Thermal and field evolution of spin dynamics in the alternating Heisenberg <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>J</mml:mi> <mml:mi>eff</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:mfrac> <mml:mn>1</mml:mn> <mml:mn>2</mml:mn> </mml:mfrac> </mml:mrow> </mml:math> spin chain <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi mathvariant="normal">Sr</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:mi mathvariant="normal">Co</mml:mi> <mml:mo>(</mml:mo> <mml:mrow> <mml:msub> <mml:mi mathvariant="normal">SeO</mml:mi> <mml:mn>3</mml:mn> </mml:msub> <mml:msub> <mml:mrow> <mml:mo>)</mml:mo> </mml:mrow> <mml:mn>3</mml:mn> </mml:msub> </mml:mrow> </mml:math>
Bibliographic record
Abstract
We present a comprehensive muon spin relaxation/rotation (\ensuremath{\mu}$\mathrm{SR}$) study of the ${\mathrm{Co}}^{2+}$-based alternating Heisenberg ${J}_{\text{eff}}=\frac{1}{2}$ spin chain system ${\mathrm{Sr}}_{2}\mathrm{Co}{({\mathrm{SeO}}_{3})}_{3}$. Low-temperature magnetic property measurements confirm a spin-singlet ground state and identify two critical fields, ${H}_{\text{C1}}$ and ${H}_{\text{C2}}$. At ${H}_{\text{C1}}$, the system evolves from the spin-singlet state to a canted antiferromagnetic phase, which persists up to ${H}_{\text{C2}}$, where the system enters a fully polarized state. This magnetically ordered phase exists between \ensuremath{\mu}${}_{0}{H}_{\text{C1}}^{\ensuremath{\perp}c}=2$ T and \ensuremath{\mu}${}_{0}{H}_{\text{C2}}^{\ensuremath{\perp}c}=3.05$ T for \ensuremath{\mu}${}_{0}H\ensuremath{\perp}c$ and between \ensuremath{\mu}${}_{0}{H}_{\text{C1}}^{///c}=2$ T and \ensuremath{\mu}${}_{0}{H}_{\text{C2}}^{///c}=3.6$ T for $H//c$, reflecting the presence of anisotropy. Additionally, \ensuremath{\mu}$\mathrm{SR}$ results provide insights into the thermal and field evolution of spin dynamics, revealing a thermal crossover in spin correlations, the reopening of a spin gap due to anisotropy above ${H}_{\text{C1}}$, and the emergence of a magnon gap above ${H}_{\text{C2}}$. These findings imply the suppressed criticality of the canted antiferromagnetic phase by anisotropy. Our study establishes ${\mathrm{Sr}}_{2}\mathrm{Co}{({\mathrm{SeO}}_{3})}_{3}$ as a model system for investigating field-driven quantum phase transitions in one-dimensional ${J}_{\text{eff}}=\frac{1}{2}$ quantum spin chains with anisotropy.
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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 | 0.010 | 0.007 |
| Meta-epidemiology (narrow) | 0.006 | 0.011 |
| Meta-epidemiology (broad) | 0.003 | 0.011 |
| Bibliometrics | 0.003 | 0.008 |
| Science and technology studies | 0.007 | 0.008 |
| Scholarly communication | 0.006 | 0.008 |
| Open science | 0.012 | 0.011 |
| Research integrity | 0.008 | 0.011 |
| Insufficient payload (model declined to judge) | 0.365 | 0.009 |
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".