Electronic and magnetic state of LaMnO3 epitaxially strained on SrTiO3 : Effect of local correlation and nonlocal exchange

Motivated by the puzzling report of the observation of a ferromagnetic insulating state in ${\mathrm{LaMnO}}₃/{\mathrm{SrTiO}}₃$ heterostructures, we calculate the electronic and magnetic state of ${\mathrm{LaMnO}}₃$, coherently matched to a ${\mathrm{SrTiO}}₃$ square substrate within a ``strained-bulk'' geometry. We employ three different density functional theory based computational approaches: (a) density functional theory (DFT) supplemented with Hubbard $U\phantom{\rule{4pt}{0ex}}(\mathrm{DFT}+U)$, (b) DFT $+$ dynamical mean-field theory (DMFT), and (c) a hybrid functional treatment of the exchange-correlation functional. While the first two approaches include local correlations and exchange at Mn sites, treated in a static and dynamic manner, respectively, the last one takes into account the effect of nonlocal exchange at all sites. We find in all three approaches that the compressive strain induced by the square substrate of ${\mathrm{SrTiO}}₃$ turns ${\mathrm{LaMnO}}₃$, from an antiferromagnet with sizable orbital polarization, to a ferromagnet with suppressed Jahn-Teller distortion, in agreement with experiment. However, while both $\mathrm{DFT}+U$ and $\mathrm{DFT}+\mathrm{DMFT}$ provide a metallic solution, only the hybrid calculations result in an insulating solution, as observed in experiment. This insulating behavior is found to originate from an electronic charge disproportionation. Our conclusions remain valid when we investigate ${\mathrm{LaMnO}}₃/{\mathrm{SrTiO}}₃$ within the experimental setup of a superlattice geometry using $\mathrm{DFT}+U$ and hybrid calculations.