Nonlinear contributions to the dynamic magnetic susceptibility of magnetic fluids

Based on our earlier analytical results for the magnetization of magnetic fluids with respect to the magnetic field strength, we propose an expansion method within the framework of mean spherical approximation (MSA) to obtain the coefficients of different nonlinear terms. Through a Fourier expansion of the frequency-dependent magnetic susceptibility the harmonic coefficients corresponding to the linear and nonlinear dynamic susceptibilities are calculated from the field expansion of magnetization. The frequency dependence of the higher order susceptibilities is determined on the basis of the Debye relaxation of magnetic dipoles. Our MSA based results are in line with the corresponding limiting case of the DebyeWeiss theory. We mapped the range of applicability of the expansion method concerning the field strength and frequencies. Our results show that under weak fields a 7th order expansion is sufficient to predict the magnitudes of the susceptibility components up to the 4th harmonic relevant for magnetic fluids. (C) 2022 The Authors. Published by Elsevier B.V.

Automated summary

In this study, we propose an expansion method within the mean spherical approximation (MSA) framework to obtain the coefficients of different nonlinear terms in magnetic fluids. The linear and nonlinear dynamic susceptibilities are calculated by Fourier expanding the frequency-dependent magnetic susceptibility and performing a field expansion of magnetization. The frequency dependence of higher order susceptibilities is determined based on the Debye relaxation of magnetic dipoles. Our results based on MSA are consistent with the limiting case of the Debye-Weiss theory. We determine the range of applicability of the expansion method in terms of field strength and frequencies, and show that a 7th order expansion is sufficient to predict the magnitudes of the susceptibility components up to the 4th harmonic relevant for magnetic fluids.