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