Fast relaxation on magnetic-dipole-forbidden spin transitions of nitrogen-vacancy centers in nanodiamonds.

Thanks to their versatility, nitrogen-vacancy (NV) centers in nanodiamonds have been widely adopted as nanoscale sensors. However, their sensitivities are limited by their short coherence times relative to NVs in bulk diamond. A more complete understanding of the origins of decoherence in nanodiamonds is critical to improving their performance. Here we present measurements of fast spin relaxation on magnetic-dipole-forbidden transitions between the $m_s = \pm1$ spin states of the NV- electronic ground state in ~40-nm nanodiamonds under ambient conditions. For frequency splittings between the $\pm1$ states of ~20 MHz or less the maximum achievable coherence time of the NV spin is ~2 orders of magnitude shorter than would be expected based on the lifetime of the $m_s = 0$ state. We attribute this fast relaxation to electric field noise. We observe a strong falloff of the relaxation rate with the splitting between $\pm1$, suggesting that, whenever possible, measurements with NVs in nanodiamonds should be performed at moderate axial magnetic fields (> 60 G). We also observe that the relaxation rate changes with time. These findings indicate that surface electric field noise is a major source of decoherence for NVs in nanodiamonds.