  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.
