Polarcatrosphy and electronic reconstructions in LaAlO$_{\mathrm{3}}$/SrMnO$_{\mathrm{3}}$ (111) digital heterostructures*

Based on extensive first-principle density functional theory calculations, we report different electronic phases at the LaAlO$_{\mathrm{3}}$/SrMnO$_{\mathrm{3}}$ (111) heterointerfaces. In the $n$-type LaAlO$_{\mathrm{3}}$/SrMnO$_{\mathrm{3}}$ (111) supperlattices, electrons transferred from LaAlO$_{\mathrm{3}}$ component distribute unevenly in SrMnO$_{\mathrm{3}}$ component and occupy Mn's e$_{\mathrm{g}}$ orbital, inducing half-metallic ferromagnetism in the framework of Zener double exchange. With increasing SrMnO$_{\mathrm{3}}$ layers, the sum of every Mn magmon keep a constant suggesting a fixed number of charge transferred from LaAlO$_{\mathrm{3}}$ component. For $p$-type superlattices, holes reside almost uniformly at the SrO$_{\mathrm{3}}$ and LaO$_{\mathrm{3}}$ plane drived by the polar electric field in the LaAlO$_{\mathrm{3}}$ and SrMnO$_{\mathrm{3}}$ component. With absence of the e$_{\mathrm{g}}$ states at the Mn sites, bulk-like G-type AFM ordering were obvious with almost imperceptible octahedron rotation and tilting. But $p$-type superlattices are metallic because of hole transfer. Our studies demonstrate the potential applications of perovskite heterointerfaces in spintronic devices.