  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.
