Large amplitude vortex gyration in Permalloy/Bi$_2$Se$_3$-like heterostructures

We consider the excitation of large amplitude gyrotropic vortex core precession in a Permalloy nanodisk by the torques originating from the in-plane microwave current flowing along the interface of the Permalloy/Bi$_2$Se$_3$ heterostructures, in which the huge charge-to-spin conversion ratio is observed cite{Mellnik-2014}. We consider analytically and by micromagnetic modelling the dependence of this excitation on the frequency and magnitude of the microwave current. The analogies of the vortex dynamics and the Landau phase transitions theory is demonstrated. These findings open the possibility to excite gyrotropic vortex motion with the current densities far lower than by any other means.