Trilinear-coupling-driven ferroelectricity in HfO2

Ferroelectricity in hafnia is often regarded as a breakthrough discovery in ferroelectrics, potentially able to revolutionize the whole field. Despite increasing interests, a deep and comprehensive understanding of the many factors driving 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 Γ3- polar mode is only weakly unstable, whereas the other two symmetry-allowed distortions, Y2+ and Y4- (showing a nonpolar and antipolar behavior, respectively), are hard modes. While none of the modes, taken alone or combined with one other mode, is able to drive the transition, the key factor in stabilizing the ferroelectric 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 HfO2 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 behavior of the Y2+ mode, which can become unstable under certain conditions (i.e., a tensile strain applied along the a direction), and an overall weakly unstable behavior for the Γ3- polar mode for all the strain conditions. In any case, a robust result emerges from our analysis: independently of the different applied strain (be it compressive or tensile, applied along the a, b, or c orthorhombic axis), the need for a simultaneous excitation of the three coupled modes remains unaltered. Finally, when applied to mimic experimental growth conditions under strain, our analysis shows a further stabilization of the ferroelectric phase with respect to the unstrained case, in agreement with experimental findings.