Magnetic field noise caused by surface paramagnetic impurities on nitrogen vacancy center diamonds

Noise is a detrimental issue for nitrogen vacancy (NV) center diamond sensing devices. The magnetic field noise is caused by both surface and bulk impurities. Here, we study the noise due to the interactions between the NV center electron spin and the surface impurity electron spins that are dissolved in a thin water layer on hydrogen (H-), oxygen (O-), or fluorine (F-) terminated surfaces. We apply the Langevin method to spin fluctuation theory to calculate and analyze the surface noise spectral density. Impurity hopping among the available sites determines the impurity relaxation time that controls the contribution of the noise either from the spin flip-flops noise only or additional spin precession noise. Our results show that O-terminated surface give a much lower surface noise than H- and F-terminated surfaces. This is because only spin flip-flop noise are present for O-terminated surface due to oxygen’s picosecond electron spin-lattice relaxation time while both spin flip-flop noise and spin precession noise are present for H- and F-terminated surfaces. Comparing to the previous work on bulk impurity noise, we find that the surface impurities are indeed a greater source of magnetic field noise than the bulk impurities.