Nonlinear magnetic susceptibility of ferrofluids

In ferrofluids, external magnetic fields can produce a nonlinearity in the dependence of magnetic susceptibilities on the field strength, due to both normal saturation and abnormal saturation. We derive the nonlinear magnetic susceptibility by using a Langevin model. Then, we investigate the nonlinear ac responses of the magnetic susceptibility by means of a perturbation expansion method and an orthogonal numerical method. The two methods are numerically shown in excellent agreement. We find that the responses are sensitive to suspension structures and field frequencies. Thus, by detecting the ac responses, it seems possible to real-time-monitor the structure of ferrofluids.