Microscopic Theory of Spin Relaxation Anisotropy in Graphene with Proximity-Induced Spin-Orbit Coupling

Inducing sizable spin--orbit interactions in graphene by proximity effect is establishing as a successful route to harnessing two-dimensional Dirac fermions for spintronics. Semiconducting transition metal dichalcogenides (TMDs) are an ideal complement to graphene because of their strong intrinsic spin--orbit coupling (SOC) and spin/valley-selective light absorption, which allows all-optical spin injection into graphene. In this study, we present a microscopic theory of spin dynamics in weakly disordered graphene samples subject to uniform proximity-induced SOC as realized in graphene/TMD bilayers. A time-dependent perturbative treatment is employed to derive spin Bloch equations governing the spin dynamics at high electronic density. Various scenarios are predicted, depending on a delicate competition between interface-induced Bychkov-Rashba and spin--valley (Zeeman-type) interactions and the ratio of intra- to inter-valley scattering rates. For weak SOC compared to the disorder-induced quasiparticle broadening, the anisotropy ratio of out-of-plane to in-plane spin lifetimes $\zeta=\tau_{s}^{\perp}/\tau_{s}^{\parallel}$ agrees qualitatively with a toy model of spins in a weak fluctuating SOC field recently proposed by Cummings and co-workers [PRL 119, 206601 (2017)]. In the opposite regime of well-resolved SOC, qualitatively different formulae are obtained, which can be tested in ultra-clean heterostructures characterized by uniform proximity-induced SOC in the graphene layer.