Controlling a Magnetic Force Microscope to Track a Magnetized Nanosize Particle

In this paper, we introduce a scheme for tracking a magnetic nanoparticle moving in three dimensions using a magnetic force microscope (MFM). The stray magnetic field of the magnetic particle induces a shift in the phase of oscillation of the tip of the MFM. We present a nonlinear feedback control law that translates the measurement of this phase shift into a trajectory for the tip of the MFM and prove that this trajectory converges to a neighborhood of the magnetic particle. The viability of the proposed tracking scheme is verified through numerical simulations of the tracking algorithm.