Simulation of butterfly loops in ferroelectric materials

Ferroelectric materials exhibit complex behaviour upon electric and mechanical loading. Their change of polarization and length is accompanied by hysteresis. The so-called butterfly loop characterizing the strain due to an applied electric field is striking. As these materials are used in technical applications as sensors, actuators, and non-volatile memory units, the ability to simulate these hysteretic phenomena is important. Here, a one-dimensional model is proposed that is capable of describing the qualitative behaviour of widely used perovskite-type ferroelectric materials.