Abstract The Pair Approximation method has been formulated for the isotropic ferromagnetic Heisenberg model with spin S = 1 . The exchange interactions of arbitrary range have been taken into account. The single-ion anisotropy has been considered as well as the external magnetic field. Within the method, the Gibbs free-energy has been derived, from which all thermodynamic properties can be self-consistently obtained. In order to illustrate the developed formalism, the numerical calculations have been performed for CrIAs planar magnetic semiconductor, a hypothetical material whose existence has been recently predicted by the Density Functional Theory-based calculations. For this model material, all the relevant thermodynamic magnetic properties have been studied. The numerical results have been presented in the figures and discussed.

中文翻译：

---

自旋 S=1 和任意相互作用范围的铁磁 Heisenberg 模型的 Pair Approximation 方法。磁性半导体CrIA的应用

摘要 对自旋 S = 1 的各向同性铁磁海森堡模型建立了对近似方法。考虑了任意范围的交换相互作用。已经考虑了单离子各向异性以及外部磁场。在该方法中，已经导出吉布斯自由能，从中可以自洽地获得所有热力学性质。为了说明发展的形式，已经对 CrIAs 平面磁性半导体进行了数值计算，这是一种假设材料，最近通过基于密度泛函理论的计算预测了其存在。对于这种模型材料，已经研究了所有相关的热力学磁性。数值结果已在图中呈现并进行了讨论。