The phenomenon of surface magnetic reconstruction (i.e. a different or
ientation of the surface spins with respect to the bulk ones) is overv
iewed in the framework of mean-field theory as an area-preserving map,
where the surfaces are introduced as appropriate boundary conditions.
In this way, the nonuniform ground state both of semi-infinite system
s and films, can be calculated very rapidly and with a great precision
for a variety of magnetic models: (i) a uniaxial antiferromagnet in a
n applied magnetic field, a model able to describe Fe/Cr(211) superlat
tices with antiferromagnetic interlayer coupling; (ii) a ferromagnet w
ith enhanced surface exchange, and with a surface anisotropy favouring
the spins to lie perpendicularly to the film surface, while the bulk
anisotropy favours in-plane alignment, a model able to describe Gd(000
1)/W(110) films.