  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 deformationof 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 (i) by a linear singularity in case of Heisenberg magnet with
bulk anisotropy only and (ii) 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.
