Figure 1

(a) $H$ dependence of $M_{[110]}$ (blue line) and $M_{[1\overline{1}0]}$ (red line) at 5 K. (b) $H$ dependence of $(dM/dH{)}_{[110]}$ (blue line) and $(dM/dH{)}_{[1\overline{1}0]}$ (red line).Reuse & Permissions

Figure 2

${\epsilon }_{[110]}$ (a), $P_{[110]}$ (b), ${\epsilon }_{[1\overline{1}0]}$ (c), and $P_{[1\overline{1}0]}$ (d) as a function of $H_{[110]}$ (blue line) and $H_{[1\overline{1}0]}$ (red line). Insets of (a) and (c): schematic experimental configurations. Inset of (d): enlargement of $P_{[1\overline{1}0]}$ as a function of $H_{[1\overline{1}0]}$. Measurements of $P_{[110]}$ and $P_{[1\overline{1}0]}$ were done with the poling $E$ of $\sim 0.54\mathrm{MV}/\mathrm{m}$.Reuse & Permissions

Figure 3

Schematic illustrations of a proposed evolution of magnetic structures by applying $H_{[1\overline{1}0]}$ (left) and $H_{[110]}$ (right) in the case of the $P_{[110]}$ measurement. Each hexagon denotes the (001) projection of a spin configuration on a TLP of ${\mathrm{Cr}}^{3+}$ ions (red, blue, and green circles). Red, blue, and green colored arrows denote spin components of 120° spin structures. Two TLP’s of ${\mathrm{O}}^{2-}$ ions (open and closed black circles) located adjacently above or below the ${\mathrm{Cr}}^{3+}$ TLP are also shown. Gray rectangles denote the spiral planes. Purple arrows and lines represent the $2^{\prime }$ axes and the projections of the $m^{\prime }$ planes, respectively. Open arrows describe the expected direction of $P$. In this figure, the initial magnetic structure is assumed to be the (110) spiral plane. By applying $E_{[110]}$, the (110) spiral plane has three kinds of domains labeled A, B, and C. The bottom, middle, and top panels denote possible domains in zero, intermediate ($\sim 4\mathrm{T}$), and sufficiently high ($\gg 9\mathrm{T}$) magnetic fields, respectively.Reuse & Permissions

Figure 4

(a) $P\mathrm{\text{−}}E$ hysteresis loops in various $H$ at 5 K for $P\Vert H\Vert$ [110]. A sweep rate of $E$ is $7.1\times {10}^{-3}\mathrm{MV}/\mathrm{m}\sec$. (b) $H$ profiles of $P$ in various $E$ at 5 K. All data were obtained in the $H$-decreasing run, and more detailed experimental procedures are shown in the text. (c) $H_r$ vs $E_r$ diagram for the $P$ reversal. Closed (open) blue circles correspond to the $P$ reversal by $E(H)$ sweeping in various $H(E)$ for $P\Vert H\Vert$ [110]. Closed (open) red squares are used for $P\Vert H\Vert$ $[1\overline{1}0]$. $E_r$ increases approximately as a function of $H_r^4$ both for the [110] and $[1\overline{1}0]$ axes.Reuse & Permissions