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Using first-principles techniques, we study the structural, magnetic andelectronic properties of (111)-oriented(LaMnO$_3$)$_{2n}$$\vert$(SrMnO$_3$)$_{n}$ superlattices of varying thickness($n=2,4,6$). We find that the properties of the thinnest superlattice ($n=2$)are similar to the celebrated half-metallic ferromagnetic alloyLa$_{2/3}$Sr$_{1/3}$MnO$_3$, with quenched Jahn-Teller distortions. Atintermediate thickness ($n=4$), the $a^{-}a^{-}a^{-}$ tilting patterntransitions to the $a^{-}a^{-}c^{+}$ tilting pattern, driven by the latticedegrees of freedom in the LaMnO$_3$ region. The emergence of the Jahn-Tellermodes and the spatial extent needed for their development play a key role inthis structural transition. For the largest thickness considered ($n=6$), weunveil an emergent separation of Jahn-Teller and volume-breathing orders in theground-state structure with the $a^{-}a^{-}c^{+}$ tilting pattern, whereas itvanishes in the antiferromagnetic configurations. The ground state of allsuperlattices is half-metallic ferromagnetic, not affected by the underlyingseries of structural transitions. Overall, these results outline athickness-induced crossover between the physical properties of bulkLa$_{2/3}$Sr$_{1/3}$MnO$_3$ and bulk LaMnO$_3$.

Emergent half-metal with mixed structural order in (111)-oriented (LaMnO$_3$)$_{2n}$|(SrMnO$_3$)$_n$ superlattices