Phase field model of domain dynamics in micron scale, ultrathin ferroelectric films: Application for multiferroic bismuth ferrite

In this work, we report a massively parallel and time domain implementation of the 3D phase field model that can reach beyond micron scale and consider for arbitrary electrical and mechanical boundary conditions. The first part of the paper describes the theory and the numerical implementation of the model. A mixed-mode approach of finite difference and finite element grid has been used for calculating the nonlocal electrostatic and elastic interactions respectively. All the local and non-local interactions are shown to scale linearly up to thousands of processors. This massive paralleling allows to compare our results directly with experiments at the same length scales where the experiments themselves are performed. The second part of the paper presents results of ferroelectric domain switching in devices based on the multi-ferroic BiFeO3. We have particularly emphasized the importance of charge driven domain growth and the effect of electrical boundary conditions that explain the temporal evolution of ferroelectric domains observed in recent experiments. We also predict a mechanism of controlling domain size in the multi-domain ferroelectric switching that could be useful for practical applications. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4754800]