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We investigate mixed-valence oxide Co$_3$O$_4$ using Co $2p3d$ resonantinelastic X-ray scattering (RIXS). By setting resonant edges at Co$^{2+}$ andCo$^{3+}$ ions, the $dd$ excitations on the two Co sites are probedselectively, providing detailed information on the local electronic structureof Co$_3$O$_4$. The $2p3d$ RIXS result reveals the $^4$T$_{2}$ excited state oftetrahedral Co$^{2+}$ site at 0.5 eV beyond the discriminative power of opticalabsorption spectroscopies. Additionally, the $^3$T$_{2g}$ excited stated at 1.3eV is uniquely identified for the octahedral Co$^{3+}$ site. Guided by clustermultiplet simulations, the ground-state character of the Co$^{2+}$ andCo$^{3+}$ site is determined to be high-spin $^4$A$_{2}$(T$_d$) and low-spin$^1$A$_{1g}$(O$_h$), respectively. This indicates that only the Co$^{2+}$ siteis magnetically active site at low-temperatures in Co$_3$O$_4$. Theligand-to-metal charge transfer analysis suggests a formation of a strongcovalent bonding between Co and O ions at the Co$^{3+}$ site, while Co$^{2+}$is rather ionic.

Revealing the site selective local electronic structure of Co$_{3}$O$_{4}$ using $2p3d$ resonant inelastic X-ray scattering