  Surface electric (charge) noise influences spin defects due to fluctuation of
the surface charge density and also the electrostatic potential at the crystal
surface. Surprisingly, the two-point correlation function of both the charged
particles' positions and the surface electrostatic potential strongly
influences the power of the polynomial decay of the electric noise spectral
density; this power is not determined solely by the character of the charge
fluctuators. Time-dependent crossover behavior near the correlation time of the
fluctuators, of the spin defect's relaxation and decoherence, provide a
quantitative fingerprint of the diffusive behavior of charged particles at the
surface.
