Non-Kitaev vs. Kitaev Honeycomb Cobaltates

TL;DR

This study clarifies the magnetic interactions in honeycomb cobaltates, showing that dominant Heisenberg interactions and negligible Kitaev interactions result from specific exchange paths, explaining discrepancies in previous theories and experiments.

Contribution

The paper derives analytical spin models for honeycomb cobaltates using ab-initio parameters, revealing the dominant exchange interactions and resolving conflicting theoretical and experimental findings.

Findings

Dominant ferromagnetic Heisenberg interaction from intraorbital $t_{2g}-t_{2g}$ exchange

Cancellation of Kitaev interactions due to competing exchange paths

Different magnetic behaviors in BCAO and Na$_3$Co$_2$SbO$_6$ based on hopping parameters

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 BaCo$_2$(AsO$_4$)$_2$ (BCAO), which calls for a 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 by {\it ab-initio} calculations for idealized honeycomb BCAO, we find that the largest intraorbital $t_{2g}-t_{2g}$ 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 $t_{2g}-e_g$ and $e_g-e_g$ contributions almost cancel each other. Exactly the same assumed-to-be-small channel also generates an antiferromagnetic Kitaev interaction, which then cancels a FM Kitaev interaction from $t_{2g}-e_g$ 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 for BCAO. However, in Na$_3$Co$_2$SbO$_6$ the intraorbital $t_{2g}-t_{2g}$ hopping is smaller and comparable to the $t_{2g}-e_g$ hopping, leading to a delicate competition between enhanced Kitaev and reduced Heisenberg interactions.