  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.
