Atomic multiplet and charge transfer screening effects in $1s$ and $2p$ core-level x-ray photoelectron spectra of early $3d$ transition-metal oxides

We present a comparative analysis of $1s$ and $2p$ core-level hard x-ray photoelectron spectroscopy (HAXPES) spectra of metallic ${\mathrm{VO}}_2$ and ${\mathrm{CrO}}_2$. Even though the V $1s$ and $2p$ spectra in ${\mathrm{VO}}_2$ show similar line shapes except for the absence/presence of a spin-orbit splitting in the core levels, the Cr $1s$ and $2p$ spectra exhibit distinct main-line shapes. The experimental HAXPES spectra are analyzed by the Anderson impurity model based on the density functional theory $+$ dynamical mean-field theory and a conventional ${\mathrm{MO}}_6$ cluster model. We examine the interplay between the formation of the intra-atomic multiplet between a core hole and valence electrons and the charge-transfer effect on the chemical bonding followed by the $1s$ and $2p$ core electron excitations. We demonstrate the advantage of $1s$ HAXPES to the routinely employed $2p$ one for distinguishing contributions of a metal-ligand and metallic screening from a state near the Fermi level in metallic early $3d$ transition-metal oxides.