Electronic structure induced reconstruction and magnetic ordering at the LaAlO$_3|$SrTiO$_3$ interface

Using local density approximation (LDA) calculations we predict GdFeO$_3$-like rotation of TiO$_6$ octahedra at the $n$-type interface between LaAlO$_3$ and SrTiO$_3$. The narrowing of the Ti $d$ bandwidth which results means that for very modest values of $U$, LDA$+U$ calculations predict charge and spin ordering at the interface. Recent experimental evidence for magnetic interface ordering may be understood in terms of the close proximity of an antiferromagnetic insulating ground state to a ferromagnetic metallic excited state.