Ab initio calculations of X-ray magnetic circular dichroism spectra within the projector augmented wave method: An implementation into the VASP code

X-ray absorption and X-ray magnetic circular dichroism (XMCD) are very powerful tools for probing the orbital and spin moments of each atomic species orbital of magnetic materials. In this work, we present the implementation of a module for computing the X-ray absorption and XMCD spectra into the VASP code. We provide a derivation of the absorption cross-section in the electric dipole approximation. The matrix elements, which make up the X-ray absorption cross-section for a given polarization of light, are then computed using either the momentum operator p or the position operator r, within the projector augmented wave method. The core electrons are described using the relativistic basis-set whereas for the valence electrons, the spin-orbit coupling is added perturbatively to the semi-relativistic Hamiltonian. We show that both the p and the r implementations lead to the same results. The results for the K-edge and L23-edges of bcc-iron are then computed and compared to experiment.