  Spin relaxation between the two lowest-lying spin-states has been studied in
the S=4 single molecule magnet Ni$_4$ under steady state conditions of low
amplitude and continuous microwave irradiation. The relaxation rate was
determined as a function of temperature at two frequencies, 10 and 27.8 GHz, by
simultaneously measuring the magnetization and the absorbed microwave power. A
strong temperature dependence is observed below 1.5 K, which is not consistent
with a direct single-spin-phonon relaxation process. The data instead suggest
that the spin relaxation is dominated by a phonon bottleneck at low
temperatures and occurs by an Orbach mechanism involving excited spin-levels at
higher temperatures. Experimental results are compared with detailed
calculations of the relaxation rate using the universal density matrix
equation.
