Magnetocrystalline anisotropy in cobalt based magnets: a choice of correlation parameters and the relativistic effects.

The dependence of the magnetocrystalline anisotropy energy (MAE) in MCo (M  =  Y, La, Ce, Gd) and CoPt on the Coulomb correlations and strength of spin orbit (SO) interaction within the GGA  +  U scheme is investigated. A range of parameters suitable for the satisfactory description of key magnetic properties is determined. We show that for a large variation of SO interaction the MAE in these materials can be well described by the traditional second order perturbation theory. We also show that in these materials the MAE can be both proportional and negatively proportional to the orbital moment anisotropy (OMA) of Co atoms. Dependence of relativistic effects on Coulomb correlations, applicability of the second order perturbation theory for the description of MAE, and effective screening of the SO interaction in these systems are discussed using a generalized virial theorem. Such determined sets of parameters of Coulomb correlations can be used in much needed large scale atomistic simulations.