Executive Summary : | The isolation of monolayers of magnetic two-dimensional (2D) materials has brought them to the forefront of spintronics research, allowing for the generation of heterostructures with added functionality and proximity-induced enhanced effects. Graphene is useful due to its long spin diffusion lengths, but the possibility of generating a heterostructure with transition metal dichalcogenides or topological insulators allows for exploration of new functionalities emerging from enhanced spin-orbit interactions. Positive induced exchange interactions in graphene with 2D magnets are surprising, as the coupling between different layers is determined by interlayer hopping interactions. However, the presence of strain complicates the description of these effects. To minimize strain in lattice mismatched heterostructures, calculations have been carried out for supercells, but even this strain is too large, and predictions are clouded by the choice of lattice parameter. To explore optimal strain in experiment and build a model of the heterostructure based on existing experimental knowledge, an approach that is missing in a substantial portion of literature that chooses convenient supercells is needed. Another aspect to investigate is the configuration involving trilayer heterostructures, where the material at the center brings in properties of the layer above and below. Enhanced spin-orbit interactions can generate a valley Zeeman effect, which involves an out-of-plane spin-orbit spin texture at K and another opposite direction at -K, analogous to what is found in transition metal dichalcogenides. Valley Zeeman fields can be varied by twisting one layer with respect to the other, with the largest value being seen between 15 and 20 degrees twist. |