-magnetic dichotomy of the thermal Hall effect in the Kitaev-Heisenberg candidate material Na${}_2$Co${}_2$TeO${}_6$
• Magnon interactions in the quantum paramagnetic phase of CoNb${}_2$O${}_6$
• Perfect kagome-lattice antiferromagnets with J${}_{eff}$ = 1/2: The Co${}^{2+}$-analogs of copper minerals volborthite and vesignieite
• Spin vestigial orders in extended Heisenberg-Kitaev models near hidden SU(2) points: Application to Na${}_2$Co${}_2$TeO${}_6$
• Suppression of Antiferromagnetic Order by Strain in Honeycomb Cobaltate: Implication for Quantum Spin Liquid
• Field and Polarization Dependent Quantum Spin Dynamics in Honeycomb Magnet Na${}_2$Co${}_2$TeO${}_6$: Magnetic Excitations and Continuum
• Comparative Raman Scattering Study of Crystal Field Excitations in Co-based Quantum Magnets
• Field-induced Kitaev multipolar liquid in spin-orbit coupled $d^2$ honeycomb Mott insulators
• Field-induced phase transitions and quantum criticality in a honeycomb antiferromagnet Na3Co2SbO6
• Anomalous continuum scattering and higher-order van Hove singularity in the strongly anisotropic S = 1/2 triangular lattice antiferromagnet
• Introducing the monoclinic polymorph of the Kitaev magnet Na${}_2$Co${}_2$TeO${}_6$
• Probing Majorana wavefunctions in Kitaev honeycomb spin liquids with second-order two-dimensional spectroscopy
• Persistent spin dynamics in magnetically ordered honeycomb cobalt oxides
• Single-crystal study of the honeycomb XXZ magnet BaCo${}_2$(PO${}_4$)${}_2$ in magnetic fields
• Ferrimagnetism from triple-q order in Na${}_2$Co${}_2$TeO${}_6$
• Ring-Exchange Interaction Effects on Magnons in Dirac Magnet CoTiO${}_3$
• Scattering phenomena for spin transport in Kitaev spin liquid
• CaCo${}_2$TeO${}_6$: A topochemically prepared 3$d^7$ honeycomb Kitaev magnet
• $J=1/2$ Pseudospins and $d$-$p$ Hybridization in the Kitaev Spin Liquid Candidates Ru$X_3$ ($X$ = Cl, Br, I)
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• Transforming from Kitaev to Disguised Ising Chain: Application to CoNb${}_2$O${}_6$
• Dynamics of fractionalized mean-field theories: consequences for Kitaev materials
• Signatures of a Quantum Critical Endpoint in the Kitaev Candidate Na${}_2$Co${}_2$TeO${}_6$
• Ground-State Phase Diagram of the Kitaev-Heisenberg Model on a Three-dimensional Hyperhoneycomb Lattice
• Suppression of the antiferromagnetic order by Zn doping in a possible Kitaev material Na${}_2$Co${}_2$TeO${}_6$
• BaCo${}_2$(AsO${}_4$)${}_2$: Strong Kitaev, After All
• Sign Changes in Heat, Spin, and Orbital Magnon Transport Coefficients in Kitaev Ferromagnets
• Field-Angle-Resolved Specific Heat in Na${}_2$Co${}_2$TeO${}_6$: Evidence against Kitaev Quantum Spin Liquid
• Topological phase diagrams of in-plane field polarized Kitaev magnets
• Active orbital degree of freedom and potential spin-orbit-entangled moments in Kitaev magnet candidate BaCo${}_2$(AsO${}_4$)${}_2$
• On the multi-$\mathbf{q}$ characteristics of magnetic ground states of honeycomb cobalt oxides
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• Disorder-induced excitation continuum in a spin-1/2 cobaltate on a triangular lattice
• Study of Staggered Magnetization in the Spin-$S$ Square-Lattice Heisenberg Model Using Spiral Boundary Conditions
• Electric field control of a quantum spin liquid in weak Mott insulators
• $J_{\mathrm{eff}}$ = 1/2 Hyperoctagon Lattice in Cobalt Oxalate Metal-Organic-Framework
• Emergent Berezinskii-Kosterlitz-Thouless and Kugel-Khomskii physics in the triangular lattice bilayer colbaltate
• Exploring rare-earth Kitaev magnets by massive-scale computational analysis
• Anomalous ferromagnetic behavior in the orthorhombic Li${}_3$Co${}_2$SbO${}_6$
• Quadrupole moments and their interactions in the triangular lattice antiferromagnet FeI${}_2$
• Cobalt-Based Pyroxenes: A New Playground for Kitaev Physics and Ising Model Realization
• Unraveling the magnetic ground-state in alkali-metal lanthanide oxide Na${}_2$PrO${}_3$
• Thermodynamic signature of the $\mathrm{SU}(4)$ spin-orbital liquid and symmetry fractionalization from the Lieb-Schultz-Mattis theorem
• Polymorphism and Magnetism in a Kitaev Honeycomb Cobaltate KCoAsO${}_4$
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• Proximity-induced sequence of field transitions in Kitaev candidate BaCo${}_2$(AsO${}_4$)${}_2$
• Spin-orbit entangled moments and magnetic exchange interactions in cobalt-based honeycomb magnets BaCo${}_2$($X$O${}_4$)${}_2$ ($X$ = P, As, Sb)
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• Exchange Interactions in Rare-earth Magnets $A_2$PrO${}_3$ ($A$= alkali metals): Revisited
• Anisotropic in-plane heat transport of Kitaev magnet Na${}_2$Co${}_2$TeO${}_6$
• Ferrimagnetism from quantum fluctuations in Kitaev materials
• Ground state and magnetic transitions of the orthorhombic antiferromagnet CaCo${}_2$TeO${}_6$
• Bond-dependent interactions and ill-ordered state in the honeycomb cobaltate BaCo${}_2$(AsO${}_4$)${}_2$
• Field-induced magnetic phases in the Kitaev candidate Na${}_3$Co${}_2$SbO${}_6$
• Optical detection of bond-dependent and frustrated spin in the two-dimensional cobalt-based honeycomb antiferromagnet Cu3Co2SbO6
• Real-time control of non-Abelian anyons in Kitaev spin liquid under energy dissipation
• Topological Majorana flat bands in the Kitaev model on a Bishamon-kikko lattice
• Quantum spin dynamics of the honeycomb magnet K${}_2$Co${}_2$TeO${}_6$ in high magnetic fields
• Phenomenological Ginzburg-Landau theory for triple-Q magnetic orders on a hexagonal lattice
• Computational exploration of a viable route to Kitaev-quantum spin liquid phase in OsCl${}_3$
• Field-induced phase transitions in the Kitaev-Heisenberg model: A sign-problem-free quantum Monte Carlo study and possible application to $\alpha$-RuCl3
• Magnetic Interactions in the Polar Ferrimagnet with a Bipartite Structure
• Competing Interactions and the Effects of Uniaxial Out-of-plane Perturbations in the Honeycomb Antiferromagnet Na${}_2$Co${}_2$TeO${}_6$
• Anisotropic magnetoelastic coupling in the honeycomb magnet Na${}_3$Co${}_2$SbO${}_6$
• Kitaev interaction and possible spin liquid state in CoI2 and Co2/3Mg1/3I2
• Spin disorder state induced by Mg${}^{2+}$ doping in a Kitaev material Na${}_3$Co${}_2$SbO${}_6$
• Direct probe of magnetic field effects on phonons by ultrasound propagation in a quasi-two-dimensional honeycomb magnet Na${}_2$Co${}_2$TeO${}_6$
• Ligand-SOC enhanced $4f^5$ Kitaev antiferromagnet: Application to ${\mathrm{SmI}}_3$
• Nesting instability of gapless U(1) spin liquids with spinon Fermi pockets in two dimensions
• Dominant Kitaev Interaction and Field-induced Quantum Disordered Phase in the Cobaltate Na${}_2$Co${}_2$TeO${}_6$
• More bridging ligands activate direct exchange: the case of anisotropic Kitaev effective magnetic interactions
• Relevance of on-site and intersite Coulomb interactions in the Kitaev-Heisenberg magnet Na${}_3$Co${}_2$SbO${}_6$
• Magnetic field effects on the Kitaev model coupled to environment
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• Crystalline water intercalation into the Kitaev honeycomb cobaltate Na${}_2$Co${}_2$TeO${}_6$
• Ising spin ladders of orthopyroxene CoGeO${}_3$
• Ferromagnetic Ferroelectricity due to Orbital Ordering