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XY magnetism, Kitaev exchange, and long-range frustration in theJeff=12honeycomb cobaltates
Physical Review B  (IF4.036),  Pub Date : 2021-10-22, DOI: 10.1103/physrevb.104.134425
Shreya Das, Sreekar Voleti, Tanusri Saha-Dasgupta, Arun Paramekanti

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 ${\mathrm{CoTiO}}_{3},$ ${\mathrm{BaCo}}_{2}{\left({\mathrm{PO}}_{4}\right)}_{2}$, and ${\mathrm{BaCo}}_{2}{\left({\mathrm{AsO}}_{4}\right)}_{2}$, using 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 ${\mathrm{Co}}^{2+}$ magnets host ${J}_{\mathrm{eff}}=1/2$ local moments with highly anisotropic $g$ factors, and we extract their full spin Hamiltonians including longer-range and anisotropic exchange couplings. For ${\mathrm{CoTiO}}_{3}$, we find a nearest-neighbor easy-plane ferromagnetic $XXZ$ model with additional bond-dependent anisotropies and interlayer exchange, which supports three-dimensional Dirac nodal line magnons. In contrast, for ${\mathrm{BaCo}}_{2}{\left({\mathrm{PO}}_{4}\right)}_{2}$ and ${\mathrm{BaCo}}_{2}{\left({\mathrm{AsO}}_{4}\right)}_{2}$, we find a strongly suppressed interlayer coupling, and significant frustration from additional third-neighbor antiferromagnetic exchange mediated by P or As. Such bond-anisotropic ${J}_{1}\text{−}{J}_{3}$ spin models can support collinear zigzag or coplanar spiral ground states. We discuss their dynamical spin correlations which reveal a gapped Goldstone mode and argue that the effective parameters of the pseudospin-$1/2$ models in these two materials may be strongly renormalized by coupling to a low-energy spin exciton. Our results call for reexamining proposals for realizing Kitaev spin liquids in the honeycomb cobaltates.