▎ 摘　　要

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 similar to 0.5 eV for pristine graphene and similar to 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 Cu-4/defective graphene, having no net magnetic moment, the spin-valley coupling prevails close to the band edges.