Even-odd effects in finite Heisenberg spin chains

Magnetic superlattices and nanowires may be described as Heisenberg spin chains of finite length N, where N is the number of magnetic units (films or atoms, respectively). We study antiferromagnetically coupled spins which are also coupled to an external field H (superlattices) or to a ferromagnetic substrate (nanowires). The model is analyzed through a two-dimensional map which allows fast and reliable numerical calculations. Both open and closed chains have different properties for even and odd N (parity effect). Open chains with odd N are known [S.Lounis et al., Phys. Rev. Lett. 101, 107204 (2008)] to have a ferrimagnetic state for small N and a noncollinear state for large N. In the present paper, the transition length N_c is found analytically. Finally, we show that closed chains arrange themselves in the uniform bulk spin-flop state for even N and in nonuniform states for odd N.