Nuclear spin-mediated relaxation mechanisms of the V B − \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\rm{V}}}_{{\rm{B}}}^{-}$$\end{document} center in hBN

Abstract The negatively charged boron vacancy ( V B − \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\rm{V}}}_{{\rm{B}}}^{-}$$\end{document} ) defect in hexagonal boron nitride has recently emerged as a promising spin qubit for sensing due to its high-temperature spin control and versatile integration into van der Waals structures. While extensive experiments have explored their coherence properties, much less is known about the spin relaxation time ( T 1 ) and its control parameter dependence. In this work, we develop a parameter-free spin dynamics model based on the cluster expansion technique to investigate T 1 relaxation mechanisms at low temperature. Our results reveal that the V B − \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\rm{V}}}_{{\rm{B}}}^{-}$$\end{document} center constitutes a strongly coupled electron spin-nuclear spin core, which necessitates the inclusion of the coherent dynamics and derived memory effects of the three nearest-neighbor nitrogen nuclear spins. Using this framework, this work closely reproduces the experimentally observed T 1 time at B = 90 G and further predicts the T 1 dependence on external magnetic field in the 0≤ B ≤2000 G interval, when the spin relaxation is predominantly driven by electron-nuclear and nuclear-nuclear flip-flop processes mediated by hyperfine and dipolar interactions. This study establishes a reliable and scalable approach for describing T 1 relaxation in V B − \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\rm{V}}}_{{\rm{B}}}^{-}$$\end{document} centers and offers microscopic insights to support future developments in nuclear-spin-based quantum technologies.