Field-dependent magnetic relaxation times of magnetic nanoparticle systems: analytic approximations supported by numerical simulations

TL;DR

This paper develops an analytic approximation for the field-dependent magnetic relaxation time of spherical magnetic nanoparticles, validated by simulations, and explores the interplay of Brownian and Ne9el relaxation mechanisms under various conditions.

Contribution

It introduces a new analytic expression for field-dependent relaxation times and compares it with empirical data and simulations, enhancing understanding of relaxation dynamics in magnetic nanoparticles.

Findings

The approximation accurately predicts relaxation times for larger particles.

The combined relaxation model matches simulation results under certain conditions.

Decoupling of relaxation mechanisms occurs at high field strengths for some particles.

Abstract

Many estimates for the magnetic relaxation time of magnetic nanoparticle systems neglect the effect of the applied field strength. This is despite many applications of magnetic nanoparticles involving relaxation dynamics under the influence of applied fields. Here, an analytic approximation for the field-dependent Brownian relaxation time of single-domain, spherical magnetic nanoparticles in an external applied field is developed mathematically. This expression is validated by comparison with existing empirically-derived expressions and by comparison to particle-level simulations that allow particle rotations. Our approximation works particularly well for larger particles. We then use the developed expression to analytically calculate the total magnetic relaxation time when both Brownian and N\'eel relaxation mechanisms are at play. Again, we show that the results match those found using particle-level simulations, this time with both particle rotations and internal magnetization dynamics allowed. However, for some particle parameters and for large field strengths, our simulations reveal that the Brownian and N\'eel relaxation mechanisms are decoupled and it is not appropriate to combine these to calculate a total relaxation time.