We observed non-exponential relaxation for a quantum tunneling molecular magnetic system at very low temperatures and argue that it results from evolving intermolecular dipole fields. At the very beginning of the relaxation, the magnetization follows a square-root time dependence. A simple model is developed for the intermediate time range that is in good agreement with the data over 4 decades in time. Detailed numerical calculations as well as measurements are presented which indicate unusual correlation effects in these systems.
PACS. 75.45.+j Macroscopic quantum phenomena in magnetic systems -61.46.+w Clusters, nanoparticles, and nanocrystalline materials -75.60.Ej Magnetization curves, hysteresis, Barkhausen and related effects Recent experiments have shown evidence of quantum tunneling of the magnetization in the molecular nanomagnetic systems Fe8 [1] and Mn12ac [2,3]. General theoretical considerations for quantum tunneling of a giant spin through its anisotropy energy barrier have been proposed during the last 10 years [4]. Both Fe8 and Mn12ac can be thought of as an ensemble of identical, iso-oriented nanomagnets of net spin S = 10 with an Ising like anisotropy. Fe8 has the advantage in terms of tunneling measurements in that its anisotropy energy barrier is approximately 24 K compared to 63 K for Mn12ac, and its crystal symmetry affords a sizable transverse anisotropy, both of which greatly enhance tunneling effects [1,4].At low enough temperatures (below 400 mK and approximately 1.8 K, respectively) both systems display a crossover from a thermal activated (over barrier) relaxation to a temperature independent relaxation [1,2] with a remarkable resonant structure of the relaxation time as a function of the external field [1,3]. Below these crossover temperatures and after saturation in a high field, only the m S = +10 state is occupied and the only way relaxation can occur (at the first resonance field B = 0) is by under barrier quantum tunneling from the m S = +10 to the m S = −10 state.Ideally, the relaxation for non interacting, identical (giant) spins would be given by an exponential function M (t) ∝ exp(−t/τ ). However, for Fe8 the data in the low temperature regime is best approximated by a stretched exponential M (t) ∝ exp(−(t/τ stretch ) β ) a