  Using a particle-based model, we simulate the behavior of a skyrmion under
the influence of asymmetric funnel geometries and ac driving at zero
temperature. We specifically investigate possibilities for controlling the
skyrmion motion by harnessing a ratchet effect. Our results show that as the
amplitude of a unidirectional ac drive is increased, the skyrmion can be set
into motion along either the easy or hard direction of the funnel depending on
the ac driving direction. When the ac drive is parallel to the funnel axis, the
skyrmion flows in the easy direction and its average velocity is quantized. In
contrast, when the ac drive is perpendicular to the funnel axis, a
Magnus-induced ratchet effect occurs, and the skyrmion moves along the hard
direction with a constant average velocity. For biharmonic ac driving of equal
amplitude along both the parallel and perpendicular directions, we observe a
reentrant pinning phase where the skyrmion ratchet vanishes. For asymmetric
biharmonic ac drives, the skyrmion exhibits a combination of effects and can
move in either the easy or hard direction depending on the configuration of the
ac drives. These results indicate that it is possible to achieve controlled
skyrmion motion using funnel geometries, and we discuss ways in which this
could be harnessed to perform data transfer operations.
