Electrostatics and domains in ferroelectric superlattices

Abstract

The electrostatics arising in ferroelectric/dielectric two-dimensional heterostructures and superlattices is revisited within a Kittel model in order to define and complete 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° domains is well understood, where 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 ≪ d ). For thinner films, a minimum is reached for w before diverging to a monodomain. Although this behaviour is known to be qualitatively unaltered when the dielectric environment of the film is modified, we consider the quantitative changes in that behaviour induced on the ferroelectric film by different dielectric settings: as deposited on a dielectric substrate, sandwiched between dielectrics, and in a superlattice of alternating ferroelectric/dielectric films. The model assumes infinitely thin domain walls, and therefore is not expected to be reliable for film thickness in the nanometre scale. The polarization field P(r) does vary in space, deviating from ± P S , following the depolarizing field in linear response, but the model does not include a polarization-gradient term as would appear in a Ginzburg–Landau free energy. The model is, however, worth characterizing, both as paradigmatic reference, and as applicable to not-so-thin films. The correct renormalization of parameters is obtained for the thick-film square-root behaviour in the mentioned settings, and the sub-Kittel regime is fully characterized. New results are presented alongside well-known ones for a comprehensive description. Among the former, a natural separation between strong and weak ferroelectric coupling in superlattices is found, which depends exclusively on the dielectric anisotropy of the ferroelectric layer.

Theory of polar domains in moiré heterostructures

“…The formation of ferroelectric domains, in oxide perovskite thin films for example, is a well-known problem which has been understood for many years. A free-standing ferroelectric thin film can form a polydomain structure in order to screen the depolarizing field arising from the polar discontinuities at the surfaces, and the behavior of the domains as a function of film thickness and perpendicular applied field can be studied in the limit of infinitely thin domain walls [50][51][52]. When the width of the domains w is less than the thickness d of the film, the domains follow Kittel's law [50,51]: w = √ l k d, where l k Kittel's length, the relevant length scale for the domains.…”

“…When the width of the domains w is less than the thickness d of the film, the domains follow Kittel's law [50,51]: w = √ l k d, where l k Kittel's length, the relevant length scale for the domains. In the limit of zero thickness, the width of the domains diverge, and a monodomain or paraelectric phase becomes more favourable [52]. Of course, in this limit, the approximation of infinitely thin walls is not appropriate.…”

Optically Induced Picosecond Lattice Compression in the Dielectric Component of a Strongly Coupled Ferroelectric/Dielectric Superlattice

“…[1,2] Key effects include the electrostatic coupling between layers, the atomic-scale structure of interfaces, strain arising from the epitaxial mismatch, and the depolarization field arising from the polarization discontinuity at interfaces between FE and DE layers. [3][4][5] At the nanometer length scale, an internal electric field polarizing the DE layers arises in response to the depolarization field in the FE layer. [6] Structural features such as the octahedral rotation pattern of the component layers can also vary at, and across, interfaces and can affect the equilibrium configuration of the electrical polarization.…”

Evolution of domain structure with electron doping in ferroelectric thin films

“…In paraelectric LaAlO 3 /SrTiO 3 interfaces, the electron gas forms a compact 2D layer adjacent to the interface while the lattice polarization points perpendicular to the interface, into the substrate [4]. On the other hand, it is a universal feature of ferroelectrics that they break up into domains to reduce the large electrostatic depolarizing fields that accompany ferroelectricity [42,43]. Which, if either, scenario applies to ferroelectric LaAlO 3 /Sr 0.99 Ca 0.01 TiO 3 interfaces?…”

“…It is known that under most conditions insulating ferroelectrics spontaneously break translational symmetry parallel to the interface and form Kittel domains [42,43] as a way of reducing the depolarizing electric fields generated by the lattice polarization [Fig. 1(b)].…”