Interpretation of magnetoelectric phase states using the praphase concept and exchange symmetry

The majority of magnetoelectric crystals show complex temperature-magnetic field or temperature-pressure phase diagrams with alternating antiferromagnetic incommensurate, magnetoelectric, and commensurate phases. Such phase diagrams occur as a result of successive magnetic instabilities with respect to different order parameters, which usually transform according to different irreducible representations (IRs) of the space group of the crystal. Therefore, in order to build a phenomenological theory of phase transitions in such magnetoelectrics one has to employ several order parameters and assume the proximity of various instabilities on the thermodynamic path. In this work we analyze the magnetoelectrics MnWO4, CuO, NaFeSi2O6, NaFeGe2O6, Cu3Nb2O8, α-CaCr2O4 and FeTe2O5Br using the praphase concept and the symmetry of the exchange Hamiltonian. We find that in all the considered cases the appearing magnetic structures are described by IRs entering into a single exchange multiplet, whereas in the cases of MnWO4 and CuO by a single IR of the space group of the praphase structure. Therefore, one can interpret the complex phase diagrams of magnetoelectrics as induced by a single IR either of the praphase or of the symmetry group of the exchange Hamiltonian. Detailed temperature-magnetic field phase diagrams of MnWO4 and CuO for certain field directions are obtained and the magnetic structures of the field-induced phases are determined.