Dynamical Magnetoelectric Coupling in Helical Magnets

We develop a theory of collective mode dynamics in the helical magnets coupled to electric polarization via spin-orbit interaction. The low-lying modes associated with the ferroelectricity are not the transverse optical phonons, but are the spin waves hybridized with the electric polarization. This hybridization leads to the Drude-like dielectric function $\epsilon (\omega )$ in the limit of zero magnetic anisotropy. There are two additional low-lying modes: phason of the spiral and rotation of helical plane along the polarization axis. Role of these low-lying modes in the neutron scattering and antiferromagnetic resonance is revealed, and a novel experiment to detect the dynamical magnetoelectric coupling is discussed.