Ferroelectricity in HfO₂ from a Coordination Number Perspective

Ferroelectricity observed in thin-film HfO2, either doped with Si, Al, and so forth or in the Hf0.5Zr0.5O2 form, has gained great technical significance. While a trilinear coupling between phonon modes could explain its ferroelectric distortion, from a practical perspective, one may be concerned with a theory that is more straightforward to predict similar ferroelectric candidates through some apparent features of HfO2 and ZrO2. In this work, we propose that the 7 cation coordination number of HfO2/ZrO2 lies at the heart of this ferroelectricity, which stems from the proper ionic radii of Hf/Zr compared with O. Among the numerous compounds with a non-centrosymmetric nature, for example, the mm2 point group, HfO2 and ZrO2 are special in that they are close to the border of 7 and 8 cation coordination, such that the 8-coordination tetragonal intermediate phase could greatly reduce the switching barrier. Other 7-coordination candidates, including SrI2, TaON, YSBr, and YOF, are also studied in comparison to HfO2/ZrO2, and six switching paths are analyzed in detail for the Pca21 phase. A rule of the preferred switching path in terms of the ionic radii ratio and coordination number has been established. We also show the possible route from the ferroelectric Pca21 phase to the monoclinic P21/c phase in HfO2, which is relevant to the fatigue phenomenon.