Atomistic theory of hybrid improper ferroelectricity in perovskites

Abstract

We discuss the so-called hybrid improper ferroelectricity (HIF) appearing in ${A}^{\ensuremath{'}}B$O${}_{3}$/${A}^{\ensuremath{'}\ensuremath{'}}B$O${}_{3}$ perovskite superlattices. By means of straightforward analytical derivations and/or associated graphical analysis, we demonstrate that two previously-proposed elemental interatomic couplings between the O${}_{6}$ octahedral rotations and the displacements of the $A$-site cations [Bellaiche and \'I\~niguez, Phys. Rev. B 88, 014104 (2013)] naturally reproduce and explain HIF in (${A}^{\ensuremath{'}}B$O${}_{3}$)${}_{1}$/(${A}^{\ensuremath{'}\ensuremath{'}}B$O${}_{3}$)${}_{1}$ superlattices composed of layers that are only one unit cell thick. Further, we show that our approach permits an easy treatment of superlattices of arbitrary stacking direction and layer thickness. In particular, this allows us to predict (i) other previously overlooked types of HIF in (${A}^{\ensuremath{'}}B$O${}_{3}$)${}_{1}$/(${A}^{\ensuremath{'}\ensuremath{'}}B$O${}_{3}$)${}_{1}$ superlattices and (ii) original and striking effects, such as the possibility of discretizing the magnitude of the spontaneous polarization in (${A}^{\ensuremath{'}}B$O${}_{3}$)${}_{m}$/(${A}^{\ensuremath{'}\ensuremath{'}}B$O${}_{3}$)${}_{n}$ systems when varying the $m$ and $n$ layer thicknesses. We further show first-principles results confirming the latter predictions.