Constituents of magnetic anisotropy and a screening of spin–orbit coupling in solids

•The screening of spin–orbit coupling and its application for magnetic anisotropy.•We test the validity of our analysis using electronic structure calculations.•Decomposition of relativistic energy and anisotropy into sites and spin components.•The microscopic origin of high anisotropy in FePt and CoPt magnets.

Using quantum mechanical perturbation theory (PT) we analyze how the energy of perturbation of different orders is renormalized in solids. We test the validity of PT analysis by considering a specific case of spin–orbit coupling as a perturbation. We further compare the relativistic energy and the magnetic anisotropy from the PT approach with direct density functional calculations in FePt, CoPt, FePd, MnAl, MnGa, FeNi, and tetragonally strained FeCo. In addition using decomposition of anisotropy into contributions from individual sites and different spin components we explain the microscopic origin of high anisotropy in FePt and CoPt magnets.