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
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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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 | 0.001 | 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) | 0.017 | 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".