  We examine skyrmions driven periodically over random quenched disorder and
show that there is a transition from reversible motion to a state in which the
skyrmion trajectories are chaotic or irreversible. We find that the
characteristic time required for the system to organize into a steady
reversible or irreversible state exhibits a power law divergence near a
critical ac drive period, with the same exponent as that observed for
reversible to irreversible transitions in periodically sheared colloidal
systems, suggesting that the transition can be described as an absorbing phase
transition in the directed percolation universality class. We compare our
results to the behavior of an overdamped system and show that the Magnus term
enhances the irreversible behavior by increasing the number of dynamically
accessible orbits. We discuss the implications of this work for skyrmion
applications involving the long time repeatable dynamics of dense skyrmion
arrays.
