First-principles study of x-ray linear dichroism at the Mn $K$ edge of LaMnO$_3$

LaMnO$_3$ shows orbital ordering of Mn $3d$ ($3x^2-r^2/3y^2-r^ 2$) states associated with the cooperative Jahn-Teller distortion. Resonant x-ray scattering measured at the Mn $K$ edge by Murakami {\it et al.}\ shows peculiar azimuth-angle dependence, indicating that the degeneracy of the Mn $4p$ states should be lifted. For its mechanism, two models have been proposed. One is the Coulomb mechanism, that is, the $3d$ orbital ordering causes the level splitting of the $4p$ states through the intra-atomic $3d$-$4p$ Coulomb interaction. The other is the Jahn-Teller mechanism: the $4p$ bands are strongly influenced by the Oxygen displacements, not by the anisotropic $3d$ charge distribution resulting from the orbital ordering. The important point to note is that these two models yield opposite way of the $4p$ splitting. To resolve this argument, very recently, Maruyama {\it et al.}\ have carried out x-ray photoabsorption measurements at the Mn $K$ edge using linearly polarized light. The energy and polarization dependence of their spectra clear up the unoccupied Mn $p$ states, apparently supporting the Jahn-Teller mechanism. Furthermore, they found interesting azimuth-angle dependence as a function of photon energy. For its interpretation, detailed band-structure information is undoubtedly necessary. In this talk, using the first-principles FLAPW calculations, we will discuss the overall feature of the measured spectra and its relation to the $3d$ orbital ordering and Jahn-Teller distortion.