  In a recent Letter, S. Lounis et al. find that the ground state of finite
antiferromagnetic nanowires deposited on ferromagnets depends on the parity of
the number N of atoms and that a collinear-noncollinear transition exists for
odd N. Authors use ab initio results and a Heisenberg model, which is studied
numerically with an iterative scheme. In this Comment we argue that the
Heisenberg model can much easier be investigated in terms of a two-dimensional
map, which allows to find an analytic expression for the transition length, a
central result of Lounis et al. (see their Fig.3).
