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>
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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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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 | 0.012 | 0.009 |
| Meta-epidemiology (narrow) | 0.006 | 0.013 |
| Meta-epidemiology (broad) | 0.002 | 0.011 |
| Bibliometrics | 0.004 | 0.008 |
| Science and technology studies | 0.008 | 0.012 |
| Scholarly communication | 0.010 | 0.013 |
| Open science | 0.013 | 0.014 |
| Research integrity | 0.013 | 0.011 |
| Insufficient payload (model declined to judge) | 0.984 | 0.011 |
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 it