A Generalized Approach to Relaxation Time of Magnetic Nanoparticles With Interactions: From Superparamagnetism to Glassy Dynamics

A novel theoretical expression for the relaxation time of magnetic nanoparticles with dipolar interactions is derived from Kramers' theory, extending the Boltzmann-Gibbs framework to incorporate Tsallis statistics. The model provides a unified description of magnetic relaxation from weakly to strongly interacting regimes. It accounts for both the decrease and the increase of the relaxation time with increasing dipolar coupling, addressing a long-standing problem in nanoparticle magnetism that cannot be consistently described by classical phenomenological models. This result also offers an innovative interpretation of the cut-off condition inherent to the Tsallis distribution in terms of a cut-off temperature, T_cut-off, which naturally characterizes the onset of glassy freezing dynamics and provides an alternative interpretation of experimental relaxation data within a non-extensive statistical framework.