Electronic, Optical, and Magnetic Properties of LiFePO<sub>4</sub>: Small Magnetic Polaron Effects
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Bibliographic record
Abstract
The electronic structure of LiFePO 4 and delithiated FePO 4 is revisited in the light of the previous calculations taking into account the coulomb correlation potential for d -electrons. The nature of the optical transitions across the energy gap is investigated. In LiFePO 4, these are intra-atomic Fe 2+ −Fe 3+ transitions suffering a strong Franck−Condon effect due to the local distortion of the lattice in FePO 4, which is indirect evidence of the formation of a small polaron. This situation contrasts with that met in the much more covalent delithiated phase, where the optical transition across the energy gap is associated with a transfer of an electron from the p-states of the oxygen to the d-states of iron ions. The small polarons in LiFePO 4 are associated with the presence of Fe 3+ ions introduced by native defects in relative concentration [Fe 3+ ]/[Fe 2+ +Fe 3+ ] = 3 × 10 - 3 in the samples known to be optimized with respect to their electrochemical properties. The nearest iron neighbors around the central polaron site are spin-polarized by the indirect exchange mediated by the electronic charge in excess. These small magnetic polarons are responsible for the interplay between electronic and magnetic properties that are quantitatively and self-consistently analyzed.
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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 | 0.000 | 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 | 0.000 | 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 it