  On the basis of a first-principles electronic structure theory of finite
temperature metallic magnetism in layered materials, we investigate the onset
of magnetic order in thin (2-8 layers) fcc-Fe films on Cu(100) substrates. The
nature of this ordering is altered when the systems are capped with copper.
Indeed we find an oscillatory dependence of the Curie temperatures as a
function of Cu-cap thickness, in excellent agreement with experimental data.
The thermally induced spin-fluctuations are treated within a mean-field
disordered local moment (DLM) picture and give rise to layer-dependent `local
exchange splittings' in the electronic structure even in the paramagnetic
phase. These features determine the magnetic intra- and interlayer interactions
which are strongly influenced by the presence and extent of the Cu cap.
