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We introduce a microscopic model for collinear multiferroics capable toreproduce, as a consequence of magnetic frustration and easy-axis anisotropy,the so-called "uudd" (or antiphase) magnetic ordering observed in several typeII multiferroic materials. The crucial role of lattice distortions in themultiferroic character of these materials is entered into the model via anindirect magnetoelectric coupling, mediated by elastic degrees of freedomthrough a pantograph mechanism. Long range dipolar interactions set electricdipoles in the antiferroelectric order. We investigate this model by means ofextensive DMRG computations and complementary analytical methods. We show thata lattice dimerization induces a spontaneous Z2 ferrielectric bulkpolarization, with a sharp switch off produced by a magnetic field above acritical value. The topological character of the magnetic excitations makesthis mechanism robust.

Topological solitons and bulk polarization switch in collinear type II multiferroics