Spin-other-orbit interaction and magnetocrystalline anisotropy

We report the effect of the two-body, spin-other-orbit interaction on the magnetocrystalline anisotropy energy of the $3d$ transition metals. The relevant energy differences were computed for bcc Fe, fcc Ni, and hcp Co using a linearized augmented plane-wave method to solve the scalar relativistic Kohn-Sham equations in the local spin-density approximation. The spin-other-orbit interaction was incorporated at the level of the Hartree approximation. Special care was taken to guarantee the correctness of our numerical procedures. We find that the spin-other-orbit interaction does indeed change the anisotropy energy, but the effect is too small to account for the disagreement with experiment found in previous calculations for all three elements.