Superparamagnetic effects in the linear magnetic response of polydisperse ensembles of nanoparticles suspended in a fluid.

Within a kinetic theory, the linear magnetic response of uniaxial single-domain particles suspended in a fluid is analyzed. The main qualitatively different types of frequency dependence of the longitudinal dynamic magnetic susceptibility of such particles are described. It is shown that superparamagnetic (related to orientation thermal fluctuations of the magnetic moment inside a particle) peculiarities of the response of a particle to a probing magnetic field are not fully determined by the ratio of anisotropy energy to thermal energy when a stationary bias field is applied. For a case where the indicated ratio is much greater than one, a simple approximate expression for the dynamic magnetic susceptibility of a particle is proposed. The developed approach is extended to polydisperse suspensions of noninteracting uniaxial nanoparticles. It is shown that polydispersity does not vanish away specific superparamagnetic features in the dynamic magnetic response of such systems. Quantitative estimates of the corresponding effects are performed in different frequency ranges of the applied field. It is demonstrated that under certain restrictions on the disperse composition of a suspension, the internal diffusion of the magnetic moment can lead to a splitting of the absorption spectrum of the system. The significant role of the bias field is revealed. In particular, it can cause an additional absorption maximum provided the particle-size distribution meets the outlined condition. Also, it enables one to assess how important it is to take into account superparamagnetism of particles: the effect of the biasing is stronger for particles with smaller anisotropy and thereby more pronounced superparamagnetic properties. A qualitative agreement of some of the inferences with the experimental data is briefly discussed.