Analyzing the Local Electronic Structure of Co$_3$O$_4$ Using 2p3d Resonant Inelastic X-ray Scattering

We present the cobalt 2p3d resonant inelastic X-ray scattering (RIXS) spectra of Co$_3$O$_4$. Guided by multiplet simulation, the excited states at 0.5 and 1.3 eV can be identified as the $^4$T$_2$ excited state of the tetrahedral Co$^{2+}$ and the $^3$T$_{2g}$ excited state of the octahedral Co$^{3+}$, respectively. The ground states of Co$^{2+}$ and Co$^{3+}$ sites are determined to be high-spin $^4$A$_2$(T$_d$) and low-spin $^1$A$_{1g}$(O$_h$), respectively. It indicates that the high-spin Co$^{2+}$ is the magnetically active site in Co$_3$O$_4$. Additionally, the ligand-to-metal charge transfer analysis shows strong orbital hybridization between the cobalt and oxygen ions at the Co$^{3+}$ site, while the hybridization is weak at the Co$^{2+}$ site.