  We have used first-principles methods to investigate the phase diagram of
multiferroic bismuth ferrite (BiFeO3 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
quasi-harmonic 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 nano-twinned polymorphs recently
predicted for BFO [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 super-tetragonal 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 quasi-harmonic scheme to investigate the
phase diagram of this complex oxide, and prospective applications are
discussed.
