Dynamics of Multiferroic Domain Wall in Spin-Cycloidal Ferroelectric ${\mathrm{DyMnO}}_3$

We report the dielectric dispersion of the giant magnetocapacitance (GMC) in multiferroic ${\mathrm{DyMnO}}_3$ 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 an extremely high relaxation rate of $\sim {10}^7{\mathrm{s}}^{-1}$ 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.

Figure 1

(a) Crystal structure of ${\mathrm{DyMnO}}_3$. (b) and (c) Magnetic structures of $bc$-cycloidal spin order (b) and $ab$-cycloidal spin order (c). (d) Magnetic-field-temperature phase diagram of ${\mathrm{DyMnO}}_3$ for the case of $\mathit{H}\parallel b$. The phase boundaries were determined from the dielectric measurements. The closed squares and circles represent the transition points in increasing and decreasing field processes, respectively. (e) Magnetic-field dependence ($\mathit{H}\parallel b$) of polarization at 10 K along the $c$ axis ($\mathit{P}\parallel c$) and the $a$ axis ($\mathit{P}\parallel a$). (f) Magnetic-field dependence ($\mathit{H}\parallel b$) of dielectric constant at 10 K along the $a$ axis at various frequencies.

Figure 2

(a) and (b) Spectra of dielectric constant at 10 K under various magnetic fields: real part (a) and imaginary part (b). (c) and (d) Magnetic-field dependence of the magnitude of the relaxation mode (c) and the relaxation rate (d) at given temperatures. Inset in (d): Temperature dependence of the relaxation rate at the flop transition, $1/{\tau }_c$ (double logarithmic plot). The solid line is a guide to the eye.

Figure 3

(a) Various multiferroic DWs conceivable in ${\mathrm{DyMnO}}_3$. The red lines represent the DW through which both the spin helicity (${\mathit{S}}_i\times {\mathit{S}}_j$) and the polarization ($P$) are reversed, while the blue lines represent the DW through which they rotate by 90°. (b) Initial $P\mathrm{\text{−}}E$ curves ($\mathit{E}\parallel a$) under various magnetic fields at 5 K, demonstrating electric-field-induced movement of multiferroic DW between the $\mathit{P}\parallel c$ ($bc$-cycloidal) and the $\mathit{P}\parallel a$ ($ab$-cycloidal) domains.

Figure 4

Calculated DW structure between the $\mathit{P}\parallel +c$ ($bc$-cycloidal) and $\mathit{P}\parallel +a$ ($ab$-cycloidal) domains for $36\times 6$ Mn sites. Blue and red arrows represent the Mn spins and the local electric polarizations, respectively. The color gradation represents the angle of local electric polarization relative to the $a$ axis. The angle becomes 45° along the DW center, which runs parallel to the $b$ axis.