Systematic investigation of dynamic nuclear polarization with boron vacancy in hexagonal boron nitride

Dynamic nuclear polarization (DNP) using the boron vacancy ($\mathrm{V_B^-}$) in hexagonal boron nitride (hBN) has gained increasing attention. Understanding this DNP requires systematically investigating the optically detected magnetic resonance (ODMR) spectra and developing a model that quantitatively describes its behavior. Here, we measure the ODMR spectra of $\mathrm{V_B^-}$ in $\mathrm{h}^{10}\mathrm{B}^{15}\mathrm{N}$ over a wide magnetic field range, including the ground state level anti-crossing (GSLAC), and compare them with the results of the Lindblad-based simulation that considers a single electron spin and three neighboring $^{15}\mathrm{N}$ nuclear spins. Our simulation successfully reproduces the experimental spectra, including the vicinity of GSLAC. It can explain the overall behavior of the magnetic field dependence of the nuclear spin polarization estimated using the Lorentzian fitting of the spectra. Despite such qualitative agreement, we also demonstrate that the fitting methods cannot give accurate polarizations. Finally, we discuss that symmetry-induced mechanisms of $\mathrm{V_B^-}$ limit the maximum polarization. Our study is an essential step toward a quantitative understanding of DNP using defects in hBN and its quantum applications.