Electronic structure of Fe$_{3}$O$_{4}$ revealed by RIXS

Magnetite (Fe$_{3}$O$_{4}$) is a prototypical example of a mixed valence compound. At 125 K, Fe$_{3}$O$_{4}$ undergoes the Verwey transition associated with charge ordering. The valence electrons order themselves over the octahedral sites (B sites) to form a Fe$^{2+}$ and Fe$^{3+}$ superstructure in the insulating phase below the transition temperature. Here we report measurements of resonant inelastic soft X-ray scattering (RIXS) to unravel the electronic structures of Fe$_{3}$O$_{4}$. By the advantage of high energy-resolution ($\Delta$E $\approx$ 80 meV) of the RIXS spectra, we found two distinctive features of magnetic excitations, coming from octahedral Fe$^{2+}$ and Fe$^{3+}$ separately. These magnetic excitations are described well by a local ionic model. The $dd$ excitations of the different Fe sites are also revealed in the RIXS spectra.