We calculate magnetic anisotropy energy of Fe and Ni by taking into account
the effects of strong electronic correlations, spin-orbit coupling, and no
ncollinearity of intra-atomic magnetization. The LDA + U method is used and
its equivalence to dynamical mean-field theory in the static limit is emph
asized. Both experimental magnitude of magnetic anisotropy energy and direc
tion 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-elect
ron spectra which are now in better agreement with experiments.