Nonlinear dynamic susceptibility of magnetic fluids in dc biased alternating magnetic fields

The dynamic response of magnetic nanoparticles to alternating (ac) magnetic fields is the basis of several promising biomedical applications, such as magnetic hyperthermia and magnetic particle imaging. In this paper, we theoretically investigate the magnetic response of an ensemble of interacting magnetic dipoles when the ac field is biased with a static dc component with arbitrary magnitude. Building on our earlier results, we propose a power series expansion based method within the framework of mean spherical approximation (MSA) to calculate the linear and higher order nonlinear susceptibilities. Moreover, an exact solution for the components of the susceptibility was also derived using the implicit MSA equations for comparison. The range of applicability of the expansion method was mapped in terms of ac field strength, frequency, and dc bias. We found that a seventh order expansion provides a good compromise between accuracy and simplicity of the analytical equations up to moderate field strengths. Using the exact MSA solution for the susceptibilities the field strength range was extended to strong fields, where the results agree qualitatively with the prediction of Fokker-Planck equation based theories.