X-ray absorption and x-ray magnetic dichroism study on Ca$_3$CoRhO$_6$ and Ca$_3$FeRhO$_6$

The valence-state of the transition-metal ions in the chain-like compounds Ca$_3$CoRhO$_6$ and Ca$_3$FeRhO$_6$ is currently an issue under debate. Using numerical simulations and x-ray absorption spectroscopy at the Rh-$L_{2,3}$, the Co-$L_{2,3}$, and the Fe-$L_{2,3}$ edges we reveal a Co$^{2+}$/Rh$^{4+}$ configuration in Ca$_3$CoRhO$_6$ and Fe$^{3+}$/Rh$^{3+}$ in Ca$_3$FeRhO$_6$. X-ray magnetic circular dichroism at the Co-$L_{2,3}$ edge shows that the Co$^{2+}$ ions carry a giant orbital moment of about $1.7\mu_B$. We attribute this to a $d_1^0d_1^2$ ground state for the high-spin Co $3d^7$ configuration in trigonal prismatic coordination. The intrachain-ferromagnetic coupling of two neighboring Co ions is mediated by a low-spin Rh$^{4+}$ ion ($S = 1/2$) in between. The results agree with our recent ab-initio study [Hua Wu {\it et al.}, Phys. Rev. B {\bf 75}, 245118 (2007)].