The Problem of Measuring Topological Charge on a Discrete Triangular Lattice

In this paper we propose the improved method for calculating topological charge of skyrmions on a discrete triangular magnetic lattice that is based on a 56× scaling up of lattice density with bilinear interpolation. We use this method to map the phase diagram of a magnetic monolayer with a triangular lattice and planar Dzyaloshinskii–Moriya interaction using local relaxation method and analyze the dependence of skyrmion density on the external magnetic field and the parameter of Dzyaloshinskii–Moriya. We also study the thermal stability of a skyrmion lattice and skyrmion gas based on a behavior of a topological charge using Monte Carlo simulation in 5 relevant cases: skyrmion gas and 4 skyrmion lattices of different skyrmion density.