Decay of time-correlations of microscopic observables in magnetic molecules

We derive a general expression for the quasielastic part of the dynamic structure factor in the presence of a heat bath, starting from the master equation applied to the full microscopic Hamiltonian. By specializing this expression to the case of the total spin, we investigate the time autocorrelation of the molecular magnetization M for three classes of magnetic molecules (antiferromagnetic rings, grids and nanomagnets), in contact with the phonon heat bath. We find that the exponential decay of the fluctuations of M, associated with the irreversible exchange of energy with the heat bath, is characterized by a single decay time for not too high temperature and field. Such fluctuations are effectively probed by nuclear magnetic resonance (NMR), and the calculations are in very good agreement with existing experimental NMR data.