Rotational dynamics of the magnetic moments in ferrofluids

We present a set of six non-linear stochastic differential equations for the six variables which are relevant for the dynamical behavior of the magnetic moments in ferrofluids, namely, the three Euler angles of the magnetic particle, the two polar angles of the magnetic moment relative to the particle and the modulus of the magnetic moment. The interaction between the magnetic particle and the solvent fluid is modeled by dissipative and random noise torques, and so is the interaction between the particle and its magnetic moment, treated as an independent physical entity. In the appropriate limits, the model system reduces to the cases of super-paramagnetic or of non-super-paramagnetic (blocked magnetic moments) particles. Numerical results show that for non-zero moment of inertia the precession of the magnetic moment around the magnetic field is accompanied by "nutation". It is also indicated how the dynamic complex susceptibility may be calculated from the equations of motion and the numerical results show that the nutation leads to a second resonance peak.