  Muon spin relaxation measurements in isotropic molecular magnets (MM) with a
spin value S ranging from 7/2 to 27/2 are used to determine the magnitude and
origin of dephasing time $\tau_\phi$ of molecular magnets. It is found that
$\tau_\phi$ ~ 10 nsec with no S or ligand dependence. This indicates a nuclear
origin for the stochastic field. Since $\tau_\phi$ is a property of the
environment, we argue that it is a number common to similar types of MM.
Therefore, $\tau_\phi$ is shorter than the Zener and tunneling times of
anisotropic MM such as Fe8 or Mn4 for standard laboratory sweep rates. Our
findings call for a stochastic Landau-Zener theory in this particular case.
