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Register a new userTrilinear coupling driven ferroelectricity in HfO$_2$
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Added by
Francesco Delodovici
Publication date
2021
fields
Physics
and research's language is
English
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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.
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In this work, we carry out first-principles calculations and lattice mode analysis to investigate the polarization switching mechanism in HfO$_2$. Because the stability of the polar orthorhombic $Pca2_1$ phase of HfO$_2$ arises from a trilinear coupling, polarization switching requires the flipping of not only the polar $Gamma_{15}^Z$ mode, but also at least one zone-boundary anti-polar mode. The coupling between the polar and anti-polar modes thus leads to substantial differences among different polarization switching paths. Specifically, our lattice-mode-coupling analysis shows that paths in which the $X_2^-$ mode is reversed involve a large activation energy, which because the $X_2^-$ mode is nonpolar cannot be directly overcome by applying an electric field. Our results show that the anti-polar $Pbca$ phase, whose structure is locally quite similar to that of the $Pca2_1$ phase, similarly cannot be transformed to this phase by an electric field as this would require local reversal of the $X_2^-$ mode pattern. Moreover, for the domain wall structure most widely considered, propagation also requires the reversal of the $X_2^-$ mode, leading to a much larger activation energy compared with that for the propagation of domain wall structures with a single sign for the $X_2^-$ mode. Finally, these first-principles results for domain wall propagation in HfO$_2$ have implications to many experimental observations, such as sluggish domain wall motion and robust ferroelectricity in thin films, and lattice mode analysis deepens our understanding of these distinctive properties of ferroelectric HfO$_2$.
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