Phase transitions of LaMnO$_3$ and SrRuO$_3$ from DFT + U based machine learning force fields simulations

Perovskite oxides are known to exhibit many magnetic, electronic and structural phases as function of doping and temperature. These materials are theoretically frequently investigated by the DFT+U method, typically in their ground state structure at $T=0$. We show that by combining machine learning force fields (MLFFs) and DFT+U based molecular dynamics, it becomes possible to investigate the crystal structure of complex oxides as function of temperature and $U$. Here, we apply this method to the magnetic transition metal compounds LaMnO$_3$ and SrRuO$_3$. We show that the structural phase transition from orthorhombic to cubic in LaMnO$_3$, which is accompanied by the suppression of a Jahn-Teller distortion, can be simulated with an appropriate choice of $U$. For SrRuO$_3$, we show that the sequence of orthorhombic to tetragonal to cubic crystal phase transitions can be described with great accuracy. We propose that the $U$ values that correctly capture the temperature-dependent structures of these complex oxides, can be identified by comparison of the MLFF simulated and experimentally determined structures.