Spin relaxometry of single nitrogen-vacancy defects in diamond nanocrystals for magnetic noise sensing

We report an experimental study of the longitudinal relaxation time (${T}_{1}$) of the electron spin associated with single nitrogen-vacancy (NV) defects hosted in nanodiamonds (NDs). We first show that ${T}_{1}$ decreases over three orders of magnitude when the ND size is reduced from 100 to 10 nm owing to the interaction of the NV electron spin with a bath of paramagnetic centers lying on the ND surface. We next tune the magnetic environment by decorating the ND surface with Gd${}^{3+}$ ions and observe an efficient ${T}_{1}$ quenching, which demonstrates magnetic noise sensing with a single electron spin. We estimate a sensitivity down to $\ensuremath{\approx}14$ electron spins detected within 10 s, using a single NV defect hosted in a 10-nm-size ND. These results pave the way towards ${T}_{1}$-based nanoscale imaging of the spin density in biological samples.