Properties of BiFeO3

   BiFeO$_3$ has draw extensive studies in past years. I will try to summarize some of its properties in this post. This post will keep update.

A nice review: 

Physics and Applications of Bismuth Ferrite,  Gustau Catalan and James F. Scott, Advanced Materials, 2009, 21, 2463-2485. 

1. Crystal Structure

Room-temperature phase of BiFeO$_3$ is classed as rhombohedral ($R3C$).

The perovskite-type unit cell has a lattice parameter, $a_{\rm rh}$, of 3.965  and a rhombohedral angle, $\alpha_{\rm rh}$, of ca. 89.3–89.48 at room temperature with ferroelectric polarization along [111]. The unit cell can also be described in a hexagonal frame of reference, with the hexagonal $c$-axis parallel to the diagonals of the perovskite cube. 

The Goldschmid tolerance factor $t=(r_{\rm Bi} +r_{\rm O})/ \sqrt{2} (r_{\rm Fe}+r_{\rm O})=0.88$, which is much smaller than 1. Therefore, the oxgen cage has to rotate so as to fit into a cell that is too small. The oxgen cage is rotated around the polar [111] axis by 11-14$^\circ$, with the directly related Fe-O-Fe angle 154-156$^\circ$. 

2. Temperature-induced phase transition for bulk BiFeO$_3$  ($\alpha \rightarrow \beta$ transition)

$T_c$ = 825 ˚C

$R3C$ $\rightarrow$  $Pbnm$

$T_c$ = 931 ˚C

$Pbnm$ $\rightarrow$  $Pm\bar{3}m$

Atomic displacements in BiFeO3 as a function of temperature: neutron diffraction study,

A. Palewicz, R. Przeniosło,I. Sosnowska and A. W. Hewat, Acta Cryst.  B63, 537–544 (2007).

Ferroelectric-Paraelectric Transition in BiFeO3: Crystal Structure of the Orthorhombic Phase, Donna C. Arnold, Kevin S. Knight, Finlay D. Morrison, and Philip Lightfoot, Phys. Rev. Lett. 102, 027602 (2009). 

BiFeO3 Crystal Structure at Low Temperatures, A. Palewicz, I. Sosnowska, R. Przeniosło and A.W. Hewat, Acta Physica Polonica A, 117, 296 (2010).

3. Pressure-induced phase transition 

Structural Properties of Multiferroic BiFeO3 under Hydrostatic Pressure, Alexei, A. Belik,
Hitoshi Yusa,  Naohisa Hirao,  Yasuo Ohishi,  and Eiji Takayama-Muromachi, Chem. Mater. 2009, 21, 3400–3405

They found three new orthorhombic phases of BiFeO3 at room temperature below 9.7 GPa. Two transitions occurs at ~4 GPa and ~7 GPa, respectively.  

$R3C$ $\rightarrow$ OI $\rightarrow$  OII $\rightarrow$ OII

Effect of high pressure on multiferroic BiFeO3, R. Haumont, P. Bouvier, A. Pashkin, K. Rabia, S. Frank, B. Dkhil, W. A. Crichton, C. A. Kuntscher, and J. Kreisel, Phys. Rev. B, 79, 184110 (2009)

Multiple high-pressure phase transitions in BiFeO3, Mael Guennou, Pierre Bouvier, Grace S. Chen, Brahim Dkhil, Raphae Haumont, Gaston Garbarino, and Jens Kreise, Phys. Rev. B,  84, 174107 (2011)

They found six phase transitions in the 0-60-GPa range. At low pressure, four transitions occurred at 4, 5, 7, and 11 GPa.  The nonpolar $Pnma$ phase remains stable over a large pressure range between 11 and 38 GPa. Two high-pressure phase transitions at 38 and 48 GPa are marked by the occurrence of larger unit cells and increase of the distortion away from the cubic parent perovskite cell.

4. Thin film BiFeO$_3$

A mechanism for the 150 μC cm$^{−2}$ polarization of BiFeO3 films based on first-principles calculations and new structural data, Dan Ricinschi, Kwi-Young Yun and Masanori Okuyama,  J. Phys.: Condens. Matter 18 (2006) L97–L105

A Strain-Driven Morphotropic Phase Boundary in BiFeO3, R. J. Zeches et. al, Science 326, 977 (2009);

Stress-induced R-MA-MC-T symmetry changes in BiFeO3 films, H. M. Christen, J. H. Nam, H. S. Kim, A. J. Hatt, and N. A. Spaldin, Phys. Rev. B 83, 144107 (2011)

With compressive strain the structural proression is rhombohedral $\rightarrow$ (R-like)  monoclinic $\rightarrow$ (T-like) monoclinic $\rightarrow$ tetragonal. When the compressive strain exceeds 4.5%,  $c/a$ ratio is near 1.25.

A phase transition close to room temperature in BiFeO3 thin films, J Kreisel, P Jadhav, O Chaix-Pluchery, M Varela, N Dix, F Sanchez and J Fontcuberta, J. Phys.: Condens. Matter 23 (2011) 342202

Multiferroic phase transition near room temperature in BiFeO3 films,  I.C. Infante et, al.
Recent experiments reveals that the T-like phase exhibits both structural, magnetic and FE phase transitions in a narrow temperature range around 360 K

5. First-principle studies

First-principles study of spontaneous polarization in multiferroic BiFeO3,

J. B. Neaton,1, C. Ederer, U. V. Waghmare, N. A. Spaldin, and K. M. Rabe, Phys. Rev. B,  71, 014113 (2005)

Theoretical investigation of magnetoelectric behavior in BiFeO3, P. Ravindran, R. Vidya, A. Kjekshus, and H. Fjellvåg, Phys. Rev. B 74, 224412 (2006)

First-principles study of ferroelectric domain walls in multiferroic bismuth ferrite

Axel Lubk, S. Gemming,  and N. A. Spaldin, Phys. Rev. B 80, 104110 (2009)

Phase Transitions in Epitaxial (-110) BiFeO3 Films from First Principles,  S. Prosandeev, Igor A. Kornev, and L. Bellaiche, Phys. Rev. Lett. 107, 117602 (2011)

6. Classical Force Field

Development of a bond-valence based interatomic potential for BiFeO3 for accurate molecular dynamics simulations, S. Liu, I. Grinberg, and A. M. Rappe, J. Phys.: Condens. Matter 25 102202 (2013)