Hyperferroelectricity in ZnO: Evidence from analytic formulation and numerical calculations

Hyperferroelectricity is an interesting phenomenon. The hexagonal ABC-type semiconductor LiZnAs was discovered to be hyperferroelectric (HFE) [Garrity et al., Phys. Rev. Lett. 112, 127601 (2014)]. ZnO is a technologically important semiconductor and possesses a wurtzite crystal structure similar to LiZnAs. It raises an intriguing question of whether ZnO is HFE. Here we use various approaches to address this important question by determining the electric equation of state, the free energy of ZnO under an open-circuit boundary condition (OCBC), and the vibration properties of a LO phonon. We find the following: (i) The $D\ensuremath{\sim}\ensuremath{\lambda}$ curve of ZnO, where $D$ is electric displacement and $\ensuremath{\lambda}=P/0.844$ is a parameter directly proportional to polarization $P$, exhibits one and only one root at $\ensuremath{\lambda}=0$. (ii) Under OCBC, the free energy of ZnO does not produce a minimum at the structural phase of nonzero polarization. (iii) The LO phonon with computed frequency ${\ensuremath{\omega}}_{\mathrm{LO}}=255\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ in centrosymmetric ZnO is not soft and does not have an imaginary frequency. These results corroborate the others and consistently lead to the conclusion that, although ZnO is interestingly on the edge of becoming a HFE, it is not yet a HFE. We further provide a physical origin explaining why ZnO is not HFE and reveal a possibility that may turn ZnO into a HFE.