Determination of nitrogen spin concentration in diamond using double electron-electron resonance

Diamond has been extensively investigated recently due to a wide range of potential applications of nitrogen-vacancy (NV) defect centers existing in a diamond lattice. The applications include magnetometry and quantum information technologies, and long decoherence time $\left(T_2\right)$ of NV centers is critical for those applications. Although it has been known that $T_2$ highly depends on the concentration of paramagnetic impurities in diamond, precise measurement of the impurity concentration remains challenging. In the present work we show a method to determine a wide range of the nitrogen concentration $\left(n\right)$ in diamond using a wide-band high-frequency electron spin resonance and double electron-electron resonance spectrometer. Moreover, we investigate $T_2$ of the nitrogen impurities and show the relationship between $T_2$ and $n$. The method developed here is applicable for various spin systems in solid and implementable in nanoscale magnetic resonance spectroscopy with NV centers to characterize the concentration of the paramagnetic spins within a microscopic volume.

Figure 1

Spin echo (SE) measurements of type-Ib and type-IIa diamond crystals. (a) SE intensity as a function of magnetic fields. The applied pulse sequence is shown in the inset. In the measurement of the type-Ib diamond, the durations of $\pi /2$ and $\pi$ pulses were 150 and 250 ns and $\tau$ was 1.$5\mu \mathrm{s}$. The data were taken with 32 averages with 20 ms of the repetition time. In the measurement of the type-IIa diamond, the durations of the $\pi /2$ and $\pi$ pulses were 250 and 450 ns and $\tau$ was $3\mu \mathrm{s}$. The data were taken with 256 averages with 20 ms of the repetition time. The magnetic field was applied along the $\left[111\right]$ direction for type-Ib crystals and the $\left[100\right]$ direction for type-IIa. (b) SE intensity as a function of $\tau$ to measure spin decoherence time $T_2$. The decays of the SE were fitted by a single exponential function to extract $T_2$ (solid lines). The data of the type-Ib (type-IIa) diamond were taken with 128 (256) averages.

Figure 2

Double electron-electron resonance (DEER) spectroscopy of the type-Ib and type-IIa diamond crystals. (a) Three-pulse DEER sequence used in the experiment, where $t_1$ and $t_2$ denote duration of $\pi /2$ and $\pi$ pulses for A spins, respectively. $t_p$ is duration of $\pi$ pulse for B spins. $T$ is the delay of $t_p$ from $t_1$. (b) and (c) DEER spectrum of N spins in type-Ib and type-IIa diamonds, respectively. The DEER signals were normalized by the SE signals. Experimental parameters were $t_1=250$ ns, $t_2=450$ ns, $t_p=450$ ns, $\tau =2.5$ $\mu \mathrm{s},T=2$ $\mu \mathrm{s}$ in case of type-Ib diamond, and $t_1=250$ ns, $t_2=450$ ns, $t_p=450$ ns, $\tau =110$ $\mu \mathrm{s},T=109.45$ $\mu \mathrm{s}$ in case of type-IIa diamond. The data of the type-Ib (type-IIa) diamond were taken with 128 (256) averages. Purple and brown dashed lines represent the best fit of experimental data using Eq. (10).

Figure 3

(a) Analyses of a single exponential SE decay with $T_2=950$ ns (cyan) using Eq. (1). 4.9, 2.9, and 2 kHz of $W_{\text{max}}$ were obtained from the fits for 60 (black square), 80 (red diamond), and 100 (pink circle) ppm of N concentrations, respectively. (b) Flip-flop rate distribution among N spins obtained using Eq. (2) for 4.9 (black), 2.9 (red), and 2 kHz (pink) of $W_{\text{max}}$.

Figure 4

Schematics for the DEER model. $L\left(\xi \right)$ is the lineshape function. ${\omega }_m$ is the center frequency of group $m$ $\left(m=1–5\right)$. ${\omega }_A$ and ${\omega }_B$ are microwave frequencies of the probe and pump pulses, respectively. $\omega$ and ${\omega }_j$ are the Larmor frequencies of A and B spins, respectively. $\delta$ and ${\delta }_j$ are frequency offsets of A and B spins from the pump and probe frequencies, respectively. A and B spins were chosen close to the probe and pump frequencies to indicate that spins can be excited by a respective pulse with a small frequency offsets. However, in general, as in our consideration, they can be anywhere within the lineshape $L$.

Figure 5

Fit results of DEER spectrum. Left top, middle, bottom panels show concentration $n$ of N spins, half-width $\mathrm{\Delta }\omega$ of inhomogeneous lineshape, and a fit error $\gamma$, respectively, as obtained from the fit at a fixed $t_{\mathrm{\Omega }}$ values. The top (bottom) panel on the right shows the result of the fit obtained at $t_{\mathrm{\Omega }}=100$ ns (305 ns). The result with $t_{\mathrm{\Omega }}=305$ ns is the best fit. The gray shaded area on the left indicates fits with a large $\gamma$.

Figure 6

(a) Summary of the obtained $\mathrm{\Delta }\omega$. (b) Summary of the obtained $t_{\mathrm{\Omega }}$. $t_2$ is the duration of the $\pi$ pulse used in the present study.

Figure 7

$1/T_2$ of N spins as a function of the N concentration. Open squares represent experimentally obtained data, the orange solid line is the best fit of the data to the model of decoherence rate described by Eq. (11). The yellow region represents the plot of Eq. (11) with the fixed ${\mathrm{\Gamma }}_C$ in the range of 150–$250\mu \mathrm{s}$ and a slope $C=0.0139$ $\mu {\mathrm{s}}^{-1}{\mathrm{ppm}}^{-1}$ as obtained from the best fit of the data. Dashed orange line shows the best fit of the data using Eq. (11) without the nuclear spin decoherence $\left(1/T_2^{{}^{13}\mathrm{C}}=0\right)$.