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

Published

January 26, 2026

Author(s)

Ronald Goldfarb

Abstract

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.

Citation

IEEE Access

Volume

14

Pub Type

Journals

Download Paper

https://doi.org/10.1109/ACCESS.2026.3657951

Local Download

Keywords

Colloids, dipole interactions, ferrofluids, impedance analyzers, magnetic relaxation, magnetic susceptibility, magnetic viscosity, magnetostatic interactions, nanoparticles, permeability, permeameters, radio frequency, standards, superparamagnetism, susceptometers, toroids.

Citation

Goldfarb, R. (2026), Radio-Frequency Toroid Susceptometry of Magnetic Nanoparticles: What Goes Around Comes Around, IEEE Access, [online], https://doi.org/10.1109/ACCESS.2026.3657951, https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=960749 (Accessed March 7, 2026)