Unraveling the Suppression of Oxygen Octahedra Rotations in $A_3{B}_2{\mathrm{O}}_7$ Ruddlesden-Popper Compounds: Engineering Multiferroicity and Beyond

The competition between polar distortions and ${B\text{O}}_6$ octahedra rotations is well known to be critical in explaining the ground state of various $AB{\mathrm{O}}_3$ perovskites. Here, we show from first-principles calculations that a similar competition between interlayer rumpling and rotations is playing a key role in layered Ruddlesden-Popper (RP) perovskites. This competition explains the suppression of oxygen octahedra rotations and hybrid improper ferroelectricity in $A_3{B}_2{\mathrm{O}}_7$ compounds with rare-earth ions in the rocksalt layer and also appears relevant to other phenomena like negative thermal expansion and the dimensionality determined band gap in RP systems. Moreover, we highlight that RP perovskites offer more flexibility than $AB{\mathrm{O}}_3$ perovskites in controlling such a competition and four distinct strategies are proposed to tune it. These strategies are shown to be promising for designing new multiferroics. They are generic and might also be exploited for tuning negative thermal expansion and band gap.

Figure 1

Schematic view of (a) $a^0{a}^0{c}^{+}$ rotations, (b) $a^{-}{b}^0{c}^0/b^0{a}^{-}{c}^0$ tilts, (c) $a^{-}{a}^{-}{c}^0$ tilts, and (d) rumpling, (e) PESs with respect to the amplitude of four distortions.

Figure 2

PESs in terms of given mode amplitudes for distinct compounds: (a) $a^0{a}^0{c}^{+}$ rotations $Q_R$ in ${\mathrm{SrTb}}_2{\mathrm{Fe}}_2{\mathrm{O}}_7$ at fixed rumpling amplitude $Q_G$, (b) $a^0{a}^0{c}^{-}$ rotations $Q_R$ in ${\mathrm{PbTiO}}_3$ at fixed polarization amplitude $Q_P$, (c) $a^{-}{a}^{-}{c}^0$ tilts $Q_T$ in ${\mathrm{SrTb}}_2{\mathrm{Fe}}_2{\mathrm{O}}_7$ at fixed rumpling amplitude $Q_G$ and (d) $a^0{a}^0{c}^{+}$ rotations $Q_R$ in ${\mathrm{Ca}}_3{\mathrm{Mn}}_2{\mathrm{O}}_7$ with and without fixed rumpling amplitude $Q_G$ as in the GS.

Figure 3

Comparison of rumpling amplitudes in the GS phase of a series of RP perovskites ($P{4}_2/mnm$ phase and $A{2}_{1}am$ phase, respectively, for compounds with $R^{3+}$ and $A^{2+}$ ions in the rocksalt layer).

Figure 4

(a)–(d) Several practical strategies to engineering rotations. PESs with respect to the amplitude of $a^0{a}^0{c}^{+}$ rotations, $a^{-}{a}^{-}{c}^0$ tilts, and $a^{-}{b}^0{c}^0/b^0{a}^{-}{c}^0$ tilts with fixed rumpling for (e) $\mathrm{Ca}{\mathrm{Tb}}_2{\mathrm{Fe}}_2{\mathrm{O}}_7$, (f) $\mathrm{Sr}{\mathrm{Tb}}_2{\mathrm{Fe}}_2{\mathrm{O}}_7$ by exchanging ${\mathrm{Tb}}^{3+}$ at the rocksalt layer with ${\mathrm{Sr}}^{2+}$ at the perovskite layer, (g) $\mathrm{Sr}{\mathrm{Tb}}_4{\mathrm{Fe}}_4{\mathrm{O}}_{13}$, and (h) $\mathrm{Sr}{\mathrm{Tb}}_2{\mathrm{Fe}}_2{\mathrm{O}}_7{\mathrm{F}}_2$.