Fig. 1: Key structural features of HfO2.
Structure of the cubic paraelectric (a) and orthorhombic ferroelectric (b) polymorphs of HfO2. In the cubic \(Fm\bar{3}m\) phase, all Hf and O atoms are equivalent by symmetry. In the ferroelectric Pca21 structure we have two symmetry-inequivalent sets of oxygen atoms –labeled OI (shown in orange) and OII (red), respectively–, while all Hf atoms are equivalent. In panel b, the black arrow indicates the positive spontaneous polarization of the structure shown, which is essentially related to the vertical downward shift of the OI atoms from their high-symmetry position in the cubic phase. In the ferroelectric state, the OI atoms have three nearest-neighboring Hf cations; the bonding distances are explicitly indicated for the OI(1) atom, which is a representative case.
