Universality of the Scaling Law for Ferroic Domains

TL;DR

This paper demonstrates a universal scaling law for ferroic domain periodicity related to crystal thickness, deriving an analytical expression applicable to ferroelectric and ferromagnetic materials, with implications for nano-devices.

Contribution

It introduces a universal scaling law for ferroic domains and provides analytical formulas for domain wall thickness and exchange constants.

Findings

Derived an analytical expression for the universal scaling factor.

Calculated domain wall thickness and exchange constants for ferroic materials.

Discussed implications for ferroelectric nano-devices and photonic crystals.

Abstract

We show how the periodicity of 180^{o} domains as a function of crystal thickness scales with the thickness of the domain walls both for ferroelectric and for ferromagnetic materials. We derive an analytical expression for the universal scaling factor and use this to calculate domain wall thickness and gradient coefficients (exchange constants) in some ferroic materials. We then use these to discuss some of the wider implications for the physics of ferroelectric nano-devices and periodically poled photonic crystals.