Muon spin relaxation studies of incommensurate magnetism and superconductivity in stage-4<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">La</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 mathvariant="normal">CuO</mml:mi></mml:mrow><mml:mrow><mml:mn>4.11</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">La</mml:mi></mml:mrow><mml:mrow><mml:mn>1.88</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Sr</mml:mi></mml:mrow><mml:mrow><mml:mn>0.12</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">CuO</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>
Bibliographic record
Abstract
We report muon spin relaxation $(\ensuremath{\mu}\mathrm{SR})$ measurements using single crystals of oxygen-intercalated stage-4 ${\mathrm{La}}_{2}{\mathrm{CuO}}_{4.11}$ (LCO:4.11) and ${\mathrm{La}}_{1.88}{\mathrm{Sr}}_{0.12}{\mathrm{CuO}}_{4}$ (LSCO:0.12), in which neutron scattering studies have found incommensurate magnetic Bragg reflections. In both systems, zero-field $\ensuremath{\mu}\mathrm{SR}$ measurements show muon spin precession below the N\'eel temperature ${T}_{N}$ with frequency 3.6 MHz at $\stackrel{\ensuremath{\rightarrow}}{T}0,$ having a Bessel function line shape, characteristic of spin-density-wave systems. The amplitude of the oscillating and relaxing signals of these systems is less than half the value expected for systems with static magnetic order in 100% of the volume. Our results are consistent with a simulation of local fields for a heuristic model with (a) incommensurate spin amplitude modulation with the maximum ordered Cu moment size of $\ensuremath{\sim}0.36{\ensuremath{\mu}}_{B},$ (b) static Cu moments on the ${\mathrm{CuO}}_{2}$ planes forming ``islands'' having typical radius $15--30 \mathrm{\AA{}},$ comparable to the in-plane superconducting coherence length, and (c) the measured volume fraction of magnetic muon sites ${V}_{\ensuremath{\mu}}$ increasing progressively with decreasing temperature below ${T}_{N}$ towards ${V}_{\ensuremath{\mu}}\ensuremath{\sim}40%$ for LCO:4.11 and 18% for LSCO:0.12 at $\stackrel{\ensuremath{\rightarrow}}{T}0.$ These results may be compared with correlation lengths in excess of $600 \mathrm{\AA{}}$ and a long range ordered moment of $0.15\ifmmode\pm\else\textpm\fi{}0.05{\ensuremath{\mu}}_{B}$ measured with neutron scattering techniques. In this paper we discuss a model that reconciles these apparently contradictory results. In transverse magnetic field $\ensuremath{\mu}\mathrm{SR}$ measurements, sensitive to the in-plane magnetic field penetration depth ${\ensuremath{\lambda}}_{\mathrm{ab}},$ the results for LCO:4.11 and LSCO:0.12 follow correlations found for underdoped, overdoped and Zn-doped high-${T}_{c}$ cuprate systems in a plot of ${T}_{c}$ versus the superconducting relaxation rate $\ensuremath{\sigma}(\stackrel{\ensuremath{\rightarrow}}{T}0).$ This indicates that the volume-integrated value of ${n}_{s}{/m}^{*}$ (superconducting carrier density / effective mass) is a determining factor for ${T}_{c},$ not only in high-${T}_{c}$ cuprate systems without static magnetism, but also in the present systems where superconductivity coexists with static spin-density-wave spin order.
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.009 | 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".