  We report on measurements of the spin lifetime of nuclear spins strongly
coupled to a micromechanical cantilever as used in magnetic resonance force
microscopy. We find that the rotating-frame correlation time of the statistical
nuclear polarization is set by the magneto-mechanical noise originating from
the thermal motion of the cantilever. Evidence is based on the effect of three
parameters: (1) the magnetic field gradient (the coupling strength), (2) the
Rabi frequency of the spins (the transition energy), and (3) the temperature of
the low-frequency mechanical modes. Experimental results are compared to
relaxation rates calculated from the spectral density of the magneto-mechanical
noise.
