Theory of anomalous x-ray scattering in orbital-ordered manganites

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 Is 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 MnO6 clusters explain the forbidden reflections observed in La0.5Sr1.5MnO4 and LaMnO3. The possibility of observing orbital waves with x-ray scattering is discussed as well.