Theoretical model for torque differential magnetometry of single-domain magnets

Abstract

We present a generic theoretical model for torque differential magnetometry (TDM)-an experimental method for determining the magnetic properties of a magnetic specimen by recording the resonance frequency of a mechanical oscillator, on which the magnetic specimen has been mounted, as a function of the applied magnetic field. The effective stiffness change, and hence the resonance frequency shift, of the oscillator due to the magnetic torque on the specimen is calculated, treating the magnetic specimen as a single magnetic domain. Our model can deal with an arbitrary magnetic free-energy density characterizing the specimen, as well as any relative orientation of the applied magnetic field, the specimen, and the oscillator. Our calculations agree well with published experimental data. The theoretical model presented here allows one to take full advantage of TDM as an efficient magnetometry method.

An all-electrical torque differential magnetometer operating under ambient conditions

“…If the prong is deflected by a small angle Θ from this direction, the magnetic moment of the specimen makes an angle θ = [H ext /(H ext + H k )]Θ with the anisotropy axis ( Fig. 8), where µ 0 H k = 2K u /M s is the anisotropy field, with the saturation magnetization M s [9,8]. Alternately, the angle between the magnetic moment and the applied magnetic field direction is Θ − θ.…”

“…We have employed quartz TFs to perform quantitative measurements via torque differential magnetometry (TDM) [9,8]. Our setup improves upon the existing TDM capabilities [9,10] by allowing 'large' specimens weighing up to several 10 µg, operation over a broad temperature and pressure range, higher sensitivity for detecting magnetic contribution to dissipation, and a simple all-electrical implementation.…”

“…1. Torque differential magnetometry [9,8] using a cantilever (a) and a quartz TF (b). On the rhs the mechanical and electrical equivalent circuits are shown.…”

“…In Sec. 5, we detail how the observed frequency shift can be used to quantify the magnetic properties of the specimen [8].…”

Damping of metallized bilayer nanomechanical resonators at room temperature

“…through elimination of metallization layers on the resonant structure or the use of different detection techniques, such as optical schemes. However, hybrid nanostructures frequently rely on such metallization films, providing functionalization for coupling mechanical resonators to other degrees of freedom [15][16][17] . For those purposes it is inevitable to acquire a deeper understanding of the metal's impact on the overall damping of the system [18][19][20][21] as well as its influence on elastic parameters 22 , especially at room temperature.…”