Tracking a nanosize magnetic particle using a magnetic force microscope

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 sensor- enabled 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.