Wiggling skyrmion propagation under parametric pumping.

We address the problem of how magnetic skyrmions can propagate along a guided direction by parametric pumping. As evidenced by our micromagnetic simulations, skyrmions can hardly be driven by either a static electric field or a static magnetic field alone. Although the magnetic anisotropy can be modified by an electric field, parametric pumping with an oscillating electric field can only excite the breathing modes. On the other hand, a static magnetic field can break rotational symmetry through the Zeeman interaction, but it cannot serve as an energy source for propelling a skyrmion. Here we found that the combination of a perpendicularly oscillating electric field and an in-plane static magnetic field can drive a skyrmion undergoing a wiggling motion along a well defined trajectory. The most efficient driving occurs when the frequency of the oscillating field is close to that of the breathing motion. The physics is revealed in a generalized Thiele equation where a net spin current excited by the parametric pumping can drive the skyrmion propagation through angular momentum transfer. Compared with other alternative proposals, our results open new possibilities for manipulating skyrmions in both metals and insulators with low-power consumption. The oscillating skyrmion motion can also be a microwave generator for future spintronic applications such as an nano-tool on a diamond Nitrogen-Vacancy center.