Directional locking and the influence of obstacle density on skyrmion dynamics in triangular and honeycomb arrays

We numerically examine the dynamics of a single skyrmion driven over triangular and honeycomb obstacle arrays at zero temperature. The skyrmion Hall angle theta (sk), defined as the angle between the applied external drive and the direction of the skyrmion motion, increases in quantized steps or continuously as a function of the applied drive. For the obstacle arrays studied in this work, the skyrmion exhibits two main directional locking angles of theta (sk) = -30 degrees and -60 degrees. We show that these directions are privileged due to the obstacle landscape symmetry, and coincide with channels along which the skyrmion may move with few or no obstacle collisions. Here we investigate how changes in the obstacle density can modify the skyrmion Hall angles and cause some dynamic phases to appear or grow while other phases vanish. This interesting behavior can be used to guide skyrmions along designated trajectories via regions with different obstacle densities. For fixed obstacle densities, we investigate the evolution of the locked theta (sk) = -30 degrees and -60 degrees phases as a function of the Magnus force, and discuss possibilities for switching between these phases using topological selection.