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We investigate spin relaxation in rippled graphene where curvature induces aZeeman-like spin-orbit coupling with opposite effective magnetic fields alongthe graphene plane in ${\bf K}$ and ${\bf K}^\prime$ valleys. The joint effectof this Zeeman-like spin-orbit coupling and the intervalley electron-opticalphonon scattering opens a spin relaxation channel, which manifests itself inlow-mobility samples with the electron mean free path being smaller than theripple size. Due to this spin relaxation channel, with the increase oftemperature, the relaxation time for spins perpendicular to the effectivemagnetic field first decreases and then increases, with a minimum of severalhundred picoseconds around room temperature. However, the spin relaxation alongthe effective magnetic field is determined by the curvature-induced Rashba-typespin-orbit coupling, leading to a temperature-insensitive spin relaxation timeof the order of microseconds. Therefore, the in-plane spin relaxation inlow-mobility rippled graphene is anisotropic. Nevertheless, in the presence ofa small perpendicular magnetic field, as usually applied in the Hanle spinprecession measurement, the anisotropy of spin relaxation is stronglysuppressed.

Electron spin relaxation in rippled graphene with low mobilities