Ferroelectricity in Pb(Zr$_{0.5}$Ti$_{0.5}$)O$_{3}$ thin films: critical thickness and 180$^\circ$ stripe domains

TL;DR

This study uses Monte Carlo simulations to explore ferroelectricity in Pb(Zr$_{0.5}$Ti$_{0.5}$)O$_{3}$ thin films, revealing a critical thickness for ferroelectricity and the formation of 180° stripe domains.

Contribution

It identifies the critical thickness for ferroelectricity and explains the formation of stripe domains in thin films using first-principles-derived simulations.

Findings

Ferroelectricity disappears below approximately 12 Å thickness.

Periodic 180° stripe domains form above the critical thickness.

Stripe period increases with film thickness.

Abstract

The ferroelectric properties of disorder Pb(Zr$_{0.5}$Ti$_{0.5}$)O$_{3}$ thin films are investigated with Monte Carlo simulations on the basis of a first-principles-derived Hamitonian. It is found that there exists a critical thickness of about three unit cells ($\sim$12 \AA) below which the ferroelectricity disappears under the condition that the in-plane polarizations are suppressed by sufficient clamping effect. Above the critical thickness, periodic $180^{\circ}$ stripe domains with out-of-plane polarizations are formed in the systems in order to minimize the energy of the depolarizaing field. The stripe period increases with increasing film thickness. The microscopic mechanism responsible for these phenomena is discussed.