  A general symmetry analysis of the optical conductivity or scattering tensor
is used to rewrite the conductivity tensor as a sum of fundamental spectra
multiplied by simple functions depending on the local magnetization direction.
Using this formalism, we present several numerical examples at the transition
metal L23 edge. From these numerical calculations we can conclude that large
deviations from the magneto-optical effects in spherical symmetry are found.
These findings are in particular important for resonant x-ray diffraction
experiments where the polarization dependence and azimuthal dependence of the
scattered Bragg intensity is used to determine the local ordered magnetization
direction.
