  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 H_ex 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 H_ex, 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
