  An effective model is developed to explain the phase diagram and the
mechanism of magnetoelectric coupling in multiferroics, $RMn_2O_5$. We show
that the nature of magnetoelectric coupling in $RMn_2O_5$ is a coupling between
two Ising-type orders, namely, the ferroelectric order in the b axis, and the
coupled magnetic order between two frustrated antiferromagnetic chains. The
frustrated magnetic structure drives the system to a
commensurate-incommensurate phase transition, which can be understood as a
competition between a collinear or col-plane order stemming from the `order by
disorder' mechanism and a chiral symmetry order. The low energy excitation is
calculated and the effect of the external magnetic field is analyzed. Distinct
features in the electromagnon spectrums in the incommensurate phase are
predicted.

Strongly Correlated Electrons;Materials Science