Relativistic spin-polarized theory of magnetoelastic coupling and magnetic anisotropy strain dependence: Application to Co/Cu(001)

A self-consistent relativistic spin-polarized version of the total-energy full-potential linearized-augmented-plane-wave (FLAPW) method is developed on the basis of a second-variation treatment of the spin-orbit coupling (SOC). As illustration, the method is applied to determine the magnetoelastic coupling, orbital magnetic moment anisotropy and magnetic anisotropy energy (MAE) of a Co overlayer on Cu(001). The MAE (-0.36 meV) calculated at the equilibrium overlayer/substrate distance is in good agreement with experiment. As discovered earlier by Wu and Freeman, we find a linear dependence of the MAE on the overlayer/substrate distance. The calculated positive effective magnetoelastic coupling coefficient (1.13 meV) is caused by a positive surface magnetoelastic anisotropy (0.23 meV). This causes a negative magnetostriction coefficient ${\lambda }_{001}=-5.20\times {10}^{-5}$ and an isotropic magnetostriction coefficient ${\lambda }_s=-5.65\times {10}^{-5}$ that is in very good agreement with previous studies based on a perturbative SOC treatment.