Landau model for the multiferroic delafossite antiferromagnets

•Symmetry considerations are used to analyze the phase diagrams of the compounds.•The competition between possible ground states is discussed.•The field induced transitions between competing states are described.

A symmetry based framework is used to describe the complex phase diagrams observed in the multiferroic delafossite compounds. A free energy Landau functional is derived from the analysis of the transformation properties of the most general incommensurate magnetic spin order parameter. A principle of maximal symmetry is invoked and the stability of each of the different higher symmetry phases considered. The competition between different potential ground states is analysed within the scope of a simplified model, which emphasizes the role of the symmetry allowed phase dependent biquadratic couplings. The cross-over between the different competing states is also discussed. The results show that the diverse set of phase diagrams that are experimentally observed in this class of triangular lattice antiferromagnets and, in particular, the stabilization of magnetically induced ferroelectric states, can be well interpreted and described within this integrated phenomenological approximation.