Theory of Anomalous X-Ray Scattering in Orbital-Ordered Manganites

Abstract

We study the theory of the anomalous x-ray scattering in relation to its role as a detector of the orbital orderings and excitations in perovskite manganites. The scattering matrix is given by virtual electron excitations in Mn from the $1s$ level to the unoccupied $4p$ level. We find that the orbital dependence of the Coulomb interaction between $3d$ and $4p$ electrons is essential to the anisotropy of the scattering factor near the $K$ edge. The calculated results in ${\mathrm{MnO}}_{6}$ clusters explain the forbidden reflections observed in ${\mathrm{La}}_{0.5}{\mathrm{Sr}}_{1.5}{\mathrm{MnO}}_{4}$ and ${\mathrm{LaMnO}}_{3}$. The possibility of observing orbital waves with x-ray scattering is discussed as well.