Biquadratic antisymmetric exchange and the magnetic phase diagram of magnetoelectric<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="normal">Cu</mml:mi><mml:mi mathvariant="normal">Fe</mml:mi><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:math>
Why this work is in the frame
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Bibliographic record
Abstract
Biquadratic antisymmetric exchange terms of the form $\ensuremath{-}{[{C}_{ij}{e}_{ij}^{\ensuremath{\alpha}}{({\mathbf{s}}_{i}\ifmmode\times\else\texttimes\fi{}{\mathbf{s}}_{j})}_{z}]}^{2}$, where ${\mathbf{e}}_{ij}$ is the unit vector connecting sites $i$ and $j$ and $\ensuremath{\alpha}=x,y$, due partially to magnetoelectric coupling effects, are shown to be responsible for the spin-flop helical phase in $\mathrm{Cu}\mathrm{Fe}{\mathrm{O}}_{2}$ at low magnetic field and temperature. Usual biquadratic symmetric exchange, likely due to magnetoelastic coupling, is found to support the stability of axial magnetic states at higher fields in this nearly-Heisenberg-like stacked triangular antiferromagnet. A model Hamiltonian which also includes substantial interplane and higher-neighbor intraplane exchange interactions reproduces the unique series of observed commensurate and incommensurate periodicity phases with increasing applied magnetic field in this highly frustrated system. The magnetic-field--temperature phase diagram is discussed in terms of a Landau-type free energy.
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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 | 0.005 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.002 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.003 |
| Science and technology studies | 0.002 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.236 | 0.003 |
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