Origin and scarcity of breathing pyrochlore lattices in spinel oxides
Bibliographic record
Abstract
Breathing pyrochlores are a unique class of materials characterized by a three-dimensional lattice of corner-sharing tetrahedra. However, unlike conventional pyrochlores where all tetrahedra are identical in size, the breathing pyrochlore lattice is composed of alternating large and small tetrahedra. Experimental realizations of the breathing pyrochlore lattice are rare but they do occur in $A$-site-ordered spinels, as in the prototype materials ${\mathrm{LiGaCr}}_{4}{\mathrm{O}}_{8}$ and ${\mathrm{LiInCr}}_{4}{\mathrm{O}}_{8}$. In this work, we demonstrate that Cr cannot be straightforwardly substituted with other magnetic transition metals while retaining the breathing pyrochlore structure. To explain this observation, we perform density functional theory (DFT) calculations to investigate the formation and stability of ${\mathrm{LiGaCr}}_{4}{\mathrm{O}}_{8}$ and ${\mathrm{LiInCr}}_{4}{\mathrm{O}}_{8}$, focusing on the energy scales associated with $A$- and $B$-site orderings as well as the magnetic exchange interactions of Cr ions. We identify the strong octahedral site preference of ${\mathrm{Cr}}^{3+}$ as a key factor in protecting the structural integrity of the pyrochlore sublattice, which in turn enables the breathing distortion to proceed. We also demonstrate that the charge order between the $A$ (Li) and ${A}^{\ensuremath{'}}$ sites (Ga or In) is maintained at all temperatures up to decomposition. Furthermore, while the magnetic exchange interactions constitute a relatively small energy scale and therefore do not play a fundamental role in the structural stability of ${\mathrm{LiGaCr}}_{4}{\mathrm{O}}_{8}$ and ${\mathrm{LiInCr}}_{4}{\mathrm{O}}_{8}$, magnetism may play a critical role in setting the magnitude of the tetrahedral distortion. Ultimately, we conclude that the scarcity of breathing pyrochlores is a consequence of the stringent requirement on site ordering for their formation.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".