XY magnetism, Kitaev exchange, and long-range frustration in the $J_{\mathrm{eff}}=1/2$ honeycomb cobaltates

Abstract

The quest for Kitaev quantum spin liquids has led to great interest in honeycomb quantum magnets with strong spin-orbit coupling. It has been recently proposed that even Mott insulators with $3d$ transition metal ions, having nominally weak spin-orbit coupling, can realize such exotic physics. Motivated by this, we study the rhombohedral honeycomb cobaltates CoTiO${}_3$, BaCo${}_2$(PO${}_4$)${}_2$, and BaCo${}_2$(AsO${}_4$)${}_2$, using $\text{ab initio}$ density functional theory, which takes into account realistic crystal field distortions and chemical information, in conjunction with exact diagonalization numerics. We show that these Co${}^{2+}$ magnets host $j_{\text{eff}}=1/2$ local moments with highly anisotropic $g$-factors, and we extract their full spin Hamiltonians including longer-range and anisotropic exchange couplings. For CoTiO${}_3$, we find a nearest-neighbor easy-plane ferromagnetic $XXZ$ model with additional bond-dependent anisotropies and interlayer exchange, which supports three-dimensional (3D) Dirac nodal line magnons. In contrast, for BaCo${}_2$(PO${}_4$)${}_2$ and BaCo${}_2$(AsO${}_4$)${}_2$, we find a strongly suppressed interlayer coupling, and significant frustration from additional third-neighbor antiferromagnetic exchange mediated by P/As. Such bond-anisotropic $J_1$-$J_3$ spin models can support collinear zig-zag or coplanar spiral ground states; we discuss their dynamical spin correlations which reveal a gapped Goldstone mode, and argue that the effective parameters of these pseudospin-$1/2$ models may be strongly renormalized by coupling to a low energy spin-exciton. Our results call for re-examining proposals for realizing Kitaev spin liquids in the honeycomb cobaltates.

Main Text: 14 pages, 9 figures ; Supplementary Material: 9 pages, 6 figures v3: added final version, journal ref

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• Non-Kitaev vs. Kitaev Honeycomb Cobaltates
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• Field-induced phase transitions and quantum criticality in a honeycomb antiferromagnet Na3Co2SbO6
• 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
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• Out-of-plane magnetic anisotropy in bulk ilmenite ${\text{CoTiO}}_3$
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• BaCo${}_2$(AsO${}_4$)${}_2$: Strong Kitaev, After All
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• Chemical tuning of a honeycomb magnet through a critical point
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• Demystifying quantum escapism on the honeycomb lattice
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• Spin-orbit driven $J_{eff}=1/2$ magnetism in a d${}^7$ triangular-lattice monolayer cobaltate
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