Self-interaction corrected relativistic theory of magnetic scattering of   x rays: Application to praseodymium
  A first-principles theory of resonant magnetic scattering of x rays is presented. The scattering amplitudes are calculated using a standard time-dependent perturbation theory to second order in the electron-photon interaction vertex. In order to calculate the cross section reliably an accurate description of the electronic states in the material under investigation is required and this is provided by the density functional theory (DFT) employing the Local Spin Density Approximation combined with the self-interaction corrections (SIC-LSD). The magnetic x-ray resonant scattering (MXRS) theory has been implemented in the framework of the relativistic spin-polarized LMTO-ASA band structure calculation method. The theory is illustrated with an application to ferromagnetic praseodymium. It is shown that the theory quantitatively reproduces the dependence on the spin and orbital magnetic moments originally predicted qualitatively (Blume, J. Appl. Phys, {\bf 57}, 3615 (1985)) and yields results that can be compared directly with experiment. 
E. Arola, M. Horne, P. Strange, H. Winter, Z. Szotek, and W.M.   Temmerman