Magnetic relaxation of mesoscopic molecules

The relaxation dynamics of nanoscale molecules such as arises from spin-lattice coupling and interaction with nuclear spins. Using a resolvent method in terms of the energy eigenstates and the first Born approximation with respect to phonon scattering, and averaging over the hyperfine field, we obtain a controlled approximation for the non-equilibrium magnetic relaxation behaviour and, in particular, for the corresponding rate. The rate is finite at T = 0, then increases linearly with T, and shows Arrhenius behaviour at higher temperature; for zero magnetic field B there are two different activation energies. The resonances as a function of B are shown to be slightly asymmetric about B = 0. Taking account of a quartic crystal field gives rise to a temperature-dependent shift of the resonant values of B. We find that, contrary to previous results, the rate is independent of the magnetic field at low but finite temperatures; for it is linear in B. Finally we compare our findings with various experimental data.