After a short review of the recent experimental data in the study of static and dynamic properties of magnetism in finite samples with attention to the surface effect, a theoretical treatment of the surface effect is presented. Different experiments are concerned: magnetization measurements, Mössbauer analysis, spin polarized photoemission, low energy electron diffraction, spin wave resonance and Brillouin scattering of spin waves. The choice of a typical Hamiltonian consistent with the experimental results is carefully made, with either a quite local surface perturbation leading to a discrete treatment or a quasi-continuous surface perturbation leading to a continuum treatment. Then the ground state of this spin Hamiltonian is derived in both cases with evidence for a surface of interface magnetic rearrangement with standard conditions. The first excited states, i.e. the one-magnon eigenstates are then derived in a quite general way, which allows non-uniformities in the sample. Several simple cases are completely treated, with, for instance, the study of the magnetic decoupling of the different parts of coupled thin films. These results enable us to discuss the temperature effects, and by means of a Tyablikov-Bogoliubov renormalization technique, high temperatures are correctly studied, including the Curie transitions. Now a careful investigation of the experimental situation compared to these theoretical results is given, with attention to new effects such as spin wave polarization and to a surface classification with evidence for "hard" and "soft" surface different behavior. © 1981.
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