A study has been made of the magnetic properties of epitaxial 6 Monolayer (ML) fcc-Fe films on Cu (100) with various thicknesses of epitaxial Cu deposited on top of the Fe. It was found that the magnetic properties undergo striking changes as a function of the Cu thickness. The easy axis of magnetization goes from being in-plane for the bare Fe to perpendicular upon the deposition of 1 ML Cu. Concurrently there is a dramatic decrease in the Kerr signal intensity at saturation. Upon depositing a second ML of Cu the Kerr signal intensity more than doubles, and the easy axis remains perpendicular. For Cu overlayers of 3 ML to 10 ML the Kerr signal intensity at saturation gradually diminishes to below the level of detectability, as if the Fe were nonmagnetic. A superlattice consisting of 60 ML Cu/ (6 ML 57Fe/10 ML Cu)×5/Cu (100) was fabricated and studied at room temperature by conversion electron Mòssbauer spectroscopy. The results confirmed that the Fe is indeed nonmagnetic. The four inner Fe layers of the 6 ML film have the same isomer shift as bulk fcc-Fe in precipitates in Cu, and the two boundary Fe layers exhibit an asymmetric quadrupole doublet.