Kitaev vs. Non-Kitaev Honeycomb Cobaltate

Since a microscopic mechanism of the Kitaev interaction in honeycomb lattice was reported, several Kitaev materials where the Kitaev interaction is dominant over other symmetry-allowed interactions have been suggested. Cobaltate with 3d⁷ is one of them, and a previous theory showed that the cancellation of exchange paths that contribute to the Heisenberg interaction makes the Kitaev to be dominant. However, recent theoretic and experimental works found leading Heisenberg and negligible Kitaev interaction in BaCo₂(AsO₄)₂. This calls for further study to clarify the origin of discrepancies.

In this work we derive the spin model using strong-coupling perturbation theory. The analytical expressions of spin interactions up to fourth order for the ideal octahedra case are provided. Incomplete cancellation of Heisenberg interactions occurs due to the presiding intraorbital hopping path together with the Hund's coupling. These second-order processes tend to be ferromagnetic (FM). Under trigonal distortions, the preeminent isotropic Heisenberg becomes an anisotorpic XXZ model. Applying our theory to BaCo₂(AsO₄)₂, the dominant FM Heisenberg is found. A way to achieve Kitaev Cobaltates is also discussed.