Strain-induced isosymmetric phase transition in ${\text{BiFeO}}_3$

We calculate the effect of epitaxial strain on the structure and properties of multiferroic bismuth ferrite, ${\text{BiFeO}}_3$, using first-principles density-functional theory. We investigate epitaxial strain corresponding to an (001)-oriented substrate and find that, while small strain causes only quantitative changes in behavior from the bulk material, compressive strains of greater than 4% induce an isosymmetric phase transition accompanied by a dramatic change in structure. In striking contrast to the bulk rhombohedral perovskite, the highly strained structure has a $c/a$ ratio of $\sim 1.3$ and five-coordinated Fe atoms. We predict a rotation of polarization from [111] (bulk) to nearly [001], accompanied by an increase in magnitude of $\sim 50\mathrm{\%}$, and a suppression of the magnetic ordering temperature. Our calculations indicate critical strain values at which the two phases might be expected to coexist and shed light on recent experimental observation of a morphotropic phase boundary in strained ${\text{BiFeO}}_3$.

Figure 1

(Color online) Left: total energy per formula unit as a function of $c/a$ ratio for three constrained $a$ parameters. Right: energy per formula unit relative to bulk BFO for the ground-state structures as a function of $a$ for $P4mm$, unrelaxed monoclinic angle $\left(\beta =90°\right)$, and relaxed monoclinic angle.

Figure 2

(Color online) Structural parameters as functions of lattice parameter/strain relative to the bulk $\text{LSDA}+U$ lattice parameter. (a) $c/a$ of the pseudocubic cell; (b) volume per formula unit; (c) Fe-O bond lengths for in-plane and out-of-plane bonds; (d) total polarization and components lying in-plane and out-of-plane. All values are for constrained monoclinic angle, $\beta =90°$.

Figure 3

(Color online) Isosymmetric phases of $Cc$ BFO: Left: tetragonal-like $T$ phase; Right: rhombohedral-like $R$ phase.

Figure 4

(Color online) Displacement mode amplitudes for dominant antiferrodistortive modes. ${\text{A}}_{4-}$ and ${\text{A}}_{5-}$ correspond to octahedral rotation and tilt, respectively.