Title: Spin-dependent photodynamics of boron-vacancy centers in hexagonal boron nitride

Abstract: The negatively-charged boron vacancy (V$_\text{B}^-$) center in hexagonal boron nitride (hBN) is currently garnering considerable attention for the design of two-dimensional (2D) quantum sensing units. Such developments require a precise understanding of the spin-dependent optical response of V$_\text{B}^-$ centers, which still remains poorly documented despite its key role for sensing applications. Here we investigate the spin-dependent photodynamics of V$_\text{B}^-$ centers in hBN by a series of time-resolved photoluminescence (PL) measurements. We first introduce a robust all-optical method to infer the spin-dependent lifetime of the excited states and the electron spin polarization of V$_\text{B}^-$ centers under optical pumping. Using these results, we then analyze PL time traces recorded at different optical excitation powers with a seven-level model of the V$_\text{B}^-$ center and we extract all the rates involved in the spin-dependent optical cycles, both under ambient conditions and at liquid helium temperature. These findings are finally used to study the impact of a vector magnetic field on the optical response. More precisely, we analyze PL quenching effects resulting from electron spin mixing induced by the magnetic field component perpendicular to the V$_\text{B}^-$ quantization axis. All experimental results are well reproduced by the seven-level model, illustrating its robustness to describe the spin-dependent photodymanics of V$_\text{B}^-$ centers. This work provides important insights into the properties of V$_\text{B}^-$ centers in hBN, which are valuable for future developments of 2D quantum sensing units.