Relaxation dynamics of multiferroic domain walls in DyMnO₃ with cycloidal spin order

Dynamic responses of various types of spin-cycloidal domain walls (DWs) have been investigated for the multiferroic compound DyMnO₃ by the dielectric measurements. By exploiting the multiferroic nature of this material, we were able to drive the spin-cycloidal DWs by an electric field and hence elucidate the dynamics in terms of the frequency-dependent dielectric susceptibility. In the 103-109-Hz range, all types of DWs exhibit relaxation motion. In some DWs, the relaxation motion presents critical behavior near the first-order flop transition of the ferroelectric spin-cycloidal plane; that is, the dielectric constant is enhanced, and the dynamics slow down. The theory of DW relaxation ascribes this behavior to the growing Larkin length. This observation of the Larkin length along with generic considerations of DW widths and flop transitions implies that the critical behavior of DW relaxation is universal in materials that exhibit a flop transition, for example, of spin or polarization. Multiferroic compounds can thus provide an ideal laboratory for the study of magnetic DW dynamics.