Two-Peak Heat Capacity Accounts for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>R</mml:mi> <mml:mi>ln</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mn>2</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> Entropy and Ground State Access in the Dipole-Octupole Pyrochlore <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:mtext>Hf</mml:mtext> </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>
Bibliographic record
Abstract
Magnetic heat capacity measurements of a high-quality single crystal of the dipole-octupole pyrochlore Ce_{2}Hf_{2}O_{7} down to a temperature of T=0.02 K are reported. These show a two-peaked structure, with a Schottky-like peak at T_{1}∼0.065 K, similar to what is observed in its sister Ce pyrochlores Ce_{2}Zr_{2}O_{7} and Ce_{2}Sn_{2}O_{7}. However, a second sharper peak is observed at T_{2}∼0.025 K, signifying the entrance to the ground state. The ground state appears to have gapped excitations, as even the most abrupt extrapolation to C_{P}=0 at T=0 K fully accounts for the Rln(2) entropy associated with the pseudospin-1/2 doublet for Ce^{3+} in this environment. The ground state could be conventionally ordered, although theory predicts a much larger anomaly in C_{P} at much higher temperatures than the measured T_{2} for expectations from an all-in, all-out ground state of the XYZ Hamiltonian for Ce_{2}Hf_{2}O_{7}. The sharp low-temperature peak could also signify a crossover from a classical spin liquid to a quantum spin liquid (QSL). For both scenarios, comparison of the measured C_{P} with NLC calculations suggests that weak interactions beyond the nearest-neighbor XYZ Hamiltonian become relevant below T∼0.25 K. The diffuse magnetic neutron scattering observed from Ce_{2}Hf_{2}O_{7} at low temperatures between T_{2} and T_{1} resembles that observed from Ce_{2}Zr_{2}O_{7}, which is well established as a π-flux quantum spin ice (QSI). Together with the peak in the heat capacity at T_{2}, this diffuse scattering from Ce_{2}Hf_{2}O_{7} is suggestive of a classical spin liquid regime above T_{2} that is distinct from the zero-entropy quantum ground state below T_{2}.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.004 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.088 | 0.014 |
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".