material becomes insulating. When the pattern of localized electrons is polar, the charge ordered state is ferroelectric. Usually the ions in such a case are magnetic and so the ferroelectric state is also multiferroic. The first proposed example of a charge ordered multiferroic was LuFe2O4, which charge orders at 330 K with an arrangement of Fe2+ and Fe3+ ions. Ferrimagnetic ordering occurs below 240 K. Whether or not the charge ordering is polar has recently been questioned, however. In addition, charge ordered ferroelectricity is suggested in magnetite, Fe3O4, below its Verwey transition, and . Magnetically-driven ferroelectricity 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 TbMnO3. In this case the polarization is small, 10−2 μC/cm2, 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 HoMnO3 and related materials. In both cases the magnetoelectric coupling is strong because the ferroelectricity is directly caused by the magnetic order. f-electron magnetism While most magnetoelectric multiferroics developed to date have conventional transition-metal d-electron magnetism and a novel mechanism for the ferroelectricity, it is also possible to introduce a different type of magnetism into a conventional ferroelectric. The most obvious route is to use a rare-earth ion with a partially filled shell of f electrons on the A site. An example is EuTiO3 which, while not ferroelectric under ambient conditions, becomes so when strained a little bit, or when its lattice constant is expanded for example by substituting some barium on the A site. Composites It remains a challenge to develop good single-phase multiferroics with large magnetization and polarization and strong coupling between them at room temperature. Therefore, composites combining magnetic materials, such as FeRh, with ferroelectric materials, such as PMN-PT, are an attractive and established route to achieving multiferroicity. Some examples include magnetic thin films on piezoelectric PMN-PT substrates and