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 whic
h 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.
We investigate analytically and numerically the synchronization dynamics of dipolarly coupled vortex based Spin-Torque Nano Oscillators (STNO) with different pillar diameters. We identify the critical interpillar distances on which synchronization oc
curs as a function of their diameter mismatch. We obtain numerically a phase diagram showing the transition between unsynchronized and synchronized states and compare it to analytical predictions we make using Thiele approach. Our study demonstrates that for relatively small diameters differences the synchronization dynamics can be described qualitatively using Adler equation. However when the diameters difference increases significantly, the system becomes strongly non-Adlerian.
Phase locking dynamics of dipolarly coupled vortices excited by spin-polarized current in two identical nanopillars is studied as a function of the interpillar distance L. Numerical study and analytical model have proved the remarkable efficiency of
magneto-static interaction to achieve phase locking. Investigating the dynamics in the transient regime towards phase locking, we extract the evolution of the locking time tau, the coupling strength {mu} and the interaction energy W. Finally, we compare this coupling energy with the one obtained by simple model.
