Spin correlations on the pyrochlore lattice
Bibliographic record
Abstract
Pyrochlores have the chemical formula A₂B₂O₇ with A, B, or both A and B magnetic. It has corner-sharing tetrahedra in the structure, therefore, frustration phenomena naturally occurs in these systems. Because of the frustration, pyrochlore have many interesting properties, including the spin glass in Y₂Mo₂O₇, spin liquid in Tb₂Ti₂O₇, disordered spin ice in Ho₂Ti₂O₇, and ordered spin ice in Tb₂Sn₂O₇. In this thesis we will focus on Tb₂Ti₂O₇. Our goal is to find the spin correlation functions between different sites of Tb ions. The Hamiltonian of Tb ions is an anisotropic nearest neighbour exchange interaction. We apply perturbation theory to the Hamiltonian, and it will separate the Hamiltonian into two parts. The unperturbed part of Hamiltonian is the spin ice Hamiltonian, and other parts of the Hamiltonian are perturbative. The perturbative parts of Hamiltonian can be written in the local coordinates to give three different terms X₂, X₃, X₄. In order to find the spin correlation function, we calculate time dependent spin operators in the interaction picture. Then we apply them to the unperturbed and perturbed terms of Hamiltonian to calculate the spin correlation functions. Finally, we discuss the neutron scattering experiment and how to apply it to test our results.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.003 | 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".