Polarization kinetics in ferroelectrics with regard to fluctuations

TL;DR

This paper models the time evolution of polarization in ferroelectrics using a Fokker-Planck approach, revealing hysteresis behavior in polarization and its gradients under external fields.

Contribution

It introduces a Fourier-based Fokker-Planck framework for analyzing polarization kinetics in ferroelectrics, enabling numerical solutions for multi-mode systems.

Findings

Demonstrates hysteresis in mean polarization

Shows hysteresis in mean squared polarization gradient

Provides numerical solutions for one and three modes

Abstract

Polarization in ferroelectrics, described by the Landau-Ginzburg Hamiltonian, is considered, based on a multi-dimensional Fokker-Planck equation. This formulation describes the time evolution of the probability distribution function over the polarization field configurations in the presence of a time dependent external field. The Fokker-Planck equation in a Fourier representation is obtained, which can then be solved numerically for a finite number of modes. Calculation results are presented for one and three modes. These results show the hysteresis of the mean polarization as well as that of the mean squared gradient of the polarization.