the ferroelectric hysteresis loop
Plot a ferroelectric's polarization against the electric field you apply to it, sweeping the field up, back down, negative, and up again, and you do not get a straight line — you get a fat closed loop. The loop is the fingerprint of ferroelectricity, and its shape is a graph of a material that remembers its own history: the polarization at any moment depends not just on the present field but on where the field has been.
Trace it starting from an unpoled sample with zero net polarization. As you raise the field, domains aligned with it grow and the polarization climbs, curving over to a saturation value P_sat where essentially all dipoles point the same way. Now reduce the field back to zero: the polarization does not fall back to zero but stays at a remanent polarization P_r, because the aligned domains hold their new orientation — the material is now poled and remembers. To erase that memory you must push the field to the opposite polarity until, at the coercive field E_c, the net polarization is driven back to zero; push further and it saturates the other way, completing the loop. Extrapolating the saturated branch back to zero field estimates the spontaneous polarization P_s, and the loop's enclosed area is the energy dissipated per cycle.
The loop is the working diagram of the field. Its P_r and E_c decide whether a ferroelectric can serve as a memory bit (two stable remanent states = a stored 1 or 0, the basis of FeRAM), and how easily a piezoelectric ceramic can be poled. But there is a notorious trap: a leaky, lossy dielectric that merely conducts a bit can trace out a rounded, loop-like curve that looks ferroelectric but is not — the so-called 'banana' artifact. A genuine loop must be confirmed by checking that it is frequency-dependent in the right way and by pulse (PUND) measurements that isolate true switchable charge; a fat rounded loop alone is not proof of ferroelectricity.
In a ferroelectric memory cell the loop is the whole device: writing a bit means driving the polarization past E_c into one saturated state, and reading it back later relies on the remanent polarization P_r still sitting there, unchanged, with the power long switched off.
Remanence (P_r) is memory; the coercive field (E_c) is how hard you must push to overwrite it. Together they are why a ferroelectric can store a bit with no power.
A rounded loop is not automatic proof of ferroelectricity. A merely leaky dielectric can mimic the shape (the 'banana' artifact), so genuine switching must be confirmed with frequency and pulse tests, not eyeballed from one curve.