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

The effect of lattice relaxation on the electronic charge density, band structure, and phase diagram in oxide heterostructure, LaTiO$_3$/SrTiO$_3$ superlattices, the structure grown and measured by Ohtomo {\it et al}.[1], is investigated using density functional theory LDA and LDA+$U$ (VASP implementation). We observe substantial ferroelectric-like distortion of TiO$_6$ octahedra at the nearest-to-La region which screens the electrostatic force originating from La$^{3+}$ ion reducing the charge density in the La-rich region. We determine the changes in the low energy electronic Hamiltonian caused by the lattice relaxation and investigate the consequences for the ground state phase diagram using the Hartree-Fock approximation. Finally, we present a detailed comparison with previous calculations which neglected the lattice effect. [2] Support from DOE ER 46169. [1]Ohtomo et al., Nature \textbf{419}, 378 (2002). [2]Okamoto and Millis, Nature (London) {\bf 428}, 630 (2004), and Phys. Rev. B {\bf 70}, 195120 (2004).