  Exponential and power law temperature dependences are widely used to fit
experimental data of magnetic relaxation time in single molecular magnets. We
derived a theory to show how these rules arise from the underling relaxation
mechanisms and to clarify the conditions for their occurrence. The theory
solves the puzzle of lower-than-expected Orbach barriers found in recent
experiments, and elucidates it as a result of the Raman process in disguise.
Our results highlight the importance of reducing the rate of direct tunneling
between the ground state doublet so as to achieve long time coherence in
magnetic molecules. To this end, large spin and small transverse magnetic
anisotropy can reduce magnitude of the transition operator, and rigid ligands
may weaken the spin-phonon coupling in that they raise the energy of
vibrational modes and better screen the acoustic phonons.
