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The independent random walk method (which is equivalent to the noninteracting spin wave method) with no further approximations was used to calculate the low temperature expansion of: (i) the local mean spin values of an isotropic Heisenberg ferromagnet for semi-infinite crystal and (ii) the spontaneous magnetization of an anisotropic Heisenberg ferromagnet for monolayer and double layer. The full low temperature expansion starting with T-3/2 term was obtained for the semi-infinite Heisenberg ferromagnet and it was shown that the spontaneous magnetization for thin films of anisotropic Heisenberg ferromagnets can exhibit a quasi-linear behaviour in certain temperature region related to the magnitude of the anisotropy.

Surface and Thin Film Magnetization of Isotropic and Anisotropic Heisenberg Ferromagnet at Low Temperatures