Time-fractional Landau–Khalatnikov model applied to numerical simulation of polarization switching in ferroelectrics

Abstract

Ferroelectrics are complex structured media that exhibit fractal properties and memory effects in terms of a number of dynamic characteristics. The most relevant applications of ferroelectrics in science and technology are associated with the primary mechanisms of polarization switching and domain structure dynamics induced by external exposure. In this study, we propose a time-fractional modification of the Landau–Ginzburg–Devonshire–Khalatnikov model to describe the dynamics of ferroelectric polarization switching. To solve the time-fractional cubic-quintic partial differential equation numerically, a computational scheme is derived. The technique combines an iterative procedure and an implicit finite-difference scheme based on an approximation of the Caputo derivative. A series of computational experiments are presented to visualize polarization switching characteristics on the example of thin films of barium titanate. A variation of the order of fractional derivative as a numerical characteristic of the memory effect allows one to “adjust” suitable regimes of simulated dynamical system. The obtained findings indicate that the generalized time-fractional model can provide better reproduction of experimental data in comparison with the classical analogue.