New theoretical developments based on a fully relativistic description
of magnetic dichroism (MXD) in X-ray absorption spectroscopy are pres
ented. It is demonstrated that it is possible to achieve within this s
ophisticated framework an unambiguous identification of the role of ex
change splitting and spin-orbit coupling for the MXD by means of model
calculations. A description of this approach that consists in the sep
arate manipulation of both sources of the MXD is presented together wi
th several applications to K-and L-2,L-3-edge-spectra of transition me
tals. All fully relativistic calculations on the MXD have been done so
far in the XANES region using the standard relativistic (kappa,mu)-re
presentation. In dealing with magnetic EXAFS (MEXAFS) it seems to be m
ore advantageous to treat the multiple scattering for the final states
in real-space adopting the (I,m(l),m(s))-representation. A correspond
ing generalization for the matrix inversion as well as the expansion t
echniques will be presented.