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We examine the dynamics of an individually driven skyrmion moving through abackground lattice of skyrmions coupled to a 2D periodic substrate as we varythe ratio of the number of skyrmions to the number of pinning sites acrosscommensurate and incommensurate conditions. As the skyrmion density increases,the skyrmion Hall angle is nonmonotonic, dropping to low or zero values incommensurate states and rising to an enhanced value in incommensurate states.Under commensuration, the driven skyrmion is channeled by a symmetry directionof the pinning array and exhibits an increased velocity. The velocityfluctuations have a narrow band signature at fillings where the skyrmion Hallangle is zero, while for incommensurate fillings, the skyrmion motion isdisordered and the velocity noise is broad band. Under commensurate conditions,multi-step depinning transitions appear and the skyrmion Hall angle is zero atlow drives but becomes finite at higher drives, while incommensurate fillingshave a single depinning transition. As the Magnus force increases,commensuration velocity peaks cross over to dips, and new directional lockingangles appear. At large Magnus forces, particularly at commensurate fillings, avelocity boost can occur in which the skyrmion moves faster than the applieddrive due to the alignment of the Magnus-induced velocity with the drivingdirection. Increase the Magnus force can produce regimes of enhanced pinningwhen the skyrmion is forced to move along a non-symmetry direction of theperiodic pinning array. This is in contrast to systems with random pinning,where increasing the Magnus force generally reduces the pinning effect. Wedemonstrate these dynamics for both square and triangular substrates, and mapout the different regimes as a function of filling fraction, pinning force, andthe strength of the Magnus force in a series of dynamic phase diagrams.

Commensuration Effects on Skyrmion Hall Angle and Drag for Manipulation of Skyrmions on Two-Dimensional Periodic Substrates