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The naturally weak spin-orbit coupling in Graphene can be largely enhanced by adatom deposition (e.g. Weeks et al. Phys. Rev. X 1, 021001 (2011)). However, the dynamics of the adatoms also induces a coupling between phonons and the electron spin. Using group theory and a tight-binding model, we systematically investigate the coupling between the low-energy in-plane phonons and the electron spin in single-layer graphene uniformly decorated with heavy adatoms. Our results provide the foundation for future investigations of spin transport and superconductivity in this system. In order to quantify the effect of the coupling to the lattice on the electronic spin dynamics, we compute the spin-flip rate of electrons and holes. We show that the latter exhibits a strong dependence on the quasi-particle energy and system temperature.
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