We investigate, via a modified mean field approach, the dynamic magnetic response of a polydisperse dipolar suspension to a weak, linearly polarised, AC field. We introduce an additional term into the Fokker-Planck equation, which takes into account dipole-dipole interaction in the form of the first order perturbation, and allows for particle polydispersity. The analytical expressions, obtained for the real and imaginary dynamic susceptibilities, predict three measurable effects: the increase of the real part low-frequency plateaux; the enhanced growth of the imaginary part in the low-frequency range; and the shift of the imaginary part maximum. Our theoretical predictions find an experimental confirmation and explain the changes in the spectrum.

Dynamic magnetic response of a ferrofluid in a static uniform magnetic fieldCitation for published version: Batrudinov, TM, Nekhoroshkova, YE, Paramonov, EI, Zverev, VS, Elfimova, EA, Ivanov, AO & Camp, PJ 2018, 'Dynamic magnetic response of a ferrofluid in a static uniform magnetic field', Physical Review E, vol. 98, no. 5. https://doi. AbstractA theory for the frequency-dependent magnetic susceptibility of a ferrofluid in a static uniform magnetic field is developed, including the dipolar interactions between the constituent particles.Interactions are included within the framework of modified mean-field theory. Predictions are given for the linear responses of the magnetization to a probing ac field both parallel and perpendicular to the static field, and are tested against results from Brownian dynamics simulations. The effects of particle concentration and dipolar coupling constant on the field-dependent static susceptibilities and the frequency dispersions are shown to be substantial, which justifies taking proper account of the interactions between particles. The theory is reliable provided that the volume concentration and dipolar coupling constant are not too large, and within the range of values for real ferrofluids.

The interweave of competing individual relaxations influenced by the presence of temperature and concentration dependent correlations is an intrinsic feature of superparamagnetic nanoparticle suspensions. This unique combination gives rise to multiple applications of such suspensions in medicine, nanotechnology and microfluidics. Here, using theory and experiment, we investigate dynamic magnetic susceptibility in a broad range of temperatures and frequencies. Our approach allows, for the first time to our knowledge, to separate clearly the effects of superparamagnetic particle polydispersity and interparticle magnetic interactions on the dynamic spectra of these systems. In this way, we not only provide a theoretical model that can predict well the dynamic response of magnetic nanoparticles systems, but also deepen the understanding of the dynamic nanoparticle self-assembly, opening new perspectives in tuning and controlling the magnetic behaviour of such systems in AC fields.

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