Nuclear relaxation rates in the herbertsmithite kagome antiferromagnets <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi mathvariant="normal">ZnCu</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi mathvariant="normal">OH</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mn>6</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">Cl</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:math>
Bibliographic record
Abstract
Local spectral functions and nuclear magnetic relaxation (NMR) rates, $1/{T}_{1}$, for the spin-half Heisenberg antiferromagnet on the Kagome lattice are calculated using the Moriyas Gaussian approximation, as well as through an extrapolation of multiple frequency moments. The temperature dependence of the calculated rates is compared with the oxygen $1/{T}_{1}$ NMR data in Herbertsmithite. We find that the Gaussian approximation for $1/{T}_{1}$ shows behavior qualitatively similar to experiments with a sharp drop in rates at low temperatures, consistent with a spin-gapped behavior. However, this approximation significantly underestimates the magnitude of $1/{T}_{1}$ even at room temperature. Rates obtained from extrapolation of multiple frequency moments give very good agreement with the room temperature NMR data with $J=195\ifmmode\pm\else\textpm\fi{}20$ K and hyperfine couplings determined independently from other measurements. The use of multiple frequency moments also leads to additional low-frequency weight in the local structure factors. The convergence of our calculations with higher-frequency moments breaks down at low temperatures, suggesting the existence of longer-range dynamic correlations in the system despite the very short range static correlations.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".