On the statistical correlations of random polarization and electric depolarization fields in ferroelectrics

TL;DR

This paper develops an exact stochastic model to analyze the time-dependent correlations of polarization fields in ferroelectrics, providing insights into nonlinear optical phenomena.

Contribution

It introduces an exactly solvable model for polarization correlations in ferroelectrics, with analytical derivations and numerical evaluations of correlation coefficients.

Findings

Derived full set of time-dependent correlation coefficients

Provided graphical visualization of correlations in 3D

Facilitated analysis of nonlinear optical effects

Abstract

A conceptual problem of the electric-field mediated polarization correlations during a stochastic formation of polarization domain structure in ferroelectrics is addressed by using an exactly solvable stochastic model of polarization development in a uniaxial ferroelectric [Phys. Rev. B 107, 144109 (2023)]. A full set of time-dependent two-point correlation coefficients between all random variables is derived analytically, evaluated numerically and presented graphically in 3D. They are particularly required for the analysis of nonlinear phenomena involving spatial dispersion like optical second harmonic generation and scattering.