Theory of Magnetic Switching of Ferroelectricity in Spiral Magnets

We propose a microscopic theory for magnetic switching of electric polarization (P) in the spin-spiral multiferroics by taking TbMnO₃ and DyMnO₃ as examples. We reproduce their phase diagrams under a magnetic field H₄ₗ by Monte Carlo simulation of an accurate spin model and reveal that competition among the Dzyaloshinskii-Moriya interaction, spin anisotropy, and spin exchange is controlled by the applied H₄ₗ, resulting in magnetic transitions accompanied by reorientation or vanishing of P. We also discuss the relevance of the proposed mechanisms to many other multiferroics such as LiCu₂O₂, MnWO₄, and Ni₃V₂O₄.