Fig. 1: Period-dependent changes in the symmetry of STO–CTO superlattices.

a, Superlattice structures calculated from DFT with coloured-bar schematics denoting the chemically (left) and structurally (right) defined interfaces. Here green, blue and cyan rectangles correspond to STO, CTO and interface layers, respectively; the same colours are used in e, f, h, i, k, l. Green, blue, grey and red circles in a, e, f, h, i, k correspond to Sr, Ca, Ti and O atoms, respectively. b–d, The [100] zone-axis SADP for SL27 (b), SL4 (c) and SL2 (d) grown on NGO. The coloured arrows correspond to ordered reflections from the three possible domains. The solid arrows indicate ordered reflections that exist and the hollow arrows indicate absences. Insets: ball-and-stick models of the orientations present with border colours matching the arrows. The red and blue arrows and insets are viewed along an out-of-phase tilt axis and the yellow are viewed along an in-phase tilt axis. In c, d, superlattice reflections are seen in the 001 direction. In b, closely spaced superlattice reflections appear as streaking of the fundamental reflections. e–m, ADF images (e, h, k), iDPC images (f, i, l) and octahedral tilt angles (g, j, m) of SL27 (e–g), SL4 (h–j) and SL2 (k–m). The legend in g illustrates the in-plane (green) and out-of-plane (black) tilt angles (θ), which are defined as half of the projected O–Ti–O bond angle . The tilt angles for a one unit-cell column are overlayed in each iDPC image to demonstrate the changing in-plane (green triangles) and out-of-plane (grey triangles) tilt angles. In g, j, m, solid and dashed curves are from experimental measurements and calculations, respectively. The error bars represent one standard deviation. Chemically abrupt interfaces are illustrated to the left of the ADF images (e, h, k) and model structures (a), illustrating the abrupt change between STO (green) and CTO (blue) layers. Chemically diffuse interfaces are illustrated to the right of the iDPC images (f, i, l) and model structures (a), illustrating the non-abrupt symmetry changes that are occurring as a result of octahedral coupling.