  In a clean Fermi liquid, due to spin up/spin down symmetry, the dc spin
current driven by a magnetic field gradient is finite even in the absence of
impurities. Hence, the spin conductivity sigma_s assumes a well-defined
collision-dominated value in the disorder-free limit, providing a direct
measure for the inverse strength of electron-electron interactions. In neutral
graphene, with Fermi energy at the Dirac point, the Coulomb interactions remain
unusually strong, such that the inelastic scattering rate comes close to a
conjectured upper bound 1/\tau_{inel} <= k_B T/\hbar, similarly as in strongly
coupled quantum critical systems. The strong scattering is reflected by a
minimum of the spin conductivity at the Dirac point, where it reaches sigma_s =
(0.121/alpha^2) * (mu_B^2/\hbar) at weak Coulomb coupling alpha. Up to the
replacement of quantum units, e^2/\hbar -> mu_s^2/\hbar, this result equals the
collision-dominated electrical conductivity obtained previously. This
accidental symmetry is, however, broken to higher orders in the interaction
strength. For gated graphene, and 2d metals in general, we show that the
transport time is parametrically smaller than the collision time. We exploit
this to compute the collision-limited sigma_s analytically as sigma_s= (1/C) *
(mu/T)^2 * (mu_B^2/\hbar) with C=4 pi^2 alpha^2 [2/3 ln(1/(2\alpha))-1] for
weak Coulomb coupling alpha.
