Mitigating surface-induced decoherence of spin sensors in nitrogen delta-doped diamond

The negatively-charged nitrogen-vacancy (NV) center in diamond is a robust nanoscale sensor of magnetic fields. To maximize their sensitivity to external spins, NVs have to be located close to the diamond surface while mitigating surface-induced decoherence. This requires a quantitative understanding of the dominant noise origins, which are currently not well understood. To address this we create shallow NVs by delta-doping during CVD growth [1] and apply scanning probe-based magnetic resonance imaging to find their depths with nm precision. We probe the noise with dynamical decoupling (DD) control of the NVs and fit their coherence decay envelopes to a spin-bath model with two contributions: bulk and surface electronic spins. The fits yield a surface spin density $\sigma_{\mathrm{s}} =$ 0.0032/nm$^{2}$ and relaxation rate 1/$\tau_{\mathrm{s}} =$ 190 kHz. We find an optimal CPMG-4 passive detection sensitivity of 250 $\mu _{\mathrm{p}}$/$\surd $Hz for an NV at 14 nm depth. Doped NVs within 10 nm of the surface were progressively decoupled from noise in the 1/$\tau _{\mathrm{s}}$ frequency regime using shorter DD inter-pulse delays, thereby enhancing their sensitivity. \\[4pt] [1] K. Ohno et al., Appl. Phys. Lett. 101, 082413 (2012).