Unexpected crystalline homogeneity from the disordered bond network in $\mathrm{La}\left(\mathrm{C}{\mathrm{r}}_{0.2}\mathrm{M}{\mathrm{n}}_{0.2}\mathrm{F}{\mathrm{e}}_{0.2}\mathrm{C}{\mathrm{o}}_{0.2}\mathrm{N}{\mathrm{i}}_{0.2}\right){\mathrm{O}}_3$ films

Designing and understanding functional electronic and magnetic properties in perovskite oxides requires controlling and tuning the underlying crystal lattice. Here we report the structure, including oxygen and cation positions, of a single-crystal, entropy stabilized perovskite oxide film of $\mathrm{La}\left(\mathrm{C}{\mathrm{r}}_{0.2}\mathrm{M}{\mathrm{n}}_{0.2}\mathrm{F}{\mathrm{e}}_{0.2}\mathrm{C}{\mathrm{o}}_{0.2}\mathrm{N}{\mathrm{i}}_{0.2}\right){\mathrm{O}}_3$ grown on $\mathrm{SrTi}{\mathrm{O}}_3$ (001). The parent materials range from orthorhombic ($\mathrm{LaCr}{\mathrm{O}}_3, \mathrm{LaMn}{\mathrm{O}}_3$, and $\mathrm{LaFe}{\mathrm{O}}_3$) to rhombohedral ($\mathrm{LaCo}{\mathrm{O}}_3$ and $\mathrm{LaNi}{\mathrm{O}}_3$), and first principles calculations indicate that these structural motifs are nearly degenerate in energy and should be highly distorted site to site. Despite this extraordinary local configurational disorder on the $B$-site sublattice, we find a structure with unexpected macroscopic crystalline homogeneity with a clear orthorhombic unit cell, whose orientation is demonstrated to be controlled by the strain and crystal structure of the substrate for films grown on $\left(\mathrm{L}{\mathrm{a}}_{0.3}\mathrm{S}{\mathrm{r}}_{0.7}\right)\left(\mathrm{A}{\mathrm{l}}_{0.65}\mathrm{T}{\mathrm{a}}_{0.35}\right){\mathrm{O}}_3$ and $\mathrm{NdGa}{\mathrm{O}}_3$ (110). Furthermore, quantification of the atom positions within the unit cell reveals that the orthorhombic distortions are small, close to $\mathrm{LaCr}{\mathrm{O}}_3$, which may be driven by a combination of disorder averaging and the average ionic radii. This is a step toward understanding the rules for designing crystal motifs and tuning functional properties through controlled configurational complexity.

Figure 1

(a) Typical unit cells for perovskites. Left: A pseudocubic cell where the dashed lines highlight a single oxygen octahedra which can be rotated about the $x$ axis by angle α, the $y$ axis by β, and the $z$ axis by γ. Center and right: The formal orthorhombic unit cells for the Pbnm and $R\overline{3}c$ structures, respectively. (b) Projections of the unit cell down the $\langle 001\rangle$ pseudocubic direction for the parent compounds of $\mathrm{La}\left(\mathrm{C}{\mathrm{r}}_{0.2}\mathrm{M}{\mathrm{n}}_{0.2}\mathrm{F}{\mathrm{e}}_{0.2}\mathrm{C}{\mathrm{o}}_{0.2}\mathrm{N}{\mathrm{i}}_{0.2}\right){\mathrm{O}}_3$. (c–e) Ionic radii (c), tolerance factor (d), and pseudocubic lattice parameter (e) versus $B$-site cation. The solid symbols are data taken from Refs. [20, 21], the open symbols represent experimental values of the parent structures from Ref. [1], and the lattice parameters from Refs. [24, 25, 26, 27]; the vertical line on Co indicates that both high spin and low spin may be favored.

Figure 2

Distribution of the $B$-O-$B$ bond angles across the supercell calculated using density functional theory for $\mathrm{L}5B\mathrm{O}$. This shows three structural motifs where the solid blue line is cubic, the dotted green line is rhombohedral, and the dashed red line is orthorhombic. The numbers listed in the parentheses are the energies for the different structural motifs relative to the lowest, which is the rhombohedral phase.

Figure 3

(a) X-ray 2θ-ω scan about the 002 peak for $\mathrm{La}\left(\mathrm{C}{\mathrm{r}}_{0.2}\mathrm{M}{\mathrm{n}}_{0.2}\mathrm{F}{\mathrm{e}}_{0.2}\mathrm{C}{\mathrm{o}}_{0.2}\mathrm{N}{\mathrm{i}}_{0.2}\right){\mathrm{O}}_3$ on $\mathrm{SrTi}{\mathrm{O}}_3$. (b) Reciprocal space map about the 113 peaks of $\mathrm{La}\left(\mathrm{C}{\mathrm{r}}_{0.2}\mathrm{M}{\mathrm{n}}_{0.2}\mathrm{F}{\mathrm{e}}_{0.2}\mathrm{C}{\mathrm{o}}_{0.2}\mathrm{N}{\mathrm{i}}_{0.2}\right){\mathrm{O}}_3$ film and $\mathrm{SrTi}{\mathrm{O}}_3$.

Figure 4

(a–c) X-ray scans of the {$\frac{1}{2}\frac{3}{2}$ 1} family of reflections corresponding to the possible $a^{-}{a}^{-}{c}^{+}, a^{-}{a}^{+}{c}^{-}$ and $a^{+}{a}^{-}{c}^{-}$ orientations for $\mathrm{L}5B\mathrm{O}$ grown on $\mathrm{SrTi}{\mathrm{O}}_3$ (a), LSAT (b), and $\mathrm{NdGa}{\mathrm{O}}_3$ (110) (c). (d–f) Schematics showing each substrate and the orientation of the orthorhombic unit cell of $\mathrm{L}5B\mathrm{O}$ on $\mathrm{SrTi}{\mathrm{O}}_3$ (d), LSAT (e), and $\mathrm{NdGa}{\mathrm{O}}_3$ (f). The labels indicate the substrate, its crystal structure, and the strain state relative to the bulk lattice parameters of $\mathrm{L}5B\mathrm{O}$ mentioned in the text, schematically represented as inward (compressive) and outward (tensile) pointing arrows.

Figure 5

(a) Pattern and possible La-displacement patterns labeled 1R, 2R, 1L, and 2L. (b) X-ray scans of the {$\frac{1}{2}\frac{1}{2}\frac{3}{2}$} family for $\mathrm{L}5B\mathrm{O}$ grown on $\mathrm{SrTi}{\mathrm{O}}_3$ which are used to distinguish the domain patterns in (a).

Figure 6

(a) Summary of experimental and fit intensities for $\mathrm{L}5B\mathrm{O}$ on $\mathrm{SrTi}{\mathrm{O}}_3$. Bottom axis shows the H K L indices for all reflections measured. Top: A symbol indicates that a given reflection was used to fit a given parameter (vertical axis). Middle: Bar chart showing experimental intensity (gray) and the final fit values (red). (b,c) γ versus α (c) and γ and α versus $n$, the iteration number during the fitting algorithm. (d) $d_1$ versus $d_2$ and (e) $d_1$ and $d_2$ versus $n$. In (b,d) the open squares are the starting values for the fit algorithm and the crossed circles are the final values, which are shown in (c,e) as dashed lines.

Figure 7

The final orthorhombic structure for $\mathrm{La}\left(\mathrm{C}{\mathrm{r}}_{0.2}\mathrm{M}{\mathrm{n}}_{0.2}\mathrm{F}{\mathrm{e}}_{0.2}\mathrm{C}{\mathrm{o}}_{0.2}\mathrm{N}{\mathrm{i}}_{0.2}\right){\mathrm{O}}_3 \mathrm{L}5B\mathrm{O}$ on $\mathrm{SrTi}{\mathrm{O}}_3$ projected along the pseudocubic axes: $\langle 100\rangle$ film direction (left), $\langle 010\rangle$ (middle), and $\langle 001\rangle$ (right).