  We report on spin transport features which are unique to high quality bilayer
graphene, in absence of magnetic contaminants and strong intervalley mixing.
The time-dependent spin polarization of propagating wavepacket is computed
using an efficient quantum transport method. In the limit of vanishing effects
of substrate and disorder, the energy-dependence of spin lifetime is similar to
monolayer graphene with a M-shape profile and minimum value at the charge
neutrality point, but with an electron-hole asymmetry fingerprint. In sharp
contrast, the incorporation of substrate-induced electron-hole puddles
(characteristics of supported graphene either on SiO2 orhBN) surprisingly
results in a large enhancement of the low-energy spin lifetime and a lowering
of its high-energy values. Such feature, unique to bilayer, is explained in
terms of a reinforced Dyakonov-Perel mechanism at the Dirac point, whereas spin
relaxation at higher energies is driven by pure dephasing effects. This
suggests further electrostatic control of the spin transport length scales in
graphene devices.
