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Motivated by the puzzling report of the observation of a ferromagneticinsulating state in LaMnO$_3$/SrTiO$_3$ heterostructures, we calculate theelectronic and magnetic state of LaMnO$_3$, coherently matched to a SrTiO$_3$square substrate within a "strained-bulk" geometry. We employ three differentdensity functional theory based computational approaches: (a) densityfunctional theory (DFT) supplemented with Hubbard U (DFT+U), (b) DFT +dynamical mean field theory (DMFT), and (c) a hybrid functional treatment ofthe exchange-correlation functional. While the first two approaches includelocal correlations and exchange at Mn sites, treated in a static and dynamicmanner, respectively, the last one takes into account the effect of non-localexchange at all sites. We find in all three approaches that the compressivestrain induced by the square substrate of SrTiO$_3$ turns LaMnO$_3$ from anantiferromagnet with sizable orbital polarization to a ferromagnet withsuppressed Jahn-Teller distortion in agreement with experiment. However, whileboth DFT+U and DFT+DMFT provide a metallic solution, only the hybridcalculations result in an insulating solution, as observed in experiment. Thisinsulating behavior is found to originate from an electronic chargedisproportionation. Our conclusions remain valid when we investigateLaMnO$_3$/SrTiO$_3$ within the experimental set-up of a superlattice geometryusing DFT+U and hybrid calculations.

Electronic and Magnetic State of LaMnO$_3$ Epitaxially Strained on SrTiO$_3$: Effect of Local Correlation and Non-local Exchange