Decoherence of ensembles of nitrogen-vacancy centers in diamond

We present a combined theoretical and experimental study of solid-state spin decoherence in an electronic spin bath, focusing specifically on ensembles of nitrogen-vacancy (NV) centers in diamond and the associated substitutional nitrogen spin bath. We perform measurements of NV spin free-induction decay (FID) times T*2 and spin-echo coherence times T2 in 25 diamond samples with nitrogen concentrations [N] ranging from 0.01 to 300 ppm. We introduce a microscopic model and perform numerical simulations to quantitatively explain the degradation of both T*2 and T2 over four orders of magnitude in [N]. Our analysis enables us to describe the NV ensemble spin coherence decay shapes as emerging consistently from the contribution of many individual NV centers.