Electrostatics and domains in ferroelectric superlattices

TL;DR

This paper revisits the electrostatics and domain formation in ferroelectric superlattices using a simplified model, revealing how domain width varies with film thickness and coupling strength, with implications for designing ferroelectric devices.

Contribution

It provides a clear theoretical framework for understanding domain behavior in ferroelectric superlattices, extending Kittel's law to complex layered structures and identifying critical coupling thresholds.

Findings

Domain width follows Kittel's law in thick films.

Deviation from Kittel's law occurs in thin films, leading to mono-domain states.

Superlattices exhibit a critical thickness ratio affecting ferroelectric coupling.

Abstract

The electrostatics arising in ferroelectric/dielectric two-dimensional heterostructures and superlatitices is revisited here within a simplest Kittel model, in order to define a clear paradigmatic reference for domain formation. The screening of the depolarizing field in isolated ferroelectric or polar thin films via the formation of 180$^{\circ}$ domains is well understood, whereby the width of the domains $w$ grows as the square-root of the film thickness $d$, following Kittel's law, for thick enough films ($w\ll d$). This behavior is qualitatively unaltered when the film is deposited on a dielectric substrate, sandwiched between dielectrics, and even in a superlattice setting, with just a suitable renormalisation of Kittel's length. As $d$ decreases, $w(d)$ deviates from Kittel's law, reaching a minimum and then diverging onto the mono-domain limit for thin enough films, always assuming a given spontaneous polarization $P$ of the ferrolectric, only modified by linear response to the depolarizing field. In most cases of experimental relevance $P$ would vanish before reaching that thin-film regime. This is not the case for superlattices. Unlike single films, for which the increase of the dielectric constant of the surrounding medium pushes the deviation from the Kittel's regime to lower values of $d$, there is a critical value of the relative thickness of ferroelectric/dielectric films in superlattices beyond which that behavior is reversed, and which defines the separation between strong and weak ferroelectric coupling in superlattices.