Fig. 2: Possible interactions of a \({{\rm{V}}}_{{\rm{B}}}^{-}\) defect in hBN.

a Spin density of the \({{\rm{V}}}_{B}^{-}\) defect, highlighting various interactions. The hyperfine interactions (Eq. (4)) are represented by gray wavy lines, while the dipole-dipole interactions between nuclear spins, including nitrogen-nitrogen, boron-boron, and nitrogen-boron interactions, are depicted by blue, pink, and green wavy lines, respectively (corresponding to the second term in Eq. (3)). The interactions of both electron and nuclear spins with an external magnetic field are present but not explicitly visualized in this figure. The spin density illustrates the localized wavefunction, which correlates with the strength of the hyperfine interaction. b Rotational invariant perpendicular hyperfine components in decreasing order plotted in a log-log scale. The steps indicate different neighboring shells. The first three nearest-neighbor nitrogen nuclei exhibit an extraordinarily strong hyperfine interaction, indicating a strongly induced spin flip-flop process.