Atomistic treatment of depolarizing energy and field in ferroelectric nanostructures

TL;DR

This paper introduces an atomistic method for accurately calculating depolarizing energy and fields in low-dimensional ferroelectric nanostructures, revealing limitations of continuum models and discovering a novel phase transition in nanodots.

Contribution

It develops an atomistic approach applicable to any low-dimensional ferroelectric structure, surpassing the accuracy of traditional continuum models and uncovering new phase behavior.

Findings

Limitations of continuum models demonstrated

Unusual phase transition observed in ferroelectric nanodots

Atomistic approach enables accurate depolarizing field calculations

Abstract

An {\it atomistic} approach allowing an accurate and efficient treatment of depolarizing energy and field in {\it any} low-dimensional ferroelectric structure is developed. Application of this approach demonstrates the limits of the widely used continuum model (even) for simple test cases. Moreover, implementation of this approach within a first-principles-based model reveals an unusual phase transition -- from a state exhibiting a spontaneous polarization to a phase associated with a toroid moment of polarization -- in a ferroelectric nanodot for a critical value of the depolarizing field.