By taking account of the non-integer number of d electrons per atom and the intra- atomic interactions of electrons, a quantum theory of ferromagnetism is given. The spontaneous magnetization and the magnetic anisotropic constant K1 in the whole temperature range are calculated by using the method of double-time Green's functions in statistical mechanics. The results obtained are better than that of the simple Heisenberg's model. The properties of the temperature dependence of K1 may be explained qualitatively.
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