Relation between the angular dependence of magnetic x-ray dichroism and anisotropic ground-state moments

We analyze the geometrical aspects of x-ray absorption spectroscopy as a function of the directions of the light polarization and the magnetization with respect to the crystalline axes of the material. Relations are derived for the angular dependence of the ground-state magnetic moments and the polarized core edge absorption signals in the presence of a second-order perturbation by an arbitrary interaction. Using the methods of the algebra of tensor operators the angular dependence can be written as a sum over different bipolar spherical harmonics. The example of second-order spin-orbit interaction in transition metals is worked out in detail. We show the importance of the magnetocrystalline anisotropy and describe a method to measure directly the anisotropy. A special choice of geometry, such as a transverse magnetic field, in combination with the sum rules for magnetic dichroism makes it possible to separate ground-state moments which cannot be distinguished in a collinear geometry. We also show that the anisotropy of the lattice can give strong variations in the observed spin to orbital magnetic moment ratio, which previously might have been ascribed to limitations in the application of the sum rules.