First-principles-based Landau-Devonshire potential for ${\mathrm{BiFeO}}_3$

The work describes a first-principles-based computational strategy for studying structural phase transitions, and in particular, for determination of the so-called Landau-Devonshire potential—the classical zero-temperature limit of the Gibbs energy, expanded in terms of order parameters. It exploits the configuration space attached to the eigenvectors of the modes frozen in the ground state, rather than the space spanned by the unstable modes of the high-symmetry phase, as done usually. This allows us to carefully probe the part of the energy surface in the vicinity of the ground state, which is most relevant for the properties of the ordered phase. We apply this procedure to ${\mathrm{BiFeO}}_3$ and perform ab initio calculations in order to determine potential energy contributions associated with strain, polarization, and oxygen octahedra tilt degrees of freedom, compatible with its two-formula unit cell periodic boundary conditions.

Figure 1

Energy profiles along selected paths in the order-parameter space of ${\mathrm{BiFeO}}_3$, connecting the cubic reference state (REF) and the ground state (${\mathbf{P}}_{\mathrm{s}},{\mathbf{A}}_{\mathrm{s}},{\mathbf{e}}_{\mathrm{s}}$). Point symbols stand for direct first-principles calculations, lines are evaluated from the present LD potential. Individual path segments are depicted in the inset and described in detail in Table 1.

Figure 2

Comparison of first-principles and LD-predicted energies for 300 randomly selected points in the order-parameters space in the vicinity of the rhombohedral ground state (coordinates falling within 20 percent around the ground state values). Monotonously increasing function stands for the direct first-principles data, ordered by the increasing total energy, while the fluctuating curve connects the corresponding energies, calculated from the LD potential.