Order by Disorder Spin Wave Gap in the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>X</mml:mi><mml:mi>Y</mml:mi></mml:math>Pyrochlore Magnet<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>Er</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mi>Ti</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>
Why this work is in the frame
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Bibliographic record
Abstract
The recent determination of a robust spin Hamiltonian for the antiferromagnetic $XY$ pyrochlore ${\mathrm{Er}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$ reveals a most convincing case of the ``Order-by-Quantum-Disorder'' mechanism for ground state selection. This mechanism relies on quantum fluctuations to remove an accidental symmetry of the magnetic ground state, and selects a particular ordered spin structure below ${T}_{N}=1.2 \mathrm{K}$. The removal of the continuous degeneracy results in an energy gap in the spectrum of spin wave excitations, long wavelength pseudo-Goldstone modes. We have measured the Order-by-Quantum-Disorder spin wave gap at a zone center in ${\mathrm{Er}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$, using low incident energy neutrons and the time-of-flight inelastic scattering method. We report a gap of $\mathrm{\ensuremath{\Delta}}=0.053\ifmmode\pm\else\textpm\fi{}0.006\text{ }\text{ }\mathrm{meV}$, which is consistent with upper bounds placed on it from heat capacity measurements and roughly consistent with the theoretical estimate of $\ensuremath{\sim}0.02\text{ }\text{ }\mathrm{meV}$, further validating the spin Hamiltonian that led to that prediction. The gap is observed to vary with the square of the order parameter, and goes to zero for $T\ensuremath{\sim}{T}_{N}$.
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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 | 0.007 | 0.006 |
| Meta-epidemiology (narrow) | 0.004 | 0.009 |
| Meta-epidemiology (broad) | 0.002 | 0.009 |
| Bibliometrics | 0.002 | 0.006 |
| Science and technology studies | 0.006 | 0.008 |
| Scholarly communication | 0.007 | 0.007 |
| Open science | 0.011 | 0.009 |
| Research integrity | 0.007 | 0.009 |
| Insufficient payload (model declined to judge) | 0.896 | 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 it