Theory of resonant X-ray scattering as a probe to detect the orbital orderings and excitations in CMR manganites

The orbital degree of freedom in transition-metal ions is recognized to be one of the indispensable ingredients to uncover anomalous electronic properties observed in several transition-metal oxides, as well as colossal magnetoresistive (CMR) manganites. Recently, much experimental development in this research field has been achieved by utilizing synchrotron radiation; orbital ordering was directly observed by resonant X-ray scattering (RXS). We theoretically study RXS as a probe to detect the orbital orderings and excitations in CMR manganites. We identify an origin of the anisotropy of the atomic scattering factor (ASF) in the orbital-ordered state and calculate the energy, polarization and orbital dependences of ASF and the scattering intensity. We develop a theory of RXS, where the scattering cross section is represented by the correlation function of the pseudospin operators for the orbital degree of freedom. Recent RXS experiments in orbital-ordered compounds are briefly reviewed.