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In this paper, we study the stability of skyrmions (SKYs) caused by thegeometric confinement (GC) effect observed in nano-domains in recentexperiments, where SKYs appear only inside the boundary and is stable at thelow magnetic field region. However, the mechanism of the GC effect is unclearfor skyrmions. We numerically find that this effect is not observed in thestandard model, in which the Dzyaloshinskii-Moriya interaction (DMI) energy isdiscretized on lattice edges, while the effect is observed in a discrete modelwhere the DMI energy is defined on lattice volume elements. In the lattermodel, the DMI energy on the surfaces effectively becomes very small comparedwith that of the inside. From this observation, we study a model with zero DMIenergy on the surfaces parallel to the external magnetic field and find thatSKY is significantly stabilized in the sample in the low magnetic field region.

Effect of Geometric Confinement on the Stabilization of Skyrmions