Stochastic dynamics of super­paramagnetic moments in poli­disperse ferrofluids

C. Scherer

Institute of Physics, Federal University of Rio Grande do Sul, Porto Alegre, Brasil

Abstract
In previous works, we studied the dynamics of the magnetic moments in ferrofluids \cite{schererBJP,scherer-matuttis, scherer-ricci}, and other authors have also dealt with this problem \cite{shliomis}. In our previous works also computational simulations have been performed. The present work differs from those in two important aspects: (i) the magnetic particles are not of uniform size, but have a lognormal distribution of diameters; (ii) the parameters used in the simulations, like magnetization, anisotropy constant, liquid viscosity, applied field, temperature, etc., correspond to the values for realistic ferrofluids (in the previous works we used values, which were convenient for the simulations). For this reason, we will briefly re-derive the equations of motion, keeping all the relevant constants in them. To avoid big powers of 10 in the simulations, we introduce an appropriate system of units. The equations of motion for the particles' rotation and for the rotation of their magnetic moments are stochastic differential equations with multiplicative noise. Therefore, they have to be interpreted as Stratonovich--Langevin equations and the roles of stochastic calculus have to be used in the simulations. In our simulations, the response functions are "measured" and from them the complex susceptibilities are calculated. We performed several simulations, varying each parameter around a standard value, in order to see how the susceptibilities are correlated with the physical constants of the material. In the conclusions of special mention is the verification that the line broadening is very big. To be explicit, the ratio of the line-width of the polydisperse to that of the monodisperse with a diameter equal to the median diameter of the polydisperse, is much bigger than the ratio of the diameter's distribution width to the median diameter. It is interesting to note that for small dispersion width of diameters the resonance frequency does not change significantly with respect to the resonance frequency of the monodisperse. Figs 7, Refs 6.