Polarization rotation in epitaxially strained perovskite-oxide superlattices

Utilizing first-principles computational techniques, we have mapped out $\Gamma$-point structural instabilities in (BaTiO$_{3}$)$_{8}$/(SrTiO$_{3}$)$_{4}$ superlattices held at varying degrees of epitaxial strain and constrained to P4mm symmetry with fully developed polarization in the out-of-plane direction. We find that at compressive strains larger than -0.5\% (with respect to a fully relaxed P4mm structure) the superlattices exhibit no structural instabilities. However, at a smaller compressive strain, an in-plane ferroelectric instability emerges in the SrTiO$_{3}$ layers. This instability is then complemented by a similar instability in the BaTiO$_{3}$ layers that develops at tensile strain of more than 0.2\%, suggesting nonzero polarization components for both in- and out-of-plane directions throughout the whole superlattice.