Comment on "Magnetism of Nanowires Driven by Novel Even-Odd Effects"

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).