Dynamic ordering and frustration of confined vortex rows studied by mode-locking experiments

The flow properties of confined vortex matter driven through disordered mesoscopic channels are investigated by mode locking (ML) experiments. The observed ML effects allow us to trace the evolution of both the structure and the number of confined rows and their match to the channel width as function of magnetic field. From a detailed analysis of the ML behavior for the case of three rows we obtain (i) the pinning frequency $f_p,$ (ii) the onset frequency $f_c$ for ML $(\propto$ ordering velocity), and (iii) the fraction $L_{\mathrm{ML}}/L$ of coherently moving three-row regions in the channel. The field dependence of these quantities shows that, at matching, where $L_{\mathrm{ML}}$ is maximum, the pinning strength is small and the ordering velocity is low, while at mismatch, where $L_{\mathrm{ML}}$ is small, both the pinning force and the ordering velocity are enhanced. Further, we find that $f_c\propto f_p^2,$ consistent with the dynamic ordering theory of Koshelev and Vinokur. The microscopic nature of the flow and the ordering phenomena will also be discussed.