Tuning the spin texture of graphene with size-specific Cu n clusters: a first-principles study

The size dependent interaction of Cu n (n = 1‒5) clusters with pristine and defective (C-vacancy) graphene is studied by employing density functional theory. The computed binding energies are in the range of ∼0.5 eV for pristine graphene and ∼3.5 eV for defective graphene, indicating a much stronger interaction in the later system. The induced spin–orbit coupling interaction, due to the proximity of the Cu n cluster, is studied with non-collinear spin-polarized simulations. The clusters cause a spin splitting in the order of few meV. The resultant low energy bands spin textures are also computed, and a spin–valley coupling in the case of even atom clusters on pristine graphene is predicted, leading to the emergence of a spin lifetime anisotropy. For defective graphene, a complete out-of-plane spin texture and a large spin splitting of 40–100 meV is obtained for Cu n (n = 1, 2, 3, 5) clusters due to local magnetic moment. On the other hand, for Cu4/defective graphene, having no net magnetic moment, the spin–valley coupling prevails close to the band edges.