Characteristic times of relaxation peaks of magnetic fluids

Abstract

The use of the Fokker–Planck equation in theoretical studies of relaxation processes in single-domain particle systems is a well-established technique. However this method has a particular disadvantage in that it can give analytical results solely in some limiting cases. An alternative method, which avoids this difficulty, is that of the use of the integral relaxation time, τ int, which is presented in this work. Complex magnetic susceptibility measurements, χ( ω)= χ′( ω)−i χ″( ω), over the frequency range 10–100 MHz, were performed on a commercial kerosene-based magnetic fluid with magnetite particles stabilized with oleic acid. Based on these measurements, the integral relaxation time, τ int, the effective relaxation time, τ eff and the maximum absorption time, τ max =(2 πf max) −1, where f max is the frequency at which χ″( ω) exhibits a maximum, were determined. These characteristic times of a relaxation peak are always different, except for the idealized case of a homogeneous system with a single relaxation time. Due to the fact that τ int can be found analytically in a wide range of parameters, without solving the Fokker–Planck equation of the stochastic process, the presented experimental method can be successfully involved in the investigation of relaxation processes in single-domain magnetic particle systems, enabling a comparison to be made between experimental and theoretical results.