Magnetization structure of a Bloch point singularity

Switching of magnetic vortex cores involves a topological transition characterized by the presence of a magnetization singularity, a point where the magnetization vanishes (Bloch point). We analytically derive the shape of the Bloch point that is an extremum of the free energy with exchange, dipolar and Landau terms. From a one parameter family of solutions, two types of singularities are distinguished, a radial one (hedgehog) corresponding to a local energy maximum, and a twisted one corresponding to a local energy minimum. Micromagnetic simulations show that the hedgehog magnetization naturally evolves to a twisted one if the size of the ferromagnet is much larger than the exchange length.