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Curvature effects are important for a proper description of the properties ofmagnetic systems. In this paper the exchange and dipolar energy of vortices ona paraboloidal shell is studied. Using analytical calculations it is shown thatthe in-plane component of vortices has larger energy on a paraboloidal shellthan in a planar disk with same thickness. On the other hand, the dipolarenergy associated to the vortex core diminishes if the vortex core is on aparaboloidal surface. This reduction in the dipolar energy may cause a vortexpinning mechanism by a paraboloidal shaped defect in a planar nanomagnet.Regarding skyrmions, by using an in-plane anisotropy approximation to thedipolar energy, it is shown that the skyrmion must have its width shrunk inorder to diminishes the magnetostatic energy and satisfy geometricalconstraints of the system.

Curvature-induced changes in the magnetic energy of vortices and skyrmions in paraboloidal nanoparticles