Magnetic Digital Flop of Ferroelectric Domain with Fixed Spin Chirality in a Triangular Lattice Helimagnet

The ferroelectric properties in a magnetic field ($H$) of varying magnitude and direction have been investigated for the triangular-lattice helimagnet ${\mathrm{CuFe}}_{1-x}{\mathrm{Ga}}_x{\mathrm{O}}_2$ ($x=0.035$). The in-plane $H$ was found to induce the rearrangement of six possible multiferroic domains. Upon every 60° rotation of in-plane $H$ around the $c$ axis, a unique 120° flop of electric polarization occurs as a result of the switch of the helical magnetic $q$ vector. The chirality of the spin helix is always conserved upon the $q$ flop. The possible origin is discussed in light of the stable structure of the multiferroic domain wall.

Figure 1

Temperature ($T$) dependence of magnetic susceptibility ($\chi$) and the [110] component of electric polarization ($P$). Magnetic field ($H$) is applied along (a),(b) [001], (c),(d) [110], and (e),(f)  $[1\overline{1}0]$, respectively. Arrows indicate the direction of the $T$ scan. In (c), a magnified profile of $\chi$ at 0.1 T (arbitrarily off-set) is also shown. (g)–(i) Three out of six possible multiferroic domains with proper-screw magnetic structure on a triangular lattice. Circled “$R$” and “$L$” denote the chirality of the spin spiral. Directions of the $P$ and magnetic $q$ vectors are also indicated. (j)–(m) Distribution of multiferroic domain(s) favored under various $H$ and electric field ($E$). The spin chirality corresponding to each $P$ domain is shown in (j).

Figure 2

$H\mathrm{\text{−}}T$ phase diagrams with $H$ parallel to (a) [001], (b) [110], and (c) $[1\overline{1}0]$ direction. Circles, triangles, squares, and diamonds are the data points obtained from $P\mathrm{\text{−}}T$, $P\mathrm{\text{−}}H$, $\chi \mathrm{\text{−}}T$, and $M\mathrm{\text{−}}H$ curves, respectively. All the data were taken from the increasing $T$ or $H$ runs [19]. Ferroelectric (FE) state is observed in the shadowed region. (d)–(f) $H$ dependence of $P$ (gray line) parallel to [110] and $M$ (black line), with $H$ applied along (d) [001], (e)  [110], and (f) $[1\overline{1}0]$ direction. $H$ was swept from 0 T to 14 T and then back to 0 T, after $T$ was lowered to 2 K at 0 T. The arrows indicate the direction of the $H$ scan.

Figure 3

(a)–(c) [110] and (d)–(f) $[1\overline{1}0]$ components of $P$ simultaneously measured in $H$ rotating within the (001) plane. ${\theta }_H$ denotes the angle between the $H$ vector and the [110] axis [see Fig. 4d]. Arrows indicate the direction of $H$ rotation. Absolute value of $P$ was determined by the $T$ scan.

Figure 4

(a) Relationship between the directions of $P$ and $H$, both confined within the (001) plane. ${\theta }_P$ (${\theta }_H$) denotes the angle between $P$ ($H$) direction and the [110] axis. (b),(c) Corresponding variations of $M$. Dashed lines indicate theoretically expected behaviors. (d) Relationship among $P$, $q$ and $H$ at ${\theta }_H=(60n)°$ ($n$: integer).