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

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, εF″, 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. The dielectrophoretic extraction of nanoparticles was evaluated via the squared electric field gradient, and a threshold, ∇E2min, 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 a 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 the magneto-dielectric effects in the ferrofluid. These findings provide insight into the interplay between the magnetic field and the 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.