The formations of individual antiferromagnetic (AF) skyrmions and AF skyrmionic lattices on two-dimensional (2D) magnets with square crystal structure are debatable in recent years, for only an isolated skyrmion can be generated in such systems if classical Monte Carlo (CMC) method is employed. For the sake, we apply here an optimized quantum Monte Carlo approach to a 2D square magnet where the AF Heisenberg exchange (HE) and Dzyaloshinskii–Moriya (DM) interactions co-exist. Consequently, the computing program converges to the equilibrium states with appreciable computational speed, and the results obtained in the last one iteration are able to accurately produce well symmetric and periodic AF skyrmionic lattices (SLs) at elevated temperatures when a considerably strong external magnetic field is exerted perpendicular to the 2D monolayer. Moreover, each of these AF SLs can be decomposed into two almost identical ferromagnetic (FM) SLs, and the distribution of topological charge density also forms symmetric lattice with the same periodicity as the AF SL, dividing the AF SL into several areas of distinct spin configurations. The reasons why the OQMC approach can work beyond CMC method are explained in the Discussion Section.

近年来，在具有方形晶体结构的二维 (2D) 磁体上形成单个反铁磁 (AF) 斯格明子和 AF 斯格明子晶格是有争议的，因为如果经典蒙特卡罗 (CMC) 方法，在此类系统中只能生成孤立的斯格明子受雇。为此，我们将优化的量子蒙特卡罗方法应用于 2D 方形磁铁，其中 AF 海森堡交换 (HE) 和 Dzyaloshinskii-Moriya (DM) 相互作用共存。因此，计算程序以可观的计算速度收敛到平衡状态，并且在最后一次迭代中获得的结果能够在相当强的外部磁场的情况下在升高的温度下准确地产生对称和周期性的 AF Skyrmionic 晶格（SLs）垂直于二维单层施加。而且，这些 AF SL 中的每一个都可以分解为两个几乎相同的铁磁 (FM) SL，并且拓扑电荷密度的分布也形成了与 AF SL 具有相同周期性的对称晶格，将 AF SL 分为几个不同自旋配置的区域。讨论部分解释了 OQMC 方法可以超越 CMC 方法的原因。