Possible existence of tristable polarization states in LiNbO3 under an open-circuit boundary condition

Hyperferroelectricity is an intriguing phenomenon in that electric polarization persists under the open-circuit boundary condition (OCBC). Using first-principles density functional calculations, we investigate the hyperferroelectric properties of ${\mathrm{LiNbO}}₃$, a technologically important ferroelectric solid. We find that (i) the longitudinal-optic ${\mathrm{A}}_{2\mathrm{u}}({\mathrm{LO}}₁)$ phonon is soft with imaginary frequency $96i\phantom{\rule{0.28em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ when centrosymmetric ${\mathrm{LiNbO}}₃$ is under OCBC, and this soft LO phonon is shown to differ drastically from the corresponding transverse-optic ${\mathrm{A}}_{2\mathrm{u}}({\mathrm{TO}}₁)$ phonon. (ii) The ${\mathrm{A}}_{2\mathrm{u}}({\mathrm{LO}}₁)$ phonon is able to yield, under OCBC, a free-energy minimum with well depth of $\ensuremath{-}9$ meV at a nonzero polarization of 0.023 C/${\mathrm{m}}²$, thereby capable of producing hyperferroelectricity. (iii) The origin that ${\mathrm{A}}_{2\mathrm{u}}({\mathrm{LO}}₁)$ is capable of inducing HyFE is determined, and it stems from the extraordinarily small mode effective charge of this soft LO phonon. This finding also provides a key guiding principle for searching and designing new hyperferroelectrics. (iv) Despite that ${\mathrm{A}}_{2\mathrm{u}}({\mathrm{LO}}₁)$ is able to induce HyFE, we find that the ground state of ${\mathrm{LiNbO}}₃$ under OCBC is nevertheless not polar, revealing that the existence of a soft LO phonon does not guarantee HyFE. (v) Interestingly, we further show that ${\mathrm{LiNbO}}₃$ under OCBC may exhibit unusual tristable polarization states, with two potential wells of depth $\ensuremath{-}23$ meV and $\ensuremath{-}1.9$ meV, respectively. Besides providing insightful knowledge for understanding HyFE in general, these results reveal that there is rich and interesting hyperferroelectric physics in ${\mathrm{LiNbO}}₃$ under OCBC, in particular.