Frequency and Polarizing Magnetic Field Dependence of the Clausius-Mossotti Factor of a Kerosene-Based Ferrofluid with Mn-Fe Nanoparticles in a Microwave Field

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Abstract
We present frequency- and magnetic field-dependent measurements of the complex dielectric permittivity ε*(f, H) of a kerosene-based ferrofluid, containing Mn0.6Fe0.4Fe2O4 nanoparticles, over 0.8–5 GHz and static fields up to ~91 kA/m. The imaginary part, ε′′F, shows a peak at a characteristic frequency that shifts towards higher frequencies with increasing H, revealing a magnetic field-dependent relaxation process, interpreted using the Maxwell–Wagner–Sillars model. Dielectrophoretic extraction of nanoparticles was evaluated via the squared electric field gradient, and a threshold, dependent on particle size was determined. Below that threshold, Brownian forces dominate, so the ferrofluid acts as a homogeneous dielectric. For this case, the Clausius-Mossotti factor (CM) was calculated for ferrofluid droplets in air and in water as a function of frequency and magnetic field. In air, CM exhibits modest but systematic magnetic field dependence, indicating magnetically modulated dielectric response at GHz frequencies. In contrast, when water is used as the reference medium, CM remains negative and essentially independent of H across the entire frequency range, suggesting that the high permittivity of water masks magneto-dielectric effects in the ferrofluid. These findings provide insight into the interplay between magnetic field and permittivity of ferrofluids, with implications for high-frequency applications. Moreover, using a λ/4 antenna connected to a network analyzer, the existence of the dielectrophoretic force acting on a ferrofluid-impregnated textile thread, at microwave frequencies, was experimentally demonstrated.

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