Néel-type antiferromagnetic skyrmionic crystals on two-dimensional square lattices investigated with optimized quantum Monte Carlo method

Abstract

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. • Optimized Monte Carlo simulating method is described and applied here. • Results obtained in last loop can produce symmetric and periodical spin textures. • AF skyrmion crystals are generated in 2D square lattices with the method. • Each AF skyrmion crystal can be decomposed into two identical FM sub-lattices. • The topological charge density forms lattice almost identical with the spin texture.