Coexistence of anomalous spin dynamics and weak magnetic order in the chiral trillium lattice <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi mathvariant="normal">K</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:mi>FeSn</mml:mi> <mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:msub> <mml:mi>PO</mml:mi> <mml:mn>4</mml:mn> </mml:msub> <mml:mo>)</mml:mo> </mml:mrow> <mml:mn>3</mml:mn> </mml:msub> </mml:mrow> </mml:math>
Bibliographic record
Abstract
Trillium lattices, in which magnetic ions form a three-dimensional chiral network of corner-sharing equilateral triangular motifs, offer a prominent platform to explore exotic quantum states. In this work, we report ground-state properties of the $S=5/2$ trillium lattice compound ${\mathrm{K}}_{2}\mathrm{FeSn}{({\mathrm{PO}}_{4})}_{3}$ through thermodynamic, electron spin resonance (ESR), and muon spin relaxation ($\ensuremath{\mu}\mathrm{SR}$) experiments. Thermodynamic and ESR measurements reveal the two-step evolution of magnetic correlations across ${T}^{*}=11\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, which results from an interplay between dominant antiferromagnetic Heisenberg interactions and subleading interactions. Below ${T}^{*}$, dc and ac magnetic susceptibilities indicate weak magnetic ordering at ${T}_{\mathrm{N}}\ensuremath{\approx}2\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ under low fields, which is suppressed for ${\ensuremath{\mu}}_{0}H\ensuremath{\ge}2$ T, consistent with a power-law dependence of magnetic specific heat at low temperatures. $\ensuremath{\mu}\mathrm{SR}$ experiments confirm the dominance of persistent spin dynamics and the absence of conventional spin freezing, supporting the subtle nature of weak magnetic ordering coexisting with strong spin fluctuations. These findings underscore the potential for realizing a classical spin-liquid ground state with exotic excitations in high-spin trillium lattice systems.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.004 | 0.000 |
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".