Compared with ferromagnetic counterparts, antiferromagnetic materials are considered as the future of spintronic applications since these materials are robust against the magnetic perturbation, produce no stray field, and display ultrafast dynamics. There are (at least) two sets of magnetic moments in antiferromagnets (AFMs) (with magnetization of the same magnitude but antiparallel directions) and ferrimagnets (with the magnetization of the different magnitude). The coupled dynamics of the bipartite collinear AFMs is modeled by a coupled system of Landau–Lifshitz–Gilbert equations with additional terms originated from the interlattice exchange, which leads to femtosecond magnetization dynamics in AFMs. In this article, we develop three Gauss–Seidel projection methods for micromagnetics simulation in AFMs and ferrimagnets. They are first-order accurate in time and second-order accurate in space, and only solve linear systems of equations with constant coefficients at each step. Femtosecond dynamics, Néel wall structure, and phase transition in the presence of an external magnetic field for AFMs are provided with the femtosecond stepsize.

中文翻译：

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反铁磁体的数值方法

与铁磁对应物相比，反铁磁材料被认为是自旋电子应用的未来，因为这些材料抗磁扰动、不产生杂散场并显示超快动力学。在反铁磁体 (AFM)（磁化强度相同但方向反平行）和亚铁磁体（磁化强度不同）中（至少）有两组磁矩。二分共线 AFM 的耦合动力学由 Landau-Lifshitz-Gilbert 方程的耦合系统建模，附加项源自晶格间交换，这导致 AFM 中的飞秒磁化动力学。在本文中，我们开发了三种 Gauss-Seidel 投影方法，用于 AFM 和亚铁磁体中的微磁模拟。它们在时间上一阶精确，在空间上二阶精确，并且每一步只求解具有常系数的线性方程组。飞秒动态、Néel 壁结构和 AFM 在外部磁场存在下的相变具有飞秒步长。