  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.
