The complex-oxides interfaces hold rich physics that have resulted in the emergence of various novel functional properties. While strain engineering has been widely used to induce many properties over the past decade, more recently the role of oxygen vacancies has increasingly drawn wider attention. In particular, research has revealed that there exists a strong coupling between strain and oxygen vacancy formation energy. This coupling can be used to alter oxygen vacancy concentration at interfaces, thereby opening another degree of freedom to control interfacial properties. In this review, we highlight recent works that have interrogated the connection between coupling and the emerging interfacial properties. The coupling has not only been used to selectively create oxygen vacancies at specific crystallographic oxygen sites but has also been used to manipulate ordering of oxygen vacancies near interfaces. In addition, recent studies have extended the existing connection between strain and octahedra distortion to oxygen vacancies, where the role of vacancies in the properties emerging due to octahedra distortion is now being unveiled. Finally, we discuss recent data-science efforts in the design and discovery of complex oxides and property prediction.

The striking observation of high electronic conductivity at the interface between two non-conducting oxide insulators has revolutionized the field of oxide interfaces.1 Since then, many novel properties such as high temperature superconductivity, colossal magnetoresistance, colossal ionic conductivity, ferromagnetic, ferroelectric, piezoelectric, and multiferroic properties have been observed.2–16 A common denominator among all thin-film structures is the presence of interfacial strain that originates due to the lattice mismatch between the two interfacing oxides. This parameter has been creatively used to tune the properties in functional oxides, broadly classified as strain engineering. Concomitantly, the presence of oxygen vacancies at interfaces has also been duly recognized. However, in the past 5 years, their role in inducing functional properties has continued to gain importance. Consequently, oxygen vacancies have now become a key focus area in the study of functional properties in complex-oxide thin films.7,17–21

Recent research has revealed that there exists a strong coupling between interfacial strain and oxygen vacancies. Multiple reports, both experimental and computational, have shown that interfacial strain impacts the thermodynamic stability of oxygen vacancies. It is commonly observed that the formation energy of oxygen vacancies generally decreases22–26 (although not always27) with tensile strain, thereby increasing the concentration of vacancies at the interfaces. Consequently, the transition elements present in functional oxides (such as in perovskites and fluorites) get reduced due to charge transfer from oxygen vacancies. The interfacial strain changes the cation-oxygen bond lengths and alters the electronic structure by affecting the cation d and O 2p electron hybridization that eventually gives rise to interesting functional properties. Thus, this coupling between interfacial strain and oxygen vacancies is now being carefully interrogated to tune functional properties in complex oxides.

In this paper, we review recent advances in the field of complex oxide interfaces at the intersection of interfacial strain and oxygen vacancies. In particular, we discuss the use of strain-vacancy coupling to induce novel properties at interfaces, oxygen-vacancy ordered structures near interfaces, computational studies on coupling between interfacial strain and vacancy formation energies, coupling between octahedra rotation, oxygen vacancies and interfacial strain, and data-science methods to predict oxygen vacancy energetics in complex oxides. Figure 1 schematically summarizes these aspects of this review paper illustrating that interfacial strain [Fig. 1(a)] can lower oxygen vacancy formation energy [Fig. 1(b)] and can lead to the formation of oxygen vacancies [Fig. 1(c)] that can form ordered networks [Fig. 1(d)] and can affect octahedral distortion [Fig. 1(e)] in complex oxides.

FIG. 1.

Schematic overview of the coupling between interfacial strain and oxygen vacancies at oxide interfaces. (a) Lattice mismatch between the thin film and the substrate can impart interfacial strain. (b) Interfacial strain can lower oxygen vacancy formation energy. Decrease in formation energy in CaMnO3 is shown in (b) [reproduced from Aschauer et al., Phys. Rev. B 88, 054111 (2013). Copyright 2013 APS]. The BO6 octahedra can elongate due to biaxial in-plane tensile strain, whereas it can compress in the vertical direction resulting in two different in-plane (IP) and out-of-plane (OP) oxygen vacancies, which can have different formation energies. (OP and IP oxygen vacancies are shown in light red and light blue.) (c) Reduced vacancy formation energy can lead to the formation of oxygen vacancies, which can (d) order to form network structures. (Oxygen vacancies are shown in white.) (e) Interfacial strain can cause octahedra distortion. The presence of oxygen vacancies can further distort the octahedra as shown in NdNiO3. The additional distortion due to vacancies can further impact functional properties (see text). Reproduced from Kim et al., Phys. Rev. B 101, 121105 (2020). Copyright APS.

FIG. 1.

Schematic overview of the coupling between interfacial strain and oxygen vacancies at oxide interfaces. (a) Lattice mismatch between the thin film and the substrate can impart interfacial strain. (b) Interfacial strain can lower oxygen vacancy formation energy. Decrease in formation energy in CaMnO3 is shown in (b) [reproduced from Aschauer et al., Phys. Rev. B 88, 054111 (2013). Copyright 2013 APS]. The BO6 octahedra can elongate due to biaxial in-plane tensile strain, whereas it can compress in the vertical direction resulting in two different in-plane (IP) and out-of-plane (OP) oxygen vacancies, which can have different formation energies. (OP and IP oxygen vacancies are shown in light red and light blue.) (c) Reduced vacancy formation energy can lead to the formation of oxygen vacancies, which can (d) order to form network structures. (Oxygen vacancies are shown in white.) (e) Interfacial strain can cause octahedra distortion. The presence of oxygen vacancies can further distort the octahedra as shown in NdNiO3. The additional distortion due to vacancies can further impact functional properties (see text). Reproduced from Kim et al., Phys. Rev. B 101, 121105 (2020). Copyright APS.

Close modal

Rare-earth nickelates display complex electronic behaviors that originate from a strong interplay between the atomic structure and electronic correlations on Ni atoms. Although metal to insulator (MIT) transition has been observed in various nickelates,20,28–30 recent works reveal that oxygen vacancies could be playing a key role in inducing this transition.20,29,31 Wang et al.29 showed that an insulating phase in NdNiO3 could be stabilized at room temperature in thin films by modulating oxygen partial pressure, which otherwise shows a metallic behavior in bulk. The creation of oxygen vacancies gradually decreases the Ni3+/Ni2+ ratio, opens the bandgap and induces a room-temperature insulating phase.32 More recently, the effect of oxygen vacancies in inducing MIT has also been observed in LaNiO3. While LaNiO3 is the only nickelate that is known to remain metal at any temperature, Golalikhani et al.20 showed that thin films of LaNiO3 up to 1.5 unit-cell thick grown on LaAlO3 show insulating behavior under varying oxygen partial pressures, thereby correlating a direct relationship between oxygen vacancies and MIT.

The effect of strain and oxygen vacancies in modulating MIT temperature has been observed in VO2. It has a MIT temperature of 68 °C that is high for most practical applications. Jeong et al.33 tuned MIT temperature during an electrolyte gating experiment. By applying an electric field, it was observed that the oxygen vacancies formed at the film–electrolyte interface; a concomitant change in the vanadium oxidation state from V4+ to V3+ was observed that confirmed the formation of oxygen vacancies. The MIT temperature was found to decrease with the formation of oxygen vacancies. Conversely, the insulating phase was recovered by annealing under oxygen atmospheres. The effect of oxygen vacancies on MIT temperature has since been observed by others.34–38 For example, Fan et al.35 showed that a combination of interfacial strain and oxygen vacancies could be used to modulate MIT in VO2. They grew thin films of VO2 on two different terminating surfaces of MgF2 to induce tensile and compressive strains in VO2. While the tensile strain in VO2 lowered the MIT temperature, the compressive strain increased it. To nullify the strain effect, they further grew thicker films and varied the oxygen partial pressure in order to introduce oxygen vacancies. The authors observed that MIT lowered uniquely due to oxygen vacancies in the fully relaxed films. Thus, both tensile strain and oxygen vacancies were found to affect MIT in VO2. Electronic structure calculations showed that oxygen vacancies act as electron donors and result in decreasing the bandgap thereby triggering the metallic behavior in VO2.34–36 

The effect of interfacial strain and the strain-oxygen vacancy coupling has also been investigated in multiferroic materials.3,19,27,39–42 YMnO3 is a multiferroic material in which non-collinear spins on Mn sites have eight configurations (Γ1–Γ8) for the magnetic ground state. Cheng et al.43 note that out of these eight, four states (Γ1–Γ4) have low energies. Intriguingly, while Γ1, Γ3, and Γ4 are found to be stable, they have no net magnetization. Thus, Γ2 is the only configuration that has non-zero magnetization that is ironically unstable. Cheng et al.43 showed that Γ2 stability could be achieved by creating specific oxygen vacancies. In YMnO3, there are four types of oxygen vacancies, i.e., OP1, OP2, OT1, and OT2, in the MnO5 cluster, and OT2 is the only vacancy via which Γ2 state can be stabilized. (OP and OT refer to in-plane and on-top oxygen atoms, respectively.) Interestingly, OT2 has higher formation energy than the other three, as per the DFT calculations by Cheng et al.43 To gain control over this specific vacancy, they found that applying axial compressive strain increases the length of the OT2–Mn bond more than that of OP–Mn and consequently leads to a decrease in the formation energy of OT2 oxygen vacancy. They induced this in-plane strain by experimentally growing YMnO3 on c-Al2O3, thereby selectively creating only OT2 vacancies. By leveraging the interplay between interfacial strain and oxygen vacancies, the authors showed a path to realize both ferroelectricity and ferromagnetism in YMnO3.

Interfacial strain has also been used to induce concentration gradients of oxygen vacancies. Guzman et al.44 used interfacial strain to induce the flexoelectric effect, i.e., electric field generated via strain gradient. They created high tensile strain in SrMnO3 by interfacing with (LaAlO3)0.3 (Sr2AlTaO6)0.7 (LSAT) that gradually decreased upward leading to a strain gradient in the film. The strain-gradient in-turn led to the formation of oxygen vacancies, creating a corresponding vacancy-concentration gradient. The signature of this oxygen vacancy gradient was revealed in the charge state of Mn that gradually changed from +3 to +4 with vacancy concentration. The presence of oxygen vacancies generated a <001>-flexoelectric component that rotated the in-plane <110>-ferroelectric polarization. This work showed that not only the interfacial strain can be used to create vacancies, but their concentration and location can also be controlled. Similar coupling among strain, oxygen vacancy, and properties is seen in various other works.40,45–49

The observation of two-dimensional electron gas (2DEG) at LaAlO3/SrTiO3 interface has been one of the groundbreaking findings in complex oxide interfaces. In the past 15 years, various reasons have been proposed to explain the phenomenon such as polar catastrophe,1,50 cation antisite formation,51–53 and oxygen vacancies.54–56 For instance, Willmott et al.51 used experimental and computational means to demonstrate that the shift in Fermi level near the interface occurred due to structural changes in the heterostructure. This shift in the Fermi level coupled with tetrahedral distortions was adjudged to be responsible for the formation of a quasi-2DEG at the LaAlO3/SrTiO3 interface. Kalabukhov et al.52 proposed that the cation defects at the interface contributed to the conductive 2DEG layer. The authors determined that this was caused by inhomogeneous distribution of La atoms in samples with LaAlO3 thickness less than four unit cells, causing intermixing of La and Sr atoms at the interface. Siemons et al.57 investigated relation between oxygen vacancies and the charge carrier density with the help of various experimental means. The samples were prepared under different growth conditions with varying oxygen partial pressure. The results showed the presence of more Ti3+ in the samples prepared at lower oxygen partial pressure, indicating that there were more oxygen vacancies. It was also shown that the sample with higher number of oxygen vacancies had a charge carrier density of 2 × 1016 cm−2 while the samples grown at higher oxygen partial pressure showed a reduction in carrier density by two orders of magnitude. Further measurements confirmed the role of oxygen vacancies at the interface contributing to the supply of charge carriers in the conductive layer in the LaAlO3/SrTiO3 interface. Liu et al.58 explored the amorphous and crystalline LaAlO3/SrTiO3 heterostructures. They deposited LaAlO3 on SrTiO3 substrates using pulsed layer deposition at room temperature and varied oxygen partial pressure during the growth. The resistance-temperature curves showed that all the samples were metallic despite being grown under different partial pressures. The conductivity at the interface was attributed to the presence of oxygen vacancies in the SrTiO3 substrate. This was supported by the loss in conductivity observed when there was reduction in oxygen vacancies caused by oxygen post-annealing. Additionally, the sheet carrier density results showed that oxygen vacancies were the primary source of charge carriers in the amorphous sample while both oxygen vacancies and polarization catastrophe were responsible for the conductive interface in unannealed crystalline LaAlO3/SrTiO3. At the LaAlO3/SrTiO3 interface, other functional properties have also been observed. Hu et al.59 investigated the dependence of magnetic behavior on oxygen vacancies in LaAlO3/SrTiO3 interfaces. Oxygen partial pressure was used to vary the content of oxygen vacancies. The authors discovered that the presence of oxygen vacancies was responsible for the ferromagnetic state in the LaAlO3/SrTiO3 interface.

Strain engineering has been widely used to tune the bandgap in semiconductors. In order to understand the interplay of strain, oxygen vacancies, and bandgap in complex oxides, Gao et al.60 deposited SrSnO3 thin films on LaAlO3 and MgO to induce compressive and tensile strain, respectively. Interestingly, both strain states led to widening of the bandgap. While the compressive strain raised the energy levels of Sn 5s orbitals, tensile strain created oxygen vacancies in SrSnO3. The formation of oxygen vacancies under tensile strain is attributed to the lowering of vacancy formation energy that has been generally widely observed.22,24–27 The coupling between interfacial strain and oxygen vacancy formation energy is as discussed in greater detail later in the paper.

Meyer et al.45 explored the dependence of superconductivity in La1.85Sr0.15CuO4 on strain relaxation and critical thickness of the films. Thin films were grown under varying tensile and compressive strain via coupling of lattice mismatch with substrates and film thickness. While the films exhibited superconductivity under compressive strain, it was suppressed when the films were under tensile strain higher than 0.25%. The authors further focused on the formation of oxygen vacancies and concluded that tensile strain facilitated oxygen non-stoichiometry in thin films. The loss in superconductivity was thus attributed to the inherent oxygen vacancies formed in La1.85Sr0.15CuO4 films during growth.

Not only there exists a thermodynamics coupling between strain and oxygen vacancy formation, there also exists a kinetics coupling between strain and oxygen vacancy migration. Large number of both experimental and computational studies have shown that oxygen vacancy migration barriers decrease with increasing tensile strain in perovskite and fluorite oxides. Consequently, both formation and diffusion of oxygen vacancies can be controlled by strain, which becomes highly useful in electrochemical applications. Studies have shown that enhanced oxygen concentration and fast ion conductivity can be achieved at heterointerfaces, thereby contributing to materials development for solid oxide fuel cells and sensors.61–74 Petrie et al.23 displayed this collective coupling in SrCoOx, where they showed that thin films of SrCoOx grown on substrates that induce tensile strain resulted in not only creating new oxygen vacancies but also enhancing ionic diffusion by lowering both the oxygen vacancy formation and migration energies simultaneously. New interfacial architectures such as vertically aligned nanocomposites75–77 and nanobrushes78 are being engineered to leverage the coupling between interfacial strain and oxygen vacancy formation and migration energies. There is large literature on coupling between strain and vacancy kinetics, and the reader is referred elsewhere for review articles.65,72,79,80

The close analysis of interfacial structures has revealed that the oxygen vacancies can order to form networks near the interfaces [Fig. 1(d)].21,81–86 It has been proposed that ordering of vacancies acts as a strain relaxation mechanism. Formation of the ordered networks has been particularly observed in ferrites and cobaltates. It has also been shown that the orientation of the ordering could also be manipulated by strain.81,87 Inoue et al.81 grew thin films of brownmillerite phase of CaFeO2.5 on four different substrates, i.e., SrTiO3, LSAT, LaAlO3, and LaSrAlO4 (LSAO). Due to the lattice parameter mismatch between the substrates and CaFeO2.5, SrTiO3 and LSAT introduced tensile strain, whereas LaAlO3 and LSAO introduced compressive strain in the films. It was observed that the compressive and tensile strains induced perpendicular and parallel ordering of oxygen vacancies along the growth direction, respectively. A contrasting ordered arrangement of vacancies due to strain illustrates that specific crystallographic directions could be manipulated for oxygen diffusion in fast-ion conductor applications.

Similar investigation was performed by Gazquez et al.82 on La0.5Sr0.5CoO3−δ (LSCO). They grew LSCO thin films on SrTiO3 (001) and LaAlO3 (001) substrates. These authors also observed the effect of the tensile strain imparted by the substrates on the orientation of vacancy ordering. Although the oxygen vacancy channels were parallel to the growth direction in LSCO/SrTiO3 (001), they were perpendicular in LSCO/LaAlO3 (001) interface. Note that while SrTiO3 imparts compressive strain, LaAlO3 imparts tensile strain based on the lattice mismatch with LSCO. It may be noted that the effect of the direction of strain (i.e., tensile or compressive) on the orientation of vacancy ordering appears to be material dependent. Under compressive strain, while the ordering of vacancies is parallel in LSCO, it is perpendicular in CaFeO2.5.81 

Zhang et al.88 further noticed that both the vacancy formation and ordering can be simultaneously achieved by interfacial strain. They grew WO3−δ films on SrTiO3 and LaAlO3, where the former imparted 4.5% tensile strain compared to 1.7% by the latter substrate. Under similar oxygen partial pressure conditions, a higher concentration of vacancies at the WO3−δ/SrTiO3 interface compared to the WO3−δ/LaAlO3 interface was observed, which is in line with the general observation of reduced vacancy formation energy under higher tensile strain. In addition, a higher level of vacancy ordering was also observed in WO3−δ/SrTiO3 compared to WO3−δ/LaAlO3. Studies have revealed similar vacancy ordering in heterostructures of fluorite oxides as well.89,90

Even more interesting oxygen vacancy features have been observed due to the coupling between interfacial strain and oxygen vacancies. Hirai et al.21 grew a 20 nm brownmillerite phase of SrFeO2.5 thin-film on perovskite DyScO3 in order to investigate the ordering of vacancies per previous studies. Interestingly, it was observed that while the vacancies indeed ordered in the rest of the film, the oxygen vacancies were disordered in SrFeO2.5 within the 2 nm vicinity of the interface in DySO3. The authors observed no change in the coordination of oxygen vacancies across the film thickness, indicating that only the order to disorder transformation of the oxygen sublattice occurred due to strain near the interface. The authors noticed that such transformation in bulk occurs at 1103 K; consequently, a high temperature phase is stabilized at low temperature via tensile strain. Nord et al.91 observed the change in structure of La0.7Sr0.3MnO3 (LSMO) thin films when grown on SrTiO3. The LSMO thin films were subjected to a 1.2% tensile strain resulting from the smaller lattice constant of LSMO compared to SrTiO3. With the combined results from DFT calculations and experiments, they found the presence of a brownmillerite phase with disordered oxygen vacancies existing within 3 nm into the thin film from the interface. Such near-interface order-to-disorder transformation of the oxygen vacancy structures due to interfacial strain (Fig. 2) possibly opens new way to unlock vacancies for fast-ion conductor applications.

FIG. 2.

Schematic illustrates that interfacial strain can alter the ordering of oxygen vacancies. The vacancies can (a) order or (b) disorder depending upon the amount of strain induced via the substrate (Vacancies are shown in white in the strained film.).

FIG. 2.

Schematic illustrates that interfacial strain can alter the ordering of oxygen vacancies. The vacancies can (a) order or (b) disorder depending upon the amount of strain induced via the substrate (Vacancies are shown in white in the strained film.).

Close modal

In our recent computational work, we have observed that tensile strain could be used to break the ordering of vacancies in fluorite δ-Bi2O3.92 Previous works had shown that vacancies in δ-Bi2O3 can order in a combined <110>–<111> manner in a 2 × 2 × 2 supercell.93–95 By applying biaxial tensile strain in DFT calculations, we observed that disordered vacancy structures become more stable compared to the ordered structure. Using molecular dynamics (MD) simulations, we then observed that, under biaxial tensile strain, there is high oxygen diffusion compared to almost no diffusion under zero strain. Similarly, we observed that the ordered structure in LaNiO2.5 could be destabilized by applying strain and metastable structures could be stabilized. These results, viewed along with the order/disorder observed experimentally, indicate that strain could be used to manipulate oxygen vacancies and metastable structures could be induced that can potentially lead to new functional properties.

In addition to coupling between interfacial strain and oxygen vacancies, the work in pyrochlore oxides (chemical formula A2B2O7) has revealed that cation ordering could also be broken by strain.92,96–98 In pyrochlores, there is an ordered arrangement of A3+ and B4+ cations and one oxygen vacancy in a unit cell. Breaking the cation chemical ordering results in unlocking the oxygen vacancy that enables fast ion conductivity in pyrochlores. Barry et al.97 grew Ho2Ti2O7 thin-films on yttria-stabilized zirconia (YSZ). Due to the lattice mismatch between the two materials, a 2% strain in the thin film was observed. Consequently, a large number of antisites near the interface, i.e., Ti sites on Ho sites and vice versa, were observed. Similarly, Yang et al.98 reported the presence of BiIr antisite defects in Bi2Ir2O7 thin films grown on YSZ. Our DFT calculations92 on Gd2Ti2O7 show that tensile strain can break the Gd and Ti ordered arrangement forming cation antisites, leading to stability of the disordered structure over the ordered structure. In parallel, our MD simulations showed significantly higher oxygen diffusivity in disordered than ordered pyrochlore in agreement with previous works.96,99,100 Cation disorder has also been observed in ion-irradiated pyrochlore samples. Using high-angle annular dark field (HAADF) imaging in scanning transmission electron microscopy (STEM),96 it was observed that a concentric disordered interphase region existed between ordered and amorphous pyrochlore regions. The disordered region had a large presence of cation antisites and was found to be under tensile strain, in agreement with DFT calculations.92,96 In summary, these studies indicate that interfacial strain can cause stability of metastable (vacancy and cation) structures near interfaces and open a pathway to influence new properties.

The formation of oxygen vacancies due to interfacial strain is correlated to its formation energy. DFT calculations have revealed that the vacancy formation energy could vary by up to 1 eV under reasonable values of strain,89 indicating that significant changes in vacancy concentration could be expected due to interfacial strain. Under tensile strain, the decrease in vacancy formation energy with increasing tensile strain is widely observed in complex oxides. Consequently, interfacial tensile strain is expected to increase vacancy concentration. However, under compressive strain, the correlation is found to be material dependent where increase, decrease, or no change in vacancy formation energies have been observed in different materials. The strain-vacancy formation energy data are available for CeO2,24,89 MnO,101 SrTiO3,22 BaTiO3,102 PbTiO3,103 LaSrCoO3,104 CaMnO3,26 SrMnO3, BaMnO3,27 LaAlO3,105 and SrCoO3 (Ref. 23), and their behaviors are discussed below.

In CeO2, vacancy formation energy decreases as the compressive strain decreases and tensile strain increases.24,89 Consequently, oxygen vacancies become more stable under tensile strain. This behavior is correlated to chemical expansion of the oxygen vacancies, where it has been observed that under tensile strain, the electrons localize on Ce atoms, leading to change in the valence state from Ce4+ to Ce3+.106–108 Since Ce3+ has larger ionic radius than Ce4+, a higher tensile strain stabilizes the vacancy formation. In contrast, an opposite behavior is observed in MnO, where the vacancy formation energy decreases as the compressive strain in the material increases. Aschauer et al.101 showed that, instead of localizing on the cation, the electrons occupy the vacancy site forming F-centers. Consequently, Mn does not reduce from Mn2+ to Mn1+, thereby demonstrating a contrasting behavior compared to CeO2.

In SrTiO3, it has been observed that the vacancy formation energy decreases under both compressive and tensile strain. Using DFT calculations, Choi et al.22 explained the behavior in relation to bandgap where it decreased irrespective of the direction of strain. The authors postulated that this correlation possibly explains the observed formation energy trend. Similar trend is observed in La0.875Sr0.125CoO3−δ as shown by Donner et al.104 Whether the correlation with bandgap exists even in La0.875Sr0.125CoO3−δ remains to be seen. Interestingly, PbTiO3 (Ref. 103) and BaTiO3 (Ref. 102) do not show the same trend as observed in SrTiO3. In these two materials, the vacancy formation energy decreases as compressive strain decreases and tensile strain increases. Formation energy increase with increasing compressive strain has been proposed to reduce oxygen vacancies in ferroelectrics where domain-wall pinning by vacancies is considered to be a vexing issue.

Biaxial strain could result in breaking the symmetry among the oxygen atoms in the BO6 octahedra, as observed in DFT calculations by Aschauer et al.26 in CaMnO3. As a result, two types of oxygen atoms, i.e., four in-plane (IP) and two out-of-plane (OP), occur under biaxial strain [Fig. 1(b)]. Consequently, the formation energy of these two crystallographically different oxygen vacancies changes under strain. Aschauer et al.26 showed that while the in-plane oxygen vacancy formation energy decreases with increasing tensile strain, that of out-of-plane remains unaltered. This is because the biaxial tensile strain increases the relaxation volume and accommodates the chemical expansion of the in-plane vacancies, whereas there is contraction in the out-of-plane dimension that does not provide such accommodation. This separation between two vacancies indicates that tensile strain can be used to modulate oxygen sites by preferentially creating vacancies at one site compared to other (as also discussed earlier in YMnO3 [Ref. 43]). In contrast, the formation energies of both vacancies remain same and unaffected under compressive strain. Aschauer et al.26 argued a competition between chemical expansion and shifts in the electronic energy levels as the underlying reason. Similar modulation of two oxygen vacancies under tensile strain was also observed in SrMnO3 and BaMnO3 (Ref. 27). Finally, both LaAlO3 (Ref. 105) and SrCoO3 (Ref. 23) show decreasing oxygen vacancy formation energy as compressive strain decreases and tensile strain increases.

The chemical expansion has been correlated to the type of B cation. Marthinsen et al.109 performed DFT calculations to understand the difference in chemical expansion between manganite and titanate perovskites. It was observed that the chemical expansion was lower in CaTiO3, SrTiO3, and BaTiO3 than their manganate counterparts, i.e., CaMnO3, SrMnO3, and BaMnO3. Similarly, Mayeshiba and Morgan25 observed higher chemical expansion in LaMnO3 compared to LaFeO3. In addition, Perry et al.110 showed that chemical expansion is proportional to the change in the B-cation radius. These studies illustrate the role of B-cation chemistry in tuning the chemical expansion in perovskites.

Mayeshiba and Morgan25 explained the underlying reasons for the general trends observed in oxygen vacancy formation energies by focusing on LaMnO3, La0.75Sr0.25MnO3, LaFeO3, and La0.75Sr0.25FeO3. While varying behaviors were observed among the four materials, the authors postulated that the trends could be explained based on the vacancy volume (i.e., chemical expansion) and elastic constants. In particular, they proposed that decreasing vacancy formation energy with increasing tensile strain was due to positive vacancy volume, in agreement with others,107,108 whereas the increase in the elastic constants increases the vacancy formation energy under compressive and tensile strains. Furthermore, they suggested that the vacancy volume and elastic constants controlled the linear portion and curvature of the formation energy curve, respectively. The authors ultimately derived an expression that directly correlates chemical expansion, elastic constants, and oxygen vacancy formation energy.

The large complexity at the interface due to chemistry, charge imbalance, growth conditions, and interfacial strain can not only lead to the formation of oxygen vacancies but also impact the stability of vacancies, such as segregation, across the interfaces. For example, He et al.111 performed DFT calculations to observe the effects of interfaces on point defects in SrTiO3/SrRuO3 superlattices. Single oxygen vacancies were placed in AO and BO2 layers of the ABO3 perovskites, and the oxygen vacancy formation energies were computed across various layers, as shown in Fig. 3. It was observed that the vacancy formation energy was lower in the AO layers compared to BO2 layers in the non-interface regions. However, at the interface, it was lower in the BO2 layer lying in the RuO2 layer, as shown in Fig. 3. It was further observed experimentally that the heterointerface structure yielded ferroelectricity despite neither of the materials shows ferroelectricity individually. The ferroelectricity in the heterointerface was attributed to the presence of oxygen vacancies at the interfaces. It was also suggested that ferroelectricity in the superlattice could be enhanced by increasing the concentration of oxygen vacancies.

FIG. 3.

DFT computed relative oxygen vacancy formation energy in AO oxygen planes and BO2 planes in SrTiO3/SrRuO3 superlattice at different locations relative to an oxygen vacancy in bulk SrTiO3. The stability of vacancies can vary significantly depending upon the planar site. (O, Sr, Ti, and Ru are shown in red, yellow, green, and blue, respectively.) Reproduced from Perry et al., J. Mater. Chem. A 3, 3602–3611 (2015). Copyright 2015 Royal Society of Chemistry.

FIG. 3.

DFT computed relative oxygen vacancy formation energy in AO oxygen planes and BO2 planes in SrTiO3/SrRuO3 superlattice at different locations relative to an oxygen vacancy in bulk SrTiO3. The stability of vacancies can vary significantly depending upon the planar site. (O, Sr, Ti, and Ru are shown in red, yellow, green, and blue, respectively.) Reproduced from Perry et al., J. Mater. Chem. A 3, 3602–3611 (2015). Copyright 2015 Royal Society of Chemistry.

Close modal

Zhang et al.112 performed the DFT study of PbTiO3/SrTiO3 interface to understand the segregation/stability of oxygen vacancy across the interface. They consider 4PbTiO3/4SrTiO3 superlattice and calculated vacancy formation energy at each layer. The calculations were performed in paraelectric and ferroelectric phases possessing octahedra rotations. It was observed that in the paraelectric phase, the vacancy formation energy is lower in PbTiO3 bulk-like region compared to SrTiO3 bulk-like region. In addition, the AO layers showed lower formation energy than the TiO2 layer. In contrast, in the ferroelectric phase, the formation energy was found to be lowest in the bulk-like region of PbTiO3, whereas it was highest at the interface in the direction of polarization. In addition, the authors showed that the octahedral rotations increased the vacancy formation energy. Overall, the authors found that the vacancy formation energy is significantly impacted by the location of the vacancy site across the interface and the rotation of the octahedra. Aidhy et al.113 performed similar calculations in the SrTiO3/MgO interface to understand the effect of strain on the vacancy formation energy across the interface structure. It was observed that when biaxial strain equivalent to the lattice parameter of SrTiO3 is applied (i.e., compressive strain in MgO whereas no strain in SrTiO3), the vacancy is found to be most stable at the interface in the TiO2 layer. However, when biaxial strain was increased, the vacancy stabilizes inside the bulk-like region of SrTiO3, thereby illustrating the effect of interfacial strain on the vacancy stability across the interface.

Comes et al.114 performed a combined experimental and DFT study on the SrTiO3/LaCrO3 interface to understand charge carrier at the interface. They found that oxygen vacancies are likely to be present at the interface instead of the bulk. Similarly, Wang et al.115 performed DFT calculations on the LaAlO3/KTaO3 interface and they observed that the oxygen vacancies are most likely to be stable at the interface, particularly in the TaO2 layer, followed by the stability at the LaO surface layer. It was found that changing the location of oxygen vacancy even to the next layer within the close vicinity of the interface could significantly impact the 2DEG and electronic properties. Zhou et al.116 performed DFT calculations to understand the effect of thickness of LaAlO3 film grown on SrTiO3. They observed that oxygen vacancy formation is most likely at the LaAlO3 surface, and the formation energy decreases as the film thickness increases. Furthermore, the formation energy becomes negative at thickness greater than four unit-cell indicating a spontaneous formation of vacancies on the LaAlO3 surface. Lee et al.78 recently studied the (111) CeO2 interface with bixbyite Y2O3 both experimentally and computationally. A 3% CeO2 lattice expansion was observed along with the presence of a large concentration (up to 10%) of oxygen vacancies at the interface with consequent reduction of Ce4+ to Ce3+. DFT calculations showed the oxygen formation energy of the vacancies to be 1.8 eV that is significantly lower than that in the bulk, leading to large segregation of vacancies at the interface. Similar observation was made by Veal et al.117 in the (001) In2O3/YSZ interface. A higher concentration of vacancies was predicted at the interface due to significantly lower vacancy formation energy compared to the bulk of either materials. These studies thus elucidate that the stability of the oxygen vacancy can vary across the interfaces. A strong coupling between interfacial strain, interface chemistry, and vacancy formation energy collectively dictates the location of vacancies at interfaces.

Many functional properties observed in perovskites are attributed to tilting/rotation of the BO6 octahedra.27,118–121 Large efforts have been made to understand the mechanisms that couple octahedra distortion and properties. Controlling the octahedra rotation has continually remained under prime spotlight, and the role of interfacial strain has been especially scrutinized. For example, Johnson-Wilke et al.105 experimentally investigated the effect of compressive and tensile strains on octahedra rotation in LaNiO3 thin films. Various substrates that imparted different amounts of strains were used. In agreement with DFT results, the authors showed that the in-plane rotation angle, α [see Fig. 1(e)], is suppressed when LaAlO3 is under compressive strain, whereas it is enhanced under tensile strain. Conversely, the opposite is observed for the out-of-plane rotation angle, γ, illustrating the octahedra rotation could be manipulated by interfacial strain. Similarly, Choquette et al.122 investigated similar coupling in the EuFeO3 thin film by growing on different substrates with strain ranging from compressive to tensile. Specific rotational patterns were observed under compressive strain, which were categorically different from that under tensile strain. More recently, the effect of crystallographic orientations (i.e., planar growth) of the substrate has been studied in various oxides, and variations in the properties have been observed, which indicate that the same substrate can qualitatively lead to different properties.123–125 

In addition to the individual effect of interfacial strain, the coupled effect of interfacial strain and oxygen vacancies on octahedra rotation has also been studied. Lu et al.126 grew SrRuO3 thin films on SrTiO3. They found that by decreasing the oxygen partial pressure, phase transformation from monoclinic to tetragonal phase could be achieved in SrRuO3. While the octahedra tilt with Glazer notation127 ab+c is observed in the stoichiometric SrRuO3 film, under reduced oxygen partial pressure, the tetragonal phase with a0a0c tilt is stabilized. It was observed that oxygen vacancies were present in SrO atomic planes that caused Ru–Ru repulsion along the c-axis. Consequently, the octahedra rotation is suppressed in a and b axes, which results in transformation from ab+c to a0a0c tilt.

The coupled effect of interfacial strain and oxygen vacancies on NiO6 octahedra has also been observed recently by Kim et al.128 in NdNiO3 grown on various substrates to induce interfacial strain. The authors performed a joint DFT and experimental study where they showed that due to biaxial strain, there is higher concentration of oxygen vacancies in tensile strained films compared to compressively strained films. The DFT calculations revealed a relatively higher octahedra distortion in the presence of oxygen vacancies [Fig. 1(e)]. In addition, the authors observed higher disproportionation of Ni–O bonds due to the presence of oxygen vacancies. Consequently, the bandgap opened up that resulted in MIT. A key difference between the work by Lu et al.126 and Kim et al.128 is that, while the oxygen vacancies in SrRuO3 were created by manipulating the oxygen partial pressure, that in NdNiO3 were created due to interfacial strain. In summary, the coupling between interfacial strain and oxygen vacancies appears to affect octahedra rotation, which ultimately impacts the functional properties. A stronger control over the coupling is expected to undoubtedly open new avenues for inducing novel properties.

Over the past two decades, DFT has been indispensable in uncovering novel properties in complex oxides. However, computational expense has continued to remain one of the main roadblocks. In the past few years, data-science-based methods, first via high-throughput calculations and now via machine learning models are opening new doors in the design and discovery of materials. The accuracy of DFT coupled with new data-science algorithms are rapidly unraveling new complex oxide chemistries and properties.121,129–135

Emery and Wolverton129 performed high-throughput calculations to predict formation energy, stability and oxygen vacancy formation in ABO3 perovskites. They performed calculations on 5329 cubic and distorted perovskites and prepared a dataset with consistent calculation parameters that could be used for training machine learning models. The authors noticed that there are 395 perovskites that are predicted to be thermodynamically stable, out of which 230 new compounds are yet to be experimentally explored.

Takahashi et al.131 used DFT and machine learning to predict bandgap in perovskites. A database of more than 15 000 materials was used to train the machine learning model, and the authors identified 18 descriptors for bandgap prediction. Using the model, the authors were able to identify 11 new Li- and Na-based perovskite materials that fall in the desired bandgap and formation energy ranges for photovoltaic applications. Similarly, Lu et al.132 identified 151 promising stable ferroelectric photovoltaic perovskites with a desirable bandgap between 0.9 and 1.7 eV out of 19 841 compositions. These studies thereby highlight the power of machine learning to identify key materials from large datasets. Rapid progress is being made in this area, and data science is widely finding high recognition as a reliable tool in fast design and discovery of new complex oxides.

In summary, the observation of various functional properties in complex oxides is now being commonly tied to oxygen vacancies. The coupling between interfacial strain and oxygen vacancies is emerging as a powerful way to control functional properties, where the concentration of oxygen vacancies in new interfaces can be tuned via strain. The presence of bi-axial interfacial strain allows inducing distinction between in-plane and out-of-plane oxygen vacancies; consequently, researchers are now rapidly gaining greater control over selectively creating oxygen vacancies at interfaces, which is opening new degrees of freedom. Recent work has also demonstrated that oxygen vacancies can be stabilized at specific sites in the vicinity of the interface via interfacial strain. A coupling between interfacial strain, oxygen vacancies, and octahedra rotation has recently been observed that is expected to further open exciting areas of research. Interfacial strain is also being used to gain control over network structures of oxygen vacancies where vacancy channels can be used to induce faster oxygen diffusion. Finally, data-science methods are making rapid strides in the field of complex oxides, and they can be expected to unveil key connections between the electronic structure, oxygen vacancies, interfacial chemistry, and functional properties in near future.

D.S.A. and K.R. acknowledge support by the National Science Foundation (NSF) under Grant No. 1929112. They also acknowledge the support of computational resources from Advanced Research Computing Center (ARCC) at the University of Wyoming. The authors declare no competing financial interests.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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