Lattice relaxation, electronic screening, and spin and orbital phase diagram of LaTiO${}_3$/SrTiO${}_3$ superlattices

The effects of lattice relaxation in LaTiO${}_3$/SrTiO${}_3$ superlattices are investigated using a combination of LDA$+U$ density functional theory, and Hartree-Fock effective Hamiltonian calculations. We find noticeable ($\sim 0.1$--0.2\mathring{A})distortionsoftheTiO$_6$ octahedra in the near-La region. The resulting screening changes the Ti $d$-electron density substantially. Tight-binding fits to the relaxed-lattice band structure, combined with Hartree-Fock calculations of the resulting model, reveal a novel phase with $xy$ orbital order, which does not occur in bulk LaTiO${}_3$, or in the hypothetical unrelaxed structure.