Dynamics of magnetization growth and relaxation in ferrofluids

The dynamics of the growth and relaxation of the magnetization in ferrofluids are determined using theory based on the Fokker-Planck-Brown equation, and Brownian-dynamics simulations. Magnetization growth starting from an equilibrium nonmagnetized state in zero field, and following an instantaneous application of a uniform field of arbitrary strength, is studied with and without interparticle interactions. Similarly, magnetization relaxation is studied starting from an equilibrium magnetized state in a field of arbitrary strength, and following instantaneous removal of the field. In all cases, the dynamics are studied in terms of the time-dependent magnetization 𝑚⁡(𝑡). The field strength is described by the Langevin parameter 𝛼, the strength of the interparticle interactions is described by the Langevin susceptibility 𝜒𝐿, and the individual particles undergo Brownian rotation with time 𝜏𝐵. For noninteracting particles, the average growth time decreases with increasing 𝛼 due to the torque exerted by the field, while the average relaxation time stays constant at 𝜏𝐵; with vanishingly weak fields, the timescales coincide. The same basic picture emerges for interacting particles, but the weak-field timescales are larger due to collective particle motions, and the average relaxation time exhibits a weak, nonmonotonic field dependence. A comparison between theoretical and simulation results is excellent for noninteracting particles. For interacting particles with 𝜒𝐿=1 and 2, theory and simulations are in qualitative agreement, but there are quantitative deviations, particularly in the weak-field regime, for reasons that are connected with the description of interactions using effective fields.