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In this paper cross-relaxation between nitrogen-vacancy (NV) centers andsubstitutional nitrogen in a diamond crystal was studied. It was demonstratedthat optically detected magnetic resonance signals (ODMR) can be used tomeasure these signals successfully. The ODMR were detected at axial magneticfield values around 51.2~mT in a diamond sample with a relatively high(200~ppm) nitrogen concentration. We observed transitions that involve magneticsublevels that are split by the hyperfine interaction. Microwaves in thefrequency ranges from 1.3 GHz to 1.6 GHz ($m_S=0\longrightarrow m_S=-1$ NVtransitions) and from 4.1 to 4.6 GHz ($m_S=0\longrightarrow m_S=+1$ NVtransitions) were used.  To understand the cross-relaxation process in more detail and, as a result,reproduce measured signals more accurately, a model was developed thatdescribes the microwave-initiated transitions between hyperfine levels of theNV center that are undergoing anti-crossing and are strongly mixed in theapplied magnetic field. Additionally, we simulated the extent to which themicrowave radiation used to induce ODMR in the NV center also inducedtransitions in the substitutional nitrogen via cross-relaxation.  The improved understanding of the NV processes in the presence of a magneticfield will be useful for designing NV-diamond-based devices for a wide range ofapplications from implementation of q-bits to hyperpolarization of largemolecules to various quantum technological applications such as field sensors.

Cross-relaxation studies with optically detected magnetic resonances in nitrogen-vacancy centers in diamond in an external magnetic field