Electrocaloric effect in relaxor ferroelectrics

A theoretical model for the electrocaloric effect (ECE) in relaxor ferroelectrics is presented. By solving a self-consistent relation for the ECE temperature change ΔT and minimizing numerically the mean field free energy for relaxors, the field and temperature dependence of ΔT is calculated. The corresponding harmonic Landau coefficient a=a(T), which differs from the ferroelectric case by always being positive, is derived from the spherical random bond-random field model, and the fourth-order coefficient b is treated as a phenomenological parameter, which can be either positive or negative. For b0, a line of field-induced first-order relaxor-to-ferroelectric phase transitions exists in relaxors, which terminates at a liquid-vapor type critical point ECP,TCP. The critical behavior close to ECP,TCP is analyzed. It is shown that near the first-order phase transition a temperature or field interval or gap formally appears, where ΔT cannot be found. However, domain formation in the coexistence range should restore the continuous behavior of the ECE observed in real systems. Finally, it is shown that the ECE responsivity R1=ΔT/E reaches a maximum near the critical point, in agreement with recent experiments.