  We study the flow of a pure spin current through zinc oxide by measuring the
spin Hall magnetoresistance (SMR) in thin film trilayer samples consisting of
bismuth-substituted yttrium iron garnet (Bi:YIG), gallium-doped zinc oxide
(Ga:ZnO), and platinum. We investigate the dependence of the SMR magnitude on
the thickness of the Ga:ZnO interlayer and compare to a Bi:YIG/Pt bilayer. We
find that the SMR magnitude is reduced by almost one order of magnitude upon
inserting a Ga:ZnO interlayer, and continuously decreases with increasing
interlayer thickness. Nevertheless, the SMR stays finite even for a
$12\;\mathrm{nm}$ thick Ga:ZnO interlayer. These results show that a pure spin
current indeed can propagate through a several nm-thick degenerately doped zinc
oxide layer. We also observe differences in both the temperature and the field
dependence of the SMR when comparing tri- and bilayers. Finally, we compare our
data to predictions of a model based on spin diffusion. This shows that
interface resistances play a crucial role for the SMR magnitude in these
trilayer structures.
