A sum rule of uniaxial anisotropy and external magnetic field for formation of Neel-type skyrmion lattices in two-dimensional ferromagnets

It is generally believed that the perpendicular magnetic anisotropy (PMA) plays an important role in stabilizing skyrmion lattices (SkL) in two-dimensional (2D) magnetic systems in which both Heisenberg exchange and Dzyaloshinskii-Moriya interactions co-exist, and the skyrmion sizes in SkLs are mainly determined by the strengths of these two intrinsic interactions. To investigate the details, we employ here a quantum computational approach we develop in recent years to simulate the Neel-type skyrmion lattices formed on a 2D PdFe/Ir(111)-like film. From our simulated results, we find that: within an external magnetic field applied normal to the film plane, the PMA is indeed able to help induce Neel-type SkLs in a wider field range; however, to stabilize the SkLs, the PMA cannot be too strong, the strengths of the external magnetic field and the maximal PMA must satisfy a sum rule since the effective perpendicular magnetic field generated by these two interactions cannot exceed a largest value. We also notice that the periodical boundary condition imposed on the FM system in simulations is able to facilitate SkL formations, and it can also modify the skyrmion size in a certain extend.