Assignment of ¹³C hyperfine interactions in the P1-center in diamond

Diamond is an attractive material due to its extreme physical properties, and has recently found a key role in the developing field of quantum bits based upon long spin coherence times at room temperature. In both natural and synthetic diamond, nitrogen is probably the dominant impurity, with the simplest configuration being substitution of a host carbon atom, which has a single unpaired electron. This defect, seen as the P1 paramagnetic resonance center, has been the subject of detailed experimental investigation, revealing the extensive interaction of the electron spin with nearby ¹³C nuclei. The interaction between the electron and nuclear spins is not only of importance in determining defect structure, but is of technological importance, such as in the main decoherence mechanism for NV centers, so understanding the coupling between ¹³C and the electron spin is of critical importance. In this paper we assess the assignment of hyperfine interactions to the various carbon sites in the vicinity of the nitrogen atom. We show that although the experimentally derived model is correct in the main, the best fit to the calculated data requires reassignment of at least one of the carbon sites.