Nuclear Spin-Mediated Relaxation Mechanisms of the V$_{B}^-$ Center in hBN

TL;DR

This paper develops a detailed, parameter-free model to understand the nuclear spin-mediated relaxation mechanisms of the V$_{B}^-$ center in hBN, matching experimental data and predicting magnetic field dependence of relaxation times.

Contribution

It introduces a comprehensive spin dynamics model incorporating nuclear spins, providing new insights into relaxation mechanisms and guiding future quantum technology applications.

Findings

Reproduces experimental T₁ times at 90 G

Predicts T₁ dependence on magnetic field up to 2000 G

Highlights the role of electron-nuclear and nuclear-nuclear flip-flops

Abstract

The negatively charged boron vacancy $V_B^-$ defect in hexagonal boron nitride (hBN) 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 $V_B^-$ 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 $B = 90\,\mathrm{G}$ and further predicts the $T_1$ dependence on external magnetic field in the $0 \le B \le 2000\,\mathrm{G}$ 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 $V_B^-$ centers and offers microscopic insights to support future developments in nuclear-spin-based quantum technologies.