MAGNETIC SUPERLATTICES, CLASSICAL SPIN CHAINS, AND THE FRENKEL-KONTOROVA MODEL

An equivalence between a simple magnetic model subject to an intrinsic ally nonconvex Heisenberg interaction and a Frenkel-Kontorova-type mod el is formulated. The magnetic model is able to reproduce the experime ntal results obtained on Fe/Cr(211) superlattices and for this reason has already attracted theoretical attention. The problem is formulated via a two-dimensional area-preserving map and the effect of the surfa ces in the magnetic model, which are introduced by appropriate boundar y conditions, is shown to be equivalent to the introduction of a disco mmensuration in a Frenkel-Kontorova-type chain. Further analogies betw een the two models are presented. The analysis is used to reconsider a nd clarify some of the features of the magnetic model and to add some contributions to its phase diagram in the space of parameters.