Insights into the phase diagram of bismuth ferrite from quasiharmonic free-energy calculations

Abstract

We have used first-principles methods to investigate the phase diagram of multiferroic bismuth ferrite (BiFeO${}_{3}$ or BFO), revealing the energetic and vibrational features that control the occurrence of various relevant structures. More precisely, we have studied the relative stability of four low-energy BFO polymorphs by computing their free energies within the quasiharmonic approximation, introducing a practical scheme that allows us to account for the main effects of spin disorder. As expected, we find that the ferroelectric ground state of the material (with $R3c$ space group) transforms into an orthorhombic paraelectric phase ($Pnma$) upon heating. We show that this transition is not significantly affected by magnetic disorder, and that the occurrence of the $Pnma$ structure relies on its being vibrationally (although not elastically) softer than the $R3c$ phase. We also investigate a representative member of the family of nanotwinned polymorphs recently predicted for BFO [S. Prosandeev et al., Adv. Funct. Mater. 23, 234 (2013)] and discuss their possible stabilization at the boundaries separating the $R3c$ and $Pnma$ regions in the corresponding pressure-temperature phase diagram. Finally, we elucidate the intriguing case of the so-called supertetragonal phases of BFO: Our results explain why such structures have never been observed in the bulk material, despite their being stable polymorphs of very low energy. Quantitative comparison with experiment is provided whenever possible, and the relative importance of various physical effects (zero-point motion, spin fluctuations, thermal expansion) and technical features (employed exchange-correlation energy density functional) is discussed. Our work attests the validity and usefulness of the quasiharmonic scheme to investigate the phase diagram of this complex oxide, and prospective applications are discussed.