Magnetic surface anisotropy of transition metals

A model calculation is presented for the computation of the magnetic surface anisotropy $K_s$ for transition metals. Special reference is made to Ni. It is demonstrated that the changes at the surface in the effective atomic potential of the different $d$ orbitals are very important in determining $K_s$. Furthermore it is shown that one must include all $d$ orbitals in the calculations. The problem is studied by successively treating the weak-hopping limit, the one-layer problem, and the surface of a semi-infinite crystal. The sign and the order of magnitude of the magnetic surface anisotropy which we find for Ni agree with the experimental results on Ni alloys. A comparison is made to earlier work on the subject.