Fundamental limits to magnetic-field sensitivity of flux-gate magnetic-field sensors

In this letter we determine the theoretical limit of the magnetic-field sensitivity of the flux-gate magnetometer. In order to do so, we have developed a model for the white noise of a flux gate based on the fundamental dynamics of the magnetic material forming the flux-gate core. Solving this model, we predict that the white noise of a physically realizable flux gate with a volume of ${\text{2×10}}^{\text{−8}} {\mathrm{m}}^{\mathrm{3}}$ is less than $\text{100\hspace{0.05em}}\mathrm{fT}/\sqrt{\mathrm{Hz}}.$ The white noise varies with the lossy susceptibility of the core and inversely with the volume. We also compare the measured white noise of a thin-film flux gate with the predictions of our model and find that the measured and predicted noise agree reasonably well.