Hysteresis Phenomena in Relaxor Ferroelectrics: Consideration of Polar Nanoregions

Hysteresis phenomena of relaxor ferroelectrics have been modeled by considering spheroidal polar nanoregions covered by a thin shell of a linear dielectric both embedded into a ferroelectric matrix. The electric field within the spheroid is described by the Landau–Ginzburg–Devonshire equation. The resulting phase transition temperature is strongly dependent on the field direction. Calculations for single spheroids are generalized for an ensemble of random oriented spheroids. Finally, the temperature dependence of P–E hysteresis curve has been described with good accuracy for 0.7PbMg1/3Nb2/3O3–0.3PbTiO3 as an exemplary relaxor ferroelectric.