Dynamic response of an ensemble of immobilized superparamagnetic interacting particles with aligned easy magnetization axes in parallel directed ac and dc magnetic fields

The paper presents a theoretical study of the dynamic magnetic response of an ensemble of interacting superparamagnetic nanoparticles with aligned easy magnetization axes, subjected to both static (dc) and alternating (ac) magnetic fields simultaneously. Such a system traditionally models soft magnetosensitive composites synthesized from liquid dispersions of magnetic nanoparticles in a strong static magnetic field, followed by the solidification of the liquid matrix. The investigation was carried out by numerically solving the Fokker-Planck-Brown equation using a modified mean-field theory that accounts for dipole-dipole interactions between particles at the level of pair correlations. It is shown that the system's dynamics are determined by the competition between the magnetic anisotropy energy, the interaction of magnetic moments with external fields, and the dipole-dipole interactions. The key spectral characteristics of the dynamic susceptibility are analyzed, namely, the low-frequency value of the real part of the susceptibility, and the value and position of the maximum of the imaginary part. A nonmonotonic regime was observed for one of these characteristics, activated when the ac and dc fields exceed critical values. Based on the numerical data, approximating formulas are proposed that relate the spectral characteristics to the amplitude of the ac field, the intensity of the dc field, and the material parameters. On one hand, these relations are in demand for optimizing the synthesis of magnetosensitive composites for biomedicine and sensing, as they allow predicting the intervals of increase and decrease in dynamic susceptibility depending on the intensity of the ac or dc fields. On the other hand, these relations can be used to determine the magnetic anisotropy constant of the magnetic filler particles from experimental measurements of the dynamic susceptibility.