A helpful classification scheme for multiferroics into so-called type-I and type-II multiferroics was introduced in 2009 by D. Khomskii.
Khomskii suggested the term type-I multiferroic for materials in which the ferroelectricity and magnetism occur at different temperatures and arise from different mechanisms. Usually the structural distortion which gives rise to the ferroelectricity occurs at high temperature, and the magnetic ordering, which is usually antiferromagnetic, sets in at lower temperature. The prototypical example is BiFeO (T=1100 K, T=643 K), with the ferroelectricity driven by the stereochemically active lone pair of the Bi ion and the magnetic ordering caused by the usual superexchange mechanism. YMnO (T=914 K, T=76 K) is also type-I, although its ferroelectricity is so-called "improper", meaning that it is a secondary effect arising from another (primary) structural distortion. The independent emergence of magnetism and ferroelectricity means that the domains of the two properties can exist independently of each other. Most type-I multiferroics show a linear magnetoelectric response, as well as changes in dielectric susceptibility at the magnetic phase transition.
The term type-II multiferroic is used for materials in which the magnetic ordering breaks the inversion symmetry and directly "causes" the ferroelectricity. In this case the ordering temperatures for the two phenomena are identical. The prototypical example is TbMnO, in which a non-centrosymmetric magnetic spiral accompanied by a ferroelectric polarization sets in at 28 K. Since the same transition causes both effects they are by construction strongly coupled. The ferroelectric polarizations tend to be orders of magnitude smaller than those of the type-I multiferroics however, typically of the order of 10 μC/cm. The opposite effect has also been reported, in the Mott insulating charge-transfer salt &ndash;. Here, a charge-ordering transition to a polar ferroelectric case drives a magnetic ordering, again giving an intimate coupling between the ferroelectric and, in this case antiferromagnetic, orders.