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

Abstract

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.

Figures (7)

• Figure 1: 2D BN material and computed spin-phonon relaxation rates of the embedded V$_{\text{B}}^{-}$ defect spin. (a) The atomic structure of freestanding monolayer BN, the AA$^\prime$-stacked hBN, where two adjacent BN layers are rotated by angle of $\pi$, and the ABC-stacked rBN, where the layers are successively shifted in the same direction by the interatomic distance. The vacant boron site is depicted as a semitransparent green ball where the spin density is localized on the three neighbor nitrogen atoms. (b) Computed two-phonon-assisted spin-phonon relaxation rates for monolayer BN, hBN and rBN. They show universal $T^2$ power-law slope at elevated temperatures with distinct shifts.
• Figure 2: Computed spin properties of V$_{\text{B}}^{-}$ as obtained in supercell model of freestanding monolayer BN. (a) The second-order spin-phonon coupling coefficients (lines) and the spectral functions (curves) for the $12\times12$ supercell size. Double-quantum transition (red) and spin-lattice dephasing (black). The out-of-plane phonon mode corresponds to the most intense spin-phonon coupling where the relative amplitude of the vibrating nitrogen atom is shown normalized to the unity (inset). (b) Temperature dependent spin-phonon relaxation rates with various supercell sizes.
• Figure 3: Computed spin properties of V$_{\text{B}}^{-}$ as obtained in $6\times6\times2$ supercell model of hBN. (a) The second-order spin-phonon coupling coefficients (lines) and the spectral function (curves). Double-quantum transition (red) and spin-lattice dephasing (black). The out-of-plane phonon mode corresponds to the most intense spin-phonon coupling where the relative amplitude of the vibrating nitrogen atom is shown as scaled with that in monolayer BN (inset). (b) Spin-phonon relaxation rates with various supercell sizes compared to experimental data from Exp1 (circles) (see Ref. gottscholl2021room) and Exp2 (squares) (see Ref. liu2025temperature).
• Figure 4: Computed spin properties of V$_{\text{B}}^{-}$ as obtained in $6\times6\times2$ supercell model of rBN. (a) Spin-phonon spectral function with double-quantum transition (red), single-quantum transition (blue), and spin-lattice dephasing (black). The out-of-plane phonon mode corresponds to the most intense spin-phonon coupling where the relative amplitude of the vibrating nitrogen atom is shown as scaled with that in monolayer BN (inset). (b) Spin-phonon relaxation rate with double-flip transition with various supercell sizes.
• Figure 5: Computed phonon density of states for pristine and defective supercells with V$_{\text{B}}^{-}$. (a) Pristine $12\times12$ monolayer BN, (b) defective $12\times12$ monolayer BN, (c) pristine $6\times6\times2$ hBN, (d) defective $6\times6\times2$ hBN, (e) pristine $6\times6\times2$ rBN, (f) defective $6\times6\times2$ rBN.