The role of ligand disorder in the long range dipolar ordering of Mn$_{12}$-ac*

The temperature dependence of the inverse magnetic susceptibility of both Mn$_{12}$-ac and Mn$_{12}$-ac-MeOH is found to give finite temperature intercepts corresponding to a Curie temperature $T_c$. This indicates a transition to a ferromagnetic phase at low temperature due to dipolar interactions. A transverse magnetic field suppresses $T_c$ to a $T=0$ quantum critical point. While the decrease of $T_c$ with transverse field, $H_\perp$, in Mn$_{12}$-ac-MeOH is consistent with mean field theory, the suppression of the ordering temperature of Mn$_{12}$-ac is more pronounced. We suggest that the different behavior is due to the ligand disorder which is known to cause a random distribution of molecular easy axis tilts in Mn$_{12}$-ac. Our experimental results can be explained in terms of random field Ising ferromagnetism (RFIFM) in a transverse field.