Geometric ferroelectricity in fluoroperovskites

We used first-principles calculations to investigate the existence and origin of the ferroelectric instability in the ABF${}_3$ fluoroperovskites. While the ground states of most $AB$F${}_3$ compounds are paraelectric ($Pnma$ phase), we find that many fluoroperovskites have a ferroelectric instability in their high-symmetry cubic structure that is of similar amplitude to that commonly found in oxide perovskites. In contrast to the oxides, however, the fluorides have nominal Born effective charges, indicating a different mechanism for the instability. We show that the instability originates from ionic size effects, and is therefore in most cases largely insensitive to pressure and strain, again in contrast to the oxide perovskites. An exception is NaMnF${}_3$, where coherent epitaxial strain matching to a substrate with equal $in$-plane lattice constants destabilizes the bulk Pnma structure, leading to a ferroelectric, and indeed multiferroic, ground state with an unusual polarization/strain response.

Figure 1

Calculated phonon-dispersion curves of cubic NaMnF${}_3$ with a $G$-type AFM order. The imaginary frequencies (unstable modes) are depicted as negative numbers. The branch colors are assigned according to the contribution of each atom to the dynamical matrix eigenvector: red for Na, green for Mn, and blue for F. In the bottom panel, the eigendisplacements at $M$, $X$, and $R$ for the modes that contribute most to the fully relaxed ground state are shown.

Figure 2

Contributions of the unstable phonon modes of the cubic high-symmetry structures to the fully relaxed ground states of Pnma Na$B$F${}_3$ fluorides [24]. Also shown are the frequency values for the FE modes in the Pnma (white squares) and cubic (white triangles) structures.

Figure 3

Left: Energy as a function of displacement for NaMnF${}_3$ with a $G$-type antiferromagnetic order for three different displacement patterns: The purple line corresponds to displacing only the Mn ions in each unit cell, the green to displacing only the Na atoms, and the blue to the full eigendisplacement of the FE soft mode (right).

Figure 4

Calculated frequency squared of the unstable FE phonon mode as a function of fractional change in cell parameter for Na$B$F${}_3$ with $B$ = Mn, V, Ni, and Zn and BaTiO${}_3$. $a$ is the varied cell parameter and $a_0$ is the PBEsol relaxed cell value.

Figure 5

Evolution of the $A$ (a), $B$ (b), F${}_{\perp }$ (c), and F${}_{\parallel }$ (d) on-site IFCs (eV/Å${}^2$) with cubic cell parameter, $a$.