Abstract
This paper describes a method to calculate the three components of statistical average of spin operators with Heisenberg model when the exchange interaction is anisotropic in z direction. By the use of many-body Green's function method, when external field is applied in both x and z directions, formalism for calculation of magnetization $〈{S}^{x}〉$ and $〈{S}^{z}〉$ are explicitly derived for spin value $S=1/2,$ 1, 3/2, 2, and 5/2. Based on the formalism, a general expression for calculation of $〈{S}^{z}〉$ for any spin value is suggested. Numerical analysis is presented for both cases of isotropic and anisotropic exchange interaction. The results of both three-dimensional and two-dimensional cases are discussed. Based on the numerical results, we suggest a method to test a film in experiments whether there is an ingredient of exchange anisotropy.
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