text: In magnetically driven multiferroics the macroscopic electric polarization is induced by long-range magnetic order which is non-centrosymmetric. Formally, the electric polarisation, , is given in terms of the magnetization,  , by
  Like the geometric ferroelectrics discussed above, the ferroelectricity is improper, because the polarisation is not the primary order parameter (in this case the primary order is the magnetisation) for the ferroic phase transition.
  The prototypical example is the formation of the non-centrosymmetric magnetic spiral state, accompanied by a small ferroelectric polarization, below 28K in TbMnO. In this case the polarization is small, 10 μC/cm, because the mechanism coupling the non-centrosymmetric spin structure to the crystal lattice is the weak spin-orbit coupling. Larger polarizations occur when the non-centrosymmetric magnetic ordering is caused by the stronger superexchange interaction, such as in orthorhombic HoMnO and related materials. In both cases the magnetoelectric coupling is strong because the ferroelectricity is directly caused by the magnetic order.