Spin-Orbital Entanglement and the Breakdown of Singlets and Triplets in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><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:msub><mml:mrow><mml:mi>RuO</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>Revealed by Spin- and Angle-Resolved Photoemission Spectroscopy
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Bibliographic record
Abstract
Spin-orbit coupling has been conjectured to play a key role in the low-energy electronic structure of ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$. By using circularly polarized light combined with spin- and angle-resolved photoemission spectroscopy, we directly measure the value of the effective spin-orbit coupling to be $130\ifmmode\pm\else\textpm\fi{}30\text{ }\text{ }\mathrm{meV}$. This is even larger than theoretically predicted and comparable to the energy splitting of the ${d}_{xy}$ and ${d}_{xz,yz}$ orbitals around the Fermi surface, resulting in a strongly momentum-dependent entanglement of spin and orbital character in the electronic wavefunction. As demonstrated by the spin expectation value $⟨\stackrel{P\vec}{{s}_{k}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{P\vec}{{s}_{\ensuremath{-}k}}⟩$ calculated for a pair of electrons with zero total momentum, the classification of the Cooper pairs in terms of pure singlets or triplets fundamentally breaks down, necessitating a description of the unconventional superconducting state of ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$ in terms of these newly found spin-orbital entangled eigenstates.
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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 | 0.003 | 0.002 |
| Meta-epidemiology (narrow) | 0.002 | 0.004 |
| Meta-epidemiology (broad) | 0.001 | 0.004 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.002 | 0.004 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.004 | 0.004 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.731 | 0.001 |
Machine scores (provisional)
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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