Tuning the probability of defect formation via substrate strains in ${\mathrm{Sr}}_2{\mathrm{FeMoO}}_6$ films

Since oxide materials like ${\mathrm{Sr}}_2{\mathrm{FeMoO}}_6$ are usually applied as thin films, we studied the effect of biaxial strain, resulting from the substrate, on the electronic and magnetic properties and, in particular, on the formation energy of point defects. From our first-principles calculations, we determined that the probability of forming point defects, like vacancies or substitutions, in ${\mathrm{Sr}}_2{\mathrm{FeMoO}}_6$ could be adjusted by choosing a proper substrate. For example, the amount of antisite disorder can be reduced with compressive strain in order to obtain purer ${\mathrm{Sr}}_2{\mathrm{FeMoO}}_6$ as needed for spintronic applications, while the formation of oxygen vacancies is more likely for tensile strain, which improves the functionality of ${\mathrm{Sr}}_2{\mathrm{FeMoO}}_6$ as a basis material of solid oxide fuel cells. In addition, we were also able to include the oxygen partial pressure in our study by using its thermodynamic connection with the chemical potential. Strontium vacancies become, for example, more likely than oxygen vacancies at a pressure of $1\mathrm{bar}$. Hence, this degree of freedom might offer in general another potential method for defect engineering in oxides aside from, e.g., experimental growth conditions like temperature or gas pressure.

Figure 1

Considered lattice structures of ${\mathrm{Sr}}_2{\mathrm{FeMoO}}_6$. (a) Tetragonal unit cell with $I4/m$ symmetry visualizing the octahedral environment of Fe and Mo formed by the oxygen atoms with colored polyhedra. (b) Top view showing the octahedra rotation denoted as $\beta$ and counted in clockwise direction for the Fe ion octahedron. (c) Side view of the $2\times 2\times 1$ supercell with $8\mathrm{f}.\mathrm{u}.$ used for the defect calculations. (d) Top view of the supercell in (c) from the gray $xy$ layer downwards. Structural figures were prepared with vesta [41].

Figure 2

Spin-resolved local density of states (LDOS) of unstrained and defect-free SFMO calculated with FSM in vasp.

Figure 3

Structural variation with biaxial strain in the lattice constants $a=b$. (a) Variation of lattice parameter $c$ and the volume of the tetragonal cell. (b) The in-plane $\left(xy\right)$ and out-of-plane $z$ bond lengths Mo-O and Fe-O. (c) Octahedra rotation angle $\beta$, visualized in (f). (d) Out-of-plane distances between Sr and O. (e), (f) Visualization of distances and angles in the tetragonal unit cell. Structural figures were prepared with vesta [41].

Figure 4

Variations of magnetic and electronic properties with biaxial strain for GGA and $\mathrm{GGA}+U$. The local magnetic moments for (a), (e) Fe ions, (b), (f) Mo ions, and (c), (g) O ions. (d), (h) Band gap in the majority-spin channel calculated from the density of states (DOS). The inset shows the DOS for unstrained defect-free SFMO. The vertical dashed line at $-4.5\%$ on the left-hand side marks the spin transition from half-metallic high-spin state to metallic low-spin state. The vertical dashed line at $5.5\%$ on the right-hand side marks the transition from ferrimagnetic (FIM) to ferromagnetic (FM) state.

Figure 5

Defect formation energy of defects in unstrained SFMO $\left(\varepsilon =0\right)$ for varying oxygen partial pressure at $T=1050{}^{\circ }\mathrm{C}$. The relative chemical potential is shown at the upper axis. The legend is given above the figure.

Figure 6

Formation energies of defects in dependence of biaxial strain and three different oxygen partial pressures. The legend is given above the figure. ${\text{V}}_{\text{Mo}}$ is out of range in (c).