Measurements of the frequency-dependent complex susceptibility χ(ω)=χ′(ω)-iχ″(ω) 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, ${\mathrm{\chi }}_{\mathrm{\parallel }}$(ω), and transverse, ${\mathrm{\chi }}_{\mathrm{\perp }}$(ω), components of the susceptibility, it is shown that the incorporation of a distribution of particle radii is required to fit the parallel component ${\mathrm{\chi }}_{\mathrm{\parallel }}$(ω) of the susceptibility, while a distribution of anisotropy constants is required to fit the resonant ${\mathrm{\chi }}_{\mathrm{\perp }}$(ω) 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 α and anisotropy constant K is demonstrated.

Measurements of the complex susceptibility, , as a function of the frequency (100 Hz–18 GHz) and polarizing field (0–90 kA m−1) at room temperature together with static magnetic measurements over the temperature range 4–300 K, are reported for a colloidal suspension of cobalt nanoparticles. The transition of the cobalt particles to the superparamagnetic state are supported by the temperature dependencies of field cooling (FC) and zero field cooling (ZFC) magnetization measurements. From these measurements, which show a typical blocking behaviour of an assembly of superparamagnetic particles with a wide distribution of blocking temperatures, the exponential pre-factor of Brown's equations for Néel relaxation, is found to be equal to 9.2 × 10−10 s. Measurement of the complex susceptibility over this broad frequency range, with an upper frequency value corresponding to three times that previously reported in our measurements on cobalt, has enabled the presence of both resonance and Néel relaxation mechanisms to be identified. From the Néel component, a further value for was evaluated and shown to be in close agreement with that obtained from the ZFC data. Data on the after-effect function, realised by Fourier transformation of the component, is also presented.

The toroidal technique is used in the determination of the complex, frequency dependent magnetic susceptibility, , of four magnetic fluids consisting of colloidal suspensions of magnetite in water with corresponding saturation magnetisation of 134 G, 107 G, 90 G and 30 G. Plots of the susceptibility components against f (Hz) over the frequency range 10 Hz to 1 MHz, are shown to have approximate Debye-type profiles with the presence of Brownian relaxation being indicated by the frequency, f max, of the maximum of the loss-peak in the profiles. Corresponding calculations of particle hydrodynamic radius indicate the presence of aggregation. An estimate of the aggregate size distribution in the samples is determined by fitting the measured susceptibility profiles to susceptibility profiles generated by the Debye equations modified by Frohlich, Cole-Cole, Normal and Lognormal distribution functions. The fits obtained from the four fitting functions are found to be similar and thus it is concluded that none of these functions offers any particular advantage over the other functions.