Strain-tuned ferroelectric transitions in HfO2: role of $${X}_{2}^{-}$$ mode in ferroelectric instabilities

Recent studies have identified HfO2 as a promising ferroelectric material for thin films, highlighting its potential as a state-of-the-art option for future ferroelectric applications. However, due to the complexity of the fabrication process, the underlying mechanism of the phase transition to Pca21 is still not fully understood. In this study, we aim to clarify the phase transition pathway by investigating the formation of the ferroelectric Pca21 phase via $${X}_{2}^{-}$$ displacement and symmetry-allowed phonon mode instability. Our results reveal that applying tensile strain regardless of direction enhances the $${X}_{2}^{-}$$ displacement and induces instabilities in the polar and antipolar modes, causing the P42/nmc phase to collapse into Pbcn or Aba2, depending on the strain direction. Emergent polar and antipolar mode displacements at the primary transition couple to $${X}_{2}^{-}$$, lowering the trilinear-coupling barrier and stabilizing Pca21. Although the $${X}_{2}^{-}$$ mode alone makes only a minor contribution, its coupling with other distortion modes governs the entire energy landscape by driving the Landau coefficients to negative values, initiating the kinetic transition pathway toward the Pca21 phase. This fundamental paradigm shift toward a mechanism governed by the $${X}_{2}^{-}$$ displacement provides a way to control the ferroelectric phase fraction in polycrystalline films under various substrate conditions via $${X}_{2}^{-}$$ engineering, paving the way for a foundation for the practical realization of ferroelectricity in device applications.