Electronic structure of CeCo$_{1-x}$Fe$_x$Ge$_3$ studied by X-ray photoelectron spectroscopy and first-principles calculations
A transformation between the magnetically ordered CeCoGe$_3$ and heavy fermion CeFeGe$_3$ is isostructural but not isoelectronic, therefore the characterization of the electronic structure of the CeCo$_{1-x}$Fe$_x$Ge$_3$ series is of special importance. We report both the experimental investigation by the X-ray photoelectron spectroscopy (XPS) measurements and the first-principles calculations within the full-potential local-orbital (FPLO) scheme based on the density functional theory. Experimentally, we investigate mainly the valence band and the Ce $3d$ spectra, both giving the possibility to conclude about the level of the $f$ states localization. Computationally, we investigate the most characteristic CeCoGe$_3$, CeCo$_{0.5}$Fe$_{0.5}$Ge$_3$, and CeFeGe$_3$ compositions. Based on the electronic band structure results, we calculate the X-ray photoelectron spectra of the valence band. We consider the effects of the spin-orbit coupling and intra-atomic Hubbard U repulsion. Furthermore, we discuss the charge distribution and occupation of valence-band orbitals. The experimentally observed evolution of the 3$d$ band with the Fe concentration is related to the decrease of the number of electrons and reduction of the 3$d$ photoionization cross-sections. Calculations indicate that charge is transferred mainly from the Ce to Ge sites and the bondings are formed mainly by the Ce 5$d$, Fe/Co 3$d$, and Ge 4$p$ and 4$s$ orbitals.