Dynamics of a Magnetic Needle Magnetometer: Sensitivity to Landau-Lifshitz-Gilbert Damping

An analysis of a single-domain magnetic needle in the presence of an external magnetic field ${\bf B}$ is carried out with the aim of achieving a high precision magnetometer. We determine the uncertainty $\Delta B$ of such a device due to Gilbert dissipation and the associated internal magnetic field fluctuations that gives rise to diffusion of the magnetic needle axis direction ${\bf n}$ and the needle orbital angular momentum. The levitation of the magnetic needle in a magnetic trap and its stability are also analyzed.