  Both the Dzyaloshiskii-Moriya interaction and the exchange-striction are
shown to affect dynamically the magnetoelectric excitations in the perovskite
multiferroic RMnO3. The exchange-striction results in a biquadratic interaction
between the spins and the transverse phonons, giving rise to quantum
fluctuations of the ferroelectric polarization P. This leads to low-lying
phonon modes that are perpendicular to P and to the helical spins at small wave
vector but are parallel to P at a wave vector close to the magnetic modulation
vector. For spin-1/2 helimagnet, the local polarization can be completely
reversed by the spin fluctuation, and so does the direction of the on-site spin
chirality, which allows for a finite differential scattering intensity of
polarized neutrons from a cycloidal magnet.
