  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.
