Interference mode-locking of 2D magnetized colloids driven by dc and ac forces in periodic pinning arrays

Using the Langevin simulation, we investigate the interference mode-locking of two-dimensional (2D) magnetized colloids on a substrate with periodic pinning centers. The colloidal particles are prepared initially in a 2D crystalline state and then driven simultaneously by direct-current (dc) and alternating-current (ac) forces. In the presence of a superimposed ac force, we find pronounced mode-locking steps in the characteristics of the averaged velocity versus dc force within a certain range of amplitude and frequency of the ac force. The mode-locking steps are attributed to an interference effect between the ac force and the modulation generated by the coherent motion of colloidal particles in a weak pinning potential. The step width Δfdc is found to oscillate in a Bessel function-like form with the amplitude of the ac force, in good agreement with previous results of vortex lattices. But, we find that Δfdc changes in an inverted parabola form with the frequency of the ac force and the substrate pinning strength as well as the interaction strength between colloidal particles. The averaged velocity at the step vstep is shown to increase linearly with the frequency of the ac force and the interaction strength between colloidal particles. The obtained results are helpful for fractionation of mesoscopic particles.