MEMS-Based Cantilever Sensor for Simultaneous Measurement of Mass and Magnetic Moment of Magnetic Particles

Abstract

This study presents a measurement approach suitable for the simultaneous determination of both the mass mp and magnetic moment µp of magnetic particles deposited on a micro electro mechanical system (MEMS) resonant cantilever balance, which is operated in parallel to an external magnetic field-induced force gradient F′(z). Magnetic induction B(z) and its second spatial derivative δ2B/δz2 is realized, beforehand, through the finite element method magnetics (FEMM) simulation with a pair of neodymium permanent magnets configured in a face-to-face arrangement. Typically, the magnets are mounted in a magnet holder assembly designed and fabricated in-house. The resulting F′ lowers the calibrated intrinsic stiffness k0 of the cantilever to k0-F′, which can, thus, be obtained from a measured resonance frequency shift of the cantilever. The magnetic moment µp per deposited particle is determined by dividing F′ by δ2B/δz2 and the number of the attached monodisperse particles given by the mass-induced frequency shift of the cantilever. For the plain iron oxide particles (250 nm) and the magnetic polystyrene particles (2 µm), we yield µp of 0.8 to 1.5 fA m2 and 11 to 19 fA m2 compared to 2 fA m2 and 33 fA m2 nominal values, respectively.