The magnetization of Ni films on Cu(100) switches from an in-plane to a perpendicular orientation at about 7 monolayers,(M. Farle et al.), Phys. Rev. B 55, 3708 (1997). whereby, as was shown by bulk calculations(O. Hjortstam et al.), Phys. Rev. B 55, 15 026 (1997). of fct Ni, tetragonal distortions seem to play an important role. A study of Ni multilayers on Cu(100) in terms of the fully ... [Show full abstract] relativistic spin-polarized screened Korringa-Kohn-Rostoker method using a `parent' fcc lattice already shows indications of such a transition, however, cannot account for the transition quantitatively. For this reason the effects of a tetragonal distortion in direction (100) will be discussed using layer-dependent structure constants.