Dipolar interaction and incoherent quantum tunneling: a Monte Carlo study of magnetic relaxation

We study the magnetic relaxation of a system of localized spins interacting through weak dipole interactions, at a temperature large with respect to the ordering temperature but low with respect to the crystal field level splitting. The relaxation results from quantum spin tunneling but is only allowed on sites where the dipole field is very small. At low times, the magnetization decrease is proportional to $\sqrt{t}$ as predicted by Prokofiev and Stamp, and at long times the relaxation can be described as an extension of a relaxed zone. The results can be directly compared with very recent experimental data on Fe_8 molecular clusters.