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Inspired by the experimental findings of an exotic ferromagnetic insulatingstate in LaMnO$_3$/SrTiO$_3$ heterostructures, we calculate the electronic andmagnetic state of LaMnO$_3$/SrTiO$_3$ superlattices with comparable thicknessesemploying ab-initio dynamical mean-field theory. Projecting on the low-energysubspace of Mn $3d$ and Ti $3d$ states, and solving a multi-impurity problem,our approach emphasizes on local correlations at Mn and Ti sites. We find thata ferromagnetic insulating state emerges due to intrinsic effects of strongcorrelations in the system, in agreement with experimental studies. We alsopredict that, due to electronic correlations, the emerging 2D electron gas islocated at the LMO side of the interface. This is in contrast to DFT resultsthat locate the electron gas on the STO side. We estimate the transitiontemperature for the paramagnetic to ferromagnetic phase transition, which maybe verified experimentally. Importantly, we also clarify that the epitaxialstrain is a key ingredient for the emergence of the exotic ferromagneticinsulating state. This becomes clear from calculations on a strained LaMnO$_3$system, also showing ferromagnetism which is not seen in the unstrained bulkmaterial.

Emergence of a ferromagnetic insulating state in LaMnO$_3$/SrTiO$_3$ heterostructures: The role of strong electronic correlations and strain