Size-dependent energy barriers of skyrmions governed by domain-wall scaling in disordered polycrystalline magnetic films

The stability of magnetic skyrmions in polycrystalline films is strongly influenced by disorder arising from grain structures, particularly through its impact on energy barriers between magnetic states. In this study, we systematically investigate the effects of intergrain exchange coupling and magnetic parameter distributions on skyrmion stability using micromagnetic simulations combined with the nudged elastic band method. We evaluate the energy barriers for skyrmion collapse, boundary annihilation, and nucleation processes, and clarify their dependence on intergrain exchange coupling. The results show that the energy barriers for both collapse and boundary annihilation increase as the intergrain exchange coupling decreases, whereas the nucleation barrier exhibits the opposite trend. Despite the different annihilation pathways, collapse and boundary annihilation exhibit nearly identical dependence on intergrain exchange coupling, with only a small difference in their absolute barrier heights. This behavior is explained by analyzing the energy landscape, where the reduction in the skyrmion-state energy is significantly larger than that in the saddle-point energy. As a result, the energy barrier increases primarily due to the stabilization of the skyrmion state rather than changes in the transition state. Furthermore, the energy barrier increases approximately linearly with the skyrmion diameter within the investigated range, reflecting a robust size-dependent scaling arising from the interplay of different energy contributions. Among the considered disorder sources, anisotropy-field variations have a much stronger impact than saturation magnetization variations. These findings provide a consistent understanding of disorder-induced modifications of skyrmion stability and offer practical insights for designing thermally stable skyrmions in realistic magnetic materials.