Symmetry, incommensurate magnetism and ferroelectricity: the case of the rare-earth manganites RMnO3

The complete irreducible co-representations of the paramagnetic space group provide a simple and direct path to explore the symmetry restrictions of magnetically driven ferroelectricity. The method consists of a straightforward generalization of the method commonly used in the case of displacive modulated systems and allows us to determine, in a simple manner, the full magnetic symmetry of a given phase originated from a given magnetic order parameter. The potential ferroic and magneto-electric properties of that phase can then be established and the exact Landau free energy expansions can be derived from general symmetry considerations. In this work, this method is applied to the case of the orthorhombic rare-earth manganites RMnO3. This example will allow us to stress some specific points, such as the differences between commensurate or incommensurate magnetic phases regarding the ferroic and magnetoelectric properties, the possible stabilization of ferroelectricity by a single irreducible order parameter or the possible onset of a polarization oriented parallel to the magnetic modulation. The specific example of TbMnO3 will be considered in more detail, in order to characterize the role played by the magneto-electric effect in the mechanism for the polarization rotation induced by an external magnetic field