Evolution of P-E loop in phase transition region of first order phase transition ferroelectrics

Polarization-electric field (E) hysteresis loop is crucial to ferroelectrics and their applications. First order phase transition ferroelectric has a transition region, where two phases coexist from ferroelectric phase at T0 to paraelectric phase at T1, and stretching to an E-enhanced phase transition temperature T2. Shape of the loops in the transition region changes with temperature confirmed by experiments. Evolution of the shape is derived by three-dimension Landau-Devonshire theory, on the basis of variations of E induced valleys of Gibbs free energy. The principles used are rotations of dipoles by the E to cause critical effect, and coupling between rotated dipoles to produce polarization hysteresis. The theoretic results exhibit that double loops converge to the origin and then separate when temperature rises through T1. The reasons for the double loops are ascribed to combination of the critical effects for the abrupt changes in polarization and the coupling effect for the hysteresis between two critical points. The theory can explain the experimental phenomena.