Kitaev-Heisenberg exchange on $t_{2g}^5e_g^2$ cobaltate platform

Abstract

The detection of considerable spin frustration in honeycomb cobalt oxide compounds indicates the presence of sizable Kitaev interactions in these systems, enlarging the pool of Kitaev spin liquid candidates. Several key questions remain to be answered, such as the magnitude of Kitaev couplings in cobaltates and how to engineer those, by either chemical or physical means. Analyzing the quantum chemistry of interacting magnetic moments in Na$_3$Co$_2$SbO$_6$, a representative $LS$-coupled $t_{2g}^5e_g^2$ Co$^{2+}$ oxide, we find that the Kitaev and off-diagonal $Γ$ interactions are substantial and antiferromagnetic but somewhat weaker than the Heisenberg contribution. Except $Γ'$, all nearest-neighbor couplings are mainly determined by Coulomb exchange, different from current representations of anisotropic interaction terms. This highlights the limits of existing anisotropic models and the need for systematic wave-function quantum chemical studies to clarify exchange mechanisms in Kitaev-Heisenberg magnets and the way of tuning intersite couplings towards the Kitaev spin liquid ground state.

Figures (2)

• Figure 1: Crystal structure of Na$_3$Co$_2$SbO$_6$. (a) Successive atomic layers. The CoO$_6$ octahedra are represented in yellow; Na and Sb species are shown in blue and green, respectively. Each Sb sits in the center of a hexagonal ring formed by Co ions. (b) Cluster employed for deriving the nearest-neighbor effective magnetic couplings. Also the SbO$_6$ octahedra are highlighted, in green. The embedding is not pictured. A different perspective is provided in Supplementary Information.
• Figure 2: Powder-averaged dynamical structure factor for Na$_3$Co$_2$SbO$_6$. Data were computed within linear spin wave theory, using the nearest-neighbor MRCI parameters from Table \ref{['couplings']} and $J_3\!=\!0.68$ meV (details: Gaussian broadening of $\sigma=0.18$ and intensity cut-off at $5/6$ of maximum intensity).