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.

• Received 9 July 2012

DOI:https://doi.org/10.1103/PhysRevB.87.014419