  Renormalized tunnel splitting with a finite distribution in the biaxial spin
model for molecular magnets is obtained by taking into account the dipolar
interaction of enviromental spins. Oscillation of the resonant tunnel splitting
with a transverse magnetic field along the hard axis is smeared by the finite
distribution which subsequently affects the quantum steps of hysteresis curve
evaluated in terms of the modified Landau-Zener model of spin flipping induced
by the sweeping field. We conclude that the dipolar-dipolar interaction drives
decoherence of quantum tunnelling in molcular magnets Fe&#8328;, which explains
why the quenching points of tunnel spliting between odd and even resonant
tunnelling predcited theoretically were not observed experimentally.
