Nonlinear contributions to the dynamic magnetic susceptibility of magnetic fluids

Abstract

• Higher order harmonic susceptibilities of magnetic fluids are obtained theoretically. • Mean spherical approximation is used with field strength expansion of magnetization. • Theoretical prediction is compared to the Langevin and Debye-Weiss limiting cases. • Field amplitude and frequency range of validity of the expanded MSA model is mapped. 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 Debye-Weiss 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.