Temperature- and Magnetic-Field-Dependent Longitudinal Spin Relaxation in Nitrogen-Vacancy Ensembles in Diamond

We present an experimental study of the longitudinal electron-spin relaxation time ($T_1$) of negatively charged nitrogen-vacancy (NV) ensembles in diamond. $T_1$ was studied as a function of temperature from 5 to 475 K and magnetic field from 0 to 630 G for several samples with various NV and nitrogen concentrations. Our studies reveal three processes responsible for $T_1$ relaxation. Above room temperature, a two-phonon Raman process dominates; below room temperature, we observe an Orbach-type process with an activation energy of 73(4) meV, which closely matches the local vibrational modes of the NV center. At yet lower temperatures, sample dependent cross-relaxation processes dominate, resulting in temperature independent values of $T_1$ from milliseconds to minutes. The value of $T_1$ in this limit depends sensitively on the magnetic field and can be tuned by more than 1 order of magnitude.

Figure 1

(a) Level structure of the NV center showing spin-triplet ground ${}^{3}A_2$ and excited ${}^{3}E$ states, as well as the singlet system involved in the optical spin-polarization mechanism. (b) Optical and microwave pulse sequence used for $T_1$ measurements. (c) Example of $T_1$ measurement. The difference in level of fluorescence for two measurements with and without a microwave $\pi$ pulse, ${\Delta }_{\mathrm{Fl}}$, is plotted as a function of dark time $\tau$ and fit to single-exponential decay.

Figure 2

(a) $1/T_1$ as a function of temperature for S2, S3, and S8 samples. Symbols represent experimental data while solid lines are global fits to the model in Eq. (1). Error bars represent the standard errors from single-exponential fits. For consistency, we also plot previously reported experimental data [22, 23]. (b) $A_1$ [Eq. (1)] versus [NV]. (c) $1/T_1$ (squares) and fluorescence intensity (circles) at 30 K versus position on the sample with a spatially varying electron irradiation dose. A magnetic field, $B\approx 25\mathrm{G}$ was applied along [100] direction for all measurements presented in this figure.

Figure 3

(a) $1/T_1$ as a function of the magnetic field $\mathbf{B}$ applied along [111] direction (the corresponding transition frequencies are shown on the upper axis) for S2 sample at two different temperatures 296 and 20 K. $1/T_1$ was measured for the subensemble of NV centers aligned with $\mathbf{B}$. Solid line represents a fit (see text). (b) Transition frequencies between magnetic sublevels of NV centers and between sublevels of N as a function of magnetic field along [111] direction. NV-NV cross relaxation occurs at 0 G and 595 G and NV-N at 514 G. Solid lines correspond to the centers aligned with [111]; dashed lines correspond to the NV centers aligned at an $\approx 109°$ to this axis.