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We calculate the properties of the 4$d$ ferromagnet SrRuO$_3$ in bulk andthin film form with the aim of understanding the experimentally observed metalto insulator transition at reduced thickness. Although the spatial extent ofthe 4$d$ orbitals is quite large, many experimental results have suggested thatelectron-electron correlations play an important role in determining thismaterial's electronic structure. In order to investigate the importance ofcorrelation, we use two approaches which go beyond the conventional localdensity approximation to density functional theory (DFT): the local spindensity approximation + Hubbard $U$ (LSDA+$U$) and the pseudopotentialself-interaction correction (pseudo-SIC) methods. We find that the details ofthe electronic structure predicted with the LSDA do not agree with theexperimental spectroscopic data for bulk and thin film SrRuO$_3$. Improvementis found by including electron-electron correlations, and we suggest that bulkorthorhombic SrRuO$_3$ is a {\it weakly strongly-correlated} ferromagnet whoseelectronic structure is best described by a 0.6 eV on-site Hubbard term, orequivalently with corrections for the self-interaction error. We also perform{\it ab initio} transport calculations that confirm that SrRuO$_3$ has anegative spin polarization at the Fermi level, due to the position of theminority Ru 4$d$ band center. Even with correlations included in ourcalculations we are unable to reproduce the experimentally observedmetal-insulator transition, suggesting that the electronic behavior ofSrRuO$_3$ ultra-thin films might be dominated by extrinsic factors such assurface disorder and defects.

Electronic properties of bulk and thin film SrRuO$_3$: a search for the metal-insulator transition