Electric-field control of the chiral magnetism of multiferroic ${\text{MnWO}}_4$ as seen via polarized neutron diffraction

The chiral components in the magnetic order in multiferroic ${\text{MnWO}}_4$ have been studied by neutron diffraction using spherical polarization analysis as a function of temperature and of external electric field. We show that sufficiently close to the ferroelectric transition at $T=12.3\text{K}$ it is possible to switch the chiral component by applying moderate electric fields at constant temperature. Full hysteresis cycles can be observed which indicate strong pinning of the magnetic order. ${\text{MnWO}}_4$, furthermore, exhibits a magnetoelectric memory effect across heating into the paramagnetic and paraelectric phase.

Figure 1

(Color online) (a) Crystal and [(b) and (c)] magnetic structure in ${\text{MnWO}}_4$; (b) and (c) show the two opposite chiral arrangements; the arrow on the bottom left of the schematic unit cell indicates the direction of the propagation vector, which is almost perpendicular to the easy axis. Note that the magnetic moments at the two Mn sites within a single unit cell are not related through the propagation vector but by the magnetic symmetry; therefore we do not add a clockwise or anticlockwise arrow. [(d) and (e)] Temperature dependence of magnetic scattering at $q_{ic}$ and $q_c$ studied with polarized neutron diffraction. The experiment was performed in the (0,1,0), $\left(-0.214,0,0.457\right)$ scattering plane; part (d) shows the magnetic scattering polarized parallel to the easy axis and that parallel to $b$ and part (e) the product of the magnetic components along these two directions, $\sqrt{{\sigma }_{yy}^{\uparrow \downarrow }}\cdot \sqrt{{\sigma }_{zz}^{\uparrow \downarrow }}$, which scales well with the ferroelectric polarization (Ref. 19).

Figure 2

(Color online) Temperature dependence of the magnetic scattering in the ${\sigma }_{xx}^{\uparrow \downarrow }$ and ${\sigma }_{xx}^{\downarrow \uparrow }$ channels measured upon cooling the ${\text{MnWO}}_4$ crystal with and without electric field. Note that the intensity in the two $xx$ spin-flip channels reflect the volumes of the two chiral arrangements shown in Figs. 1b, 1c. [(a)–(d)] After first cooling in negative electric field the cycles were successively recorded by cooling in $-3500$, 0, $+3500$, and 0 V. [(e)–(h)] Before starting the second run of thermal cycles, we heated the sample up to room temperature and then measured the cooling cycles in $+3500$, 0, $-3500$, and 0 V.

Figure 3

(Color online) Hysteresis curves of the chiral ratio as a function of external electric field at constant temperature; [(a)–(d)] hysteresis cycles were recorded after electric-field cooling in $E=-2000\text{V}$ [only the lower cycle in (a)] was recorded after cooling in $+2000\text{V}$. [(e)–(l)] Hysteresis curves were recorded after cooling in $-3500\text{V}$; (m) and (n) present the electric-field-induced difference in the chiral ratio and the width of the hysteresis measured at the middle value as function of temperature, respectively.