Crystal structure and electronic properties of bulk and thin film brownmillerite oxides

The equilibrium structure and functional properties exhibited by brownmillerite oxides, a family of perovskite-derived structures with alternating layers of $B{\mathrm{O}}_6$ octahedra and $B{\mathrm{O}}_4$ tetrahedra, viz., ordered arrangements of oxygen vacancies, is dependent on a variety of competing crystal-chemistry factors. We use electronic structure calculations to disentangle the complex interactions in two ferrates, ${\mathrm{Sr}}_2{\mathrm{Fe}}_2{\mathrm{O}}_5$ and ${\mathrm{Ca}}_2{\mathrm{Fe}}_2{\mathrm{O}}_5$, relating the stability of the equilibrium (strain-free) and thin film structures to both previously identified and herein newly proposed descriptors. We show that cation size and intralayer separation of the tetrahedral chains provide key contributions to the preferred ground state. We show the bulk ground-state structure is retained in the ferrates over a range of strain values; however, a change in the orientation of the tetrahedral chains, i.e., a perpendicular orientation of the vacancies relative to the substrate, is stabilized in the compressive region. The structure stability under strain is largely governed by maximizing the intraplane separation of the dipoles generated from rotations of the ${\mathrm{FeO}}_4$ tetrahedra. Lastly, we find that the electronic band gap is strongly influenced by strain, manifesting as an unanticipated asymmetric-vacancy alignment dependent response. This atomistic understanding establishes a practical route for the design of functional electronic materials in thin film geometries.

Figure 1

The removal of chains of oxygen atoms (colored in black) from the $AB{\mathrm{O}}_3$ perovskite structure (a) results in the vacancy ordered $A_2{B}_2{\mathrm{O}}_5$ brownmillerite structure (b), which consists of alternating layers of $B{\mathrm{O}}_4$ tetrahedra and $B{\mathrm{O}}_6$ octahedra along the $b$ direction. The undistorted rows of $B{\mathrm{O}}_4$ tetrahedra can then twist (c) to create left- or right-handed chains (colored blue and red, respectively).

Figure 2

The hypothetical high symmetry brownmillerite structure (a) is defined as having no octahedral or tetrahedral rotations, and has the $Imma$ space group. Relative ordering of tetrahedral chains results in three different low-symmetry structures. If all chains are of the same handedness, the structure is polar $I2bm$ (b); alternation of left- and right-handed chains within each layer results in centric $Pbcm$ (c), while alternation between each layer gives centric $Pnma$ (d). The $A$-site cations are omitted from the low-symmetry structures for clarity.

Figure 3

When brownmillerite structures are placed under epitaxial strain, the oxygen-deficient layers can order (a) parallel or (b) perpendicular to the substrate, with the pseudocubic orientations shown in (c) and (d), respectively.

Figure 4

(a) The three characteristic angles of the $A_2{B}_2{\mathrm{O}}_5$ brownmillerite structure. Rotations of the tetrahedral chains, of the octahedral network, and between the tetrahedral and octahedral layers are given by ${\mathrm{\Phi }}_T,{\mathrm{\Phi }}_O$, and ${\mathrm{\Phi }}_{OT}$, respectively. These three angles are sufficient to describe the case when the tetrahedral chains order parallel to the substrate under biaxial strain. In (b) the perpendicular orientation, however, the changes in the out-of-plane lattice parameter owing to the strain state split the octahedral and tetrahedral rotation angles.

Figure 5

The intralayer chain separation in the brownmillerite structure. The average separation distance is given by $R$, which is defined as the average of the two distances between Fe atoms of different chains $(d_1$ and $d_2)$.

Figure 6

Energy of the different tetrahedral chain ordered ${\mathrm{Sr}}_2{\mathrm{Fe}}_2{\mathrm{O}}_5$ (a) and ${\mathrm{Ca}}_2{\mathrm{Fe}}_2{\mathrm{O}}_5$ (b) structures as a function of epitaxial strain (top panels). In both cases, the parallel vacancy ordering (filled symbols) is stabilized under tensile strain, while perpendicular (empty symbols) is stabilized under compressive. This change in stabilization occurs at the point where either the parallel or perpendicular phase maximizes the average intralayer tetrahedral chain separation $(R$, middle panels) and minimizes the octahedral distortion effect $(\mathrm{\Delta }$, bottom panels).

Figure 7

The effect of strain on the tilt angles (as defined in Fig. 4) of the different ${\mathrm{Sr}}_2{\mathrm{Fe}}_2{\mathrm{O}}_5$ (left) and ${\mathrm{Ca}}_2{\mathrm{Fe}}_2{\mathrm{O}}_5$ (right) structures with both parallel and perpendicular vacancy orientation.

Figure 8

The band gap of (a) ${\mathrm{Sr}}_2{\mathrm{Fe}}_2{\mathrm{O}}_5$ and (b) ${\mathrm{Ca}}_2{\mathrm{Fe}}_2{\mathrm{O}}_5$ are strongly influenced by epitaxial strain; the electronic gap for thin film structures with vacancies ordered parallel to the substrate (filled symbols) increases as tensile strain increases, but decreases in the perpendicular orientation (empty symbols). This electronic structure response occurs owing to the manner in which strain affects the angle between the tetrahedral and octahedral layers. The $Pbcm$ structure of ${\mathrm{Sr}}_2{\mathrm{Fe}}_2{\mathrm{O}}_5$ with vacancies parallel to the substrate, for example, has a $\sim 0.3$ eV larger band gap under (c) 2% tensile strain when compared to (d) 2% compressive strain as seen by the change in the atom-resolved densities of states.

Figure 9

The effect of different stress stimuli [ionic size or chemical pressure (captured by $\tau )$ and epitaxy] on various structural descriptors, which combine to produce the equilibrium crystal structure in (a) perovskite and (b) brownmillerite oxides.