Calculations of the cubic models of two solid solutions LaGa_0.5Fe_0.5O₃ and LaAl_0.5Fe_0.5O₃ have been performed within the hybrid density functional theory. Multiple configurations have been considered for the solid solutions resulting from a different distribution of Fe atoms over the p-metal (Ga or Al) positions accounting for different spin orientation for Fe atoms themselves. It was demonstrated that 27 structures for both LaGa_0.5Fe_0.5O₃ and LaAl_0.5Fe_0.5O₃ should be treated to account for all the possible configurations in case of cubic 2 × 2 × 2 supercell. Optimized geometry, energy, and electron properties were calculated for all the obtained configurations_. Statistical weights and probabilities were estimated for each symmetry non-equivalent configuration of the solid solutions within the canonical ensemble. A new parameterization for the dilute Ising model has been proposed. In this model, we account for non-magnetic contributions, which are absent in the simple Ising model, using the lattice approach based on the concept of interchange energy. Two model parameters (the magnetic coupling constant and interchange energy) were fitted to the calculated total energies of all considered configurations of both solid solutions. The dilute Ising model confirmed the benefit of Fe-clustering in doped lanthanum gallate against aluminate. Different signs of the estimated interchange energy enable us to explain the reasons for such differences.

在混合密度泛函理论中，已经对两种固溶体LaGa _0.5 Fe _0.5 O ₃和LaAl _0.5 Fe _0.5 O ₃的立方模型进行了计算。对于固溶体已经考虑了多种构型，这是由于Fe原子在p-金属（Ga或Al）位置上的分布不同而造成的，这说明了Fe原子本身的自旋取向不同。已证明LaGa _0.5 Fe _0.5 O ₃和LaAl _0.5 Fe _0.5 O _3的27种结构在立方2×2×2超级电池的情况下，应考虑所有可能的配置。针对所有获得的构型，计算出最佳的几何形状，能量和电子性质_。对规范集合内固溶体的每个对称非等价构型，估计统计权重和概率。提出了一种针对稀伊辛模型的新参数化方法。在此模型中，我们使用基于交换能量概念的晶格方法来解决简单的Ising模型中不存在的非磁性影响。将两个模型参数（磁耦合常数和交换能量）拟合到两种固溶体所有考虑构型的计算总能量。稀的Ising模型证实了Fe簇合物在掺杂的没食子酸镧中对抗铝酸盐的好处。估计交换能量的不同符号使我们能够解释这种差异的原因。