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 TbMnO3, 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 10−2 μC/cm2. The opposite effect has also been reported, in the Mott insulating charge-transfer salt –. 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. Symmetry and coupling The formation of a ferroic order is always associated with the breaking of a symmetry. For example, the symmetry of spatial inversion is broken when ferroelectrics develop their electric dipole moment, and time reversal is broken when ferromagnets become magnetic. The symmetry breaking can be described by an order parameter, the polarization P and magnetization M in these two examples, and leads to multiple equivalent ground states which can be selected by the appropriate conjugate field; electric or magnetic for ferroelectrics or ferromagnets respectively. This leads for example to the familiar switching of magnetic bits using magnetic fields in magnetic data storage. Ferroics are often characterized by the behavior of their order parameters under space inversion and time reversal (see table). The operation of space inversion reverses the direction of polarisation (so the phenomenon of polarisation is space-inversion antisymmetric) while leaving the magnetisation invariant. As a result, non-polar ferromagnets and ferroelastics are invariant under space inversion whereas polar ferroelectrics are not. The operation of time reversal, on the other hand, changes the sign of M (which is therefore time-reversal antisymmetric), while the sign of P remains invariant. Therefore, non-magnetic ferroelastics and ferroelectrics are invariant under time reversal whereas ferromagnets are not. Magnetoelectric multiferroics are both space-inversion and time-reversal anti-symmetric since they are both ferromagnetic and ferroelectric. The combination of symmetry breakings in multiferroics can lead to coupling between the order parameters, so that one ferroic property can be manipulated with the conjugate field of the other. Ferroelastic ferroelectrics, for example, are piezoelectric, meaning that an electric field can cause a shape change or a pressure can induce a voltage, and ferroelastic ferromagnets