Numerical simulation of two-dimensional magnetic skyrmion structures

Magnetic systems, in which due to competition between the direct Heisenberg exchange and the Dzyaloshinskii–Moriya interaction, magnetic vortex structures — skyrmions appear, were studied using the Metropolis algorithm.
The conditions for the nucleation and stable existence of magnetic skyrmions in two-dimensional magnetic films in the frame of the classical Heisenberg model were considered in the article. A thermal stability of skyrmions in a magnetic film was studied. The processes of the formation of various states in the system at different values of external magnetic fields were considered, various phases into which the Heisenberg spin system passes were recognized. The authors identified seven phases: paramagnetic, spiral, labyrinth, spiral-skyrmion, skyrmion, skyrmion-ferromagnetic and ferromagnetic phases, a detailed analysis of the configurations is given in the article.
Two phase diagrams were plotted: the first diagram shows the behavior of the system at a constant $D$ depending on the values of the external magnetic field and temperature $(T, B)$, the second one shows the change of the system configurations at a constant temperature $T$ depending on the magnitude of the Dzyaloshinskii–Moriya interaction and external magnetic field: $(D, B)$.
The data from these numerical experiments will be used in further studies to determine the model parameters of the system for the formation of a stable skyrmion state and to develop methods for controlling skyrmions in a magnetic film.