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We numerically study the stability and morphology of geometrically confined skyrmions in nanodots using Finsler geometry (FG) modeling technique. The FG model dynamically implements anisotropies in ferromagnetic interaction, Dzyaloshinskii-Moriya interaction, and magneto-elastic coupling in response to mechanical stresses. Without the stresses, there exists a geometrically confined effect originating from the surface effect of small nanodots, in which skyrmions are stabilized under a low external magnetic field. This surface effect is enhanced by radial stresses, which significantly reduce the surface DMI compared to the bulk DMI. The radial stresses also alter the interactions to be anisotropic. Owing to these position- and direction-dependent interactions, incomplete skyrmions emerge at the center of the nanodots under the tensile stress. In addition to the incomplete skyrmions, target skyrmions are observed under the compressive stress. Our numerical results indicate that the strain-enhanced surface effect and the strain-induced interaction anisotropies suitably explain the skyrmion stability in nanodots with zero magnetic field., Comment: 38 page, 14 figures

Geometric confinement (GC) of skyrmions in nanodomains plays a crucial role in skyrmion stabilization. This confinement effect decreases the magnetic field necessary for skyrmion formation and is closely related to the applied mechanical stresses. However, the mechanism of GC is unclear and remains controversial. Here, we numerically study the effect of GC on skyrmion stabilization and find that zero Dzyaloshinskii-Moriya interaction (DMI) coupling constants imposed on the boundary surfaces of small thin plates cause confinement effects, stabilizing skyrmions in the low-field region. Moreover, the confined skyrmions are further stabilized by tensile strains parallel to the plate, and the skyrmion phase extends to the low-temperature region. This stabilization occurs due to the bulk anisotropic DMI coupling constant caused by lattice deformations. Our simulation data are qualitatively consistent with reported experimental data on skyrmion stabilization induced by tensile strains applied to a thin plate of the chiral magnet ${\rm Cu_2OSeO_3}$., Comment: 33 pages, 16 figures

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., Comment: 6 pages, 5 figures