Using local-spin density calculations performed in the generalized-gradient
approximation we have examined the possibility that Mn monolayers epitaxia
lly grown on Cu(111) substrates represent a physical realization of the fru
strated antiferromagnetic planar (AFP) model. Indeed, we find that the nonc
ollinear ground state of the AFP model with +/- 120 degrees orientations of
the nearest-neighbors is also the ground state of Mn/Cu(111). However, due
to the rather long-range antiferromagnetic interactions, the energetic pre
ference over a raw-wise antiferromagnetic order is only very weak.