Abstract
The ferromagnetic phase transition in ultra-thin films and surfaces is studied by the Green function method based upon the Heisenberg model (S>or=1) with the out-of-plane spin orientation of the atoms in the surfaces. A model calculation shows that the order parameter (spontaneous magnetization) changes with the atomic planes in the ferromagnetic films but the Curie temperatures of the atomic planes are all the same; the Curie temperature of ultra-thin films may be higher or lower than the bulk Curie temperature which depends on the fact that the spin is pinned to some degree at the surfaces. It is impossible for an ordered surface phase to coexist with a disordered bulk phase and it is also impossible for a disordered surface phase to coexist with an ordered bulk phase in homogeneous films or a bulk magnet.
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