MEAN-FIELD STUDY OF SURFACE AND INTERFACE PROPERTIES IN TERMS OF NONLINEAR MAPS

In systems with free surfaces and interfaces, the absence of translational invariance may result in a completely different behavior with respect to the corresponding bulk system, so that many new and interesting phenomena may take place, as for example, the occurrence of a surface reconstruction phenomenon, characterized by an order at the surface different from the one which occurs deep in the sample. This article reviews the mean-field approach to surface and interface properties as a problem in nonlinear dynamics. We focus our attention on magnetic films and superlattices, whose properties are studied in terms of area-preserving maps; the emphasis is put on the effect of the surfaces, which are introduced as appropriate boundary condition, and which let exotic solution become physically relevant, though the infinitely extended system is trivially solvable. The importance of the discreteness of the lattice and of chaotic regimes in the map phase space is stressed. Some specific applications are given: (i) the magnetic field dependence of the ground state of semi-infinite uniaxial antiferromagnets and films, so that the anomalous behavior of the magnetic susceptibility experimentally observed in Fe/Cr(211) superlattices is easily accounted for as related to the chaotic nature of the corresponding map; (ii) the ground state and the temperature dependence of the magnetization of a ferromagnet with an enhanced surface exchange, and with a surface anisotropy favoring the spins to lie perpendicularly to the film plane, while a bulk anisotropy favors an in plane spin configuration.