We use the self-consistent harmonic approximation (SSCHA) with machine learning interatomic potentials to calculate the effect of 18O substitution on the properties of quantum paraelectric SrTiO3 (STO). We find that calculations including both quantum and anharmonic effects are able to reproduce the experimentally observed isotope effect, in which replacement of 16O by 18O induces the ferroelectric state, and demonstrate that the ferroelectric phase transition in ST18O can be reproduced in a purely displacive manner. We calculate the ferroelectric soft mode frequency as a function of volume, lattice parameters and temperature for ST16O and ST18O, and find that the phase space in which ST16O shows quantum paraelectric behaviour, while ST18O becomes ferroelectric is narrow. Our study shows that machine learning interatomic potentials enable temperature-dependent simulations that include quantum and anharmonic phonon effects, however quantitative prediction of phase diagrams remains challenging due to a lack of universally accurate electronic structure methods.
@article{arxiv.2508.10735,
title = {Machine-Learning-enabled ab initio study of quantum phase transitions in SrTiO$_3$},
author = {Jonathan Schmidt and Nicola A. Spaldin},
journal= {arXiv preprint arXiv:2508.10735},
year = {2025}
}