Dipolar-octupolar correlations and hierarchy of exchange interactions in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi mathvariant="normal">Ce</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:msub> <mml:mi mathvariant="normal">Hf</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:msub> <mml:mi mathvariant="normal">O</mml:mi> <mml:mn>7</mml:mn> </mml:msub> </mml:math>
Bibliographic record
Abstract
High-resolution neutron spectroscopy on <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:msub> <a:mi mathvariant="normal">Ce</a:mi> <a:mn>2</a:mn> </a:msub> <a:msub> <a:mi mathvariant="normal">Hf</a:mi> <a:mn>2</a:mn> </a:msub> <a:msub> <a:mi mathvariant="normal">O</a:mi> <a:mn>7</a:mn> </a:msub> </a:math> reveals a correlated state characterized by distinct dipolar scattering signals—quasielastic and inelastic contributions consistent with ‘photon’ and ‘spinon’ excitations in quantum spin ice. These signals coexist with weak octupolar scattering. Fits of thermodynamic data using numerical methods indicate a dominant octupolar exchange, <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:msub> <e:mi>J</e:mi> <e:mi>x</e:mi> </e:msub> </e:math> or <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"> <f:msub> <f:mi>J</f:mi> <f:mi>y</f:mi> </f:msub> </f:math> , with substantial dipolar <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:msub> <g:mi>J</g:mi> <g:mi>z</g:mi> </g:msub> </g:math> and minute dipole-octupole <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"> <h:msub> <h:mi>J</h:mi> <h:mrow> <h:mi>x</h:mi> <h:mi>z</h:mi> </h:mrow> </h:msub> </h:math> couplings. The <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"> <i:msub> <i:mi>J</i:mi> <i:mrow> <i:mi>x</i:mi> <i:mi>z</i:mi> </i:mrow> </i:msub> </i:math> value is corroborated by an independent fit of the neutron scattering amplitude balance between dipolar and octupolar ‘photon’ contributions, highlighting its importance to understand neutron scattering results in this family. <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"> <j:msub> <j:mi mathvariant="normal">Ce</j:mi> <j:mn>2</j:mn> </j:msub> <j:msub> <j:mi mathvariant="normal">Hf</j:mi> <j:mn>2</j:mn> </j:msub> <j:msub> <j:mi mathvariant="normal">O</j:mi> <j:mn>7</j:mn> </j:msub> </j:math> enriches the landscape of dipole-octupole pyrochlore physics, and reveals a ‘quantum multipolar liquid’ where hybrid correlations involve multiple terms in the moment series expansion, opening questions regarding their intertwining and hierarchy in quantum phases.
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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 | 0.003 | 0.002 |
| Meta-epidemiology (narrow) | 0.003 | 0.005 |
| Meta-epidemiology (broad) | 0.002 | 0.006 |
| Bibliometrics | 0.001 | 0.004 |
| Science and technology studies | 0.003 | 0.003 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.005 | 0.007 |
| Research integrity | 0.002 | 0.007 |
| Insufficient payload (model declined to judge) | 0.165 | 0.004 |
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".