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---has remained largely unexplored. In this study, we present a systematic first-principles investigation of the negatively charged boron-vacancy (${\mathrm{V}}_{\text{B}}^{\ensuremath{-}}$) defect in monolayer boron nitride (BN), as well as in ${\mathrm{AA}}^{\ensuremath{'}}$-stacked hexagonal BN (hBN) and ABC-stacked rhombohedral BN (rBN). Our results reveal that the ${T}_{1}$ times of ${\mathrm{V}}_{\text{B}}^{\ensuremath{-}}$ in monolayer BN and hBN are nearly identical at room temperature. Surprisingly, despite the symmetry reduction in rBN that opens additional spin relaxation channels, ${\mathrm{V}}_{\text{B}}^{\ensuremath{-}}$ 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 ${\mathrm{V}}_{\text{B}}^{\ensuremath{-}}$ in rBN offers enhanced spin coherence properties, making it a promising candidate for quantum technology applications.