Experimental and theoretical profiles of the frequency-dependent complex susceptibility of systems containing nanometer-sized magnetic particles

Abstract

Measurements of the frequency-dependent complex susceptibility \ensuremath{\chi}(\ensuremath{\omega})=\ensuremath{\chi}\ensuremath{'}(\ensuremath{\omega})-i\ensuremath{\chi}\ensuremath{''}(\ensuremath{\omega}) of ferrofluids and magnetic tape are presented and compared with susceptibility profiles generated by means of classical models. In the case of ferrofluids, fitting is realized by means of a combination of the equations of Raikher and Shliomis and of Debye. These equations are for monodispersed particles, and as ferrofluids consist of polydispersed particles, it is demonstrated that to achieve a good fit to the experimental data it is necessary to provide for both a distribution of particle radii r and anisotropy constant K. In terms of the parallel, ${\mathrm{\ensuremath{\chi}}}_{\mathrm{\ensuremath{\parallel}}}$(\ensuremath{\omega}), and transverse, ${\mathrm{\ensuremath{\chi}}}_{\mathrm{\ensuremath{\perp}}}$(\ensuremath{\omega}), components of the susceptibility, it is shown that the incorporation of a distribution of particle radii is required to fit the parallel component ${\mathrm{\ensuremath{\chi}}}_{\mathrm{\ensuremath{\parallel}}}$(\ensuremath{\omega}) of the susceptibility, while a distribution of anisotropy constants is required to fit the resonant ${\mathrm{\ensuremath{\chi}}}_{\mathrm{\ensuremath{\perp}}}$(\ensuremath{\omega}) component. Susceptibility data for magnetic tape are fitted to the equations of Landau and Lifshitz, suitably adapted to provide for a distribution of K alone. The usefulness of the fitting technique in ascertaining average values of the damping parameter \ensuremath{\alpha} and anisotropy constant K is demonstrated.