Non-Kitaev versus Kitaev honeycomb cobaltates

Abstract

Recently, honeycomb cobaltates with $3{d}^{7}$ were proposed to display Kitaev physics despite weak spin-orbit coupling. However, other theoretical and experimental works found leading XXZ Heisenberg and negligible Kitaev interactions in ${\mathrm{BaCo}}_{2}{({\mathrm{AsO}}_{4})}_{2}$ (BCAO), which calls for further study to clarify the origin of the discrepancies. Here we derive the analytical expressions of the spin model using strong-coupling perturbation theory. With tight-binding parameters obtained with ab initio calculations for idealized honeycomb BCAO, we find that the largest intraorbital ${t}_{2g}\ensuremath{-}{t}_{2g}$ exchange path, which was assumed to be small in the earlier theory proposal, leads to a ferromagnetic (FM) Heisenberg interaction. This becomes the dominant interaction, as other ${t}_{2g}\ensuremath{-}{e}_{g}$ and ${e}_{g}\ensuremath{-}{e}_{g}$ contributions almost cancel each other. Exactly the same assumed-to-be-small channel also generates an antiferromagnetic Kitaev interaction, which then cancels the FM Kitaev interaction from ${t}_{2g}\ensuremath{-}{e}_{g}$ paths, resulting in a small Kitaev interaction. Under the trigonal distortion, the preeminent isotropic Heisenberg becomes an anisotropic XXZ model, as expected, which is the case in BCAO. However, when ${t}_{2g}\ensuremath{-}{e}_{g}$ and intraorbital ${t}_{2g}\ensuremath{-}{t}_{2g}$ hoppings are similar in size such as in ${\mathrm{Na}}_{3}{\mathrm{Co}}_{2}{\mathrm{SbO}}_{6}$, the Kitaev interaction may become comparable to the Heisenberg interaction. A way to achieve the Kitaev cobaltates is also discussed.