  We investigate the spin relaxation and decoherence in a single-electron
graphene quantum dot with Rashba and intrinsic spin-orbit interactions. We
derive an effective spin-phonon Hamiltonian via the Schrieffer-Wolff
transformation in order to calculate the spin relaxation time T_1 and
decoherence time T_2 within the framework of the Bloch-Redfield theory. In this
model, the emergence of a non-monotonic dependence of T_1 on the external
magnetic field is attributed to the Rashba spin-orbit coupling-induced
anticrossing of opposite spin states. A rapid decrease of T_1 occurs when the
spin and orbital relaxation rates become comparable in the vicinity of the
spin-mixing energy-level anticrossing. By contrast, the intrinsic spin-orbit
interaction leads to a monotonic magnetic field dependence of the spin
relaxation rate which is caused solely by the direct spin-phonon coupling
mechanism. Within our model, we demonstrate that the decoherence time T_2 ~ 2
T_1 is dominated by relaxation processes for the electron-phonon coupling
mechanisms in graphene up to leading order in the spin-orbit interaction.
Moreover, we show that the energy anticrossing also leads to a vanishing pure
spin dephasing rate for these states for a super-Ohmic bath.
