Memory effects and KWW relaxation of the interacting magnetic nano-particles

TL;DR

This paper models the slow relaxation behavior of interacting magnetic nano-particles, demonstrating that their relaxation deviates from Debye and follows KWW stretched exponential dynamics influenced by memory effects, aligning with experimental observations.

Contribution

It introduces a simple operator formalism model for the relaxation of interacting nano-particles, highlighting the role of memory effects in KWW relaxation behavior.

Findings

Relaxation deviates from Debye and follows KWW in the presence of memory effects.

Frequency and temperature dependence are consistent with experimental data.

The model provides a pedagogical tool for understanding slow relaxation in nano-particle systems.

Abstract

The nano-particle systems under theoretically and experimentally investigation because of the potential applications in the nano-technology such as drug delivery, ferrofluids mechanics, magnetic data storage, sensors, magnetic resonance imaging, and cancer therapy. Recently, it is reported that interacting nano-particles behave as spin-glasses and experimentally show that the relaxation of these systems obeys stretched exponential i.e., KWW relaxation. Therefore, in this study, considering the interacting nano-particle systems we model the relaxation and investigate frequency and temperature behaviour depends on slow relaxation by using a simple operator formalism. We show that relaxation deviates from Debye and obeys to KWW in the presence of the memory effects in the system. Furthermore, we obtain the frequency and temperature behaviour depend on KWW relaxation. We conclude that the obtained results are consistent with experimental results and the simple model, presented here, is very useful and pedagogical to discuss the slow relaxation of the interacting nano-particles.