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

In systems with free surfaces and interfaces, the absence of translati onal invariance may result in a completely different behavior with res pect to the corresponding bulk system, so that many new and interestin g phenomena may take place, as for example, the occurrence of a surfac e reconstruction phenomenon, characterized by an order at the surface different from the one which occurs deep in the sample. This article r eviews the mean-field approach to surface and interface properties as a problem in nonlinear dynamics. We focus our attention on magnetic fi lms and superlattices, whose properties are studied in terms of area-p reserving maps; the emphasis is put on the effect of the surfaces, whi ch are introduced as appropriate boundary condition, and which let exo tic solution become physically relevant, though the infinitely extende d 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 dependen ce of the ground state of semi-infinite uniaxial antiferromagnets and films, so that the anomalous behavior of the magnetic susceptibility e xperimentally observed in Fe/Cr(211) superlattices is easily accounted for as related to the chaotic nature of the corresponding map; (ii) t he ground state and the temperature dependence of the magnetization of a ferromagnet with an enhanced surface exchange, and with a surface a nisotropy favoring the spins to lie perpendicularly to the film plane, while a bulk anisotropy favors an in plane spin configuration.