Magnetic field dependence of $V_B^-$ Defects in hexagonal boron nitride

The interface with spin defects in hexagonal boron nitride has recently become a promising platform and has shown great potential in a wide range of quantum technologies. Varieties of spin properties of $V_B^-$ defects in hexagonal boron nitride (hBN) have been researched widely and deeply, like their structure and coherent control. However, little is known about the influence of off-axis magnetic fields on the coherence properties of $V_B^-$ defects in hBN. Here, by using the optically detected magnetic resonance (ODMR) spectroscopy, we systematically investigated the variations in ODMR resonance frequencies under different transverse and longitudinal external magnetic field, respectively. In addition, we measured the ODMR spectra under off-axis magnetic fields of constant strength but various angles, and observed that the splitting of the resonance frequencies decreases as the angle increases, aligning with our theoretical calculation based on the Hamiltonian, from which we come up with a solution of detecting the off-axis magnetic field angle. Through Rabi oscillation measurements, we found that the off-axis magnetic field suppresses the spin coherence time. These results are crucial for optimizing $V_B^-$ defects in hBN, establishing their significance as robust quantum sensors for quantum information processing and magnetic sensing in varied environments.