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We investigated the mechanism of magnetic noise due to both surface and bulkimpurities. For surface noise, we apply the Langevin method to spin fluctuationtheory to calculate the noise for paramagnetic surface impurities absorbed in athin layer of water. We find that the mechanisms generating noise are spin flipand spin precession which depend on impurity spin relaxation and spinprecession time. For the bulk noise, we consider carbon-13 and nitrogen asimpurities and employ the correlated-cluster expansion to calculate noise.Carbon-13 noise is a few orders of magnitude larger than nitrogen due to thehigher impurity density in the typical NV center diamond system. We also findthat the noise in the secular approximation underestimates noise under lowapplied magnetic field. Overall, the major source of magnetic field noise isspin precession noise, which is more than five orders of magnitude larger thanthe spin flip noise.

Magnetic field noise analyses generated by the interactions between a nitrogen vacancy center diamond and surface and bulk impurities