First-principles calculation of magnetic x-ray dichroism in Fe and Co multilayers

A relativistic, spin-polarized band theory of magnetic x-ray dichroism (MXD) in solids is briefly described. Calculated circular and linear dichroic x-ray absorptions at the ${\mathit{L}}_{2,3}$ edges from bulk Fe and Co as well as from their multilayers [${\mathrm{Fe}}_2$ ${\mathrm{Cu}}_6$ (001), ${\mathrm{FeAg}}_5$ (001), ${\mathrm{Co}}_2$Pd(Pt${)}_4$ (111), and ${\mathrm{Co}}_2$ ${\mathrm{Cu}}_6$ (001)] are presented. Large circular MXD is predicted in both the bulks and the multilayers while linear MXD due to magnetocrystalline anisotropy is found to be small (within 1%). Nevertheless, linear MXD due to a photon polarization change is about 3–8 %. The orbital magnetization sum rule of B. T. Thole et al., [Phys. Rev. Lett. 68, 1943 (1992)] is found to give orbital magnetic moments too small by about 20–35 %. We note that for each ion species, there is a simple linear relationship between the integrated circular MXD signal and the orbital magnetic moment, and we propose that one uses this linear relationship to measure the orbital magnetic moment of an ion in magnetic solids. The recently proposed spin magnetization sum rule [P. Carra et al., Phys. Rev. Lett. 70, 694 (1993)] is found to give rather accurate spin magnetic moments for the Co systems (errors within 15%). However, it does not hold qualitatively for highly anisotropic systems such as Fe multilayers.