Even-odd effects in finite Heisenberg spin chains

TL;DR

This paper investigates how the parity of the number of spins in finite Heisenberg chains affects their magnetic states, revealing distinct behaviors for even and odd chain lengths through analytical and numerical methods.

Contribution

It provides an analytical determination of the transition length for odd chains and characterizes the different magnetic configurations in open and closed chains based on parity.

Findings

Open odd chains exhibit ferrimagnetic and noncollinear states depending on length.

Closed chains show uniform spin-flop states for even N and nonuniform states for odd N.

Analytical expression for the transition length N_c in odd chains.

Abstract

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.