Transient retrograde motion of spin wave driven skyrmions in magnetic nanotracks

The motion of a skyrmion driven by propagating spin waves in a thin film track with interfacial perpendicular magnetic anisotropy and Dzyaloshinskii-Moriya interaction was investigated by numerical micromagnetic simulations. At long simulation times, we find that the skyrmion always moves in the direction of the spin-wave propagation. At shorter times, rather than observing skyrmion motion in a single direction, the skyrmion shows transient retrograde motion when the track width is wider than 50 nm (for Gilbert damping $\ensuremath{\alpha}=0.02$) or $\ensuremath{\alpha}<0.06$ (for a track width of 100 nm). A simple treatment of spin-wave-driven skyrmion motion based on the Thiele equation predicts that the skyrmion will be pulled back towards the source of the spin waves because of the gyrotropic and dissipative effects. The forward motion away from the spin wave source can be explained by also considering the effect of a repulsive force from the edges of the track when the skyrmion is in close contact with it. We discuss these effects quantitatively in terms of the spin-wave transmission and reflection coefficients of the skyrmion.