Phase transitions and antiferroelectricity in $\mathrm{BiFe}{\mathrm{O}}_3$ from atomic-level simulations

The structural and polar properties of $\mathrm{BiFe}{\mathrm{O}}_3$ at finite temperature are investigated using an atomistic shell model fitted to first-principles calculations. Molecular dynamics simulations show a direct transition from the low-temperature $R3c$ ferroelectric phase to the Pbnm orthorhombic phase without evidence of any intermediate bridging phase between them. The high-temperature phase is characterized by the presence of two sublattices with opposite polarizations, and it displays the characteristic double-hysteresis loop under the action of an external electric field. The microscopic analysis reveals that the change in the polar direction and the large lattice strains observed during the antiferroelectric-ferroelectric phase transition originate from the interplay between polarization, oxygen octahedron rotations, and strain. As a result, the induced ferroelectric phase recovers the symmetry of the low-temperature $R3c$ phase.

Figure 1

Total energy at different configuration obtained with the model (solid lines) and with $\mathrm{LDA}+U$ calculations (dotted lines). (a) Energy as functions of atomic displacements from the Imma phase towards the Pbnm (left) and $R3c$ (right) ones. Atoms are moved following the pattern of the LDA relaxed structure, which is taken as the unit. All calculations were done in a 40-atom cubic cell with $a=7.80\AA$. (b) Energy as function of the volume for relaxed Pbnm and $R3c$ structures.

Figure 2

Phase diagram of $\mathrm{BiFe}{\mathrm{O}}_3$ at zero pressure resulting from the MD simulations. Thermal evolution of the lattice parameters (a), net polarization, $P$, and order parameter associated with the antiferroelectric order along the $z$ direction, ${\mathit{P}}^{\mathrm{AF}}$ (b), and the oxygen octahedral rotation parameters describing antiphase, ${\mathit{\omega }}^{\mathrm{R}}$, and in-phase ${\mathit{\omega }}^{\mathrm{M}}$, tilting along the $z$ direction (c).

Figure 3

Distributions of local polarizations corresponding to the Pbnm phase at 1100 K. The superscripts correspond to the sublattices in which the system can be decomposed. Inset: time evolution of one unit-cell polarization along the [110] direction.

Figure 4

Polarization (a) and strains (b) as function of the electric field obtained from the Pbnm phase at 1100 K. The field is applied along [110] directions, and arrows indicate field changes.

Figure 5

Decomposed sublattice polarizations (a) and oxygen octahedral rotation (b) as function of the applied electric field.