Dynamical-mean-field cluster-correlation expansion of NV- spin-echo decoherence in a realistic substitutional-nitrogen bath
Abstract
The Hahn-echo time T2 of nitrogen-vacancy (NV-) ensembles in nitrogen-rich diamond follows the empirical relation T2·[N] = 160 μs ppm, and this relation does not depend on the magnetic field between 2 and 30 mT. Cluster-correlation-expansion (CCE) calculations solve the spin dynamics exactly within small groups of spins. When they treat the Overhauser field of the surrounding P1 centres, that is, the field that these electron spins produce, as frozen, they overestimate T2 at high field by up to a factor of two. This excess was recently attributed to additional dark defects. We show that the excess comes mostly from the frozen field. In our model the P1 centres outside each cluster flip-flop in pairs: two centres exchange their spin states and conserve their total Sz. Kinetic Monte Carlo generates these events at golden-rule rates, which follow from the dipolar Hamiltonian without adjustable parameters, and each cluster evolves in the resulting time-dependent field. This dynamical mean field lies between the static-mean-field and mean-field-free limits. For a 14N P1 bath it reduces T2·[N] at 30 mT from 264 ± 16 to 188 ± 12 μs ppm and gives 167 ± 11 μs ppm at 10 mT, 1.7 and 0.4 standard deviations from experiment, with no dark spins. When each centre jumps independently, T2·[N] is 147 ± 9 μs ppm at 30 mT; the correlation of the flip-flop partners thus lengthens T2 by 20-30 percent at high field. The Overhauser field is neither frozen nor averaged out by fast motion: 68-83 percent of its autocorrelation survives 200 μs. At 2.5 mT, where the P1 electron and nucleus hybridise, T2 stays below experiment for any choice of rates. Part of the field dependence therefore remains: T2 rises by a factor 1.69 ± 0.07 instead of 2.15 ± 0.08 from 2.5 to 30 mT.
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BibTeX
@misc{shinei2026dynamicalmeanfield,
title = {{Dynamical-mean-field cluster-correlation expansion of NV$^-$ spin-echo decoherence in a realistic substitutional-nitrogen bath}},
author = {Chikara Shinei},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.02528},
eprint = {2611.02528},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.02528},
}
RIS
TY - UNPB
TI - Dynamical-mean-field cluster-correlation expansion of NV^- spin-echo decoherence in a realistic substitutional-nitrogen bath
AU - Chikara Shinei
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.02528
UR - https://arxiv.org/abs/2611.02528
AB - The Hahn-echo time T_2 of nitrogen-vacancy (NV^-) ensembles in nitrogen-rich diamond follows the empirical relation T_2·[N] = 160 μs ppm, and this relation does not depend on the magnetic field between 2 and 30 mT. Cluster-correlation-expansion (CCE) calculations solve the spin dynamics exactly within small groups of spins. When they treat the Overhauser field of the surrounding P1 centres, that is, the field that these electron spins produce, as frozen, they overestimate T_2 at high field by up to a factor of two. This excess was recently attributed to additional dark defects. We show that the excess comes mostly from the frozen field. In our model the P1 centres outside each cluster flip-flop in pairs: two centres exchange their spin states and conserve their total S_z. Kinetic Monte Carlo generates these events at golden-rule rates, which follow from the dipolar Hamiltonian without adjustable parameters, and each cluster evolves in the resulting time-dependent field. This dynamical mean field lies between the static-mean-field and mean-field-free limits. For a ^14N P1 bath it reduces T_2·[N] at 30 mT from 264 ± 16 to 188 ± 12 μs ppm and gives 167 ± 11 μs ppm at 10 mT, 1.7 and 0.4 standard deviations from experiment, with no dark spins. When each centre jumps independently, T_2·[N] is 147 ± 9 μs ppm at 30 mT; the correlation of the flip-flop partners thus lengthens T_2 by 20-30 percent at high field. The Overhauser field is neither frozen nor averaged out by fast motion: 68-83 percent of its autocorrelation survives 200 μs. At 2.5 mT, where the P1 electron and nucleus hybridise, T_2 stays below experiment for any choice of rates. Part of the field dependence therefore remains: T_2 rises by a factor 1.69 ± 0.07 instead of 2.15 ± 0.08 from 2.5 to 30 mT.
ER -