Single-Crystal Diffuse Neutron Scattering Study of the Dipole-Octupole Quantum Spin-Ice Candidate <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>Ce</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> <mml:msub> <mml:mrow> <mml:mi>Zr</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> <mml:msub> <mml:mrow> <mml:mi mathvariant="normal">O</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>7</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> : No Apparent Octupolar Correlations Above <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>T</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0.05</mml:mn> <mml:mtext> </mml:mtext> <mml:mtext> </mml:mtext> <mml:mi mathvariant="normal">K</mml:mi> </mml:mrow> </mml:math>
Bibliographic record
Abstract
The insulating magnetic pyrochlore <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mrow> <a:msub> <a:mrow> <a:mi>Ce</a:mi> </a:mrow> <a:mrow> <a:mn>2</a:mn> </a:mrow> </a:msub> </a:mrow> <a:msub> <a:mrow> <a:mi>Zr</a:mi> </a:mrow> <a:mrow> <a:mn>2</a:mn> </a:mrow> </a:msub> <a:msub> <a:mrow> <a:mi mathvariant="normal">O</a:mi> </a:mrow> <a:mrow> <a:mn>7</a:mn> </a:mrow> </a:msub> </a:mrow> </a:math> has gained attention as a quantum spin-ice candidate with dipole-octupole character that arises from the crystal-electric-field ground-state doublet for the <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"> <d:mrow> <d:msup> <d:mrow> <d:mi>Ce</d:mi> </d:mrow> <d:mrow> <d:mn>3</d:mn> <d:mo>+</d:mo> </d:mrow> </d:msup> </d:mrow> </d:math> Kramers ion. This dipole-octupole character permits both spin-ice phases based on magnetic dipoles and those based on more-exotic octupoles. This work reports low-temperature neutron diffraction measurements on single-crystal <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"> <f:mrow> <f:mrow> <f:msub> <f:mrow> <f:mi>Ce</f:mi> </f:mrow> <f:mrow> <f:mn>2</f:mn> </f:mrow> </f:msub> </f:mrow> <f:msub> <f:mrow> <f:mi>Zr</f:mi> </f:mrow> <f:mrow> <f:mn>2</f:mn> </f:mrow> </f:msub> <f:msub> <f:mrow> <f:mi mathvariant="normal">O</f:mi> </f:mrow> <f:mrow> <f:mn>7</f:mn> </f:mrow> </f:msub> </f:mrow> </f:math> with <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mi>Q</i:mi> </i:math> coverage both at low <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mi>Q</k:mi> </k:math> , where the magnetic form factor for dipoles is near maximal, and at high <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mi>Q</m:mi> </m:math> , covering the region where the magnetic form factor for <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:mrow> <o:msup> <o:mrow> <o:mi>Ce</o:mi> </o:mrow> <o:mrow> <o:mn>3</o:mn> <o:mo>+</o:mo> </o:mrow> </o:msup> </o:mrow> </o:math> octupoles is near maximal. This study was motivated by recent powder neutron diffraction studies of other Ce-based dipole-octupole pyrochlores, <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:mrow> <q:mrow> <q:msub> <q:mrow> <q:mi>Ce</q:mi> </q:mrow> <q:mrow> <q:mn>2</q:mn> </q:mrow> </q:msub> </q:mrow> <q:msub> <q:mrow> <q:mi>Sn</q:mi> </q:mrow> <q:mrow> <q:mn>2</q:mn> </q:mrow> </q:msub> <q:msub> <q:mrow> <q:mi mathvariant="normal">O</q:mi> </q:mrow> <q:mrow> <q:mn>7</q:mn> </q:mrow> </q:msub> </q:mrow> </q:math> and <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"> <t:mrow> <t:mrow> <t:msub> <t:mrow> <t:mi>Ce</t:mi> </t:mrow> <t:mrow> <t:mn>2</t:mn> </t:mrow> </t:msub> </t:mrow> <t:msub> <t:mrow> <t:mi>Hf</t:mi> </t:mrow> <t:mrow> <t:mn>2</t:mn> </t:mrow> </t:msub> <t:msub> <t:mrow> <t:mi mathvariant="normal">O</t:mi> </t:mrow> <t:mrow> <t:mn>7</t:mn> </t:mrow> </t:msub> </t:mrow> </t:math> , which each showed temperature-dependent diffuse diffraction at high <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"> <w:mi>Q</w:mi> </w:math> , interpreted as arising from octupolar correlations. Our measurements use an optimized single-crystal diffuse scattering instrument that allows us to screen against strong Bragg scattering from <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"> <y:mrow> <y:mrow> <y:msub> <y:mrow> <y:mi>Ce</y:mi> </y:mrow> <y:mrow> <y:mn>2</y:mn> </y:mrow> </y:msub> </y:mrow> <y:msub> <y:mrow> <y:mi>Zr</y:mi> </y:mrow> <y:mrow> <y:mn>2</y:mn> </y:mrow> </y:msub> <y:msub> <y:mrow> <y:mi mathvariant="normal">O</y:mi> </y:mrow> <y:mrow> <y:mn>7</y:mn> </y:mrow> </y:msub> </y:mrow> </y:math> . The temperature-difference neutron diffraction reveals a low- <bb:math xmlns:bb="http://www.w3.org/1998/Math/MathML" display="inline"> <bb:mi>Q</bb:mi> </bb:math> peak consistent with dipolar spin-ice correlations reported in previous work, and an alternation between positive and negative net intensity at higher <db:math xmlns:db="http://www.w3.org/1998/Math/MathML" display="inline"> <db:mi>Q</db:mi> </db:math> . These features are consistent with our numerical-linked-cluster calculations using pseudospin interaction parameters previously reported for <fb:math xmlns:fb="http://www.w3.org/1998/Math/MathML" display="inline"> <fb:mrow> <fb:mrow> <fb:msub> <fb:mrow> <fb:mi>Ce</fb:mi> </fb:mrow> <fb:mrow> <fb:mn>2</fb:mn> </fb:mrow> </fb:msub>
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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 | 0.009 | 0.007 |
| Meta-epidemiology (narrow) | 0.006 | 0.012 |
| Meta-epidemiology (broad) | 0.003 | 0.012 |
| Bibliometrics | 0.003 | 0.008 |
| Science and technology studies | 0.009 | 0.010 |
| Scholarly communication | 0.009 | 0.010 |
| Open science | 0.014 | 0.014 |
| Research integrity | 0.010 | 0.011 |
| Insufficient payload (model declined to judge) | 0.801 | 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 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".