Langevin dynamic simulations of fast remagnetization processes in ferrofluids with internal magnetic degrees of freedom

In this paper we present a model which allows numerical studies of ferrofluid dynamics taking into account the internal magnetic degrees of freedom of the ferrofluid particles. In standard ferrofluid models the magnetic moment of a ferrofluid particle is supposed to be fixed with respect to the particle itself, which corresponds to the limit of an infinitely high single-particle magnetic anisotropy. In contrast to this strongly simplifying assumption, we take into account that in real ferrofluids the magnetic moments of ferrofluid particles are allowed to rotate with respect to the particles themselves. Our model results in a system of equations of motion describing both magnetic and mechanical degrees of freedom, where the ‘magnetic’ equations are coupled with the ‘mechanical’ equations via (i) the interparticle distances determining the magnetodipolar interaction fields and (ii) orientations of the particle anisotropy axes with respect to their magnetic moments which define the mechanical torque on the particle. Using our model we have studied the ferrofluid magnetization dynamics for various particle concentrations, i.e., for various magnetodipolar interaction strengths. In particular, we present numerical results (a) the magnetization relaxation of a ferrofluid after the external field is switched off and (b) the frequency dependence of the ferrofluid AC susceptibility. Comparing these results with the corresponding dependences obtained for the rigid dipoles model, we demonstrate that for magnetic anisotropy values typical for commonly used ferrofluid materials (like magnetite) the inclusion of ‘magnetic’ degrees of freedom is qualitatively essential to obtain a correct description of the ferrofluid dynamics.