Dynamics and thermalization of the nuclear spin bath in the single-molecule magnet<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Mn</mml:mi><mml:mn>12</mml:mn></mml:msub><mml:mtext>−</mml:mtext><mml:mi>ac</mml:mi></mml:mrow></mml:math>: Test for the theory of spin tunneling
Bibliographic record
Abstract
The description of the tunneling of a macroscopic variable in the presence of a bath of localized spins is a subject of great fundamental and practical interest, and is relevant for many solid-state qubit designs. Most of the attention is usually given to the dynamics of the ``central spin'' (i.e., the qubit), while little is known about the spin bath itself. Here, we present a detailed study of the dynamics of the nuclear spin bath in the ${\mathrm{Mn}}_{12}\text{\ensuremath{-}}\mathrm{ac}$ single-molecule magnet, probed by NMR experiments down to very low temperatures $(T\ensuremath{\simeq}20\phantom{\rule{0.3em}{0ex}}\mathrm{mK})$. The results are critically analyzed in the framework of the Prokof'ev-Stamp theory of nuclear-spin-mediated quantum tunneling. We find that the longitudinal relaxation rate of the $^{55}\mathrm{Mn}$ nuclei in ${\mathrm{Mn}}_{12}\text{\ensuremath{-}}\mathrm{ac}$ becomes roughly $T$ independent below $T\ensuremath{\simeq}0.8\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ and can be strongly suppressed with a longitudinal magnetic field. This is consistent with the nuclear relaxation being caused by quantum tunneling of the molecular spin, and we attribute the tunneling fluctuations to the minority of fast-relaxing molecules present in the sample. The transverse nuclear relaxation is also $T$ independent for $T<0.8\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, and can be explained qualitatively and quantitatively by the dipolar coupling between like nuclei in neighboring molecules. This intercluster nuclear spin diffusion mechanism is an essential ingredient for the global relaxation of the nuclear spin bath. We also show that the isotopic substitution of $^{1}\mathrm{H}$ by $^{2}\mathrm{H}$ leads to a slower nuclear longitudinal relaxation, consistent with the decreased tunneling probability of the molecular spin. Finally, we demonstrate that even at the lowest temperatures---where only $T$-independent quantum tunneling fluctuations are present---the nuclear spins remain in thermal equilibrium with the lattice phonons, and we investigate the time scale for their thermal equilibration. After a review of the theory of macroscopic spin tunneling in the presence of a spin bath, we argue that most of our experimental results are consistent with that theory, but the thermalization of the nuclear spins is not. This calls for an extension of the spin-bath theory to include the effect of spin-phonon couplings in the nuclear-spin-mediated tunneling process.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.004 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.065 | 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 teacher head, 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".