  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.
