  Using a particle-based model, we examine the collective dynamics of skyrmions
interacting with a funnel potential under dc driving as the skyrmion density
and relative strength of the Magnus and damping terms are varied. For driving
in the easy direction, we find that increasing the skyrmion density reduces the
average skyrmion velocity due to jamming of skyrmions near the funnel opening,
while the Magnus force causes skyrmions to accumulate on one side of the funnel
array. For driving in the hard direction, there is a critical skyrmion density
below which the skyrmions become trapped. Above this critical value, a clogging
effect appears with multiple depinning and repinning states where the skyrmions
can rearrange into different clogged configurations, while at higher drives,
the velocity-force curves become continuous. When skyrmions pile up near the
funnel opening, the effective size of the opening is reduced and the passage of
other skyrmions is blocked by the repulsive skyrmion-skyrmion interactions. We
observe a strong diode effect in which the critical depinning force is higher
and the velocity response is smaller for hard direction driving. As the ratio
of Magnus force to dissipative term is varied, the skyrmion velocity varies in
a non-linear and non-monotonic way due to the pile up of skyrmions on one side
of the funnels. At high Magnus forces, the clogging effect for hard direction
driving is diminished.
