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Localized and mixed valence state of Ce $4f$ in superconducting and ferromagnetic CeO$_{1-x}$F$_{x}$BiS$_{2}$ revealed by x-ray absorption and photoemission spectroscopy

We have performed Ce $L_3$-edge x-ray absorption spectroscopy (XAS) and Ce $4d$-$4f$ resonant photoemission spectroscopy (PES) on single crystals of CeO$_{1-x}$F$_x$BiS$_2$ for $x=0.0$ and 0.5 in order to investigate the Ce $4f$ electronic states. In the Ce $L_3$-edge XAS, mixed valence of Ce was found in the $x=0.0$ sample and the F-doping suppresses it, which is consistent with the results on polycrystalline samples. As for the resonant PES, we found that the Ce $4f$ electrons in both $x=0.0$ and $0.5$ systems respectively form a flat band at 1.0 eV and 1.4 eV below the Fermi level and there is no contribution to the Fermi surfaces. Interestingly, Ce valence in CeOBiS$_2$ deviates from Ce$^{3+}$ even though Ce $4f$ electrons are localized, indicating the Ce valence is not in a typical valence fluctuation regime. We assume that localized Ce $4f$ in CeOBiS$_2$ is mixed with the unoccupied Bi $6p_z$, which is consistent with the previous local structural study. Based on the analysis of the Ce $L_3$-edge XAS spectra using Anderson's impurity model calculation, we found that the transfer integral becomes smaller increasing the number of Ce $4f$ electrons upon the F substitution for O.