Coupled Spin-Phonon Excitations in Helical Multiferroics

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.