Complex spin texture of Dirac cones induced via spin-orbit proximity effect in graphene on metals

Abstract: We use large-scale DFT calculations to investigate with unprecedented detail the so-called spin-orbit (SO) proximity effect in graphene adsorbed on the Pt(111) and Ni(111)/Au semi-infinite surfaces, previously studied via spin and angle resolved photoemission (SP-ARPES) experiments. The key finding is that, due to the hybridization with the metal's bands, the Dirac cones manifest an unexpectedly rich spin texture including out-of-plane and even radial in-plane spin components at (anti)crossings where local gap openings and deviations from linearity take place. Both the continuum character of the metallic bands and the back folding associated to the moir\'e patterns enhance the spin texture and induce sizable splittings which, nevertheless, only become giant (~100 meV) at anticrossing regions; that is, where electronic transport is suppressed. At the quasilinear regions the splitted bands typically disperse with different broadenings and tend to cross with their magnetization continuously changing in order to match that at the edges of the upper and lower gaps. As a result, both the splittings and spin direction become strongly k dependent. The SO manifests in an analogous way for the spin-polarized G/Au/Ni(111) system, although here the magnetic exchange interactions dominate inducing small splittings (~10 meV) in the $\pi$ bands while the SO mainly introduces a small Rashba splitting in the Dirac cones as their magnetization acquires a helical component. While revealing such complex spin texture seems challenging from the experimental side, our results provide an important reference for future SP-ARPES measurements of similar graphene based systems extensively investigated for applications in spintronics.