Magnetic structure of high-order skyrmion number produced in a nanodisk via micromagnetic simulation with long-range dipole-dipole interaction

Numerical simulations have shown that skyrmion-like domains with a skyrmion number of 2 can deviate from the analytically predicted single-core form, especially in systems with long-range interactions; therefore, higher-order skyrmion states may also exhibit nontrivial and previously unreported structures. Exploring these configurations may provide new insights into the diversity of topological magnetic textures and the role of competing interactions in stabilizing complex spin structures. This study investigates the magnetic structures of skyrmion-like domains produced in a circular magnetic nanodisk based on the numerical simulations of the Landau-Lifshitz-Gilbert equation, including long-range dipole-dipole interactions. By initializing the domain wall with magnetic moments following different integer-winding patterns, stable magnetic states with high-order skyrmion numbers are obtained. For skyrmion numbers equal to or greater than positive 2, the relaxed states consistently exhibit a multicore structure consisting of a central core and several surrounding outer cores. These configurations resemble interconnected structures comprising multiple skyrmions and antiskyrmion-like domains. By contrast, for negative skyrmion numbers, the domain stabilizes into a simpler configuration with only a single inner core and no outer cores; this configuration closely resembles previously known analytical forms. The contrasting features between the states of the positive and negative skyrmion numbers can be explained by the orientation of the demagnetizing field in the domain generated by the domain wall. These findings indicate that controlling the transitions between these states would facilitate the development of skyrmion-number-based devices with multiple stable magnetic states.