The use of fractional derivation in modeling ferroelectric dynamic hysteresis behavior over large frequency bandwidth

The present article proposes a dynamical model to obtain ferroelectric hysteresis dynamics based on fractional derivatives. The consideration of a fractional derivative term widely increases the frequency bandwidth of the accuracy of the traditional hysteresis models. As a consequence, the model is suited for successfully taking into account the well-known scaling relations of the ferroelectric hysteresis area, < A >, versus the frequency, f, and field amplitude, E-0. Under low frequency excitation, simulation tests provided good results regarding the comparison of the fractional model, experimental results and the well-known nonentire power law < A >infinity f(1/3)E(0)(2/3) (where < A > represents the hysteresis loop area). These results were followed by comparing the hysteresis area obtained from the fractional model with that from the well known scaling relations as f ->infinity, and the results were proposed as validation of the high frequency behavior. Next, the model was tested on large frequency bandwidths (>6 decades) and validated with success using the comparison between simulation tests and the only experimental results available in literature obtained in such conditions by Liu [J. Phys.: Condens. Matter 16, 1189 (2004)] for BNT thin film samples. (C) 2010 American Institute of Physics. [doi: 10.1063/1.3393814]