Topological skyrmion dynamics driven by spin-transfer torque

Magnetic solitons can exist either as static (vortices, bubbles, skyrmions, etc.) or dynamical (droplets, vortex pair, etc.) states in both conservative and dissipative magnetic systems. In this paper, it is shown that a perpendicular spin current, in the presence of the Dzyaloshinskii Moriya interaction and strong perpendicular anisotropy, induces the rotation of the spins from the hedgehog like to the vortex like texture in the topological droplet state and excites low frequency topological modes. The topological character of these spin wave excitations results from the synchronized dynamics between the 360o rotation of the spin of the outer droplet domain and the expansion shrinking of the droplet core. A quantitative description of topological modes is given according to an analytical model based on the linearization of the equations of motion and is confirmed by micromagnetic simulations. The analytical approach shows directly how in the topological droplet state, dynamics is linked to topology. The definition of topological degeneracy permits to study in a more exhaustive way the dynamical properties of topological defects and, more generally, of physical systems having topological behaviour. The theoretical results could open the route for experiments based on the giant magnetoresistance effect able to detect the topological modes in magnetic solitons and for the design of a further generation of nanoscale microwave oscillators.