The frequency shift of ¹²⁹Xe and ¹³¹Xe nuclei in NMR sensors caused by weak temperature gradients

The nuclear magnetic resonance (NMR) sensor is the core sensor of the inertial navigation system. Compared with the traditional mechanical and optical fiber angle velocity sensors, it has the advantages of higher precision and smaller volume. It is a new direction for the development of gyroscopes in the future. In this study, we have found the frequency shift phenomenon of ¹²⁹Xe and ¹³¹Xe in the NMR sensors caused by weak temperature gradients. The temperature characteristic of NMR sensors is one of the most important research interests, which is of great significance for improving the performance and indicators of sensors. Most papers have studied the frequency shift in the NMR sensors’ cell under strong temperature gradients, and it is rarely used under weak temperature gradients. Others study the frequency shift in the NMR sensors’ cell by magnetic field characteristics. In multiple experiments, we found that the frequency shift increases with the rise of temperature gradients, which caused by the relative concentration gradients between the Xe isotopes. Therefore, a new model is proposed based on the thermal diffusion and relative concentration to explain the frequency shift. The model contains alkali electronic spin polarization and relative concentration gradients is used in COMSOL software to simulate the frequency shift phenomenon. The error between simulations and experiments is 2.29% under 0.1 K temperature. It can be seen that the simulation results are consistent with experiments under weak temperature gradients. This study provides a good reference for analyzing the frequency shift of NMR sensors under weak temperature gradients.