Hysteresis Loop — Ferroelectric Polarization

Landau-Devonshire free energy with double-well potential

Material Parameters

E = 0.000
P = 0.000
State: —

The Landau free energy for a ferroelectric:

F(P) = α(T-Tc)P²/2 + βP⁴/4

Below Tc, the double-well creates two stable polarization states ±Pₛ. An applied field E tilts the landscape, causing sudden switching at the coercive field.

The enclosed area of the P-E loop is the energy dissipated per cycle — the signature of switching loss in capacitors and memories.