Vortex core reversal in magnetic particle is essentially influenced by a surface anisotropy. Under the action of a perpendicular static magnetic field the vortex core undergoes a shape deformation of pillow- or barrel-shaped type, depending on the type of the surface anisotropy. This deformation plays a key point in the switching mechanism: we predict that the vortex polarity switching is accompanied by a linear singularity in case of Heisenberg magnet with bulk anisotropy only and by a point singularities in case of surface anisotropy or exchange anisotropy. We study in details the switching process using spin-lattice simulations and propose a simple analytical description using a wired core model, which provides an adequate description of the Bloch point statics, its dynamics and the Bloch point mediated switching process. Our analytical predictions are confirmed by spin-lattice simulations for Heisenberg magnet and micromagnetic simulations for nanomagnet with account of a dipolar interaction.

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