Resonant x-ray scattering in manganites: Study of the orbital degree of freedom

The orbital degree of freedom of electrons and its interplay with spin, charge and lattice degrees of freedom are some of the central issues in colossal magnetoresistive manganites. The orbital degree of freedom has until recently remained hidden, since it does not couple directly to most experimental probes. Development of synchrotron light sources has changed the situation; by the resonant x-ray scattering (RXS) technique the orbital ordering has successfully been observed. In this article, we review progress in the recent studies of RXS in manganites. We start with a detailed review of the RXS experiment applied to the orbital-ordered manganites and other correlated electron systems. We derive the scattering cross section of RXS, where the tensor character of the atomic scattering factor (ASF) with respect to the x-ray polarization is stressed. Microscopic mechanisms of the anisotropic tensor character of the ASF are introduced and numerical results of the ASF and the scattering intensity are presented. The azimuthal angle scan is a unique experimental method to identify RXS from the orbital degree of freedom. A theory of the azimuthal angle and polarization dependence of the RXS intensity is presented. The theoretical results show good agreement with the experiments in manganites. Apart from the microscopic description of the ASF, a theoretical framework of RXS to relate directly to the 3d orbital is presented. The scattering cross section is presented by the correlation function of the pseudo-spin operator for the orbital degree of freedom. A theory is extended to the resonant inelastic x-ray scattering and methods to observe excitations of the orbital degree of freedom are proposed.