Internal and Brownian mode-coupling effects in thetheory of magnetic relaxation and ferromagnetic resonance offerrofluids

Abstract

It is shown how the Langevin equation for the motion of themagnetization of a ferrofluid particle with uniaxial anisotropyin a strong uniform applied field reduces to those governingthe Néel (i.e. the solid-state or internal) mechanism ofreorientation of the magnetic moment in the non-axiallysymmetric potential created when a field is applied at an angleto the easy axis and a Larmor-like equation for the transversemotion. The field angle, unlike in the solid-state problem, isa function of the time due to the torques imposed by the fluidcarrier. The Langevin equation for the Brownian rotationalmotion of the particle itself reduces to that describing Debyerelaxation in the applied field but is coupled to the magneticmotion via the external field. The results indicate that the dissipation parameter of the internal solid-state mechanism isaugmented by the external stochastic torques imposed by thecarrier. However, the effect appears to be negligible becauseof the ratio of the Brownian (Debye) time to the free Néeldiffusion time. Furthermore, just as in the pure solid-stateprocess, pronounced precession-aided longitudinal relaxation andferromagnetic resonance effects, having their origin in thebreaking of the axial symmetry due to the strong field, willoccur. The precession-aided relaxation disappears for weakfields since the potential becomes axially symmetric. Moreover,the equations of motion of the magnetic moment and the particlecompletely decouple and the overall decay function is simply theproduct of the decay functions of the internal (Néel) andDebye processes. It appears that the ferromagnetic resonance inthis instance is accurately described by the known solid-stateresults, since the Brownian relaxation time greatly exceeds theeffective relaxation times of the internal dipole andquadrupole modes associated with the ferromagnetic resonance.This conclusion is reinforced by the favourable agreement of theweak-field result with experimental observations of the complex susceptibility of four ferrofluid samples.