Dynamics of ferroelectric domains

Abstract

The goal of this thesis is to explore a simple and general framework for domain analysis in ferroelectric thin films. In this work I construct mathematical and numerical description of complex ferroelectric systems and use it to advance our knowledge and understanding of domains. I state that the main theoretical tool we have employed is an appropriate Landau-Ginzburg-Devonshire (LGD) model, and its time-dependent generalizations. I analyze four types of domains - (i) 1800, (ii) 900, (iii) vortex-antivortex and (iv) fractal. A nonlinear domain dynamics is observed in intrinsically pinned ferroelectric films while growing fractal domains occur under the influence of an external electric field. I measure fractal Hausdorff dimension by detecting the edges of the domain images by means of the standard Canny algorithm. Hausdorff dimension which is computed numerically shows a very good quantitative agreement with experiments. To understand dynamics, I compute the areal velocity of the domains as a function of the applied field and find different regions of nonlinearities that qualitatively agree with experiments. I also generate vortex-antivortex-vortex (V-AV-V) triplet by applying an inhomogeneous transverse field in the x-y plane. A specific boundary condition is used to maintain the sanctity of the vortex states i.e. the net polarization in the boundary is always ensured to be zero. I also use the Ginzburg-Landau-Devonshire free energy theory to construct a set of time-dependent differential equations in order to model the dynamics of interaction between the tip of an Atomic Force microscope (AFM) and the surface of a ferroelectric thin film. I obtain growth and nucleation pattern of ferroelectric domains under the AFM tip. To conclude, the construction of an appropriate domain model is an important step towards understanding the technologically important ferroelectric materials. We have confirmed our results by double-checking with experimental data and also with other alternate theoretical approaches.