  Secondary batteries are important energy storage devices for a mobile
equipment, an electric car, and a large-scale energy storage. Nevertheless,
variation of the local electronic state of the battery materials in the charge
(or oxidization) process are still unclear. Here, we investigated the local
electronic state of cobalt-hexacyanoferrate (Na$_x$Co[Fe(CN)$_6$]$_{0.9}$), by
means of resonant inelastic X-ray scattering (RIXS) with high energy resolution
(~100 meV). The L-edge RIXS is one of the most powerful spectroscopic technique
with element- and valence-selectivity. We found that the local electronic state
around Co$^{2+}$ in the partially-charged
Na$_{1.1}$Co$^{2+}$$_{0.5}$Co$^{3+}$$_{0.5}$[Fe$^{2+}$(CN)$_6$]$_{0.9}$ film (x
= 1.1) is the same as that of the discharged
Na$_{1.6}$Co$^{2+}$[Fe$^{2+}$(CN)$_6$]$_{0.9}$ film (x = 1.6) within the energy
resolution, indicating that the local electronic state around Co$^{2+}$ is
invariant against the partial oxidization. In addition, the local electronic
state around the oxidized Co$^{3+}$ is essentially the same as that of the
fully-charged film
Co$^{3+}$[Fe$^{2+}$(CN)$_6$]$_{0.3}$[Fe$^{3+}$(CN)$_6$]$_{0.6}$ (x = 0.0) film.
Such a strong localization of the oxidized Co$^{3+}$ state is advantageous for
the reversibility of the redox process, since the localization reduces extra
reaction within the materials and resultant deterioration.
