Octahedral coupling in (111)- and (001)-oriented La$_{2/3}$Sr$_{1/3}$MnO$_3$/SrTiO$_3$ heterostructures

Rotations and distortions of oxygen octahedra in perovskites play a key role in determining their functional properties. Here we investigate how octahedral rotations can couple from one material to another in La$_{2/3}$Sr$_{1/3}$MnO$_3$/SrTiO$_3$ epitaxial heterostructures by first principles density functional theory (DFT) calculations, emphasizing the important differences between systems oriented perpendicular to the (111)- and (001)-facets. We find that the coupling length of out-of-phase octahedral rotations is independent of the crystalline facet, pointing towards a steric effect. However, the detailed octahedral structure across the interface is significantly different between the (111)- and (001)-orientations. For (001)-oriented interfaces, there is a clear difference whether the rotation axis in SrTiO$_3$ is parallel or perpendicular to the interface plane, while for the (111)-interface the different rotations axes in SrTiO$_3$ are symmetry equivalent. Finally, we show that octahedral coupling across the interface can be used to control the spatial distribution of the spin density.