Longitudinal relaxation and thermoactivation of quantum superparamagnets

The relaxation mechanisms of a quantum nanomagnet are discussed in the framework of linear response theory. We use a spin Hamiltonian with a uniaxial potential barrier plus a Zeeman term. The spin, having arbitrary S, is coupled to a bosonic environment (phonons). From the eigenstructure of the relaxation matrix, we identify two main mechanisms: namely, thermal activation over the barrier, with a time scale Lambda(-1)(1), and a faster dynamics inside the potential wells, with characteristic time Lambda(-1)(w). This permits to introduce a simple analytical formula for the response, which agrees well with exact numerical results and covers experiments even under moderate to strong fields in the superparamagnetic range. In passing, we generalize known classical results for a number of quantities (e.g., integral relaxation times, initial decay time, Kramers' rate), results that are recovered in the limit S ->infinity.