Modelling of toroidal moment switching and dynamics in ferromagnetic nanorings

Switching between right and left vortex magnetization states in annular ferromagnetic nanostructures, was studied. The study was performed by numerically solving the modified Landau-Lifshitz equation with consideration of the effect of spin transfer and full-scale consideration of the magnetostatic field, exchange energy, and anisotropy energy. The dynamics of magnetization reversal of the ferromagnetic nanoring, caused by the electric current flowing perpendicularly to the object plane and penetrating the structure, was studied taking into account two mechanisms of the current effect on magnetization: by the Oersted field and spin transfer. It was found that the presence of the spin polarization both perpendicular and parallel to the nanoring plane decreases the critical current at which the object is switched by an order of magnitude. It was shown that the toroidal moment \(\vec T\) is a convenient characteristic for describing magnetization reversal processes in annular magnetic nanostructures.