Core-shell Fe-Fe3C nanoparticles: Magnetic hyperthermia effect and equilibrium susceptibility

Iron-cementite (Fe–Fe 3 C) “core–shell” magnetic nanoparticles embedded in a carbon matrix were synthesized via solid-state pyrolysis of ferrocene. The average nanoparticle diameter is approximately 20 nm, with a composition ratio of Fe to Fe 3 C of about 2:1, which correlates well with the saturation magnetization ( M s ) measured at room temperature. The efficacy of magnetic hyperthermia as a function of nanoparticle concentration, as well as the frequency and amplitude of the alternating magnetic field, was systematically investigated. The Rosensweig theory was applied to calculate the relaxation time (τ) as 2.9 × 10⁻⁷ seconds by fitting the frequency-dependent specific loss power (SLP) values at a constant frequency. Using this approach, the equilibrium magnetic susceptibility (χ₀) was also estimated at 0.22 ± 0.03 through approximations of frequency-dependent SLP values at a fixed magnetic field amplitude. Additionally, χ₀ was determined at 0.33 ± 0.04 by fitting the field-dependent SLP data at a constant frequency, incorporating a conservative estimate of field-dependent susceptibility based on the Langevin model. Both methods yielded χ₀ values that overlap with the experimental value of 0.27 ± 0.03 within their respective error margins. These results suggest that the primary assumptions of the employed theoretical model are consistent with the experimental conditions. A numerical model simulating a single nanoparticle embedded in a fluid was developed using COMSOL Multiphysics to compare with the experimental concentration-dependent SLP data. The obtained results enable determination of the critical concentration in suspensions, beyond which the assumption of non-interacting particles no longer holds. • Synthesis of core-shell, Fe–Fe₃C, magnetic nanoparticles (MNPs). • The specific loss power (SLP) of MNPs was systematically investigated. • The equilibrium magnetic susceptibility (χ₀) were calculated based on SLS data. • The (χ₀) was experimentally determined. • Good fitting between experimental and calculated χ₀ values was obtained.