Isotope shift, a systematic error arising from the alkali polarization field generated by the spin-exchange collisions between the Xe and alkali-metal atoms, has been observed in many ${}^{129}\mathrm{Xe}-{}^{131}\mathrm{Xe}$ comagnetometer studies. This isotope shift constitutes a major source of systematic error that ultimately limits the measurement precision and long-term stability of comagnetometers. In this work we present a comprehensive analysis of how a spatially inhomogeneous alkali polarization field induces the isotope shift through the diffusion motion of Xe atoms. We identify two primary physical mechanisms responsible for the isotope shift: the mismatch of the wall relaxation rates and the large difference of the gyromagnetic ratios between ${}^{129}\mathrm{Xe}$ and ${}^{131}\mathrm{Xe}$ spins. Focusing on the alkali polarization field produced by a Gaussian pump beam, we perform detailed analytical and numerical evaluations of the magnitude and stability of the isotope shift. These results offer practical guidance for optimizing the experimental working point, thereby enhancing the absolute accuracy and long-term stability of ${}^{129}\mathrm{Xe}-{}^{131}\mathrm{Xe}$ comagnetometers and nuclear magnetic resonance gyroscopes.

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• Atomic & molecular processes in external fields
• Nuclear & electron resonance
• Quantum metrology
• Atomic ensemble
• Diffusion & random walks