Orbital Ordering, Jahn-Teller Distortion, and Anomalous X-Ray Scattering in Manganates

We demonstrate with LSDA $+U$ calculations that x-ray scattering at the $K$ edge of Mn is sensitive to orbital ordering in one energy range and Jahn-Teller distortion in another. Contrary to what is suggested by atomic or cluster models used to date we show that band structure effects rather than local Coulomb interactions dominate the polarization dependence of the $K$ edge scattering and therefore it is sensitive to nearest neighbor bond length distortions and next nearest neighbor orbital occupation. Based on this we propose a new mechanism for $K$ edge x-ray scattering in the manganates which we suggest is also applicable to transition metal compounds in general.