Microscopic mechanisms behind hyperferroelectricity

Hyperferroelectrics are observing a growing interest thanks to their unique property to retain a spontaneous polarization even in the presence of a depolarizing field, corresponding to zero macroscopic displacement field $(\mathbf{D}=0)$ conditions. Hyperferroelectricity is ascribed to the softening of a polar $LO$ mode, but the microscopic mechanisms behind this softening are not totally resolved. Here, by means of phonon calculations and force constants analysis, performed in two classes of hyperferroelectrics, the ${\mathrm{ABO}}_3$-LiNbO3-type systems and the hexagonal-ABC systems, we unveil the common features in the dynamical properties of a hyperferroelectric that lead the $LO$ instability: negative or vanishing on-site force constant associated to the cation driving the $LO$ polar mode and a destabilizing cation-anion interaction; both induced by short-range forces. We also predict a possible enhancement of the hyperferroelectric properties under increasing external positive pressures: pressure strengthens the destabilizing short-range interactions, inducing a stronger $LO$ mode instability and the increase of the longitudinal mode effective charges associated to the unstable $LO$ mode. This suggests an eventual enhancement of the $\mathbf{D}=0$ polarization under compressive strain.

Figure 1

The paraelectric $R\overline{3}c$ structure of ${\mathrm{ABO}}_3\text{−}{\mathrm{LiNbO}}_3$-type oxides in its conventional hexagonal unit cell (the primitive rhombohedral unit cell inset). A atoms are in green color, B atoms in blue, and O atoms in red.

Figure 2

(a) In the paraelectric $R\overline{3}c$ phase, Li is undercoordinated (surrounded with three in-plane oxygens). (b) In the ferroelectric $R3c$, Li displaces toward the out-of-plane oxygens cage along the $z$-direction, optimizing its coordination from III to VI.

Figure 3

(a), (c), (e), and (g) Evolution of $LO1$ mode frequency with pressure. (b), (d), (f), and (h) Evolution of the total ($zz$) on-site IFC of A atoms with pressure, together with its LR and SR parts.

Figure 4

(a)–(c) Evolution of Li displacement (in atomic unit) with pressure in $TO1$, $TO2$, and $TO3$ polar modes. (d)–(f) Evolution with pressure of the overlap of the $LO1$ mode with $TO1$, $TO2$ and $TO3$ modes.

Figure 5

ABC-hexagonal cell in the paraelectric $P{6}_3/mmc$ and polar $P{6}_{3}mc$(186) phases.