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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.