Atomic, electronic, and ferroelectric properties of manganite R MnO 3 ( R = Ho , Er , Tm , Lu ) in hexagonal and orthorhombic phases

Using first-principles calculations, we perform a systematic study of the energetic, atomic, electronic, and ferroelectric properties of the late rare-earth manganites $R{\text{MnO}}_{3}$ $(R=\text{Ho},\text{Er},\text{Tm},\text{Lu})$ in both hexagonal and orthorhombic structures. The hexagonal phase is confirmed to be energetically preferred over the orthorhombic phase. The calculations show that the size of the band gap of the hexagonal manganites is improved when the triangularly frustrated Mn magnetic moments are properly treated. As $R$ approaches the end of the rare-earth series, the polarization in the hexagonal phase increases whereas that in the orthorhombic phase remains practically unchanged. We conclude that the driving force of ferroelectricity in the hexagonal phase is the asymmetric movement of $R$ ions from the centrosymmetric structure. On the other hand, the underlying $E$-type ordering is the origin of the ferroelectricity observed in the orthorhombic phase. The interplay among the ferroelectricity, magnetic ordering, and lattice structure for the two phases is also discussed in detail.