  We show that ac driven skyrmions interacting with an asymmetric substrate
provide a realization of a new class of ratchet system which we call a vector
ratchet that arises due to the effect of the Magnus term on the skyrmion
dynamics. In a vector ratchet, the dc motion induced by the ac drive can be
described as a vector that can be rotated clockwise or counterclockwise
relative to the substrate asymmetry direction. Up to a full $360^{\circ}$
rotation is possible for varied ac amplitudes or skyrmion densities. In
contrast to overdamped systems, in which ratchet motion is always parallel to
the substrate asymmetry direction, vector ratchets allow the ratchet motion to
be in any direction relative to the substrate asymmetry. It is also possible to
obtain a reversal in the direction of rotation of the vector ratchet,
permitting the creation of a reversible vector ratchet. We examine vector
ratchets for ac drives applied parallel or perpendicular to the substrate
asymmetry direction, and show that reverse ratchet motion can be produced by
collective effects. No reversals occur for an isolated skyrmion on an
asymmetric substrate. Since a vector ratchet can produce motion in any
direction, it could represent a new method for controlling skyrmion motion for
spintronic applications.
