The magnetic anisotropy energy of Ni-n/Cu(100) is calculated in terms of th
e spin-polarized fully relativistic Korringa-Kohn-Rostoker method including
surface relaxation by using 2D structure constants originally described fo
r low-energy electron diffraction calculations. Investigating different rel
axations, an explanation for the reorientation transition from in-plane to
perpendicular can be given. For a relaxation of -5.5% (c/a = 0.945) this re
orientation occurs at about seven layers of Ni and yields second order term
s to the magnetic anisotropy energy that are in excellent agreement with ex
periment. [S0031-9007(98)08322-7].