Anharmonic Thermodynamics Redefines Metastability and Parent Phases in Ferroelectric HfO₂

Hafnia (HfO₂) is a silicon-compatible dielectric material, yet stabilizing its desired but metastable ferroelectric phase remains challenging. Phase stability predictions by density functional theory (DFT) have provided crucial guidance, but most simulations neglected or only treated finite temperature effects with (quasi)harmonic approximation due to the high computational cost of DFT. Here, we develop a machine learning force field and perform thermodynamic calculations for HfO₂ using self-consistent phonon theory to address growing evidence of anharmonicity. Our results reveal that the ferroelectric orthorhombic phase oIII exhibits metastability below 0.1k_BT under most conditions within the simulated regime of temperature and pressure (600 ≤ T ≤ 1500 K and 0 ≤ p ≤ 7.5 GPa), contradicting previous harmonic predictions of metastability above 1500 K at ambient pressure. We further report evidence for the temperature- and pressure-dependent ferroelectric parent phase despite efforts to identify a universal one. This study highlights the importance of anharmonicity and provides an effective approach to its treatment in the design of HfO₂-based ferroelectrics.