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

TL;DR

This study combines ab initio calculations and exact diagonalization to analyze honeycomb cobaltates, revealing complex magnetic interactions and frustration that challenge simple Kitaev spin liquid models.

Contribution

It provides detailed spin Hamiltonians for honeycomb cobaltates, highlighting the role of anisotropic exchange and frustration, and questions the realization of Kitaev spin liquids in these materials.

Findings

CoTiO$_3$ hosts a 3D Dirac nodal line magnon system.

BaCo$_2$(PO$_4$)$_2$ and BaCo$_2$(AsO$_4$)$_2$ exhibit strong frustration and suppressed interlayer coupling.

The effective pseudospin-$1/2$ models may be significantly renormalized by spin-exciton interactions.

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 $\textit{ab initio}$ 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.