Topological spin textures of antiskyrmionic crystals in two-dimensional magnetic monolayers

The topological textures of a two-dimensional (2D) magnetic monolayer, where ferromagnetic (FM) Heisenberg exchange (HE) and anisotropic Dzyaloshinskii-Moriya (DM) interactions coexist, are investigated with a quantum computational method. We find from our calculated results that when the external magnetic field, exerted perpendicularly to the 2D magnetic monolayer, is gradually increased, FM helical, antiskyrmionic and antivortical lattices (abbreviated as HL, ASL and AVL respectively), spin textures consisting of skyrmions and bimerons, and those of pure bimerons, are induced on the magnetic monolayer successively. The antiskyrmionic lattice states prevail over a broad area in the $T-H$ phase diagram, and the wavelengths of the ASLs and AVLs change discontinuously with the increasing external magnetic field. For comparison, two sets of formulas are used to calculate the topological charge $Q_{\mathrm{av}}$ per particle-like spin texture, and the topological charge density, ${\rho }_i$, over the monolayer. Consequently, the calculated ${\rho }_i$ contour of every ASL and AVL also forms periodical and symmetric crystals that coincides well with the corresponding spin texture, and divides the ASL or AVL into serval areas with distinct spin structures. For the ASL and spin textures consisting of skyrmions and bimerons, if the formulas of Berg and M. Lüscher (1981) are applied and every bimeron is treated as a skyrmion, the averaged $Q_{\mathrm{av}}$ per antiskyrmion and per bimeron are all equal to 1. We also explain why the quantum method is able to work beyond the classical ones.