Fig. 1: The origin of the ferroelectricity in fluorite MO2 (M = Hf, Zr).
From: Point-defect-driven flattened polar phonon bands in fluorite ferroelectrics
a Calculated difference of total energy ΔE for crystal m-phase, o-phase, t-phase, and c-phase for fluorite MO2 (M = Hf, Zr). ΔE =Eother-phase-Em-phase (in unit meV per formular unit MO2, meV/f.u.), green and red spheres indicate Hf/Zr and O, respectively. b, c Phonon dispersion spectra of c-HfO2 and c-ZrO2 and their symmetry-lowering steps. The blue dots labeled Γ15, X5, and X’2 indicate the primary instability modes in Γ and X wave vectors. d The phonon modes Γ15, X5, and X’2 correspond to transformations to polar-, antipolar-, and t-phase, respectively. The Γ15 and X5 modes condense in phase with equal magnitude to generate an orthorhombic structure that is periodically sandwiched between dead spacer layers. The arrows denote the polarization due to the displacement of oxygen atoms. e, f The above two inset images show the orthorhombic structures with polarization up and polarization down respectively (indicated by the dashed rectangular region) and periodically sandwiched between spacer layer. The green spheres indicate Hf/Zr, while the red spheres indicate oxygen.
