Muon Knight Shift as a Precise Probe of the Superconducting Symmetry of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>Sr</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>RuO</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>4</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> </mml:mrow> </mml:math>
Bibliographic record
Abstract
Muon spin rotation (μSR) measurements of internal magnetic field shifts, known as the muon Knight shift, are used for determining pairing symmetries in superconductors. While this technique has been especially effective for f-electron-based heavy-fermion superconductors, it remains challenging in d-electron-based superconductors such as Sr_{2}RuO_{4}, where the Knight shift is intrinsically small. Here, we report high-precision muon Knight shift measurements of superconducting Sr_{2}RuO_{4}. We observe that using multiple pieces of crystals, a common practice in μSR measurements, induces a substantial paramagnetic shift below the superconducting transition temperature, T_{c}, when a weak magnetic field is applied. We attribute such an unresolved paramagnetic shift to stray fields generated by neighboring diamagnetic crystals. To avoid this, one piece of crystal was used in this Letter. We experimentally determine the muon Knight shift of Sr_{2}RuO_{4} in the normal state to be -116±7 ppm. By combining the observed muon Knight shift with independently determined bulk magnetization data from the same crystal used in μSR and carefully separating various contributions to the shift, we confirm a significant reduction in the spin Knight shift below T_{c}, consistent with spin-singlet-like pairing. This result constitutes the precise muon Knight shift measurement in a d-electron-based superconductor. Our results highlight the potential of μSR as a powerful complementary technique to the established method of nuclear magnetic resonance for probing the spin susceptibility in superconductors.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.007 | 0.001 |
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".