  We propose a microscopic magneto-electric model in which the coupling between
spins and electric dipoles is mediated by lattice distortions. The magnetic
sector is described by a spin S=1/2 Heisenberg model coupled directly to the
lattice via a standard spin-Peierls term and indirectly to the electric dipole
variables via the distortion of the surrounding electronic clouds. Electric
dipoles are described by Ising variables for simplicity. We show that the
effective magneto-electric coupling which arises due to the interconnecting
lattice deformations is quite efficient in one-dimensional arrays. More
precisely, we show using bosonization and extensive DMRG numerical simulations
that increasing the magnetic field above the spin Peierls gap, a massive
polarization switch-off occurs due to the proliferation of soliton pairs. We
also analyze the effect of an external electric field $E$ when the magnetic
system is in a gapped (plateau) phase and show that the magnetization can be
electrically switched between clearly distinct values. More general
quasi-one-dimensional models and two-dimensional systems are also discussed.
