  The coupling between magnetic order and ferroelectricity has been under
intense investigation in a wide range of transition-metal oxides. The strongest
coupling is obtained in so-called magnetically-induced multiferroics where
ferroelectricity arises directly from magnetic order that breaks inversion
symmetry. However, it has been difficult to find non-oxide based materials in
which these effects occur. Here we present a study of copper dimethyl sulfoxide
dichloride (CDC), an organo-metallic quantum magnet containing $S = 1/2$ Cu
spins, in which electric polarization arises from non-collinear magnetic order.
We show that the electric polarization can be switched in a stunning hysteretic
fashion. Because the magnetic order in CDC is mediated by large organic
molecules, our study shows that magnetoelectric interactions can exist in this
important class of materials, opening the road to designing magnetoelectrics
and multiferroics using large molecules as building blocks. Further, we
demonstrate that CDC undergoes a magnetoelectric quantum phase transition where
both ferroelectric and magnetic order emerge simultaneously as a function of
magnetic field at very low temperatures.
