Interplay between charge ordering and geometric ferroelectricity in $\mathrm{Lu}{\mathrm{Fe}}_2{\mathrm{O}}_4/\mathrm{LuFe}{\mathrm{O}}_3$ superlattices

Oxide superlattices have drawn great attention owing to the intriguing coupling among elastic, electrical, and magnetic orderings at the interfaces and the emergence of improper ferroelectricity. Here, superlattices composed of hexagonal $\mathrm{LuFe}{\mathrm{O}}_3$ $\left(\mathrm{h}\text{−}\mathrm{LuFe}{\mathrm{O}}_3\right)$ and $\mathrm{Lu}{\mathrm{Fe}}_2{\mathrm{O}}_4$ are investigated via density functional theory calculations. h-$\mathrm{LuFe}{\mathrm{O}}_3$ is a well-known multiferroic material that is stable only in thin film or doped bulk state, while $\mathrm{Lu}{\mathrm{Fe}}_2{\mathrm{O}}_4$ is a charge ordered (CO) material where the existence of ferroelectricity is still a controversy. We have found that the CO-induced polarizations in $\mathrm{Lu}{\mathrm{Fe}}_2{\mathrm{O}}_4$ layers coexist with the geometric polarizations in $\mathrm{h}\text{−}\mathrm{LuFe}{\mathrm{O}}_3$ layers in the ${\left(\mathrm{Lu}{\mathrm{Fe}}_2{\mathrm{O}}_4\right)}_m/{\left(\mathrm{LuFe}{\mathrm{O}}_3\right)}_n$ superlattices with different periodicities, and the ferroelectric states are generally preferred over the antiferroelectric states for $\mathrm{Lu}{\mathrm{Fe}}_2{\mathrm{O}}_4$ in superlattices. The out-of-plane polarizations in h-$\mathrm{LuFe}{\mathrm{O}}_3$ and $\mathrm{Lu}{\mathrm{Fe}}_2{\mathrm{O}}_4$ layers tend to be aligned in parallel, and the overall polarization increases with the ratio of $\mathrm{h}\text{−}\mathrm{LuFe}{\mathrm{O}}_3$. The influence of layered polarizations on the local electrostatic potential is not significant except the detected small trend caused by the CO-induced polarization within a FeO bilayer. Additionally, the local electronic structures show that the Fermi level position in a certain layer can be tuned by the valences of Fe in this layer and the polarization distributions in neighboring layers. $\mathrm{Lu}{\mathrm{Fe}}_2{\mathrm{O}}_4$ layers sandwiched between thick $\mathrm{h}\text{−}\mathrm{LuFe}{\mathrm{O}}_3$ layers are more susceptible. The calculated configurations of the superlattices are supported by atomic-resolution transmission electron microscopy experiments. Our results pave the way for tunable ferroelectricity in superlattice systems and create a playground for manipulating the coupling between various degrees of freedom.

Figure 1

(a) Atomic structure and sketch of each block for the $\mathrm{Lu}{\mathrm{Fe}}_2{\mathrm{O}}_4$ unit cell viewed along the [100] zone axis. The three blocks in a unit cell are labeled with A, B, and C with different gray levels. When the mirror reflection through the (001) plane is performed for $\mathrm{Lu}{\mathrm{Fe}}_2{\mathrm{O}}_4$, the arrangement of the three blocks is reversed, as $\overline{\mathrm{C}}$, $\overline{\mathrm{B}}$, and $\overline{\mathrm{A}}$. (b) Atomic structure and sketch of each block for the $\mathrm{h}\text{−}\mathrm{LuFe}{\mathrm{O}}_3$ paraelectric unit cell, denoted with O and O′. The unit cell center has different choices in which the coordinates of the atoms are different. According to the in-plane positions of Fe ions in the unit cell, the $\mathrm{h}\text{−}\mathrm{LuFe}{\mathrm{O}}_3$ blocks are sorted as ${\mathrm{O}}_1$, ${\mathrm{O}}_2$, and ${\mathrm{O}}_3$ plot with different colors, which are the same in nature. Using certain $\mathrm{Lu}{\mathrm{Fe}}_2{\mathrm{O}}_4$ blocks and $\mathrm{h}\text{−}\mathrm{LuFe}{\mathrm{O}}_3$ blocks, the superlattices (c) 1111, (d) 2121, (e) 2212, (f) 2323, (g) 3232, (h) 3131, and (i) (1313) are built, which are the seven smallest and typical superlattices. Note that the choices of $\mathrm{Lu}{\mathrm{Fe}}_2{\mathrm{O}}_4$ and $\mathrm{h}\text{−}\mathrm{LuFe}{\mathrm{O}}_3$ blocks must be matched and satisfy the out-of-plane stacking rule. Big cyan spheres and solid cyan circles both represent Lu ions, medium golden spheres and solid golden circles both represent Fe ions, and small red ions represent O ions which have been omitted in the block sketches.

Figure 2

(a) Charge ordered (CO) unit cell of $\mathrm{Lu}{\mathrm{Fe}}_2{\mathrm{O}}_4$ with CO-induced ferroelectricity. (b) CO unit cell of $\mathrm{Lu}{\mathrm{Fe}}_2{\mathrm{O}}_4$ with CO-induced antiferroelectricity. (c) Ferroelectric $\mathrm{h}\text{−}\mathrm{LuFe}{\mathrm{O}}_3$ unit cell with downward polarization. (d) Ferroelectric $\mathrm{h}\text{−}\mathrm{LuFe}{\mathrm{O}}_3$ unit cell with upward polarization. Here, different colors of Fe ions represent different valences, and hollow arrows represent the polarization directions of the corresponding $\mathrm{Lu}{\mathrm{Fe}}_2{\mathrm{O}}_4$ or $\mathrm{h}\text{−}\mathrm{LuFe}{\mathrm{O}}_3$ blocks. (e) Six types of polarization arrangements for a certain $m_1{n}_1{m}_2{n}_2$ superlattice. To be specific, the lower (upper) $\mathrm{Lu}{\mathrm{Fe}}_2{\mathrm{O}}_4$ layer contains $m1$ ($m2$) $\mathrm{Lu}{\mathrm{Fe}}_2{\mathrm{O}}_4$ blocks, and the lower (upper) $\mathrm{h}\text{−}\mathrm{LuFe}{\mathrm{O}}_3$ layer contains $n1$ ($n2$) $\mathrm{h}\text{−}\mathrm{LuFe}{\mathrm{O}}_3$ blocks. Black arrows aside the $\mathrm{Lu}{\mathrm{Fe}}_2{\mathrm{O}}_4$ or $\mathrm{h}\text{−}\mathrm{LuFe}{\mathrm{O}}_3$ blocks represent the polarization direction along the $c$ axis of the layers. The ↕ arrow indicates that the $\mathrm{Lu}{\mathrm{Fe}}_2{\mathrm{O}}_4$ layer is antiferroelectric.

Figure 3

The relaxed average polarizations for the lower $\mathrm{Lu}{\mathrm{Fe}}_2{\mathrm{O}}_4$ layers, lower $\mathrm{h}\text{−}\mathrm{LuFe}{\mathrm{O}}_3$ layers, upper $\mathrm{Lu}{\mathrm{Fe}}_2{\mathrm{O}}_4$ layers, and upper $\mathrm{h}\text{−}\mathrm{LuFe}{\mathrm{O}}_3$ layers in the seven superlattices with all the polarizations initially pointing down (↓↓↓↓).

Figure 4

Local polarizations of all the blocks in the lower $\mathrm{Lu}{\mathrm{Fe}}_2{\mathrm{O}}_4$, lower $\mathrm{LuFe}{\mathrm{O}}_3$, upper $\mathrm{Lu}{\mathrm{Fe}}_2{\mathrm{O}}_4$, and upper $\mathrm{LuFe}{\mathrm{O}}_3$ layers for the seven considered superlattices in their most stable final states. The periodicities of the superlattices are labeled in the right of the horizontal axes. The exact values of the polarizations are marked at the end of the bars representing the block polarizations in units of $\mu \mathrm{C}\mathrm{c}{\mathrm{m}}^{\text{–}2}$.

Figure 5

Planar average electrostatic potential along the $c$ axis (gray line) and macroscopic-averaged local electrostatic potential over 2.92 Å (read line) as functions of the distance from the bottom plane. The corresponding superlattice systems are denoted in the panels. The positions of Fe and Lu ions at the $c$ axis are also labeled aside the potential curves. The local $c$ components of the block-resolved polarizations are plot with blue-magenta bars overlying at the central position of each block for reference.

Figure 6

Sketches of the electrostatic potential variation caused by polarization and charge ordering (CO). (a) Depolarization field induced by a sizeable polarization leads to high (low) electrostatic potential for electrons at the tail (head) of the polarization. (b) Unbalanced charges in each FeO plane of a FeO bilayer cause different electrostatic potentials for electrons. CO-induced polarization in the bilayer is represented by the arrow with gradient colors.

Figure 7

(a)–(e) Total densities of states (TDOS) and projected densities of states (PDOS) on O $2p$ orbitals and Fe $3d$ orbitals. The corresponding superlattice systems are denoted in the panels. The top panels are the TDOS and PDOS for the whole superlattice structures. The local TDOS and PDOS for each block are shown below the top panels. Taking 3131-↓↓↑↑ structure for example, the eight DOS panels (except for the top one) correspond to those of the eight blocks in Fig. 1 in a one-by-one manner. In the $\mathrm{h}\text{−}\mathrm{LuFe}{\mathrm{O}}_3$ layers, there are only O $2p$ states and ${\mathrm{Fe}}^{3+}$ $3d$ states; therefore, the latter are shown with green shades. In the $\mathrm{Lu}{\mathrm{Fe}}_2{\mathrm{O}}_4$ layers, the Fe $3d$ states are divided into ${\mathrm{Fe}}^{3+}$ $d$ states and ${\mathrm{Fe}}^{2+}$ $d$ states. Note that the DOS from Lu atoms are not plotted here. The Fermi energy is pinned in each superlattice system and set as 0. (f) Sketch of the $3d$ orbital occupancy for ${\mathrm{Fe}}^{2+}$ and ${\mathrm{Fe}}^{3+}$ ions, respectively, where a red arrow represents a $3d$ spin-down or spin-up electron.

Figure 8

(a) Low magnification high-angle annular dark field scanning transmission electron microscopy (HAADF-STEM) image of the $\mathrm{Lu}{\mathrm{Fe}}_2{\mathrm{O}}_4$ sample. (b) The high-resolution HAADF image magnified from the white outlined rectangle region in (a). (c) The corresponding superlattice structure of the white dash rectangle region in (b). The image is viewed along the [100] zone axis. (d) The integrated intensity profile from the top to the bottom for the white dash rectangle region in (b). (e) The high-resolution HAADF image from the [210] zone axis. (f) Corresponding superlattice along the [210] zone axis. Note that, in (c) and (f), the displacements of Lu atoms are not illustrated.