Geometric ferroelectricity in rare-earth compounds RGaO3 and RInO3

We have studied the stability and ferroelectric properties of hexagonal $R{\text{GaO}}_{3}$ and $R{\text{InO}}_{3}$ ($R$: rare-earth elements) by first-principles calculations. Computed spontaneous polarization in the series shows a systematic increase with the rare-earth elements, with values being larger in $R{\text{InO}}_{3}$ than in the corresponding $R{\text{GaO}}_{3}$. The largest polarization found is about $10\text{ }\ensuremath{\mu}\text{C}/{\text{cm}}^{2}$ for ${\text{ErInO}}_{3}$, which is about twice as large as those observed in hexagonal $R{\text{MnO}}_{3}$. The polarization can be further increased by applying in-plane compressive stress. The Born effective charges of constituent ions in the compounds are found to be similar to their formal values, implying that the ferroelectric displacements are merely driven by the ionic size effect. A transition to the high-symmetry phase at around 1500 K was confirmed in ${\text{GdInO}}_{3}$ and ${\text{DyInO}}_{3}$ by in situ high-temperature powder x-ray diffractometry. The present systems should belong to the family of geometric ferroelectrics.