  We perform an investigation on the spin relaxation for $n$-type ZnO (0001)
quantum wells by numerically solving the kinetic spin Bloch equations with all
the relevant scattering explicitly included. We show the temperature and
electron density dependence of the spin relaxation time under various
conditions such as impurity density, well width, and external electric field.
We find a peak in the temperature dependence of the spin relaxation time at low
impurity density. This peak can survive even at 100 K, much higher than the
prediction and measurement value in GaAs. There also exhibits a peak in the
electron density dependence at low temperature. These two peaks originate from
the nonmonotonic temperature and electron density dependence of the Coulomb
scattering. The spin relaxation time can reach the order of nanosecond at low
temperature and high impurity density.
