Effect of Geometric Confinement on the Stabilization of Skyrmions

In this paper, we study the stability of skyrmions (SKYs) caused by the geometric confinement (GC) effect observed in nano-domains in recent experiments, where SKYs appear only inside the boundary and is stable at the low magnetic field region. However, the mechanism of the GC effect is unclear for skyrmions. We numerically find that this effect is not observed in the standard model, in which the Dzyaloshinskii-Moriya interaction (DMI) energy is discretized on lattice edges, while the effect is observed in a discrete model where the DMI energy is defined on lattice volume elements. In the latter model, the DMI energy on the surfaces effectively becomes very small compared with that of the inside. From this observation, we study a model with zero DMI energy on the surfaces parallel to the external magnetic field and find that SKY is significantly stabilized in the sample in the low magnetic field region.