Simulation and Quantitative Clarification of AC Susceptibility of Magnetic Fluid in Nonlinear Brownian Relaxation Region

The nonlinear Brownian rotational relaxation of magnetic fluids for the case of large excitation field was studied in relation to its biomedical applications. The Fokker–Planck equation, which describes the nonlinear behavior of magnetic fluids, was solved by numerical simulation when a large step or a sinusoidal field was applied. Deviations from the Debye theory were quantitatively clarified. First, it was shown that the response time of the magnetic fluids became shorter than the Brownian relaxation time for a larger excitation field, which can be expressed in terms of the field-dependent Brownian relaxation time. Next, the amplitude of the ac susceptibility became lower for larger excitation fields, and the frequency characteristic of the ac susceptibility moved to a higher frequency compared with that predicted by the Debye theory. Finally, higher harmonics occurred with increasing excitation fields. Approximate equations, that describe such nonlinear behaviors reasonably well, were also obtained. These equations are expected to be useful for developing biosensors based on Brownian relaxation.