Hyperfine interaction in the ground state of the negatively charged nitrogen vacancy center in diamond

The ${}^{14}\text{N}$, ${}^{15}\text{N}$, and ${}^{13}\text{C}$ hyperfine interactions in the ground state of the negatively charged nitrogen vacancy $\left({\text{NV}}^{-}\right)$ center have been investigated using electron-paramagnetic-resonance spectroscopy. The previously published parameters for the ${}^{14}\text{N}$ hyperfine interaction do not produce a satisfactory fit to the experimental ${\text{NV}}^{-}$ electron-paramagnetic-resonance data. The small anisotropic component of the ${\text{NV}}^{-}$ hyperfine interaction can be explained from dipolar interaction between the nitrogen nucleus and the unpaired-electron probability density localized on the three carbon atoms neighboring the vacancy. Optical spin polarization of the ${\text{NV}}^{-}$ ground state was used to enhance the electron-paramagnetic-resonance sensitivity enabling detailed study of the hyperfine interaction with ${}^{13}\text{C}$ neighbors. The data confirmed the identification of three equivalent carbon nearest neighbors but indicated the next largest ${}^{13}\text{C}$ interaction is with six, rather than as previously assumed three, equivalent neighboring carbon atoms.

Figure 1

Projection of the nitrogen vacancy center in diamond on the $\left(1\overline{1}0\right)$ plane. The grey disc represents a nitrogen atom and the other circles represent carbon atoms. The larger circles represent carbon atoms located above the plane of the paper and the smaller dashed circles represent carbon atoms below the plane of the paper. The labels on the carbon atoms denote sets of equivalent neighbors.

Figure 2

First harmonic EPR spectra of the half-field, $M_S=-1\to 1$, transitions for the ${}^{14}\text{N}{\text{V}}^{-}$ defect with the magnetic field $\mathbf{B}$ applied along $⟨110⟩$. The squares show the experimental data points recorded for the ${}^{14}\text{N}$-doped sample A and the lines show the simulated spectrum using (a) the parameters from He et al. (Ref. 24) and (b) the parameters determined in this study. The spectrum is complicated due to the similar magnitudes of the nitrogen hyperfine, nuclear Zeeman, and quadrupole interactions, which results in considerable nuclear spin-state mixing such that $m_I$ is no longer a good quantum number.

Figure 3

First harmonic EPR spectra of the half-field, $M_S=-1\to 1$, transitions with the magnetic field $\mathbf{B}$ applied along $⟨001⟩$ for (a) ${}^{14}\text{N}{\text{V}}^{-}$ and (b) ${}^{15}\text{N}{\text{V}}^{-}$. The squares represent the experimental data points measured in (a) sample A and (b) sample C. The lines show the simulated spectrum using the hyperfine parameters determined in this study. The experimental spectrum in (b) is modulation broadened, which is accounted for in the fit through pseudomodulation. Note how the confusion of lines due to spin-state mixing resulting from the similarity in magnitude of the ${}^{14}\text{N}$ hyperfine, nuclear Zeeman, and quadrupole interactions in (a) simplifies to the two line spectrum of (b) with clear $m_I=\frac{1}{2}$ lower field and $m_I=-\frac{1}{2}$ higher field lines when ${}^{14}\text{N}$ is substituted with ${}^{15}\text{N}$.

Figure 4

Optically excited EPR spectrum from the ${}^{15}\text{N}$-doped sample B recorded with the magnetic field $\mathbf{B}$ applied along $⟨111⟩$, showing the $M_S=0\to 1$ transitions for the defects with their axes parallel to the magnetic field. The upper black line shows the second-harmonic experimental spectrum and the lower grey line shows the simulated spectrum using the spin-Hamiltonian parameters from Tables . The intensities of the ${}^{13}\text{C}$ satellites in the simulated spectrum correspond to three and six equivalent C-atom positions.

Figure 5

Projection of the nitrogen vacancy center in diamond on the (111) plane, showing equivalent sets of C neighbors. The labeling system is the same as that used in Fig. 1.