Based on a total energy search among the complete set of $2^{n-1\mathrm{}}$ collinear spin states for $n$ ( $n=1,\dots ,6\mathrm{}$) monolayers (ML) of fcc Fe on Cu(100) by use of the generalized gradient approximation combined with the full-potential linearized augmented plane-wave method, we find ferromagnetism for 1, 2, and 3 ML fcc-Fe/Cu(100), bilayer antiferromagnetism for even numbers of layers (4 and 6 ML), and the coexistence of several spin states for an odd number of layers (5 ML). The results are consistent with the experimental situation and a possible spin-spiral ground state of fcc Fe. Effects of band narrowing, relaxations, interface mixing, and surface steps are addressed.

• Received 14 April 1997

DOI:https://doi.org/10.1103/PhysRevLett.79.507