Orbital ordering, Jahn-Teller distortion, and resonant x-ray scattering   in KCuF3
  The orbital, lattice, and spin ordering phenomena in KCuF3 are investigated by means of LDA+U calculations, based on ab-initio pseudopotentials.We examine the Cu-3d orbital ordering and the associated Jahn-Teller distortion in several different spin-ordered structures of KCuF3. The ground state is correctly predicted to be an A-type antiferromagnetic structure, and the calculated Jahn-Teller distortion agrees also well with experiment. Concerning the orbital ordering, we find that even for a highly ionic compound such as KCuF3, the orbital-order parameter is significantly reduced with respect to its nominal value due to Cu(3d)--F(2p) hybridization. We also calculate the Cu K-edge resonant x-ray scattering spectra for Bragg reflections associated with orbital order. Consistent with previous studies, we find that the resonant signal is dominated by the structural anisotropy in the distribution of the F neighbors of the resonant Cu atom, and that the Cu-3d orbital ordering has only a minor influence on the spectra. Our LDA+U results, however, also indicate that a change in the magnetic structure has a small influence on the Jahn-Teller distortion, and hence on the resonant spectrum, in the conventional (room-temperature) crystallographic structure of KCuF3. This may indicate that the large change observed experimentally in the resonant signal near the N\'eel temperature is related to a low-temperature structural transformation in KCuF3. 
N. Binggeli and M. Altarelli