Fig. 1: \({{{{{{{{\rm{V}}}}}}}}}_{{{{{{{{\rm{B}}}}}}}}}^{-}\) electron spin resonance spectra in isotopically distinct hBN samples.

a Schematic of an individual \({{{{{{{{\rm{V}}}}}}}}}_{{{{{{{{\rm{B}}}}}}}}}^{-}\) center (red spin) in an isotopically purified h¹⁰B¹⁵N crystal. \(\hat{z}\) is defined along the c-axis (perpendicular to the lattice plane) and \(\hat{x}\) and \(\hat{y}\) lie in the lattice plane, with \(\hat{x}\) oriented along one of the three \({{{{{{{{\rm{V}}}}}}}}}_{{{{{{{{\rm{B}}}}}}}}}^{-}\) Nitrogen bonds. The table lists the nuclear spin quantum number (\({{{{{{{\mathcal{I}}}}}}}}\)), gyromagnetic ratio (γ_n), and overall electronic spin transition width (\(\propto 2| {\gamma }_{n}{{{{{{{\mathcal{I}}}}}}}}|\)) of the four stable atomic isotopes in hBN. b Energy level diagram of the \({{{{{{{{\rm{V}}}}}}}}}_{{{{{{{{\rm{B}}}}}}}}}^{-}\) electronic ground state coupled to the three nearest-neighbor ¹⁵N nuclear spins (\({{{{{{{\mathcal{I}}}}}}}}=\frac{1}{2}\)) under an external magnetic field B_z. For each electronic spin transition \(\left|{m}_{s}=0\right\rangle \leftrightarrow \left|{m}_{s}=\pm 1\right\rangle\), the hyperfine interaction leads to four distinct resonances with total nuclear spin magnetic quantum number \(\sum {m}_{I}=\{-\frac{3}{2},-\frac{1}{2},\frac{1}{2},\frac{3}{2}\}\) of degeneracy {1, 3, 3, 1}. c Measured ESR spectra of \({{{{{{{{\rm{V}}}}}}}}}_{{{{{{{{\rm{B}}}}}}}}}^{-}\) in h¹⁰B¹⁵N and naturally abundant hBN_nat at magnetic field B_z ≈ 87 G. Solid lines represent multi-peak Lorentzian fits, and shaded regions represent numerically simulated transitions considering the 36 nearest nuclear spins (18 nitrogen and 18 boron atoms; see Methods). Insets: ESR spectra at B_z = 0 G. Source data are provided as a Source Data file.