Strongly momentum-dependent screening dynamics in La$_{0.5}$Sr$_{1.5}$MnO$_4$ observed with resonant inelastic x-ray scattering

We report strongly momentum-dependent local charge screening dynamics in CE-type charge, orbital, and spin ordered La$_{0.5}$Sr$_{1.5}$MnO$_4$, based on Mn K-edge resonant inelastic x-ray scattering data. Through a comparison with theoretical calculations, we show that the observed momentum dependence reflects highly localized, nearest neighbor screening of the transient local charge perturbation in this compound with an exciton-like screening cloud, rather than delocalized screening. The size of the screening cloud is estmated to be about 0.4-0.5 interatomic distances.