Low-Temperature Quantum Relaxation in a System of Magnetic Nanomolecules

We argue that to explain recent resonant tunneling experiments on crystals of ${\mathrm{Mn}}_{12}$ and ${\mathrm{Fe}}_8$, particularly in the low-T limit, one must invoke dynamic nuclear spin and dipolar interactions. The low- $T$, short-time relaxation will then have a $\sqrt{t/\tau }$ form, where $\tau$ depends on the nuclear $T_2$, on the tunneling matrix element ${\Delta }_{10}$ between the two lowest levels, and on the initial distribution $N\left(\xi \right)$ of internal fields in the sample, which depends strongly on sample shape. We also give results for the long-time relaxation.