Dynamics of Multiferroic Domain Wall in Spin-Cycloidal Ferroelectric DyMnO$_{3}$

We report the dielectric dispersion of the giant magnetocapacitance (GMC) in multiferroic DyMnO$_{3}$ over a wide frequency range. The GMC is found to be attributable not to the softened electromagnon but to the electric-field-driven motion of multiferroic domain wall (DW). In contrast to conventional ferroelectric DWs, the present multiferroic DW motion holds extremely high relaxation rate of $\sim$$10^{7}$ s$^{-1}$ even at low temperatures. This mobile nature as well as the model simulation suggests that the multiferroic DW is not atomically thin as in ferroelectrics but thick, reflecting its magnetic origin.