Enhanced magnetic moment discrimination for multiplex nanoparticle quantification via dual-frequency nonlinearity probing

Advanced applications of Magnetic nanoparticles (MNPs) in biomedicine based on multiplex MNP distinction require accurate, model-agnostic characterization of their magnetic moment distributions (MMDs). However, the resolving power of conventional MMD reconstruction from a static magnetization curve remains literarily underexplored. Moreover, due to particle-particle interactions, the response of the particle mixture might differ from the linear combination of the original constituents. We explore resolution enhancement in magnetic-moment space by directly probing higher-order magnetization derivatives, benefiting from their ever-increasing field-domain localization. Nonetheless, the direct derivative probing, as it is inevitably conducted dynamically, poses an interpretive problem for the origin of the nonlinearities. Spectral symmetries arising solely under dual-frequency excitation reflect the corresponding origins of amplitude- and rate-related nonlinearities. Using a dedicated experimental setup capable of synchronous demodulation of intermodulation terms, the method is tested on commercial MNP samples and benchmarked with conventional AC-susceptometry and static magnetization data. The binary mixture ratio was quantified with 8.9% deviation, without any prior information about the initial constituents differing by a factor of 3 in their average magnetic moments, potentially allowing the accommodation of three independent contrast channels for multiplex MNP applications as well as qualitatively probing magnetic interaction effects.