  We introduce a microscopic model for collinear multiferroics capable to
reproduce, as a consequence of magnetic frustration and easy-axis anisotropy,
the so-called "uudd" (or antiphase) magnetic ordering observed in several type
II multiferroic materials. The crucial role of lattice distortions in the
multiferroic character of these materials is entered into the model via an
indirect magnetoelectric coupling, mediated by elastic degrees of freedom
through a pantograph mechanism. Long range dipolar interactions set electric
dipoles in the antiferroelectric order. We investigate this model by means of
extensive DMRG computations and complementary analytical methods. We show that
a lattice dimerization induces a spontaneous Z2 ferrielectric bulk
polarization, with a sharp switch off produced by a magnetic field above a
critical value. The topological character of the magnetic excitations makes
this mechanism robust.
