XY magnetism, Kitaev exchange, and long-range frustration in the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>J</mml:mi><mml:mi>eff</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:mfrac></mml:math> honeycomb cobaltates
Shreya Das, Sreekar Voleti, Tanusri Saha‐Dasgupta, Arun Paramekanti
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 ${\mathrm{CoTiO}}_{3},$ ${\mathrm{BaCo}}_{2}{({\mathrm{PO}}_{4})}_{2}$, and ${\mathrm{BaCo}}_{2}{({\mathrm{AsO}}_{4})}_{2}$, 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 ${\mathrm{BaCo}}_{2}{({\mathrm{PO}}_{4})}_{2}$ and ${\mathrm{BaCo}}_{2}{({\mathrm{AsO}}_{4})}_{2}$, we find a strongly suppressed interlayer coupling, and significant frustration from additional third-neighbor antiferromagnetic exchange mediated by P or As. Such bond-anisotropic ${J}_{1}\text{\ensuremath{-}}{J}_{3}$ 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.