Non-Kitaev vs. Kitaev Honeycomb Cobaltates

Abstract

Recently, honeycomb cobaltates with 3$d^7$ were proposed to display Kitaev physics despite weak spin-orbit coupling. However, other theoretical and experimental works found leading XXZ Heisenberg and negligible Kitaev interactions in BaCo${}_2$(AsO${}_4$)${}_2$ (BCAO), which calls for a further study to clarify the origin of the discrepancies. Here we derive the analytical expressions of the spin model using strong-coupling perturbation theory. With tight binding parameters obtained by {\it ab-initio} calculations for idealized honeycomb BCAO, we find that the largest intraorbital $t_{2g}-t_{2g}$ exchange path, which was assumed to be small in the earlier theory proposal, leads to a ferromagnetic (FM) Heisenberg interaction. This becomes the dominant interaction, as other $t_{2g}-e_g$ and $e_g-e_g$ contributions almost cancel each other. Exactly the same assumed-to-be-small channel also generates an antiferromagnetic Kitaev interaction, which then cancels a FM Kitaev interaction from $t_{2g}-e_g$ paths, resulting in a small Kitaev interaction. Under the trigonal distortion, the preeminent isotropic Heisenberg becomes an anisotropic XXZ model as expected, which is the case for BCAO. However, in Na${}_3$Co${}_2$SbO${}_6$ the intraorbital $t_{2g}-t_{2g}$ hopping is smaller and comparable to the $t_{2g}-e_g$ hopping, leading to a delicate competition between enhanced Kitaev and reduced Heisenberg interactions.

10 pages, 4 figures

References in corpus (20)

• 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
• On the Origin of Zigzag Magnetic Order in Iridium Oxide Na2IrO3
• Scattering Continuum and Possible Fractionalized Excitations in $\alpha$-RuCl${}_3$
• Magnetic order in $\alpha$-RuCl${}_3$: a honeycomb lattice quantum magnet with strong spin-orbit coupling
• Long range magnetic ordering in Na${}_2$IrO${}_3$
• Kitaev magnetism in honeycomb RuCl3 with intermediate spin-orbit coupling
• Pseudospin exchange interactions in d^7 cobalt compounds: Possible realization of the Kitaev model
• Kitaev-Heisenberg Hamiltonian for High-Spin $d^7$ Mott Insulators
• Hidden symmetries of the extended Kitaev-Heisenberg model: Implications for honeycomb lattice iridates A2IrO3
• Kitaev interactions in the Co honeycomb antiferromagnets Na${}_3$Co${}_2$SbO${}_6$ and Na${}_2$Co${}_2$TeO${}_6$
• Geometrical frustration versus Kitaev interactions in BaCo${}_2$(AsO${}_4$)${}_2$
• Dominant Kitaev interactions in the honeycomb materials Na${}_3$Co${}_2$SbO${}_6$ and Na${}_2$Co${}_2$TeO${}_6$
• Magnetic Couplings in Edge-Sharing High-Spin $d^7$ Compounds
• Spin-orbital entangled state and realization of Kitaev physics in 3d cobalt compounds: a progress report
• Ab initio guided minimal model for the "Kitaev" material BaCo${}_2$(AsO${}_4$)${}_2$: Importance of direct hopping, third-neighbor exchange and quantum fluctuations
• EDRIXS: An open source toolkit for simulating spectra of resonant inelastic x-ray scattering
• Significant thermal Hall effect in the 3$d$ cobalt Kitaev system $N{a}_{2}C{o}_{2}Te{O}_6$
• Theoretical analysis of single-ion anisotropy in $d^3$ Mott insulators
• Strategy to Extract Kitaev Interaction using Symmetry in Honeycomb Mott Insulators

Cited by in corpus (31)

• Beyond Kitaev physics in strong spin-orbit coupled magnets
• Magnetic ground state of the Kitaev Na${}_2$Co${}_2$TeO${}_6$ spin liquid candidate
• Kitaev Quantum Spin Liquids
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• Suppression of Antiferromagnetic Order by Strain in Honeycomb Cobaltate: Implication for Quantum Spin Liquid
• Comparative Raman Scattering Study of Crystal Field Excitations in Co-based Quantum Magnets
• Persistent spin dynamics in magnetically ordered honeycomb cobalt oxides
• Anomalous continuum scattering and higher-order van Hove singularity in the strongly anisotropic S = 1/2 triangular lattice antiferromagnet
• Microscopic Roadmap to a Yao-Lee Spin-Orbital Liquid
• CaCo${}_2$TeO${}_6$: A topochemically prepared 3$d^7$ honeycomb Kitaev magnet
• Transforming from Kitaev to Disguised Ising Chain: Application to CoNb${}_2$O${}_6$
• BaCo${}_2$(AsO${}_4$)${}_2$: Strong Kitaev, After All
• Field-Angle-Resolved Specific Heat in Na${}_2$Co${}_2$TeO${}_6$: Evidence against Kitaev Quantum Spin Liquid
• Cobalt-Based Pyroxenes: A New Playground for Kitaev Physics and Ising Model Realization
• Proximity-induced sequence of field transitions in Kitaev candidate BaCo${}_2$(AsO${}_4$)${}_2$
• Polymorphism and Magnetism in a Kitaev Honeycomb Cobaltate KCoAsO${}_4$
• Spin-orbit entangled moments and magnetic exchange interactions in cobalt-based honeycomb magnets BaCo${}_2$($X$O${}_4$)${}_2$ ($X$ = P, As, Sb)
• Quantum Spin Liquids in Weak Mott Insulators with a Spin-Orbit Coupling
• Bond-dependent interactions and ill-ordered state in the honeycomb cobaltate BaCo${}_2$(AsO${}_4$)${}_2$
• Optical detection of bond-dependent and frustrated spin in the two-dimensional cobalt-based honeycomb antiferromagnet Cu3Co2SbO6
• Field-induced magnetic phases in the Kitaev candidate Na${}_3$Co${}_2$SbO${}_6$
• Order-by-disorder from Schwinger bosons in a frustrated honeycomb ferromagnet
• Crystalline water intercalation into the Kitaev honeycomb cobaltate Na${}_2$Co${}_2$TeO${}_6$
• More bridging ligands activate direct exchange: the case of anisotropic Kitaev effective magnetic interactions
• Trigonal distortion in the Kitaev candidate honeycomb magnet BaCo2(AsO4)2
• Relevance of on-site and intersite Coulomb interactions in the Kitaev-Heisenberg magnet Na${}_3$Co${}_2$SbO${}_6$
• Spin-orbit driven $J_{eff}=1/2$ magnetism in a d${}^7$ triangular-lattice monolayer cobaltate
• Thermal and quantum fluctuations in extended Kitaev-Yao-Lee spin-orbital model
• 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
• Ligand-SOC enhanced $4f^5$ Kitaev antiferromagnet: Application to ${\mathrm{SmI}}_3$