Spin-Orbit-Mediated Spin Relaxation in Graphene

We investigate how spins relax in intrinsic graphene. The spin-orbit coupling arises from the band structure and is enhanced by ripples. The orbital motion is influenced by scattering centers and ripple-induced gauge fields. Spin relaxation due to Elliot-Yafet and Dyakonov-Perel mechanisms and gauge fields in combination with spin-orbit coupling are discussed. In intrinsic graphene, the Dyakonov-Perel mechanism and spin flip due to gauge fields dominate and the spin-flip relaxation time is inversely proportional to the elastic scattering time. The spin-relaxation anisotropy depends on an intricate competition between these mechanisms. Experimental consequences are discussed.

Figure 1

(a) Dyakonov-Perel spin relaxation: The SO coupling induces a momentum dependent effective field ${\overrightarrow{B}}_{\parallel }$ which changes direction randomly after scattering events, leading to spin relaxation. ${\overrightarrow{B}}_{\parallel }$ is “in plane” so spins directed perpendicular to the plane relax faster than as spins in the plane. (b) Gauge-field spin relaxation: Gauge fields due to ripples (light and gray blue areas) induce an effective field ${\mathcal{B}}_{\perp }$, which for a finite SO coupling leads to spin relaxation. ${\overrightarrow{B}}_{\perp }$ is “out of plane” so spins directed perpendicular to the plane relax slower than spins in the plane.