High-sensitivity magnetometers play a crucial role in various domains, including fundamental physics, biomedical imaging, and navigation. Levitated diamonds containing nitrogen-vacancy centers exhibit significant potential for magnetic sensing due to their high mechanical quality factor and long spin coherence time. However, previous studies have predominantly focused on electron-spin-based measurements of alternating current magnetic fields. In this paper, we propose an approach for direct current magnetic-field measurement based on the Berry phase generated by three-dimensional rotation. We analyze the adiabatic evolution of the ${}^{14}\mathrm{N}$ nuclear spin inside a levitated three-dimensional rotating diamond with frequencies around $\mathrm{MHz}$. Our finding reveals that the Berry phase exhibits high sensitivity to external parameters near rotation-induced nuclear spin resonance. Using this mechanism, we theoretically demonstrate that a static magnetic-field sensitivity of ${10}^{-7}\mathrm{T}/\sqrt{\mathrm{Hz}}/\sqrt{N}$ is achievable as experimental techniques continue to mature.

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• Berry curvature
• Magnetometry
• Quantum sensing
• Rotation sensing
• Nitrogen vacancy centers in diamond