Magnetocrystalline anisotropy and orbital polarization in ferromagnetic transition metals

The magnetocrystalline anisotropy energies (MAEs) of the ferromagnetic metals bcc Fe, fcc and hcp Co, and fcc Ni have been calculated by using the {\it ab initio} tight-binding method. Disentangling the strong correlation among the $d$ orbitals with the Hamiltonian in the local spin-density approximation, we have investigated the orbital polarizations induced by the Hubbard $U$ and Racah $B$. The experimental MAE of fcc Ni is found with the value of $U$ close to that determined from experiments and used in other theories. With the optimized values of $U$ and $J$, both the MAEs and the orbital moments for Fe and Co are in close agreement with experiment.