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 proper ties observed in several transition-metal oxides, as well as colossal magne toresistive (CMR) manganites. Recently, much experimental development in th is research field has been achieved by utilizing synchrotron radiation; orb ital ordering was directly observed by resonant X-ray scattering (RXS). We theoretically study RXS as a probe to detect the orbital orderings and exci tations in CMR manganites. We identify an origin of the anisotropy of the a tomic scattering factor (ASF) in the orbital-ordered state and calculate th e energy, polarization and orbital dependences of ASF and the scattering in tensity. 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 compo unds are briefly reviewed. (C) 2001 Elsevier Science B.V. All rights reserv ed.