A Landau theory of ferroelectric nanoribbons

Abstract

Most of the work involving the Landau-Devonshire theory of ferroelectrics has been either for bulk materials or thin films. By extending such calculations to two dimensions it is possible to consider a ferroelectric strip. If the thickness and width of the strip are small compared to the surface are of the corresponding surfaces it is expected that the spontaneous polarisation near the surfaces will be different from that at points further inside the strip. This paper will show how Landau-Devonshire theory can be applied to such a strip. This is of particular interest now with increasing focus on nanoscale dimensions, where these size effects are expected to be more pronounced. Thus the work will concern relevant strips whose thickness and length are on the nanoscale but whose length is much greater, and from now on will mostly be referred to as nanoribbons. After showing how spontaneous polarisation profiles can be calculated, an outline will be given of how Maxwell's equations together with Landau-Khalatnikov dynamical equations can be brought in to study the interaction of the nanoribbon with incident electromagnetic waves. The work here forms a fundamental basis for numerical analysis of ferroelectric strips and will be useful in future computer aided design implementations which require modelling of ferroelectric elements.