Surface spin hopping dynamics on diamond surfaces*

Unpaired surface electronic spins (dark spins) on a diamond surface, arising from dangling bonds, are recognized as a major source of magnetic noise, and they limit the practical utility of NV-based quantum sensors. To either suppress these dark spins or harness them as a quantum resource, a comprehensive understanding of their dynamics is crucial. Recent experimental observations have indicated that surface dark spins can change their positions between measurements, with approximately 80% of them undergoing hopping [1].

Consequently, any static model for these surface spins is inadequate for accurately describing their dynamics. Utilizing experimentally derived density data for dark spins on a diamond surface, we present a reliable model based on multisite spin-hopping that effectively accounts for both coherent (tunneling) and incoherent (hopping) dynamics. Our study shows how the dynamics of dark spins affects the decoherence of near-surface NV center spin qubits. We also uncover how the stretched exponent of the coherence function, which characterizes the noise of the qubit environment, depends on the inter-spin distances on the surface and the depth of the NV center.

Our results provide a way to accurately describe surface spin noise and underscore the potential of spin qubits for characterizing both the static and dynamical properties of interacting surface spin baths.