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 derived. The effects of strong correlations are studied along several paths in $(U,J)$ parameter space. 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. The modified one-electron spectra by strong correlations are emphasized in conjunction with magnetic anisotropy.
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