When most materials are electrically polarized, the polarization induced, P, is almost exactly proportional to the applied external electric field E; so the polarization is a linear function.  This is called linear dielectric polarization (see figure). Some materials, known as paraelectric materials, show a more enhanced nonlinear polarization (see figure). The electric permittivity, corresponding to the slope of the polarization curve, is not constant as in linear dielectrics but is a function of the external electric field.
In addition to being nonlinear, ferroelectric materials demonstrate a spontaneous nonzero polarization (after entrainment, see figure) even when the applied field E is zero. The distinguishing feature of ferroelectrics is that the spontaneous polarization can be reversed by a suitably strong applied electric field in the opposite direction; the polarization is therefore dependent not only on the current electric field but also on its history, yielding a hysteresis loop.  They are called ferroelectrics by analogy to ferromagnetic materials, which have spontaneous magnetization and exhibit similar hysteresis loops.
Typically, materials demonstrate ferroelectricity only below a certain phase transition temperature, called the Curie temperature (T) and are paraelectric above this temperature: the spontaneous polarization vanishes, and the ferroelectric crystal transforms into the paraelectric state. Many ferroelectrics lose their pyroelectric properties above T completely, because their paraelectric phase has a centrosymmetric crystal structure.