## 3 Results and Discussion
### Electronic Properties
The analysis of atom- and orbital-projected band structures and PDOS for both the spin-up and -down channels indicates that the occurrence of oxygen vacancies results in the generation of localized defect states in the bandgap of ZnO (Figure 4a,b). These states are inhabited by Zn-4s electrons and predominantly influenced by the proximity of Zn atoms to the oxygen vacancies. One can also notice that the presence of oxygen vacancies in 2D ZnO leads to a shift of both VBM and CBM positions, suggesting the Schottky barrier alteration. In this regard, the 1V\({}_{\text{O}}\)-2D ZnO/graphene structure has \(p\)-type Schottky contact (\(\Phi_{\text{n}}<\Phi_{\text{p}}\)). On the other hand, the 2V\({}_{\text{O}}\)-2D ZnO/graphene heterostructure \(\Phi_{\text{p}}\) becomes  
Figure 5: Atom- and orbital-projected band structures and PDOS of the spin-up and -down channels for the (**a**) 1 Fe-2 DZnO/graphene and (**b**) 2 Fe-2 DZnO/graphene heterostructures. The size of each circle corresponds proportionally to the orbital contribution of each band. even more negative (\(-0.016\) eV), suggesting a transition from \(p\)-type Schottky contact to \(p\)-type ohmic contact. Similar to a pristine 2 DZnO/graphene heterostructure, the nature of the band structure and PDOS for spin-up and -down channels for vacancy-containing complexes was basically the same. This contrast with the Fe-doped 2 DZnO/graphene heterostructures, where the band structures exhibited strong spin polarizations (Figure 5a,b). More specifically, the Dirac point energy of graphene in spin-up and -down directions was approximately \(-0.619\) and \(-0.643\) eV for the 1 Fe-2 DZnO/graphene heterostructure and \(-0.663\) and \(-0.691\) eV for the 1 Fe-2 DZnO/graphene heterostructure. Another important observation was that Fe dopants were found to introduce additional states in the ZnO bandgap only in the spin-down direction. Remarkably, the Fe-related defect states were in the close vicinity to the Fermi level. This was probably the main reason for a strong charge transfer between Fe-doped 2D ZnO and graphene. From Table 1 and Figure 5, it is also seen that there is a pronounced spin-asymmetry of Schottky barriers in Fe-doped 2 DZnO/graphene heterostructures. Considering the spin-down channels, it is clear that \(\Phi_{p}\) is equal to zero for both 1 Fe-2 DZnO/graphene and 2 Fe-2 DZnO/graphene heterostructures, pointing out the \(p\)-type ohmic behavior of the vdW contacts. Concomitantly, the values of \(\Phi_{\rm n}\) for the spin-up channels were less than the \(\Phi_{\rm p}\) values, indicating that an \(n\)-type Schottky contact was formed in the spin-up direction in the Fe-doped 2 DZnO/graphene heterostructures. It is striking to note that the barriers for spin-up holes and electrons differed significantly from each other. Eventually, this may affect the spin-dependent charge transport through the interface [41]. This is referred to as the spin-filter effect [42; 43; 44], which arises from the difference in the tunneling rates of electrons/holes with opposite-spin orientations, i.e., spin-up and -down. To date, this investigation primarily focused on the electronic properties of complex structures. It is justifiable to posit that the formation of these structures entailed reciprocal interactions between zinc oxide and graphene, as exemplified by the previously mentioned displacement of graphene's Dirac point. Nevertheless, in the realm of developing devices based on these heterostructures, the extent of graphene's impact on the band structure of zinc oxide became a pertinent question. To address this, additional calculations with a specific emphasis on free-standing ZnO monolayers were conducted. The band structures of free-standing monolayers of zinc oxide are presented in Figures S6-S11 (Supplementary Material). Overall, these findings demonstrate a qualitative agreement with the results obtained for zinc oxide monolayers supported by graphene.