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

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.