Importance of Correlation Effects on Magnetic Anisotropy in Fe and Ni

We calculate magnetic anisotropy energy of Fe and Ni by taking into account the effects of strong electronic correlations, spin-orbit coupling, and non-collinearity of intra--atomic magnetization. The LDA+U method is used and its equivalence to dynamical mean--field theory in the static limit is emphasized. Both experimental magnitude of MAE and direction of magnetization are predicted correctly near U=1.9 eV, J=1.2 eV for Ni and U=1.2 eV, J=0.8 eV for Fe. Correlations modify the one--electron spectra which are now in better agreement with experiments.