4$f$ electron temperature driven ultrafast electron localization
Valence transitions in strongly correlated electron systems are caused by orbital hybridization and Coulomb interactions between localized and delocalized electrons. The transition can be triggered by changes in the electronic structure and is sensitive to temperature variations, applications of magnetic fields, and physical or chemical pressure. Launching the transition by photoelectric fields can directly excite the electronic states and thus provides an ideal platform to study the correlation among electrons on ultrafast timescales. The EuNi$_2$(Si$_{0.21}$Ge$_{0.79}$)$_2$ mixed-valence metal is an ideal material to investigate the valence transition of the Eu ions via the amplified orbital hybridization by the photoelectric field on sub-picosecond timescales. A direct view on the 4$f$ electron occupancy of the Eu ions is required to understand the microscopic origin of the transition. Here we probe the 4$f$ electron states of EuNi$_2$(Si$_{0.21}$Ge$_{0.79}$)$_2$ at the sub-ps timescale after photoexcitation by X-ray absorption spectroscopy across the Eu $M_5$-absorption edge. The observed spectral changes due to the excitation indicate a population change of total angular momentum multiplet states $J$ = 0, 1, 2, and 3 of Eu$^{3+}$, and the Eu$^{2+}$ $J$ = 7/2 multiplet state caused by an increase in 4$f$ electron temperature that results in a 4$f$ localization process. This electronic temperature increase combined with fluence-dependent screening accounts for the strongly non-linear effective valence change. The data allow us to extract a time-dependent determination of an effective temperature of the 4$f$ shell, which is also of great relevance in the understanding of metallic systems' properties, such as the ultrafast demagnetization of ferromagnetic rare-earth intermetallics and their all-optical magnetization switching.