Cobalt spin state and hyperfine interaction in ferromagnetic insulating LaCoO$_3$ thin films*

At low temperatures, bulk LaCoO$_3$ is a non-metallic diamagnet. In contrast, thin-film LaCoO$_3$ experiencing a tensile epitaxial strain is a ferromagnetic insulator in the same temperature range. It is difficult to properly describe this phenomenon with density functional theory (DFT) calculations, even with the Hubbard $U$ correction. Previous calculations have found ferromagnetic conducting thin-film LaCoO$_3$ with all Co ions in the intermediate-spin (IS) state, incompatible with experimental data. In this work, using the DFT+$U$ approach, we show that a strained LaCoO$_3$ thin film can be stabilized in a ferromagnetic insulating state. We also predict the electric field gradient (EFG) at the Co nucleus in the magnetic thin film, which can be helpful in identifying Co spin states via nuclear magnetic resonance (NMR) spectroscopy.