Skyrmion to ferromagnetic state transition: A description of the topological change as a finite-time singularity in the skyrmion dynamics

Abstract : We investigate the topological change in a Belavin-Polyakov skyrmion under the action of a spin-polarized current. The dynamics is described by the Schrödinger equation for the electrons carrying the current coupled to the Landau-Lifshitz equation for the evolution of the magnetic texture in a square lattice. We show that the addition of an exchange dissipation term tends to smooth the transition from the skyrmion state to the ferromagnetic state. We demonstrate that this topological change in the continuum dissipationless limit can be described as a self-similar finite-time singularity by which the skyrmion core collapses.