Trilinear coupling driven ferroelectricity in HfO$_2$

TL;DR

This study reveals that trilinear coupling among specific lattice modes stabilizes ferroelectricity in HfO₂, with strain conditions further enhancing the ferroelectric phase, providing a comprehensive theoretical understanding of its stabilization mechanism.

Contribution

The paper introduces a Landau-theory-based analysis combined with first-principles simulations to identify trilinear mode coupling as the key factor in stabilizing ferroelectricity in HfO₂, extending understanding to strain effects.

Findings

Trilinear coupling among three modes stabilizes ferroelectricity.

Strain conditions can destabilize or stabilize specific modes.

Ferroelectric phase is stabilized under strain, aligning with experiments.

Abstract

Ferroelectricity in hafnia is often regarded as a breakthrough discovery in ferroelectrics, potentially able to revolutionize the whole field. Despite increasing interests, a comprehensive understanding of the many factors driving the ferroelectric stabilization is still lacking. We here address the phase transition in terms of a Landau-theory-based approach, by analyzing symmetry-allowed distortions connecting the high-symmetry paraelectric tetragonal phase to the low-symmetry polar orthorhombic phase. By means of first-principles simulations, we find that the $\Gamma_{3-}$ polar mode is only weakly unstable, whereas the other two symmetry-allowed distortions, non-polar Y$_{2+}$ and anti-polar Y$_{4-}$ are hard modes. None of the modes, taken alone or combined with one other mode, is able to drive the transition: the key factor in stabilizing the polar phase is identified as the strong trilinear coupling among the three modes. Furthermore, the experimentally acknowledged importance of substrate-induced effects in the growth of HfO$_2$ ferroelectric thin films, along with the lack of a clear order parameter in the transition, suggested the extension of our analysis to strain effects. Our findings suggest a complex behaviour of the Y$_{2+}$ mode, which become unstable under certain strain conditions and an overall unstable behaviour for the $\Gamma_{3-}$ polar mode for all the strain states. A robust result emerges from our analysis: independently of the different applied strain (compressive or tensile, applied along orthorhombic axes), the need of a simultaneous excitation of the three coupled modes remain unaltered. Finally, when applied to mimic experimental growth conditions under strain, our analysis show a further stabilization of the ferroelectric phase with respect to the unstrained case, in agreeement with experimental findings.