Approaches for modeling magnetic nanoparticle dynamics

TL;DR

This paper reviews various modeling approaches for magnetic nanoparticle dynamics, including deterministic and stochastic methods, thermal effects, and approximate models, to better understand their magnetization behavior in biological applications.

Contribution

It provides a comprehensive summary of existing modeling techniques for magnetic nanoparticle dynamics, highlighting their theoretical foundations and practical approximations.

Findings

Comparison of deterministic and stochastic models

Inclusion of thermal fluctuations in magnetization modeling

Derivation of simplified models for specific regimes

Abstract

Magnetic nanoparticles are useful biological probes as well as therapeutic agents. There have been several approaches used to model nanoparticle magnetization dynamics for both Brownian as well as N\'eel rotation. The magnetizations are often of interest and can be compared with experimental results. Here we summarize these approaches including the Stoner-Wohlfarth approach, and stochastic approaches including thermal fluctuations. Non-equilibrium related temperature effects can be described by a distribution function approach (Fokker-Planck equation) or a stochastic differential equation (Langevin equation). Approximate models in several regimes can be derived from these general approaches to simplify implementation.