We use the self-consistent harmonic approximation with machine learning interatomic potentials to calculate the effect of ${}^{18}\mathrm{O}$ substitution on the properties of quantum paraelectric ${\mathrm{SrTiO}}_3$ (STO). We find that calculations including both quantum and anharmonic effects are able to reproduce the experimentally observed isotope effect, in which the replacement of ${}^{16}\mathrm{O}$ by ${}^{18}\mathrm{O}$ induces the ferroelectric state, and we demonstrate that the ferroelectric phase transition in $\mathrm{ST}{}^{18}\mathrm{O}$ can be reproduced in a purely displacive description. We calculate the ferroelectric soft mode frequency as a function of volume, lattice parameters, and temperature for $\mathrm{ST}{}^{16}\mathrm{O}$ and $\mathrm{ST}{}^{18}\mathrm{O}$ and find that the phase space in which $\mathrm{ST}{}^{16}\mathrm{O}$ shows quantum paraelectric behavior, while $\mathrm{ST}{}^{18}\mathrm{O}$ becomes ferroelectric, is narrow. Our Letter shows that machine learning interatomic potentials enable temperature-dependent simulations that include quantum and anharmonic phonon effects and that quantitative prediction of the phase diagram in the case of STO is limited by the accuracy of the underlying electronic structure method.

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• Ferroelectricity
• Phonons
• Quantum phase transitions
• Structural phase transition
• Ferroelectrics
• Paraelectrics
• First-principles calculations
• Machine learning categories