Surface and interface effects in oxygen-deficient SrMnO3 thin films grown on SrTiO3

Complex oxide functionality, such as ferroelectricity, magnetism or superconductivity is often achieved in epitaxial thin-film geometries. Oxygen vacancies tend to be the dominant type of defect in these materials but a fundamental understanding of their stability and electronic structure has so far mostly been established in the bulk or strained bulk, neglecting interfaces and surfaces present in a thin-film geometry. We investigate here, via density functional theory calculations, oxygen vacancies in the model system of a SrMnO3 (SMO) thin film grown on a SrTiO3 (STO) (001) substrate. Structural and electronic differences compared to bulk SMO result mainly from undercoordination at the film surface. The changed crystal field leads to a depletion of subsurface valence-band states and transfer of this charge to surface Mn atoms, both of which strongly affect the defect chemistry in the film. The result is a strong preference of oxygen vacancies in the surface region compared to deeper layers. Finally, for metastable oxygen vacancies in the substrate, we predict a spatial separation of the defect from its excess charge, the latter being accommodated in the film but close to the substrate boundary. These results show that surface and interface effects lead to significant differences in stability and electronic structure of oxygen vacancies in thin-film geometries compared to the (strained) bulk.

In Fig. S1a, we show the layer-resolved projected density of states for the SMO portion of the thin-film-substrate system. We focused on a small energy range around the Fermi level as opposed to the broader range shown in Fig. 1a of the main text. This more clearly shows the depletion of the subsurface valence band states and the modification of the surface electronic structure as discussed in the main text.
In Fig. S1b we show, for comparison, the density of states of bulk SMO and the contribution of different d states to the valence and conduction bands respectively. Figure S1. a) Total and projected layer-resolved density of states for the stoichiometric SrMnO3 thin film part of the interface shown in Fig. 1a) of the main text. b) Contribution of different d states to the valence and conduction bands of bulk SrMnO3.
Electronic Supplementary Material (ESI) for Physical Chemistry Chemical Physics. This journal is © the Owner Societies 2022 2 In Figs. S2a) and b) we show the density of states in deeper layers of the SMO film (layer 3 in Fig. 1 in the main text) and the STO substrate (layer 7 in Fig. 1 in the main text) respectively. Our results show that the electronic structure of these layers is virtually unchanged compared to the bulk density of states of the two materials shown in Figs. S2c) and d) respectively.

S2. EFFECT OF FILM SYMMETRY
In Fig. S3, we show the layer-resolved projected density of states for an asymmetric SrMnO 3 slab with a MnO 2 top surface and a SrO bottom surface as well as for a symmetric slab with two MnO 2 surfaces. The key result is that when both surfaces are MnO 2 -terminated and allowed to relax, they develop the same electronic structure as the top surface of the asymmetric slab. Since in the symmetric slab, no spurious electric field due to the presence of two different surface terminations is present, we associate the changed surface electronic structure with crystal-field changes from octahedral to square pyramidal, as mentioned in the main text, rather than it being an artifact associated with the asymmetric geometry of the film.   Fig. S4 reports the formation energies of an oxygen vacancy in different layers and for different charge states (neutral = 0, singly = +1 and doubly = +2 ionized). For SMO an n-doped limit with the Fermi energy close to the conduction band edge is most relevant. In this limit, although the 0/+1 charge transition level moves closer to the conduction band edge in deeper layers, the neutral charge state remains most stable for all investigated layers. Figure S4. Formation energy of oxygen vacancies in different charge states (neutral = 0, singly = +1 and doubly = +2 ionized) in a) the surface MnO2 layer, b) the first SrO layer and c) the second MnO2 layer.

S4. CELL-SIZE EFFECT
To test for cell-size effects, we computed an oxygen vacancy in the top-most SrO layer in a larger 320-atom √ 2× √ 2×1 supercell of the cells used throughout the rest of the manuscript. Reciprocal mesh-sampling was reduced to 4 × 4 × 1 in this case and all other computational parameters kept the same. We obtain an oxygen vacancy formation energy of 0.42 eV, which is only 5% smaller than in the smaller cell (0.44 eV), showing that defect-defect interactions are already small for the cells used throughout the manuscript. Moreover, the electronic structure of the defect in the larger cell (see Fig. S5) is very similar to the one in the smaller cell (see Fig. 3a of the main text). Figure S5. Total and projected layer-resolved density of states for VO in the first SrO layer computed in a 320-atom √ 2× √ 2×1 supercell of the cells used throughout the rest of the manuscript.