Theoretical study of the magnetization dynamics of non-dilute ferrofluids

TL;DR

This study provides a theoretical analysis of how magnetodipolar interactions influence the magnetization relaxation and ac-susceptibility in moderately concentrated ferrofluids, showing increased relaxation times and susceptibility shifts.

Contribution

It introduces an analytical model using a second order virial expansion to describe magnetization dynamics, validated against numerical simulations for certain concentrations.

Findings

Magnetodipolar interactions increase initial magnetization relaxation time.

Interactions cause an increase in the imaginary part of ac-susceptibility.

The virial expansion model agrees well with simulations up to specific particle concentrations.

Abstract

The paper is devoted to the theoretical investigation of the magnetodipolar interparticle interaction effect on remagnetization dynamics in moderately concentrated ferrofluids. We consider a homogeneous (without particle aggregates) ferrofluid consisting of identical spherical particles and employ a rigid dipole model, where magnetic moment of a particle is fixed with respect to the particle itself. In particular, for the magnetization relaxation after the external field is instantly switched off, we show that the magnetodipolar interaction leads to the increase of the initial magnetization relaxation time. For the complex ac-susceptibility we find that the this interaction leads to an overall increase of the imaginary susceptibility part and shifts the peak on its frequency dependence towards lower frequencies. Comparing results obtained with our analytical approach (second order virial expansion) to numerical simulation data (Langevin dynamics method), we demonstrate that the employed virial expansion approximation gives a good qualitative description of the ferrofluid magnetization dynamics and provides a satisfactory quantitative agreement with numerical simulations for the dc magnetization relaxation - up to the particle volume fraction c ~ 10% and for the ac-susceptibility - up to c ~ 5 %.