Frequency shifts in noble-gas magnetometers

We have investigated anomalous frequency variations -- not due to external magnetic fields -- in a two-species $^3$He -$^{129}$Xe magnetometer, as seen in several recent experiments. We controlled the transverse and longitudinal magnetization of the two species with NMR pulse sequences and measured the correlated frequency and comagnetometer shifts. We set upper limits on frequency shifts induced by transverse magnetization and rule these out as the source of observed comagnetometer shifts. We see a species dependent frequency shift that depends on longitudinal magnetization and causes a shift in the comagnetometer implementation. The longitudinal shift is of an appropriate size to explain the comagnetometer variation as being dominated by the decay of residual longitudinal magnetization. Our measurements are also consistent with the recent observation of a scalar interaction between $^3$He and $^{129}$Xe by Limes et al. We find $kappa_mathrm{HeXe} = -0.009 pm 0.0004$, and present the first measurement of the scalar shift induced by $^{129}$Xe on $^3$He corresponding to $kappa_mathrm{XeHe} = -0.007 pm 0.001$.