  Using a particle based model, we investigate the skyrmion dynamical behavior
in a channel where the upper wall contains divots of one depth and the lower
wall contains divots of a different depth. Under an applied driving force,
skyrmions in the channels move with a finite skyrmion Hall angle that deflects
them toward the upper wall for $-x$ direction driving and the lower wall for
$+x$ direction driving. When the upper divots have zero height, the skyrmions
are deflected against the flat upper wall for $-x$ direction driving and the
skyrmion velocity depends linearly on the drive. For $+x$ direction driving,
the skyrmions are pushed against the lower divots and become trapped, giving
reduced velocities and a nonlinear velocity-force response. When there are
shallow divots on the upper wall and deep divots on the lower wall, skyrmions
get trapped for both driving directions; however, due to the divot depth
difference, skyrmions move more easily under $-x$ direction driving, and become
strongly trapped for $+x$ direction driving. The preferred $-x$ direction
motion produces what we call a Magnus diode effect since it vanishes in the
limit of zero Magnus force, unlike the diode effects observed for asymmetric
sawtooth potentials. We show that the transport curves can exhibit a series of
jumps or dips, negative differential conductivity, and reentrant pinning due to
collective trapping events. We also discuss how our results relate to recent
continuum modeling on a similar skyrmion diode system.
