Combining photoemission and optical spectroscopies for reliable valence determination in YbS and Yb metal

Hard x-ray photoemission and optical spectroscopies have been performed on YbS and Yb metal to determine the precise $f$-electron occupation. A comparison of the photoemission spectra with the energy loss functions in bulk and surface, obtained from optical reflectivity, enables us to distinguish between the energy loss satellite of Yb${}^{2+}$ peak and Yb${}^{3+}$ multiplet. The results clearly indicate a purely divalent Yb state except for the surface of YbS. We demonstrate that the present method is highly reliable in identifying the electronic structure and the mean valence in $f$-electron systems.