Magnetic Reversal of Electric Polarization with Fixed Chirality of Magnetic Structure in a Chiral-Lattice Helimagnet ${\mathrm{MnSb}}_2{\mathrm{O}}_6$

The correlation between magnetic and dielectric properties has been investigated for the single crystal of the chiral triangular-lattice helimagnet ${\mathrm{MnSb}}_2{\mathrm{O}}_6$. We found that the spin-spiral plane in the ground state has a considerable tilting from the (110) plane and that the sign of the spin-spiral tilting angle is coupled to the clockwise or counterclockwise manner of spin rotation and accordingly to the sign of magnetically induced electric polarization. This leads to unique magnetoelectric responses such as the magnetic-field-induced selection of a single ferroelectric domain as well as the reversal of electric polarization just by a slight tilting of the magnetic field direction, where the chiral nature of the crystal structure plays a crucial role through the coupling of the chirality between the crystal and magnetic structures. Our results demonstrate that crystallographic chirality can be an abundant source of novel magnetoelectric functions with coupled internal degrees of freedom.

Figure 1

(a) Crystal structure of ${\mathrm{MnSb}}_2{\mathrm{O}}_6$ with the chiral trigonal space group $P321$. The compatible symmetry elements [twofold rotation axes (2) along the $⟨110⟩$ directions and threefold rotation axis (closed triangle) along the [001] direction] are also indicated. (b) Temperature dependence of magnetic susceptibility for $H\parallel [110]$ and $H\parallel [001]$. (c) Schematic illustration of the helical magnetic structure in the ground state of ${\mathrm{MnSb}}_2{\mathrm{O}}_6$, with its spin-spiral plane tilted from the (110) plane by angle ${\theta }_t$. The application of twofold rotation around the [110] axis gives an equivalent magnetic structure as shown in (d). These two domains [i.e., the ($+$) and ($-$) domains] are characterized by the opposite sign of spin-spiral tilting angle ${\theta }_t$ and magnetically induced electric polarization $P\parallel [1\overline{1}0]$. The views from the [$1\overline{1}0$] direction are also shown in (e) and (f). (g) Six equivalent helimagnetic domains characterized by different orientations of the spin-spiral plane (purple bold bars). The sign of ${\theta }_t$ for each domain is expressed by ($+$) and ($-$). The corresponding orientations of magnetically induced electric polarization $P\parallel ⟨1\overline{1}0⟩$ are also indicated with blue arrows. (h),(i) Examples of the favored domain configuration under the specific external $H$ having both in-plane and out-of-plane components (red arrows and symbols).

Figure 2

(a) $H$-direction dependence of the magnetic susceptibility measured at 4 K with various magnitudes of $H$. Here, $H$ is rotated within the ($1\overline{1}0$) plane, and ${\theta }_H$ is defined as the angle between the [110] axis and $H$ direction. Before each measurement, the sample is cooled down from 20 to 4 K with ${\mu }_{0}H=2\mathrm{T}$ at ${\theta }_H=0°$, and then the magnitude of $H$ is tuned at the target value to align the threefold helimagnetic domains. The data are arbitrarily shifted along the vertical axes. (b) Calculated versus observed intensities for both the nuclear and magnetic reflections obtained by single-crystal neutron diffraction experiments for the magnetic structure shown in Fig. 1 with ${\theta }_t\sim 18°$. For the details of the neutron diffraction experiments, see Supplemental Material [28].

Figure 3

Magnetic field dependence of magnetization $M$ for (a) $H\parallel [001]$ and (b) $H\parallel [110]$, measured at various temperatures after the zero field cooling. The corresponding $H$ derivatives of $M$ are plotted in (c) and (d), whose anomalies represent spin-flop transitions and domain selections, respectively. The data are arbitrarily shifted along the vertical axes. Based on the anomalies found in the $M-T$ (squares) and $M-H$ (circles) profiles, $H-T$ magnetic phase diagrams are summarized in (e) and (f).

Figure 4

(a) $H$-direction dependence of polarization current $I$ and (b) corresponding electric polarization $P$, measured along the [$1\overline{1}0$] direction at 4 K with various magnitudes of $H$. The definition of ${\theta }_H$ is common with the case for Fig. 2, and all the measurements were performed after once applying in-plane ${\mu }_{0}H\sim 2\mathrm{T}$ at 4 K. The arrows indicate the direction of $H$ rotation, and the data are arbitrarily shifted along the vertical axes. Here, theoretically expected behaviors based on Eq. (1) under the assumption of $({\overrightarrow{S}}_i\times {\overrightarrow{S}}_j)\parallel \overrightarrow{H}$ are also plotted with a dashed line. (c)–(f) Schematic illustration of the $H$-induced $(+)/(-)$ domain switching. (c) and (d) are for the case of ${\theta }_H\sim (180n)°$, and (e) and (f) for the case of ${\theta }_H\sim (180n+90)°$. Depending on the magnitude of $H$, different behaviors of $P$ generation can be observed for the respective cases.