Insulating state and the importance of the spin-orbit coupling in Ca$_3$CoRhO$_6$

TL;DR

This study highlights the crucial role of spin-orbit coupling in opening the band gap and influencing magnetic properties in Ca$_3$CoRhO$_6$, contrasting it with Ca$_3$FeRhO$_6$ which is explained by traditional band theory.

Contribution

It demonstrates that spin-orbit coupling is essential for understanding the insulating state and magnetic moments in Ca$_3$CoRhO$_6$, providing a new perspective on its electronic structure.

Findings

Ca$_3$FeRhO$_6$ is a band insulator with high-spin Fe$^{3+}$ and low-spin Rh$^{3+}$.

Ca$_3$CoRhO$_6$ has a Co$^{2+}$ tendency with orbital degeneracy.

Spin-orbit coupling lifts degeneracy and significantly enhances magnetic moments.

Abstract

We have carried out a comparative theoretical study of the electronic structure of the novel one-dimensional Ca$_3$CoRhO$_6$ and Ca$_3$FeRhO$_6$ systems. The insulating antiferromagnetic state for the Ca$_3$FeRhO$_6$ can be well explained by band structure calculations with the closed shell high-spin $d^5$ (Fe$^{3+}$) and low-spin $t_{2g}^{6}$ (Rh$^{3+}$) configurations. We found for the Ca$_3$CoRhO$_6$ that the Co has a strong tendency to be $d^7$ (Co$^{2+}$) rather than $d^6$ (Co$^{3+}$), and that there is an orbital degeneracy in the local Co electronic structure. We argue that it is the spin-orbit coupling which will lift this degeneracy thereby enabling local spin density approximation + Hubbard U (LSDA+U) band structure calculations to generate the band gap. We predict that the orbital contribution to the magnetic moment in Ca$_3$CoRhO$_6$ is substantial, i.e. significantly larger than 1 $\mu_B$ per formula unit. Moreover, we propose a model for the contrasting intra-chain magnetism in both materials.