Spin interaction and magnetism in cobaltate Kitaev candidate materials: An <i>ab initio</i> and model Hamiltonian approach

Abstract

In the quest for materials hosting Kitaev spin liquids, much of the efforts have been focused on the fourth- and fifth-row transition metal compounds, which are spin-orbit coupling--assisted Mott insulators. Here we study the structural and magnetic properties of $3d$ transition metal oxides, ${\mathrm{Na}}_{2}{\mathrm{Co}}_{2}{\mathrm{TeO}}_{6}$ and ${\mathrm{Na}}_{3}{\mathrm{Co}}_{2}{\mathrm{SbO}}_{6}$. The partial occupancy of sodium in former compound is addressed using a cluster expansion, and a honeycomb lattice of sodiums is found to be energetically favored. Starting from the ab initio band structures, a many-body second-order perturbation theory leads to a pseudospin-$\frac{1}{2}$ Hamiltonian with estimated magnetic interactions. We show that the experimentally observed zigzag magnetic state is stabilized only when the first-neighbor Kitaev coupling dominates over the Heisenberg term, both of which are highly suppressed due to presence of ${e}_{g}$ orbitals. A third-neighbor Heisenberg interaction is found dominant in both these compounds. We also present a phase diagram for ${\mathrm{Na}}_{2}{\mathrm{Co}}_{2}{\mathrm{TeO}}_{6}$ by varying the electron-electron and spin-orbit interactions. The computed spin excitation spectra are found to capture essential features of recent experimental magnon spectrum, lending support to our results.