Measurement of paramagnetic spin concentration in a solid-state system 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 ($T_2$) 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 preset work, we show a method to determine a wide range of the nitrogen concentration ($n$) 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.