Phase transition and thermal order-by-disorder in the pyrochlore antiferromagnet Er<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mrow/><mml:mn>2</mml:mn></mml:msub></mml:math>Ti<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mrow/><mml:mn>2</mml:mn></mml:msub></mml:math>O<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mrow/><mml:mn>7</mml:mn></mml:msub></mml:math>: A high-temperature series expansion study
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Bibliographic record
Abstract
We use a high-temperature series expansion method to study the phenomenon of thermal order-by-disorder in the rare-earth pyrochlore material Er${}_{2}$Ti${}_{2}$O${}_{7}$ on its approach to the critical temperature ${T}_{c}$. We show that its anisotropic exchange parameters, ${{J}_{e}}$, characterizing an effective spin-1/2 model and recently determined from high-field inelastic neutron scattering spectra, describe very well the thermodynamic properties of the material in the paramagnetic phase and near ${T}_{c}$. While different $\mathbit{q}=0$ $XY$ order-parameter susceptibilities show a high degree of degeneracy, a nonlinear susceptibility, related to the sixth power of the order parameter, reveals a thermal order-by-disorder selection of the same noncollinear ``${\ensuremath{\psi}}_{2}$ state'' as found in Er${}_{2}$Ti${}_{2}$O${}_{7}$. Our results provide a rather definite quantitative demonstration that thermal order-by-disorder is operating at ${T}_{c}$ in this frustrated quantum spin-1/2 antiferromagnetic material.
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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 | 0.004 | 0.002 |
| Meta-epidemiology (narrow) | 0.004 | 0.006 |
| Meta-epidemiology (broad) | 0.002 | 0.005 |
| Bibliometrics | 0.001 | 0.004 |
| Science and technology studies | 0.004 | 0.004 |
| Scholarly communication | 0.004 | 0.006 |
| Open science | 0.005 | 0.004 |
| Research integrity | 0.004 | 0.006 |
| Insufficient payload (model declined to judge) | 0.011 | 0.006 |
Machine scores (provisional)
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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 it