Precise Measurement of Magnetic Field Gradients from Free Spin Precession Signals of $^{3}$He and $^{129}$Xe Magnetometers

We report on precise measurements of magnetic field gradients extracted from transverse relaxation rates of precessing spin samples. The experimental approach is based on the free precession of gaseous, nuclear spin polarized $^3$He and $^{129}$Xe atoms in a spherical cell inside a magnetic guiding field of about 400 nT using LT$_C$ SQUIDs as low-noise magnetic flux detectors. The transverse relaxation rates of both spin species are simultaneously monitored as magnetic field gradients are varied. For transverse relaxation times reaching 100 h, the residual longitudinal field gradient across the spin sample could be deduced to be$|\vec{\nabla}B_z|=(5.6 \pm 0.4)$ pT/cm. The method takes advantage of the high signal-to-noise ratio with which the decaying spin precession signal can be monitored that finally leads to the exceptional accuracy to determine magnetic field gradients at the sub pT/cm scale.