Earth's field diamond vector magnetometry with isotropic magnetic flux concentrators

Vector magnetometers based on the optically detected magnetic resonance (ODMR) of nitrogen-vacancy centers in diamond are being developed for applications such as navigation and geomagnetism. However, at low magnetic fields, such as that on Earth (~50 {\mu}T), diamond magnetometers suffer from spectral congestion whereby ODMR peaks are not easily resolved. Here, we experimentally investigate a potential solution of using an isotropic, three-dimensional magnetic flux concentrator to amplify Earth's field without altering its direction. The concentrator consists of six ferrite cones, in a face-centered cubic arrangement, centered about a diamond. We vary the direction of a 50 {\mu}T applied field and record and fit the resulting ODMR spectra. By comparing the fitted fields to those of a reference fluxgate magnetometer, we characterize the angular response of the diamond magnetometer and quantify absolute errors in the field magnitude and angle. We find that the enhancement factor is nearly isotropic, with a mean of 19.05 and a standard deviation of 0.16, when weighted by solid angle coverage. Gradient broadening of the ODMR lines is sufficiently small that the spectra are well resolved for nearly all field directions, alleviating spectral congestion. For ~98% of the total 4{\pi} solid angle, Cram\'er-Rao lower bounds for magnetic field estimation uncertainty are within a factor of 2 of those of the fully-resolved case, indicating minimal deadzones. We track the stability of the magnetometer over six hours and observe variations less than or approximately 40 nT/hour, limited by temperature drift. Our study presents a new route for diamond vector magnetometry at Earth's field, with potential applications in geomagnetic surveys, anomaly detection, and navigation.