The magnetization of a Mn-12-acetate single crystal was measured with
a cantilever magnetometer to temperatures below 60 mK. Contrary to exp
ectations we did not observe steps in the hysteretic magnetization wit
h indices higher than 11. The data suggest a significant degree of hig
her-order anisotropy. The fourth-order term appears to be about - 3 x
10(-4)k(B). Both hysteresis in magnetization at different ramping rate
s of the field, and relaxation at different fixed values of the magnet
ic field were studied. The relaxation is found to be logarithmic below
1 K, and not single exponential. We contend that the process of magne
tization reversal is initiated by tunneling across the anisotropy barr
ier from a weak population in excited levels from which they can easil
y tunnel across the barrier, and that the consequent emission and reab
sorption of phonons helps to promote a significant fraction of the spi
ns to these excited levels. [S0163-1829(98)02525-9].