Strain-induced structural transitions in (111)-oriented (LaMnO$_3$)$_{2n}|$(SrMnO$_3$)$_n$ superlattices
By means of first-principles electronic structure calculations, we hereby investigate the structural transitions induced by epitaxial strain in (111)-oriented (LaMnO$_3$)$_{2n}|$(SrMnO$_3$)$_n$ superlattices, with $n=2,4,6$. All superlattices in the explored range of strain are shown to prefer a half-metallic ferromagnetic order where the local magnetic moments are coupled to volume-breathing distortions. More in detail, our results reveal that thickness plays a crucial role in the response to epitaxial strain, which is particularly evident in the resulting tilt pattern of the oxygen octahedra. The thinnest superlattice, for $n=2$, always adopts the $a^-a^-a^-$ tilt pattern and the competing $a^-a^-c^+$ tilt pattern can be stabilized as a metastable state only in presence of compressive strain. Instead, the superlattice with $n=4$ favours the $a^-a^-c^+$ tilt pattern at equilibrium conditions, but the in-phase rotations around the third pseudocubic axis are so fragile that the $a^-a^-a^-$ pattern is recovered under a tiny amount of either compressive or tensile strain. The superlattice with $n=6$ exhibits a more nuanced behaviour: compressive strain drives a transition from $a^-a^-c^+$ to $a^-a^-a^-$, whereas tensile strain preserves the $a^-a^-c^+$ tilt pattern and significantly accentuates the structural differences between the two inequivalent sublattices within this symmetry. In fact, the Jahn-Teller distortions are quenched in one of the sublattices, leading to enhanced volume-breathing distortions and corresponding enhanced charge and spin oscillations. This suggests that Hund's physics may be more relevant in this regime of tensile strain, maximizing the interplay between strong electronic correlations and structural effects.