The time dependence of switching multiferroic domains in MnWO4 has been studied by timeresolved polarized neutron diffraction. Inverting an external electric field inverts the chiral magnetic component within rise times ranging between a few and some tens of milliseconds in perfect agreement with macroscopic techniques. There is no evidence for any faster process in the inversion of the chiral magnetic structure. The time dependence is well described by a temperature-dependent rise time suggesting a well-defined process of domain reversion. As expected, the rise times decrease when heating towards the upper boundary of the ferroelectric phase. However, switching also becomes faster upon cooling towards the lower boundary, which is associated with a first-order phase transition.

The control of ferroelastic, ferroelectric, and ferromagnetic domains through the corresponding fields has led to numerous applications taken for granted nowadays. Ferrotoroidal order on the other hand has been less explored due to its more complex character and due to the peculiar field needed to control it. LiFeSi 2 O 6 exhibits a ferrotoroidal order that is particularly simple to analyze. By performing neutron-diffraction experiments with spherical polarization analysis we show that crossed electric and magnetic fields allow us to control ferrotoroidal moments.

By comprehensive neutron diffraction measurements we have studied the magnetic structure of aegirine (NaFeSi 2 O 6 ) in and above its multiferroic phase. Natural aegirine exhibits two magnetic transitions into incommensurate magnetic order with a propagation vector of k inc = (0, ∼ 0.78,0). Between 9 and 6 K, we find a transverse spin-density wave with moments pointing near the c direction. Below 6 K, magnetic order becomes helical and spins rotate in the ac plane. The same irreducible representation is involved in the two successive transitions. In addition, the ferroelectric polarization P appearing along the b direction cannot be described by the most common multiferroic mechanism but follows P ∝ S i × S j . Synthetic NaFeSi 2 O 6 does not exhibit the pure incommensurate helical order but shows coexistence of this order with a commensurate magnetic structure. By applying moderate pressure to natural aegirine, we find that the incommensurate magnetic ordering partially transforms to the commensurate one, underlining the nearly degenerate character of the two types of order in NaFeSi 2 O 6 .

Abstract. The control of multiferroic domains through external electric fields has been studied by dielectric measurements and by polarized neutron diffraction on singlecrystalline TbMnO 3 . Full hysteresis cycles were recorded by varying an external field of the order of several kV/mm and by recording the chiral magnetic scattering as well as the charge in a sample capacitor. Both methods yield comparable coercive fields that increase upon cooling.

Polarized neutron scattering experiments reveal that type-II multiferroics allow for controlling the spin chirality by external electric fields even in the absence of long-range multiferroic order. In the two prototype compounds TbMnO 3 and MnWO 4 , chiral magnetism associated with soft overdamped electromagnons can be observed above the long-range multiferroic transition temperature T MF , and it is possible to control it through an electric field. While MnWO 4 exhibits chiral correlations only in a tiny temperature interval above T MF , in TbMnO 3 chiral magnetism can be observed over several kelvin up to the lock-in transition, which is well separated from T MF . DOI: 10.1103/PhysRevLett.119.177201 Multiferroic materials with coupled magnetic and ferroelectric order bear considerable application potential [1,2]. In type-II multiferroics, magnetic order directly induces ferroelectric polarization and giant magnetoelectric coupling. External magnetic fields imply a flop of electric polarization, and electric fields can control chiral magnetic domains [1][2][3][4][5]. Various neutron experiments [6][7][8][9][10][11][12] as well as resonant and nonresonant x-ray studies [13,14] show that cooling in electric fields enforces a monodomain chiral state, and varying external electric fields at constant temperature drives the chiral magnetic order [9][10][11][12], which corresponds to the most promising application as a data storage medium. In addition, time resolved soft x-ray diffraction showed that chiral magnetism can be manipulated by THz-radiation pulses at an electromagnon energy [15].So far, studies of the multiferroic coupling and hysteresis curves were restricted to the phases with long-range magnetic order on bulk or film materials [16], while only small multiferroic blocks would be vital for applications. Also, from the fundamental point of view, one may ask whether multiferroic hysteresis and control can be achieved in short-range systems above the long-range static multiferroic transition, and how far spin chirality persists above the static and long-range multiferroic order. The mixed system Ni 0.42 Mn 0.58 TiO 3 already indicates that magnetoelectric coupling can persist in cluster systems with competing magnetic structures [17], but until now there has been no information about the control and multiferroic coupling of chiral ordering that is limited in space and time. Here, we study two prototype type-II multiferroics, TbMnO 3 [1, 3,4] and MnWO 4 [18-20], above the long-range ferroelectric transition at zero electric field T MF , where it is still possible to pole and control chiral magnetic correlations. Although the two materials exhibit a similar sequence of magnetic transitions, it turns out that only in TbMnO 3 can chiral scattering be controlled over a large temperature interval of several kelvin.TbMnO 3 (MnWO 4 ) both exhibit a first magnetic transition at T N ¼ 42 K (13.5 K), followed by a second transition at lower temperature, at which cycloid order develops at T MF ¼ 27.6 K (12.6 K). For ...