Order Parameters and Phase Diagram of MultiferroicRMn2O5

The generic magnetic phase diagram of multiferroic $R{\mathrm{Mn}}_2{\mathrm{O}}_5$ (with $R=\mathrm{Y}$, Ho, Tb, Er, Tm), which allows different sequences of ordered magnetic structures for different $R$’s and different control parameters, is described using order parameters which explicitly incorporate the magnetic symmetry. A phenomenological magnetoelectric coupling is used to explain why some of these magnetic phases are also ferroelectric. Several new experiments, which can test this theory, are proposed.