Effects of oxygen vacancies on the electronic structure of the (LaVO3)6/SrVO3 superlattice: a computational study

By means of first principles calculations, we comprehensively investigate the stability of O vacancies at the different possible sites in the (LaVO3)6/SrVO3 superlattice and their effect on the electronic structure. Formation energy calculations demonstrate that O vacancies are formed most easily in or close to the SrO layer. We show that O vacancies at these energetically favorable sites conserve the semiconducting character of the superlattice by reducing V4+ ions next to the SrO layer to V3+ ions, while all other sites result in a metallic character.


Introduction
O vacancies in transition metal oxides are becoming increasingly critical in device applications, since they act as electron donors and therefore can strongly perturb the electronic structure [1][2][3]. On the other hand, as the O vacancy concentration may be reversibly controlled by an external electric field or by epitaxial strain, the electronic conductivity and magnetism of transition metal oxides can be tuned without introducing other impurities [4,5]. Numerous experimental and theoretical works have investigated the formation and diffusion of O vacancies (and the induced effects on the electronic and magnetic properties) in transition metal oxide thin films [5][6][7][8] and heterostructures [9][10][11], while the role of O vacancies in superlattices is still a developing field. For the LaAlO 3 /SrTiO 3 heterostructure (of non-magnetic insulators), for example, the consequences of O vacancies for the formation of a two-dimensional electron gas or even superconductivity at the interface, as found experimentally, have been studied in [12][13][14][15]. O vacancies also play a decisive role for the magnetic ordering in this heterostructure [15,16]. LaVO 3 /SrVO 3 superlattices with different periodicities are attracting a lot of interest in recent years, particularly due to magnetic features that do not exist in the bulk compounds [17][18][19][20][21][22]. It also has been reported that the saturation magnetization of (LaVO 3 ) m /SrVO 3 superlattices is larger for even than for odd values of m [18]. The key for understanding the experimental situation may be the observation of simultaneous appearance of both V 3+ ions (as in bulk LaVO 3 ) and V 4+ ions (as in bulk SrVO 3 ) at the interface of the (LaVO 3 ) 6 /(SrVO 3 ) 3 superlattice in [22]. Under the assumption that there are no O vacancies, first principles calculations show that these V 3+ and V 4+ ions form a checkerboard pattern adjacent to the SrO layer [23]. However, in a real sample, O vacancies are inevitable during the growth process [24], which may affect the electronic reconstruction of the V ions and, thus, the properties of the superlattice. In addition, it can be expected that the location of an O vacancy with respect to the SrO layer is important for its influence on the electronic structure. In order to clarify the role of O vacancies in the (LaVO 3 ) 6 /SrVO 3 superlattice, which has been investigated experimentally in [18], we thus introduce in the present work such vacancies in different distances from the SrO layer and study their stability. This will allow us to determine the induced charge transfer as well as the effects on the electronic properties. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
Spin polarized first principles calculations are performed employing the projector augmented wave method [25,26] (pseudopotentials with the following cores: He for O, Ne 3s 2 for V, Ar 3d 10 for Sr, and Kr 4d 10 for La) of the Vienna ab initio simulation package [27][28][29][30]. The generalized gradient approximation (Perdew-Burke-Ernzerhof [31,32]) is adopted for the exchange-correlation functional and the electronic correlations in the V 3d orbitals are taken into account by an effective onsite interaction parameter of 3 eV [33]. The cut-off energy of the plane wave basis is chosen as 500 eV. We have checked that a higher cut-off energy of 650 eV results for the pristine (LaVO 3 ) 6 /SrVO 3 superlattice in a total energy difference of less than 0.05 eV and a change in the band gap of less than 0.01 eV. The Brillouin zone is sampled on a 9×9×1 k-mesh, for which we have confirmed convergence. The total energy of the self-consistency calculations is converged to 1×10 −5 eV and the atomic positions are relaxed until the forces on all atoms have declined below 0.02 eV Å −1 .
We form a single O vacancy in the (LaVO 3 ) 6 /SrVO 3 superlattice by removing 1 out of the 42 O atoms. This represents a sufficiently low defect concentration that only the atomic coordinates have to be relaxed, while the lattice constants can be adopted from the pristine superlattice without relaxation.
However, the shortest distance between O vacancies (through the periodic boundary conditions) is only 5.5 Å in our simulation cell, implying that the interaction between the defects is not yet fully negligible. Lowering the defect concentration, on the other hand, would require a larger simulation cell, which is computationally not treatable as a consequence of a very slow convergence behavior. A superlattice with thinner LaVO 3 slab also is not an alternative, because the experimental situation would no longer be modeled and the interfaces at the two ends of the slab would start interacting. Due to the epitaxial strain present in the (LaVO 3 ) 6 /SrVO 3 superlattice, the magnetic order is found to be A-type antiferromagnetic throughout the superlattice except for ferromagnetic coupling of the two VO 2 layers next to the SrO layer, which is in agreement with the results reported in [27]. For comparison, we also study O deficient bulk LaVO 3 using the lattice constants of the superlattice and enforcing A-type antiferromagnetic ordering. The formation energy of an O vacancy is calculated as where E defective is the total energy of the O deficient superlattice, E O 2 the total energy of a gas phase O 2 molecule (triplet ground state), and E pristine the total energy of the pristine superlattice.

Results and discussion
Our calculations for bulk LaVO 3 result in a band gap of 1.39 eV, which is close to the experimental value of 1.1 eV as reported in [34]. We consider for the (LaVO 3 ) 6 /SrVO 3 superlattice all inequivalent O vacancy sites: four sites in each of the VO 2 layers L1 to L4 (OV L ), see figure 2(a), and two sites in each LaO layer in between them (OV B ). The O vacancy formation energies obtained for these sites are summarized in figure 2(b). In the bulk-like region of the superlattice (L3, L4) the values are similar to our results for OV L and OV B in bulk LaVO 3 , compare the dotted lines in figure 2(b). They decrease gradually when we approach layer L1, showing that O vacancies are formed more easily towards the interface of the superlattice. A similar behavior has been reported in [35] for the LaAlO 3 /SrTiO 3 interface. Interestingly, we find a change in the electronic character of the superlattice as function of the distance of the O vacancy from the SrO layer, see figure 2(c): while O vacancies in the bulk-like region of the superlattice give rise to metallic states, those located close to the interface (layer L2 are closer) conserve the original semiconducting state. In addition, within the semiconducting regime, the band gap grows gradually towards the interface.
We first analyze the metallic state of the defective superlattice. Since the different O vacancy sites of this regime, compare figure 2, behave similarly, we study as first example an O vacancy in layer L3 in more detail. The total DOS and band structure obtained for this case are illustrated in figures 3(a) and (b), respectively. The pristine (LaVO 3 ) 6 /SrVO 3 superlattice is predicted to exhibit a band gap of 0.70 eV, while figure 3 shows for the superlattice with O vacancy in layer L3 a significant number of electronic states at the Fermi energy (mainly spin majority states, but also spin minority states). In figure 4 further insight is provided by projecting the DOS on the 3d orbitals of individual V atoms in layers L1 and L3. In the case of the pristine (LaVO 3 ) 6 /SrVO 3 superlattice, V 3+ ions (sites V1b and V1c) and V 4+ ions (sites V1a and V1d) form a checkerboard pattern next to the SrO layer. Everywhere else we have V 3+ ions. In the case of defective bulk LaVO 3 , as discussed earlier, the excess charge enters mainly the d x y 2 2 or d z r orbitals of the two V ions next to the O vacancy, whereas in the superlattice a substantial part of this charge does not stay at sites V3c and V3d but is transferred to a V 4+ ion at the interface (site V1d, see figure 4(d)), resulting in a partially occupied band. Correspondingly, the d x y orbitals become partially occupied at sites V3c and V3d. The metallic character thus is induced by the interplay between the O vacancy and the interface, which, of course, is impossible in the case of defective bulk LaVO 3 due to the absence of V 4+ ions (while a comparable situation is realized in La 1−x Sr x VO 3 solid solutions with mixed V 3+ and V 4+ states and in appropriately doped LaVO 3 , i.e., the discovered mechanism may play a role). As a consequence of the charge transfer, we find that the magnetic moment is reduced from 1.96 to 1.86 μ B for sites V3c and V3d but enhanced from 1.10 to 1.46 μ B for site V1d. As second example for the metallic regime, we study an O vacancy between layers L2 and L3, which demonstrates that the described charge transfer phenomenon is not limited to OV L but also occurs for OV B . The metallic character of the superlattice is clearly visible in figure 5, and figure 6 indicates charge transfer from sites V2c and V3c (located next to the O vacancy) to the V 4+ ion at site V1d. The magnetic moment turns out to be 1.30 μ B at site V1d, 1.88 μ B at site V2c, and 1.91 μ B at site V3c. We note that site V2c (layer L2) is closer to the V 4+ ion than site V3c (layer L3) so that the reduction of its magnetic moment (from 1.96 μ B ) is slightly more pronounced.
Turning to the semiconducting regime of the defective superlattice, compare figure 2, we address as example an O vacancy in layer L1, located between sites V1c and V1d. According to the total DOS and band structure, see figures 7(a) and (b), respectively, this defect conserves the semiconducting character of the superlattice but the band gap is reduced from 0.70 to 0.51 eV. In figure 8 we show the DOS projected on the 3d orbitals of the V atoms in layer L1. We find that the excess charge due to the O vacancy results in a 3d 2 configuration for site V1d,

Conclusion
We have studied the stability of O vacancies at different sites in the (LaVO 3 ) 6 /SrVO 3 superlattice. It turns out that the formation energy decreases gradually from the bulk-like region of the superlattice towards the SrO layer (interface). An O vacancy in the bulk-like region leads to charge accumulation on the two neighboring V atoms as well as to charge transfer to the V 4+ ions in the checkerboard pattern at the interface. As a consequence, partially filled bands are generated which give rise to a metallic character of the superlattice. This mechanism plays no role in the case of bulk LaVO 3 , since there are no V 4+ ions that could accept additional charge. On the other hand, it may be speculated that the discovered mechanism becomes relevant, for example, for La 1−x Sr x VO 3 solid solutions with mixed V 3+ and V 4+ states and for appropriately doped LaVO 3 . When the O vacancy is located within a range of not more than two VO 2 layers next to the SrO layer, surprisingly, the semiconducting state of the superlattice is conserved despite the O deficiency. This finding has been explained in terms of a perturbation of the V 3+ -V 4+ checkerboard pattern that is present in the (LaVO 3 ) 6 /SrVO 3 superlattice in the VO 2 layers next to the SrO layer. Instead of partial charge transfer, as in the case of bulk-like O vacancies, here V ions at the interface change their oxidation state fully from 4+ to 3+ and in that way are able to absorb the entire excess charge resulting from the O deficiency. The conservation of the semiconducting character is an immediate consequence of this observation.