Spin-Relaxation of Dipolar-Coupled Nitrogen-Vacancy Centers : The role of Double-flip Processes

We study relaxation processes of the spins of dipolar-coupled negatively charged nitrogen vacancy (NV$^-$) centers under transverse electric and magnetic fields. Specifically, we uncover regimes where flip-flop, double-flip processes as well as mixing induced by local electric fields play a significant role in NV-NV cross-relaxation. Our results are relevant for understanding decoherence in many-body spin systems as well as for high sensitivity magneto- and electro-metry with long-lived interacting solid-state spins. As a proof of principle, we present an orientation and microwave-free magnetometer based on cross-relaxation.