Orbital ordering in the manganites: Resonant x-ray scattering predictions at the manganeseLIIandLIIIedges

It is proposed that the observation of orbital ordering in manganite materials should be possible at the $L_{\mathrm{II}}$ and $L_{\mathrm{III}}$ edges of manganese using x-ray resonant scattering. If performed, dipole selection rules would make the measurements much more direct than the disputed observations at the manganese K edge. They would yield specific information about the type and mechanism of the ordering not available at the K edge, as well as permitting the effects of orbital ordering and Jahn-Teller ordering to be detected and distinguished from one another. Predictions are presented based on atomic multiplet calculations, indicating distinctive dependence on energy, as well as on polarization and on the azimuthal angle around the scattering vector.