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

Using first-principles techniques, we study the structural, magnetic and electronic 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 alloy La$_{2/3}$Sr$_{1/3}$MnO$_3$, with quenched Jahn-Teller distortions. At intermediate thickness ($n=4$), the $a^{-}a^{-}a^{-}$ tilting pattern transitions to the $a^{-}a^{-}c^{+}$ tilting pattern, driven by the lattice degrees of freedom in the LaMnO$_3$ region. The emergence of the Jahn-Teller modes and the spatial extent needed for their development play a key role in this structural transition. For the largest thickness considered ($n=6$), we unveil an emergent separation of Jahn-Teller and volume-breathing orders in the ground-state structure with the $a^{-}a^{-}c^{+}$ tilting pattern, whereas it vanishes in the antiferromagnetic configurations. The ground state of all superlattices is half-metallic ferromagnetic, not affected by the underlying series of structural transitions. Overall, these results outline a thickness-induced crossover between the physical properties of bulk La$_{2/3}$Sr$_{1/3}$MnO$_3$ and bulk LaMnO$_3$.