Formation mechanism and energy interaction of spontaneous skyrmion in nanodisks

•Phase diagram of magnetic moment distribution under different intrinsic properties.•Eani, Eex, Ed account for 40~80%, 10~20%, 10~40% of Etot when skyrmions are formed.•Spontaneous skyrmion equilibrium states can exist generally in certain materials.•Various domain structures can be controlled by adjusting the material parameters. Topological spin textures, such as magnetic skyrmion, have great promises in data storage applications due to their inherent stability. Contrary to the general idea, simulation results here indicate that spontaneous skyrmion equilibrium states can exist generally in certain materials without the assistance of Dzyaloshinskii-Moriya interaction, external fields or defects. The spin configurations are closely related to the variations of the magnetocrystalline anisotropy K1, exchange interaction A, and saturation magnetization MS. The system with low anisotropy is conducive to the formation of vortex, while a single domain can be formed in the large range of K1 and A in the system with small MS. Landau-Lifshitz-Gilbert equation is used to investigate the variations of different interaction energies in the formation of topological domains. In the range where skyrmions are formed, the anisotropic energy, exchange energy and demagnetization energy account for 40 ~ 80%, 10 ~ 20%, 10 ~ 40% of the total energy. Meanwhile, a phase diagram of equilibrium magnetic moment distribution under different intrinsic properties is obtained. The K1, A and MS values of skyrmions range from 1.6 ~ 2.5 × 105 J/m3, 1.6 ~ 6.8 × 10-12 J/m, and 7.1 ~ 8.8 × 105 A/m in this simulation. By adjusting the material parameters, various competing interactions in magnetic nanostructures can be controlled to form skyrmion textures, which provide important insights for understanding the formation mechanism of nontrivial topological domains.