In the previous chapter we mentioned the current interest in combining magnetic behavior with additional desirable properties, and looked at the examples of semiconducting transport and robust insulation. In this chapter we continue this philosophy with a discussion of the so-called multiferroics, which combine magnetic ordering with other kinds of ferroic ordering – ferroelectricity, ferroelasticity, and ferrotoroidicity. We will focus in particular on the combination of magnetism and ferroelectricity, which is appealing because of its potential for magnetoelectric response, that is, the control and tuning of magnetism using electric fields, and vice versa.

The formal definition of a multiferroic is a material that displays two or more primary ferroic orderings simultaneously. The well-established primary ferroics are: the ferromagnets, which have a spontaneous magnetization that is switchable using an applied magnetic field and which we have focused on in this text so far; the ferroelectrics, with their spontaneous electric polarization that is switchable by an applied electric field; and the ferroelastics, which have a spontaneous strain that is switchable by an applied mechanical stress. Recently the ferrotoroidics have been proposed, using symmetry arguments, to complete the classes of primary ferroics. Let's begin by comparing the properties of the ferroelectrics, ferroelastics, and ferrotoroidics with the ferromagnets that we have already discussed in detail.