Highly-confined spin-polarized two-dimensional electron gas in SrTiO${}_3$/SrRuO${}_3$ superlattices

We report first principles characterization of the structural and electronic properties of (SrTiO${}_3$)${}_5$/(SrRuO${}_3$)${}_1$ superlattices. We show that the system exhibits a spin-polarized two-dimensional electron gas, extremely confined to the 4$d$ orbitals of Ru in the SrRuO${}_3$ layer. Every interface in the superlattice behaves as a minority-spin half-metal ferromagnet, with a magnetic moment of $\mu$ = 2.0 ${\mu }_{\mathrm{B}}$/SrRuO${}_3$ unit. The shape of the electronic density of states, half metallicity and magnetism are explained in terms of a simplified tight-binding model, considering only the $t_{2g}$ orbitals plus (i) the bi-dimensionality of the system, and (ii) strong electron correlations.