  Here we report the measurement of the interfacial spin accumulation induced
by the spin Hall effect in Pt and W thin films using magneto-optical Kerr
microscopy. We show that the Kerr rotation has opposite sign in Pt and W and
scales linearly with current density. By comparing the experimental results
with ab-initio calculations of the spin Hall and magneto-optical Kerr effects,
we quantitatively determine the current-induced spin accumulation at the Pt
interface as $5*10^{-12} \mu_B$A$^{-1}$cm$^2$ per atom. From
thickness-dependent measurements, we determine the spin diffusion length in a
single Pt film to be $11 \pm 3$ nm, which is significantly larger compared to
that of Pt adjacent to a magnetic layer.
