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

TL;DR

This paper analyzes how Gilbert damping affects the sensitivity and stability of a magnetic needle magnetometer, providing insights into its precision limits and internal magnetic fluctuations.

Contribution

It offers a detailed theoretical analysis of the impact of Landau-Lifshitz-Gilbert damping on the performance and stability of a magnetic needle magnetometer.

Findings

Uncertainty in magnetic field measurement due to Gilbert dissipation quantified.

Internal magnetic field fluctuations cause diffusion of the needle's axis and angular momentum.

Stability conditions for levitating magnetic needles are derived.

Abstract

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.