Simple microscopic model for magneto-electric coupling in type-II antiferromagnetic multiferroics

We present a simple two-dimensional model in which the lattice degrees of freedom mediate the interactions between magnetic moments and electric dipoles. This model reproduces basic features, such as a sudden electric polarization switch-off when a magnetic field is applied and the ubiquitous dimerized distortion patterns and magnetic $\uparrow \uparrow \downarrow \downarrow$ ordering, observed in several multiferroic materials of different composition. The list includes E-type manganites, RMnO${}_3$, nickelates such as in YNiO${}_3$ and other materials under strain, such as TbMnO${}_3$. In spite of its simplicity, the model presented here captures the essence of the origin of multiferroicity in a large class of type II multiferroics.