Figure 4

Vortex hopping between wells.

(a), Vortex trajectories in wells 1 to 6 (solid symbols) and hopping events between the wells shown schematically by dashed lines with a color matching the original well. The hopping between the wells results in hysteretic closed-loop trajectories that vary upon repeated cycles of the full loop and of the sub-loops. (b), The restoring force of the wells F_dc = −F_r(x) with the hopping events (dashed lines with a color matching the original well). The vortex jumps to the right (left) when a positive (negative) applied force exceeds the restoring force. The vortex stops at a position where the restoring force of the new well equals the applied force (dashed lines are horizontal). Well 6 exists only at positive forces and well 3 only at negative forces. The jumps to the right from well 3 to well 4 occur against the direction of the driving force when the value of the applied force drops below the minimum restoring force of well 3. (c), 2D potential due to a random distribution of defects, marked by ×, of equal U₀ = 0.66 eV and average density of 200 µm⁻². The stationary trajectories upon tilting the potential are shown by the solid lines and the dynamic escape trajectories by dashed lines with colors matching the source well. (e–j), Selected B_ac(x,y) images from a movie (S6) of the ac vortex response to F_ac = 93.1 fN ptp in different wells at the indicated values of F_dc. The gray scale spans 20 µT in all images.