Unconventional magnetic vortex structures observed in micromagnetic simulations

Very simple complex functions can give good approximate descriptions of two-dimensional magnetic vortex structures. By rotating all the spins of a common vortex by the same angle in the plane, abnormal vortex structures are obtained, which we term unconventional vortex structures. Compared to conventional vortices, unconventional vortices are usually not energetically favorable due to the generation of volume charges. Under certain circumstances, however, unconventional vortices can be formed in order to minimize the total energy of the system. In micromagnetic simulations, unconventional vortex structures are observed in two magnetic systems discussed in the paper: a cylindrical Permalloy disk with thickness much greater than the exchange length; and the crossing region of two perpendicular long, thin-film Permalloy wires