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

## TL;DR

This study investigates how epitaxial strain affects the electronic and magnetic properties of LaMnO$_3$ on SrTiO$_3$, revealing that non-local exchange interactions are crucial for accurately predicting its insulating state.

## Contribution

It compares local and non-local exchange approaches in DFT-based methods to explain the insulating ferromagnetic state of strained LaMnO$_3$.

## Key findings

- Strain induces ferromagnetism and suppresses Jahn-Teller distortion in LaMnO$_3$.
- Only hybrid functional calculations reproduce the insulating state observed experimentally.
- Electronic charge disproportionation underpins the insulating behavior.

## Abstract

Motivated by the puzzling report of the observation of a ferromagnetic insulating state in LaMnO$_3$/SrTiO$_3$ heterostructures, we calculate the electronic and magnetic state of LaMnO$_3$, coherently matched to a 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 (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 non-local exchange at all sites. We find in all three approaches that the compressive strain induced by the square substrate of SrTiO$_3$ turns LaMnO$_3$ from an antiferromagnet with sizable orbital polarization to a ferromagnet with suppressed Jahn-Teller distortion in agreement with experiment. However, while both DFT+U and DFT+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 LaMnO$_3$/SrTiO$_3$ within the experimental set-up of a superlattice geometry using DFT+U and hybrid calculations.