Magnetic-Field Induced Competition of Two Multiferroic Orders in a Triangular-Lattice Helimagnet ${\mathrm{MnI}}_2$

Magnetic and dielectric properties with varying magnitude and direction of magnetic-field $H$ have been investigated for a triangular-lattice helimagnet ${\mathrm{MnI}}_2$. The in-plane electric polarization $P$ emerges in the proper screw magnetic ground state below 3.5 K, showing the rearrangement of six possible multiferroic domains as controlled by the in-plane $H$. With every 60° rotation of $H$ around the [001] axis, discontinuous 120° flop of the $P$ vector is observed as a result of the flop of magnetic modulation vector $q$. With increasing the in-plane $H$ above 3 T, however, the stable $q$ direction changes from $q\Vert ⟨1\overline{1}0⟩$ to $q\Vert ⟨110⟩$, leading to a change of $P$-flop patterns under rotating $H$. At the critical field region ($\sim 3\mathrm{T}$), due to the phase competition and resultant enhanced $q$ flexibility, the $P$ vector smoothly rotates clockwise twice while the $H$ vector rotates counterclockwise once.

Figure 1

(a)–(c) The $T$ dependence of $\chi$, $ϵ$, and $P$ under various magnitudes of $H$. (d) The (001) projection of a triangular-lattice layer of ${\mathrm{Mn}}^{2+}$ ions (large circles) and two adjacent ${\mathrm{I}}^{-}$ layers (small open or filled circles) located above or below it. The symmetry elements at Mn site are also indicated: reflection mirror ($m$), twofold rotation axis (2) and threefold rotation axis along the [001]-axis with inversion center (a triangle with a small circle). (e) The crystal axes of ${\mathrm{MnI}}_2$. (f) The proper screw magnetic order with in-plane modulation vector $q\Vert ⟨1\overline{1}0⟩$, which appears in low-$H$ region. The remaining symmetry element and the allowed $P$ direction are also indicated. (g) Six possible multiferroic domains with $P\Vert ⟨110⟩$. Corresponding magnetic $q$ vector and spin chirality (denoted as $R$ or $L$) are also indicated. (h) and (i) Favorable domain distribution under various sets of $E$ and $H$. (j)–(l) The analogous diagrams for the proper screw magnetic order with $q\Vert ⟨110⟩$, which emerges in the high-$H$ region (see text).

Figure 2

(a) [110] and (b) $[1\overline{1}0]$ components of $P$ simultaneously measured at 2.3 T as functions of the $H$ direction around the [001] axis. (c) Relationship between the directions of $P$ and $H$. Arrows indicate the direction of the $H$ rotation. (d) Schematic illustration of the observed development of the $P$ vector under rotating $H$. Corresponding data sets taken at 3 T [(e)–(h)] and 5 T [(i)–(l)] are also shown (see text).

Figure 3

(a) ${\theta }_H$ dependence of $\chi$ ($=M/H$) measured with various magnitudes of $H$. (b) $T\mathrm{\text{−}}H$ phase diagram for $H$ applied parallel to $[1\overline{1}0]$, determined by various $T$ and $H$ scans of $M$, $ϵ$, and $P$. FE nature is observed in the shadowed region. The transition point (denoted as $\times$ with a horizontal error bar) separating the two screw magnetic phases with different $q$ vectors as indicated in Figs. 1f, 1j is determined from the result of ${\theta }_H$ scans for $P$ and $M$. Horizontal bars indicate a provisional phase boundary.