Microscopic theory of spin relaxation anisotropy in graphene with proximity-induced spin-orbit coupling

We present a microscopic theory of spin dynamics in weakly disordered graphene with uniform proximity-induced spin-orbit coupling (SOC). A time-dependent perturbative treatment is employed to derive the spin Bloch equations governing the spin dynamics at high electronic density for arbitrary ratio λSOC/η, where η is the disorder-induced quasiparticle broadening and λSOC is the largest spin-orbit energy scale. Rich scenarios are predicted, depending on a delicate competition between interface-induced Bychkov-Rashba and spin-valley interaction. In the motional narrowing regime of weak SOC (λSOC ≪ η), the anisotropy ratio of out-of-plane to in-plane spin lifetimes ζ = τ⊥s / τ∥s agrees qualitatively with a toy model of spins in a fluctuating SOC field proposed recently by Cummings and co-workers Phys. Rev. Lett. 119, 206601 (2017). For well-resolved SOC (λSOC ≳ η), the spin dynamics is characterized by fast damped oscillations with spins relaxing on the timescale of a single scattering event. In this regime, qualitatively different formulas for ζ are obtained, which can be useful to model spin transport in ultraclean van der Waals heterostructures.