  The possibility of transporting spin information over long distances in
graphene, owing to its small intrinsic spin-orbit coupling (SOC) and the
absence of hyperfine interaction, has led to intense research into spintronic
applications. However, measured spin relaxation times are orders of magnitude
smaller than initially predicted, while the main physical process for spin
dephasing and its charge-density and disorder dependences remain unconvincingly
described by conventional mechanisms. Here, we unravel a spin relaxation
mechanism for nonmagnetic samples that follows from an entanglement between
spin and pseudospin driven by random SOC, which makes it unique to graphene.
The mixing between spin and pseudospin-related Berry's phases results in fast
spin dephasing even when approaching the ballistic limit, with increasing
relaxation times away from the Dirac point, as observed experimentally. The SOC
can be caused by adatoms, ripples or even the substrate, suggesting novel spin
manipulation strategies based on the pseudospin degree of freedom.
