Radio-Frequency Toroid Susceptometry of Magnetic Nanoparticles: What Goes Around Comes Around

The intrinsic magnetic susceptibility of noninteracting magnetic nanoparticles is calculated from the measured complex radio-frequency susceptibility of dipolar-coupled particles in colloidal suspension. The susceptibility, derived from the impedance of toroidal specimens in a shorted coaxial transmission line, requires no adjustment for demagnetizing factors. Three established models for interacting superparamagnetic particles - the Weiss molecular-field model, the Onsager model, and the modified mean-field model - are extended to magnetically viscous particles at frequencies above their Néel relaxation frequency. Magnetic figures of merit for nanoparticles are the real and imaginary parts of complex intrinsic susceptibility scaled by particle concentration. The work seeks to promote standard characterization methods for interlaboratory comparison of realistic distributions of magnetic nanoparticles at radio frequencies.