New classes of systematic effects in gas spin co-magnetometers

Atomic co-magnetometers are widely used in precision measurements searching for spin interactions beyond the Standard Model. We describe a new $^3$He-$^{129}$Xe co-magnetometer probed by Rb atoms and use it to identify two general classes of systematic effects in gas co-magnetometers, one associated with diffusion in second-order magnetic field gradients and another due to temperature gradients. We also develop a general and practical approach for calculating spin relaxation and frequency shifts due to arbitrary magnetic field gradients and confirm it experimentally.