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Orbital degree of freedom of electrons and its interplay with spin, chargeand lattice degrees of freedom are one of the central issues in colossalmagnetoresistive manganites. The orbital degree of freedom has until recentlyremained hidden, since it does not couple directly to most of experimentalprobes. Development of synchrotron light sources has changed the situation; bythe resonant x-ray scattering (RXS) technique the orbital ordering hassuccessfully been observed . In this article, we review progress in the recentstudies of RXS in manganites. We start with a detailed review of the RXSexperiments applied to the orbital ordered manganites and other correlatedelectron systems. We derive the scattering cross section of RXS where thetensor character of the atomic scattering factor (ASF) with respect to thex-ray polarization is stressed. Microscopic mechanisms of the anisotropictensor character of ASF is introduced and numerical results of ASF and thescattering intensity are presented. The azimuthal angle scan is a uniqueexperimental method to identify RXS from the orbital degree of freedom. Atheory of the azimuthal angle and polarization dependence of the RXS intensityis presented. The theoretical results show good agreement with the experimentsin manganites. Apart from the microscopic description of ASF, a theoreticalframework of RXS to relate directly to the 3d orbital is presented. Thescattering cross section is represented by the correlation function of thepseudo-spin operator for the orbital degree of freedom. A theory is extended tothe resonant inelastic x-ray scattering and methods to observe excitations ofthe orbital degree of freedom are proposed.Comment: 47 pages, 24 figures, submitted to Rep. Prog. Phy

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