Inertial effects in the complex magnetic susceptibility of a ferrofluid in the presence of a dc bias field

The Euler-Langevin equation for rotational Brownian motion of a particle in a form appropriate to magnetic relaxation of ferrofluids (suspensions of single domain ferromagnetic particles) in the presence of a de bias external magnetic field is used to include the inertia of particles, It is shown, by averaging the Langevin equation corrected for inertia, how approximate analytic expressions for the transverse and longitudinal components of the complex magnetic susceptibility may be calculated directly from that equation with the aid of linear response theory. The method allows one to bypass the Fokker-Planck equation entirely. Sum rules for integrated absorption of electromagnetic radiation in suspensions of ferromagnetic particles are also deduced.