Towards understanding the special stability of ${\mathrm{SrCoO}}_{2.5}$ and ${\mathrm{HSrCoO}}_{2.5}$

Reversible hydrogen incorporation was recently attested [Lu et al., Nature (London) 546, 124 (2017)] in ${\mathrm{SrCoO}}_{2.5}$, the brownmillerite phase (BM) of strontium cobalt oxide (SCO), opening new avenues in catalysis and energy applications. However, existing theoretical studies of BM-SCO are insufficient, and that of ${\mathrm{HSrCoO}}_{2.5}$, the newly reported hydrogenated SCO (H-SCO) phase, is especially scarce. In this work, we demonstrate how the electron-counting model can be used in understanding the phases, particularly in explaining the stability of the oxygen-vacancy channels, and in examining the Co valance problem. Using density-functional theoretical methods, we analyze the crystalline, electronic, and magnetic structures of BM- and H-SCO. Based on our structure search, we discovered stable phases with large band gaps ($>1$ eV) for both BM-SCO and H-SCO, agreeing better with experiments on the electronic structures. Our calculations also indicate limited charge transfer from H to O, which may explain the special stability of the H-SCO phase and the reversibility of H incorporation observed in experiments. Contrary to the initial study, our calculations also suggest intrinsic antiferromagnetism of H-SCO, showing how the measured ferromagnetism has possible roots in hole doping.

Figure 1

Illustrations of the (a) BM-SCO and (b) H-SCO phases; the different Co and O sites are color coded here for illustrative purpose.

Figure 2

Schematics of the first BZ (in thin lines) and the IBZ (in thicker lines) of the BM-SCO and H-SCO phases, with the high-symmetry points labeled.

Figure 3

Plots of the band gap energy $E_{\text{g}}$ of H-SCO, if any, against the $U$ parameter, for the (a) LDA and (b) PBE-GGA functionals; band gaps estimated from the eigenvalues of the highest-occupied and lowest-unoccupied bands on the $2\times 5\times 5k$-point mesh.

Figure 4

Plot of the magnetic coupling energy $\mathrm{\Delta }{F}_{\text{AFM}-\text{FM}}/N_{\text{Co}}$ of H-SCO against the $U$ parameter, for both the LDA and PBE-GGA functionals.

Figure 5

Illustration of the distribution of the longer ${\mathrm{Co}}_{\left(6\right)}–{\mathrm{O}}_{\left(6\right)}$ bonds (overlaid with gray arrows) in phase-1 BM-SCO; note how the bond arrangements about the two circled ${\mathrm{Co}}_{\left(6\right)}$ centers, $\left(\frac{1}{2},\frac{1}{2},\frac{1}{2}\right)$ apart in direct coordinates, are different. Also shown: definitions of the ${\mathrm{O}}_{\left(\mathrm{Sr}\right)}–{\mathrm{Co}}_{\left(4\right)}–{\mathrm{O}}_{\left(\mathrm{Sr}\right)}$ bond angles ${\theta }_1$ and ${\theta }_2$.

Figure 6

Plots of the band structures of (a) phase-1 and (b) phase-2 BM-SCO near the band edges, with spin-up (-down) bands in red (color)/light gray (gray scale) solid lines [blue (color)/dark gray (gray scale) dotted lines].

Figure 7

Single-H adsorption sites, viewed along the $\left[00\overline{1}\right]$ direction; adsorbed H and surrounding atoms boxed as visual aid. Relative free energies $\mathrm{\Delta }F$ of the $1\times 2\times 2$ supercells are also listed above each figure. OVCs are marked with crosses in (a).

Figure 8

Fully hydrogenated H-SCO primitive cells and their relative free energies $\mathrm{\Delta }F$ per formula of ${\mathrm{HSrCoO}}_{2.5}$. The eight arrows in each subfigure indicate the approximate orientations of the ${\mathrm{O}}_{\left(\mathrm{Sr}\right)}-\mathrm{H}$ bonds.

Figure 9

Plot of the band structure of H-SCO near the band edges, with spin-up (-down) bands in red (color)/light gray (gray scale) solid lines [blue (color)/dark gray (gray scale) dotted lines].

Figure 10

Schematics of the energy splitting of the Co-$d$ orbitals.