Microscopic polarization and magnetization fields: Including spin effects
Bibliographic record
Abstract
We extend a microscopic theory of polarization and magnetization to include the spin degree of freedom of the electrons. We include a general spin orbit coupling and Zeeman interaction term to account for the modifications to the dynamics upon treating the electrons as spinful particles. We find a contribution to the magnetization due to the intrinsic angular momentum of the electrons. Additionally, the charge current gains a component transverse to both this intrinsic magnetization and the electric field of the crystal lattice. The microscopic polarization and magnetization fields are introduced throughout an extended system using a set of orthogonal orbitals associated with each site. As well free charge and current density fields are introduced associated with charge movement from site to site. The sites act as natural expansion points for the microscopic fields allowing for the evaluation of multipole moments associated with the polarization and magnetization fields. Associated with the dipole moments are the respective macroscopic polarization and magnetization fields, from which we can extract various response tensors. We focus on topologically trivial insulators in the limit of uniform fields to recover the magnetoelectric polarizability (MP) tensor, which contains the accepted expression for the orbital magnetoelectric polarizability (OMP) tensor as well as an added explicitly spin dependent contribution. This general framework can then be extended to finite frequency responses.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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".