Abstract
The magnetic structures of the incommensurate phases of the prototypic multiferroic MnWO${}_{4}$ are analyzed using superspace symmetry formalism. This approach shows in a very simple way the relation between the magnetic symmetry of the incommensurate phases and any tensorial property, such as ferroelectricity. The magnetic structures have been redetermined by single-crystal neutron diffraction experiments, which revealed fine details of the AF3 and AF2 magnetic structures. The spin modulations of the two manganese ions of the basic unit cell are symmetry-related in the paraelectric incommensurate-magnetic structure (AF3)---they are not forced to be collinear but they must have opposite chirality---while in the multiferroic phase (AF2) they become symmetry independent. It is due to this symmetry break that the electric polarization arises along the $b$ axis.
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