LAUSR

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 CoTiO3, BaCo2(PO4)2, and BaCo2(AsO4)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 Co magnets host Jeff =1/2 local moments with highly anisotropic g-factors, and we extract their full spin Hamiltonians including longer-range and anisotropic exchange couplings. For CoTiO3, 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 BaCo2(PO4)2 and BaCo2(AsO4)2, we find a strongly suppressed interlayer coupling, and significant frustration from additional third-neighbor antiferromagnetic exchange mediated by P/As. Such bond-anisotropic J1-J3 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 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 re-examining proposals for realizing Kitaev spin liquids in the honeycomb cobaltates.