Title: Soft magnon contributions to dielectric constant in spiral magnets with domain walls

Abstract: Competing magnetic exchange interactions often result in non-collinear magnetic states, such as spin spirals, which break the inversion symmetry and induce ferroelectric polarization. The resulting strong interactions between magnetic and dielectric degrees of freedom lead to a technologically important possibility to control magnetic order by electric fields and to electromagnons, magnetic excitations that can be excited by an electric dipole of the electromagnetic field. Here we study the effects of chiral domain walls on magnetoelectric properties of spiral magnets. We use a quasi-1D model Hamiltonian with competing Heisenberg exchange interactions, leading to a spin spiral, and Dzyaloshinskii-Moriya interactions, that couple spins and electric dipoles and mix magnon and phonon excitations. The results suggest that low frequency dielectric anomalies in spiral magnets, such as TbMnO3 and MnWO4, may originate from hybrid magnon - polar phonon excitations associated with domain walls.