Analytic solution for the nonlinear response of magnetic nanoparticles to large amplitude oscillatory fields

Ilg, P. ORCID: https://orcid.org/0000-0002-7518-5543 (2025) Analytic solution for the nonlinear response of magnetic nanoparticles to large amplitude oscillatory fields. Physical Review E, 111 (5). 055411. ISSN 2470-0053 doi: 10.1103/PhysRevE.111.055411

Abstract/Summary

Nonlinear responses of physical systems to strong perturbations are notoriously difficult to tackle analytically. Here, we present analytic results for the nonlinear response of magnetic nanoparticles to large amplitude oscillatory magnetic fields based on a particular model for the magnetization dynamics. A number of characteristic features of the in-phase and out-of-phase higher-harmonic response are found and analyzed. In particular we find that the magnitude of higher harmonic contributions Rn depends on the field amplitude and frequency only via a single scaling variable that combines the two quantities. The decrease of |Rn|with increasing order nof harmonics is a key quantity monitored in biomedical applications such as magnetic particle spectroscopy and magnetic particle imaging. Except for the first few harmonics, we find that this decrease is exponential with a rate that depends on the scaling variable only. For not too high frequencies and not loo large amplitudes, we find that these exact results for one particular model of magnetization dynamics hold approximately also for other, more frequently used models. Our results therefore offer not only deeper insight into strongly nonlinear responses of magnetic nanoparticles, especially for higher harmonics that are very difficult to determine numerically, but also suggest analyzing data in terms of a scaling variable.

Item Type	Article
URI	https://centaur.reading.ac.uk/id/eprint/122527
Identification Number/DOI	10.1103/PhysRevE.111.055411
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	American Physical Society
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