Directional Mode-Locking of Dynamics of Two-Dimensional Superparamagnetic Colloidal System in a Periodic Pinning Array

Using Langevin simulations,we study numerically the directional mode-locking of the dynamics of twodimensional superparamagnetic colloidal system in a periodic pinning array.When the colloidal particles are initially commensurate with the pinning sites,there appear mode-locking steps in the average velocity of colloidal particles along certain directions of the external driving force.With an increase in the pinning strength,the width of the step increases linearly but the velocity at the step decreases parabolically.