We report results of density-functional theory calculations on the structur
al, magnetic, and electronic properties of (1 x 1) structures of Co on Cu(0
01) for coverages up to two monolayers. In particular we discuss the tenden
cy towards phase separation in Co islands and the possibility of segregatio
n of Cu on top of the Co film. A sandwich structure consisting of a bilayer
Co film covered by 1 monolayer of Cu is found to be the lowest-energy conf
iguration. We also discuss a bilayer c(2 x 2) alloy which may form due to k
inetic reasons, or be stabilized at strained surface regions. Furthermore,
we study the influence of magnetism on the various structures and, e.g., fi
nd that Co adlayers induce a weak spin-density wave in the copper substrate
.