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