  We compute the relaxation rate of the spin density of heavy quarks in a
perturbative QCD plasma to leading-log order in the coupling constant $g$. The
spin relaxation rate $\Gamma_s$ in spin hydrodynamics is shown to be
$\Gamma_s\sim g^4\log(1/g)T (T/M)^2$ in the heavy-quark limit $T/M\ll 1$, which
is smaller than the relaxation rate of other non-hydrodynamic modes by
additional powers of $T/M$. We demonstrate three different methods to evaluate
the spin relaxation rate: 1) the Green-Kubo formula in the spin hydrodynamic
regime, 2) the spin density correlation function in the strict hydrodynamic
limit, and 3) quantum kinetic theory of the spin distribution function in
momentum space. We highlight the interesting differences between these methods,
while they are ultimately connected to each other by the underlying
Ward-Takahashi identity for the non-conserved spin density.
