The following describes the mechanisms that are known to circumvent this contraindication between ferromagnetism and ferroelectricity. Lone-pair-active In lone-pair-active multiferroics, the ferroelectric displacement is driven by the A-site cation, and the magnetism arises from a partially filled d shell on the B site. Examples include bismuth ferrite, BiFeO3, BiMnO3 (although this is believed to be anti-polar), and PbVO3. In these materials, the A-site cation (Bi3+, Pb2+) has a so-called stereochemically active 6s2 lone-pair of electrons, and off-centering of the A-site cation is favoured by an energy-lowering electron sharing between the formally empty A-site 6p orbitals and the filled O 2p orbitals. Geometric ferroelectricity In geometric ferroelectrics, the driving force for the structural phase transition leading to the polar ferroelectric state is a rotational distortion of the polyhedra rather than an electron-sharing covalent bond formation. Such rotational distortions occur in many transition-metal oxides; in the perovskites for example they are common when the A-site cation is small, so that the oxygen octahedra collapse around it. In perovskites, the three-dimensional connectivity of the polyhedra means that no net polarization results; if one octahedron rotates to the right, its connected neighbor rotates to the left and so on. In layered materials, however, such rotations can lead to a net polarization. The prototypical geometric ferroelectrics are the layered barium transition metal fluorides, BaMF4, M=Mn, Fe, Co, Ni, Zn, which have a ferroelectric transition at around 1000K and a magnetic transition to an antiferromagnetic state at around 50K. Since the distortion is not driven by a hybridisation between the d-site cation and the anions, it is compatible with the existence of magnetism on the B site, thus allowing for multiferroic behavior. A second example is provided by the family of hexagonal rare earth manganites (h-RMnO3 with R=Ho-Lu, Y), which have a structural phase transition at around 1300 K consisting primarily of a tilting of the MnO5 bipyramids. While the tilting itself has zero polarization, it couples to a polar corrugation of the R-ion layers which yields a polarisation of ~6µC/cm2. Since the ferroelectricity is not the primary order parameter it is described as improper. The multiferroic phase is reached at ~100K when a triangular antiferromagnetic order due to spin frustration arises. Charge ordering Charge ordering can occur in compounds containing ions of mixed valence when the electrons, which are delocalised at high temperature, localize in an ordered pattern on different cation sites so that the