  Inter-valence charge transfer (IVCT) is electron transfer between two metal
$M$ sites differing in oxidation states through a bridging ligand: $M^{n+1} +
M'^{m} \rightarrow M^{n} + M'^{m+1}$. It is considered that IVCT is related to
the hopping probability of electron (or the electron mobility) in solids. Since
controlling the conductivity of ferromagnetic semiconductors (FMSs) is a key
subject for the development of spintronic device applications, the manipulation
of the conductivity through IVCT may become a new approach of band engineering
in FMSs. In Ru-doped cobalt ferrite CoFe$_2$O$_4$ (CFO) that shows
ferrimagnetism and semiconducting transport properties, the reduction of the
electric resistivity is attributed to both the carrier doping caused by the Ru
substitution for Co and the increase of the carrier mobility due to
hybridization between the wide Ru $4d$ and the Fe $3d$ orbitals. The latter is
the so-called IVCT mechanism that is charge transfer between the mixed valence
Fe$^{2+}$/Fe$^{3+}$ states facilitated by bridging Ru $4d$ orbital: Fe$^{2+}$ +
Ru$^{4+}$ $\leftrightarrow$ Fe$^{3+}$ + Ru$^{3+}$. To elucidate the emergence
of the IVCT state, we have conducted x-ray absorption spectroscopy (XAS) and
resonant photoemission spectroscopy (RPES) measurements on non-doped CFO and
Co$_{0.5}$Ru$_{0.5}$Fe$_2$O$_4$ (CRFO) thin films. The observations of the XAS
and RPES spectra indicate that the presence of the mixed valence
Fe$^{2+}$/Fe$^{3+}$ state and the hybridization between the Fe $3d$ and Ru $4d$
states in the valence band. These results provide experimental evidence for the
IVCT state in CRFO, demonstrating a novel mechanism that controls the electron
mobility through hybridization between the $3d$ transition-metal cations with
intervening $4d$ states.
