Domain walls (DWs) in ferroic materials, across which the order parameter abruptly changes its orientation, can host emergent properties that are absent in the bulk domains. Using a broadband ($10^6-10^{10}$ Hz) scanning impedance microscope, we show that the electrical response of the interlocked antiphase boundaries and ferroelectric domain walls in hexagonal rare-earth manganites ($h-RMnO_3$) is dominated by the bound-charge oscillation rather than free-carrier conduction at the DWs. As a measure of the rate of energy dissipation, the effective conductivity of DWs on the (001) surfaces of $h-RMnO_3$ at GHz frequencies is drastically higher than that at dc, while the effect is absent on surfaces with in-plane polarized domains. First-principles and model calculations indicate that the frequency range and selection rules are consistent with the periodic sliding of the DW around its equilibrium position. This acoustic-wave-like mode, which is associated with the synchronized oscillation of local polarization and apical oxygen atoms, is localized perpendicular to the DW but free to propagate along the DW plane. Our results break the ground to understand structural DW dynamics and exploit new interfacial phenomena for novel devices.
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