First-principles study of competing ferroelectric and antiferroelectric instabilities in BaTiO3/BaO superlattices

We report a first-principles study of (BaTiO${_3}$)$_m$/(BaO)$_n$ superlattices for a wide range of periodicities $m/n$. We show that such a system develops a polar zone-center instability for sufficiently large \textit{m}/\textit{n} ratio, which can be understood, at least qualitatively, from a simple electrostatic model and should lead to a ferroelectric ground-state. However, the analysis of the phonon dispersion curves also points out the appearance of stronger antiferroelectric instabilities at the zone boundaries around $m=4$, before the critical ratio for ferroelectricity is reached and which still dominate beyond it. The dominant character of the anti-ferroelectric instability is explained from the depolarizing field which hardens the ferroelectric mode. This analysis allows us to predict that, (BaTiO${_3}$)$_m$/(BaO)$_n$ superlattices should present an antiferroelectric ground state for $m$ larger than 4, which should smoothly evolve to a multidomain structure for increasing $m$ values and only become ferroelectric for large $m$.