# Dynamics of magnetic nano particles in a viscous fluid driven by rotating magnetic fields

## TL;DR

This paper investigates the rotational behavior of magnetic nanoparticles in viscous fluids under rotating magnetic fields, combining theoretical analysis and numerical simulations to understand their dynamics and phase lag.

## Contribution

It introduces a comprehensive analysis of nanoparticle dynamics considering thermal noise and magnetic anisotropy, providing new analytical formulas applicable to various field strengths and frequencies.

## Key findings

- Magnetic moment locks to anisotropy axis at high anisotropy energy.
- Analytical and numerical results show perfect agreement for rotating magnetic fields.
- Formulas are valid for a wide range of magnetic field strengths and frequencies.

## Abstract

The rotational dynamics of magnetic nano particles in rotating magnetic fields in the presence of thermal noise is studied both theoretically and by performing numerical calculations. Kinetic equations for the dynamics of particles with uniaxial magnetic anisotropy are studied and the phase lag between the rotating magnetic moment and the driving field is obtained. It is shown that for large enough anisotropy energy the magnetic moment is locked to the anisotropy axis so that the particle behaves like a rotating magnetic dipole. The corresponding rigid dipole model is analyzed both numerically by solving the appropriate Fokker-Planck equation and analytically by applying an effective field method. In the special case of a rotating magnetic field applied analytic results are obtained in perfect agreement with numerical results based on the Fokker-Planck equation. The analytic formulas derived are not restricted to small magnetic fields or low frequencies and are therefore important for applications. The illustrative numerical calculations presented are performed for magnetic parameters typical for iron oxide.