Our aim of this work is to study the magnetic properties of a bi-layer borophene structure, using Monte Carlo simulations under the Metropolis algorithm. Such a system is formed by two layers. The first one contains 126 atoms with spin σ = ± 3/2, ± 1/2 and 84 atoms with spins S = ± 1, 0 while the second one contains 84 atoms with spin σ = ± 3/2, ± 1/2 and 126 atoms with spins S = ± 1, 0. We establish, in various planes, the ground-state phase diagrams. Furthermore, we present the thermal variation of the total magnetization and total susceptibility for several values of exchange coupling interactions and crystal field. It is found that the increase in both exchange coupling interactions leads to an almost linear increase in transition temperature in one hand and, on the other hand, to a decrease in the corresponding crystal field transition.

中文翻译：

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具有混合自旋的双层硼烯结构的磁性：蒙特卡罗研究

我们这项工作的目的是在 Metropolis 算法下使用蒙特卡罗模拟研究双层硼烯结构的磁性。这样的系统由两层构成。第一个包含 126 个自旋 σ = ± 3/2, ± 1/2 的原子和 84 个自旋 S = ± 1, 0 的原子，而第二个包含 84 个自旋 σ = ± 3/2, ± 1/2 的原子和 126 个自旋 S = ± 1, 0 的原子。我们在不同的平面上建立了基态相图。此外，我们展示了交换耦合相互作用和晶体场的几个值的总磁化强度和总磁化率的热变化。发现两种交换耦合相互作用的增加一方面导致转变温度几乎线性增加，另一方面导致相应晶场转变的减少。