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Geometric curvature of nanoscale magnetic shells brings aboutcurvature-induced anisotropy and Dzyaloshinskii-Moriya interaction (DMI). Here,we derive equations to describe the profile of the magnetic vortex state in aspherical cap. We demonstrate that the azimuthal component of magnetizationacquires a finite tilt at the edge of the cap, which results in the increase ofthe magnetic surface energy. This is different compared to the case of a closedspherical shell, where symmetry of the texture does not allow any tilt ofmagnetization at the equator of the sphere. Furthermore, we analyze the size ofthe vortex core in a spherical cap and show that the presence of thecurvature-induced DMI leads to the increase of the core size independent of theproduct of the circulation and polarity of the vortex. This is in contrast tothe case of planar disks with intrinsic DMI, where the preferred direction ofcirculation as well as the decrease or increase of the size of vortex core isdetermined by the sign of the product of the circulation and polarity withrespect to the sign of the constant of the intrinsic DMI.

Impact of curvature-induced Dzyaloshinskii-Moriya interaction on magnetic vortex texture in spherical caps