Maxwell relation, giant (negative) electrocaloric effect, and polarization hysteresis

The electrocaloric effect (ECE) in dielectrics is characterized by the isothermal entropy change ΔS and adiabatic temperature change ΔT induced by changes of external electric fields. The Maxwell relation, which relates changes of polarization P with temperature T (pyroelectric coefficient) under a fixed electric field E to ΔS for finite intervals in E, provides a convenient way to deduce the ECE from polarization data P(T, E). Hence, this method, known as the indirect method, is widely used in ECE studies in ferroelectrics. Here, we first present the thermodynamic consideration for the Maxwell relation. We then use the indirect method and P(T, E) from bipolar and unipolar polarization curves to deduce the ECE in the normal ferroelectric phase of a P(VDF-TrFE) copolymer. The deduced ECE using the P(T, E) from bipolar polarization curves exhibits a giant negative ECE. In contrast, the directly measured ECE in the same polymer shows the weak and normal ECE. We discuss the constraints of the indirect method and its relation to the polarization-electric field curves measured in practical ferroelectric materials.