Tuning incommensurate charge order in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>Ba</mml:mi> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>−</mml:mo> <mml:mi>x</mml:mi> </mml:mrow> </mml:msub> <mml:msub> <mml:mi>Sr</mml:mi> <mml:mi>x</mml:mi> </mml:msub> <mml:msub> <mml:mi>Al</mml:mi> <mml:mn>4</mml:mn> </mml:msub> </mml:mrow> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>Ba</mml:mi> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>−</mml:mo> <mml:mi>y</mml:mi> </mml:mrow> </mml:msub> <mml:msub> <mml:mi>Eu</mml:mi> <mml:mi>y</mml:mi> </mml:msub> <mml:msub> <mml:mi>Al</mml:mi> <mml:mn>4</mml:mn> </mml:msub> </mml:mrow> </mml:math>
Bibliographic record
Abstract
The BaAl$_4$-type structure family is home to a vast landscape of interesting and exotic properties, with descendant crystal structures hosting a variety of electronic ground states including magnetic, superconducting and strongly correlated electron phenomena. BaAl$_4$ itself hosts a non-trivial topological band structure, but is otherwise a paramagnetic metal. However, the other members of the $A$Al$_4$ family ($A$= alkali earth), including SrAl$_4$ and EuAl$_4$, exhibit symmetry-breaking ground states including charge density wave (CDW) and magnetic orders. Here we investigate the properties of the solid solution series Ba$_{1-x}$Sr$_x$Al$_4$ and Ba$_{1-y}$Eu$_y$Al$_4$ using transport, thermodynamic and scattering experiments to study the evolution of the charge-ordered state as it is suppressed with Ba substitution to zero near 50% substitution in both systems. Neutron and x-ray diffraction measurements reveal an incommensurate CDW state in SrAl$_4$ with $c$-axis-oriented ordering vector (0, 0, 0.097) that evolves with Ba substitution toward a shorter wavelength. A similar progression is observed in the Ba$_{1-y}$Eu$_y$Al$_4$ series that also scales with the ordering temperature, revealing a universal correlation between charge-order transition temperature and ordering vector that points to a critical wavevector that stabilizes CDW order in both systems. We study the evolution of the phonon band structure in the Ba$_{1-x}$Sr$_x$Al$_4$ system, revealing the suppression of the CDW phase matches the suppression of a phonon instability at precisely the same momentum as observed in experiments, confirming the electron-phonon origin of charge order in this system.
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How this classification was reachedexpand
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 | 0.015 | 0.013 |
| Meta-epidemiology (narrow) | 0.008 | 0.016 |
| Meta-epidemiology (broad) | 0.004 | 0.015 |
| Bibliometrics | 0.005 | 0.013 |
| Science and technology studies | 0.012 | 0.014 |
| Scholarly communication | 0.011 | 0.011 |
| Open science | 0.018 | 0.016 |
| Research integrity | 0.014 | 0.014 |
| Insufficient payload (model declined to judge) | 0.739 | 0.015 |
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; both teacher heads agree on what is shown here.
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".