Magnetocrystalline anisotropy energy in cubic Fe, Co, and Ni: Applicability of local-spin-density theory reexamined

We report an ab initio investigation of the magnetocrystalline anisotropy energy (MAE) in bcc Fe and fcc Co and Ni. We introduce the spin-orbit scaling (SOS) technique, which, in combination with the force theorem, we use to achieve numerically converged MAE's. From these MAE's, and from MAE's which we separately obtain from total energy calculations, we investigate the ability of energy band theory based upon the local-spin-density approximation to describe the MAE in the cubic $3d$ metals. The SOS technique yields the correct easy axis for Fe and Co, but a vanishing MAE for Ni. Our total energy calculations on a smaller number of 3.7×10⁵ k points predict the correct easy axis in Fe, Co, and also Ni.