Tracking a nanosize magnetic particle using a magnetic force microscope

Abstract

A scheme for tracking nano-sized magnetic particles using a magnetic force microscope (MFM) is introduced. The stray magnetic field of the particle induces a shift in the phase of the oscillation of the MFM tip. The magnitude of this shift depends on the distance between the tip and the particle and can be expressed as a spatial field. We present a control law which steers the tip to a level set of this field. The approach is based on the previous work of two of the authors on a novel method for mapping unknown potential fields using sensorenabled mobile robots. Because the method involves geometric properties of the field and its domain, it is not surprising that it can be applied to problems where the characteristic length scales are small. Additionally, we introduce to the original control law an adaptive term to compensate for uncertainties in the parameter values in the model of the magnetic force. The efficacy of this approach is illustrated through simulation. This approach to tracking will provide the capability to investigate the dynamics of single molecules with a higher resolution (in both space and time) than is currently possible.

Tracking a magnetic nanoparticle in 3-D with a magnetic force microscope

“…The sensitivity of this response is maximized when the tip is driven near its original natural frequency ω = ω 0 . From (2), this corresponds to φ = π 2 . Then, setting ω = ω 0 in (4) gives:…”

“…We note that in previous work [2], we used a similar approach to develop a control law to track a given level set ∆Φ = const near the extremum. That law required knowledge of model parameters that in general are difficult to determine.…”

“…Motivated by this ability, we introduce a feedback control law which steers the tip of the MFM to remain in a neighborhood of a single magnetic particle. This works builds upon a previous effort of the authors [2]. The contribution of the present paper is a new algorithm which does not depend on detailed a priori information about the nanoparticle and which is designed to operate in 3-D.…”