Ferroelectricity from coupled cooperative Jahn-Teller distortions and octahedral rotations in ordered Ruddlesden-Popper manganates

Density functional theory and group-theoretical methods are used to explore the origin for ferroelectricity in cation ordered ${\mathrm{LaSrMnO}}_4$ with the Ruddlesden-Popper structure. The equilibrium phase exhibits the polar $Pca{2}_1$ space group where small polar displacements of $d^4{\mathrm{Mn}}^{3+}$ coexist with antiferrodistortive octahedral rotations and Jahn-Teller distortions. We find that the octahedral rotations and Jahn-Teller distortion stabilize the polar structure and induce polar displacements through high-order anharmonic interactions among the three modes, making ${\mathrm{LaSrMnO}}_4$ a hybrid-improper ferroelectric material. The rotations result from the ionic size mismatch between $A$ cations and Mn whereas the Jahn-Teller distortions are energetically favored owing to the coupling between the local $e_g$ orbital polarization of the two nearest-neighboring Mn cations in the two-dimensional ${\mathrm{MnO}}_2$ sheets. Our results indicate that anharmonic interactions among multiple centric modes can be activated by cation ordering to induce polar displacements in layered oxides, making it a reliable approach for realizing acentric properties in artificially constructed materials.

Figure 1

(a) The ${\mathrm{LaSrMnO}}_4$ structure with random occupancy of La and Sr on the $A$ site. (b) A layered cation ordered ${\mathrm{LaSrMnO}}_4$ structure with subsequent monoxide LaO and SrO planes alternating along the $c$ axis. (c) Schematic of the collinear $A$-type antiferromagnetic structure. (d) Polar $(Q_{{\mathrm{\Gamma }}_5^{-}}$) and (e) rotation $\left(Q_{M_1}\right)$ distortions present in the ground phase; (black) arrows indicate the relative direction of the atomic displacements. In all panels, gray and red spheres correspond to the equatorial and apical oxygen atoms coordinating Mn, respectively.

Figure 2

Relative energy of LSMO for increasing amplitude of the (a) polar $\left(Q_{{\mathrm{\Gamma }}_5^{-}}\right)$, (b) rotation $\left(Q_{M_1}\right)$, and (c) Jahn-Teller $\left(Q_{M_4}\right)$ distortions. Independent of other modes, only the antiferrodistortive (b) and (c) modes are energetically favorable.

Figure 3

(a) Schematic of the Jahn-Teller distortion $\left(Q_{M_4}\right)$, which alters only the equatorial oxygen atoms in the $ab$ plane. The model also mediates the interaction between two nearest-neighbor Mn sites. (b) Orbital polarization of Mn(1) $\left({\mathcal{P}}_1\right)$ and Mn(2) $\left({\mathcal{P}}_2\right)$ sites against the Jahn-Teller distortion mode amplitude. In the presence of $Q_{M_4}$ distortion, the Mn crystallographic site is equivalent, but the Mn $e_g$ polarization is site dependent. Both ${\mathcal{P}}_1$ and ${\mathcal{P}}_2$ polarizations are equivalent at zero distortion amplitude (gray open circle) when the structure has the $P4/nmm$ symmetry. At high distortion values, Mn(1) to Mn(2) coupling is removed.

Figure 4

Group-subgroup relations with calculated energy stabilities for ordered ${\mathrm{LaSrMnO}}_4$ fully relaxed within the specified symmetry. The structural transition $P4/nmm\to Pca{2}_1$ can be realized by coupling at least two of the $Q_{{\mathrm{\Gamma }}_5^{-}},Q_{M_1}$, and $Q_{M_4}$ distortions. Shaded (pink) boxes with rounded corners indicate polar symmetries.

Figure 5

Stable magnetic configurations calculated for the $Pca{2}_1$ ground phase. Each arrow is centered on a Mn site: The color represents the direction of the magnetic component corresponding to the crystallographic axis shown in the upper left. (a)–(c) Ferromagnetic orderings. (d) Collinear antiferromagnetic ordering $L{A}_a$. (e)–(k) Antiferromagnetic ordering with weak-ferromagnetic component $M_i$; arrows terminated with a diamond correspond to the weak-ferromagnetic component whereas solid shaded arrows in (i)–(k) correspond to the main magnetic component lying on the $\left(ab\right),\left(bc\right)$, and $\left(ac\right)$ planes, respectively.