## 3 Results and Discussion
### Electronic Properties
Specifically, the conduction band of pristine 2D ZnO primarily consists of Zn 4s states, while the valence band is predominantly dominated by O \(2p\) states, with a reduced contribution from Zn-related states (Figure S6, Supplementary Material). However, the presence of oxygen vacancies leads to the formation of localized Zn 4s states above the valence band maximum, which is primarily composed of O \(2p\) states (Figures S7 and S8, Supplementary Material). Turning our attention to free-standing monolayers of zinc oxide doped with iron (Figures S9 and S10, Supplementary Material), there was a noticeable tendency for the emergence of Fe-doped electronic states in close proximity to the Fermi level, albeit only in the spin-down direction. Furthermore, through a comprehensive comparative analysis of the band structures of zinc oxide monolayers in the presence and absence of graphene (Figures S11-S15, Supplementary Material), several significant observations were made. Firstly, the presence of graphene induced an upward shift of the valence band maximum and conduction band minimum for both pristine 2D ZnO and 2V\({}_{\rm O}\)-2D ZnO systems. Secondly, an actual narrowing of the band gap occurred in the 1V\({}_{\rm O}\)-2D ZnO system. Lastly, systems containing iron exhibited a shift of Fe-related states closer to the Fermi level. These distinct characteristics can be directly attributed to the interfacial charge transfer occurring between the ZnO monolayer and graphene. Bearing in mind that the defects can induce magnetism in the otherwise non-magnetic ZnO material, it would be interesting to find out whether there was an effect of the oxygen vacancies and Fe dopants on the spin-density distribution in the 2D ZnO/grapheneheterostructure. For this purpose, the spin density determined as a difference between the spin-\(\alpha\) (spin-up) and spin-\(\beta\) (spin-down) densities was predicted for all considered heterostructures (Figure 6). Before proceeding to the discussion of the results, it is important to emphasize that neutral oxygen vacancies were not expected to introduce additional magnetic moments in the 2D ZnO. This is because they have spin-zero ground states in ZnO [45]. On the other hand, Fe doping of ZnO is a common strategy to achieve a high spin density in ZnO-based materials [46; 47; 48]. In this regard, as opposed to very low spin densities for pristine and V\({}_{\text{O}}\)-containing systems displayed with an isosurface value of 10\({}^{-5}\), high spin densities demonstrated for Fe-containing systems are represented by isosurfaces corresponding to 0.001. The spin density plots for pristine 2D ZnO/graphene and 1V\({}_{\text{O}}\)-2D ZnO/graphene heterostructures show the spin density is localized entirely in all oxygen atoms (Figure 6a,b), while, for the ZnO/graphene heterostructure, the spin density is additionally redistributed around the oxygen vacancy sites (Figure 6c). A completely different picture appears in the presence of Fe dopants (Figure 6d,e). Particularly, spin density is mainly localized on the Fe atoms and their adjacent oxygen neighbors, indicating the formation of localized magnetic moments within the ZnO nanosheet due to the presence of Fe atoms. Furthermore, spin-density localization was even observed on the carbon atoms of graphene. This underlines the critically important role of Fe dopants in inducing the magnetism in the 2D ZnO/graphene vdW heterostructure.