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

TL;DR

This paper introduces a new theoretical model for magnetic nanoparticle relaxation times that unifies weakly and strongly interacting regimes using Tsallis statistics, addressing longstanding issues in nanoparticle magnetism.

Contribution

It extends classical models by incorporating non-extensive Tsallis statistics to describe relaxation dynamics across different interaction strengths.

Findings

The model explains both decrease and increase of relaxation time with dipolar interactions.

It introduces a cut-off temperature T_cut-off for glassy freezing dynamics.

The approach aligns well with experimental relaxation data.

Abstract

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.