ferroelectricity
Most insulators are dead until you apply a field: no field, no polarization. A ferroelectric is alive. Even with no field applied, it carries a built-in electric polarization — a permanent, one-directional separation of charge frozen into the crystal — and, crucially, you can flip that polarization to the opposite direction by applying a strong enough field, and it stays flipped. It is the electrical twin of a permanent magnet you can re-magnetize; the name 'ferroelectric' is borrowed from ferromagnetism by analogy and, confusingly, has nothing to do with iron.
The built-in polarization is called the spontaneous polarization, P_s, and it appears because below a certain temperature the crystal spontaneously distorts so that its centre of positive charge no longer sits on top of its centre of negative charge. In barium titanate the small Ti4+ ion, which sits centred in a cage of six oxygens above 130 degrees C, slides slightly off-centre below it — like a marble that rolls into one of two shallow dimples. Because there are two (in fact several) equivalent off-centre positions, the polarization can point either way, and a field can push the ion from one dimple to the other, switching P. This switchability is the defining test: a material with a fixed built-in polarization that cannot be reversed (like ordinary quartz) is merely polar, not ferroelectric.
Ferroelectricity is the engine behind a whole class of electroceramics. The easily-polarized lattice gives the giant dielectric constants of capacitor ceramics; the switchable polarization gives two stable states for non-volatile ferroelectric memory (FeRAM); and every ferroelectric is automatically also piezoelectric and pyroelectric, so this one property underlies sensors, actuators, and infrared detectors too. A key honesty about the family tree: the 32 crystal classes nest — all ferroelectrics are pyroelectric, all pyroelectrics are piezoelectric, but not the reverse. Ferroelectricity also requires a non-centrosymmetric structure, and it vanishes entirely above a material-specific temperature, the Curie point, where the crystal snaps back to its undistorted, non-polar form.
Cool a crystal of barium titanate through 130 degrees C and watch it come alive: above that temperature it is an ordinary cubic insulator, but just below it the lattice stretches slightly along one axis, the titanium ion shifts off-centre, and a spontaneous polarization switches on that a modest field can now flip back and forth.
The signature of ferroelectricity is not just a built-in polarization but a switchable one — reversible by a field, and lost above the Curie point.
'Ferro' misleads: ferroelectrics need contain no iron, and iron itself is not ferroelectric. The name only marks the mathematical analogy to ferromagnetism — a hysteresis loop and a Curie point.