Contribution of particle inertial effects to resonance in ferrofluids

Abstract

The effect of the moment of inertia of single domain ferromagnetic particles on the frequency-dependent complex susceptibility ?(?)=??(?)-i???(?) of ferrofluids is reported. It is demonstrated that particle inertial effects that arise from rotational Brownian motion can give rise to a resonant behavior, which is indicated by the real component ??(?) becoming negative at a frequency substantially lower than the Larmor frequency. This provides a possible explanation for previously published data that display such an effect in the 10 to 100 MHz region. The Langevin treatment of Brownian motion is used to incorporate thermal agitation into a model which represents, for the purpose of analysis, a typical ferroparticle, P, as a composite particle comprising a magnetic particle, Pm (assumed to be spherical), which may rotate inside and in contact with a concentric rigid sphere, Ps, representing the surfactant, so that Pm and Ps may have different angular velocities about a common center. This leads to a three-dimensional form of the itinerant oscillator model in the small oscillation approximation. The model predicts inertia corrected Debye relaxation in the form of the Rocard equation that arises for Pm and Ps rotating as a unit, and resonance behavior arising from the relative motion of Pm and Ps.