Spin-Phonon Relaxation of Boron-Vacancy Centers in Two-Dimensional Boron Nitride Polytypes

Two-dimensional (2D) materials hosting color centers and spin defects are emerging as key platforms for quantum technologies. However, the impact of reduced dimensionality on the spin-lattice relaxation time ($T_1$) of embedded defect spins -- critical for quantum applications -- remains largely unexplored. In this study, we present a systematic first-principles investigation of the negatively charged boron-vacancy (V$_{\text{B}}^-$) defect in monolayer boron nitride (BN), as well as in AA$^\prime$-stacked hexagonal BN (hBN) and ABC-stacked rhombohedral BN (rBN). Our results reveal that the $T_1$ times of V$_{\text{B}}^-$ in monolayer BN and hBN are nearly identical at room temperature. Surprisingly, despite the symmetry reduction in rBN opening additional spin relaxation channels, V$_{\text{B}}^-$ exhibits a longer $T_1$ compared to hBN. We attribute this effect to the stiffer out-of-plane phonon modes in rBN, which activate spin-phonon relaxation at reduced strength. These findings suggest that V$_{\text{B}}^-$ in rBN offers enhanced spin coherence properties, making it a promising candidate for quantum technology applications.