Sum Rules and Fundamental Spectra of Magnetic X-Ray Dichroism in Crystal Field Symmetry

The sumrules for X-ray absorption and photoemission [Thole et al ., Phys. Rev. Lett. 68 (1992) 1943; 70 (1993) 2499] which relate the integrated signals of the magnetic circular and linear dichroism to the orbital magnetic moment and quadrupole moment are generalized to point group symmetry. The polarization dependence of the spectra is obtained by separating the geometry from the physical properties. The number of fundamental spectra is equal to the number of total symmetric representations of the recoupled moment in the point group. Cylindrical symmetry is particularly simple because it has the natural basis lm. The presented results can be useful for measurements of magnetic materials that contain transition metal, rare earth or actinide ions using linearly and circularly polarized X-rays.