Resonant inelastic x-ray scattering from charge and orbital excitations in manganites

We present a theory of the resonant inelastic x-ray scattering (RIXS) of electronic excitations in orbital ordered manganites. The charge and orbital excitations of the Mn $3d$ electron result from the Coulomb interactions in the intermediate scattering state. The scattering cross section is formulated in terms of the Liouville operator method in which the local and itinerant natures of the excitations are taken into account on an equal footing. This permits the cross section to be written in the charge and orbital correlation functions associated with a factor describing local electronic excitations. The RIXS spectra are calculated numerically as functions of momentum and the polarization of the x ray. Our calculations show that RIXS provides an excellent means by which to study the unique electronic excitations in correlated electron systems with orbital degeneracy.