Hartree-Fock study of orbital magnetic moments in 3d and 5f magnets and X-ray magnetic circular dichroism

The spin (M_s) and orbital magnetic moments (M_o) of the uranium 5f state in the ferromagnetic compound uranium sulfide (US) and of the cobalt 3d state in various transition-metal superlattices are calculated on the basis of a tight-binding model, in which the intra-atomic f-f or d-d multipole interaction is taken into account using the Hartree-Fock (HF) approximation. The parameters in the model are determined on the basis of available first-principles calculations. For US, the calculated ratio M_o/M_s and magnetic circular dichroism spectrum for U M_4,5 absorption are in good agreement with the experimental results. Inclusion of the expectation values of the spin-off-diagonal operators in addition to the number operators in the 5f state is found to be crucially important when describing the 5f magnetic state. A difference in enhancement of M_o of the Co atom between the Co/Pd and Co/Cu superlattices is discussed on the basis of a semi-quantitative calculation, assuming ferromagnetism.