Spin‐multislice simulation of an electron inside the objective lens of a TEM
Bibliographic record
Abstract
Spin filtering of an unpolarized beam in a TEM is a fascinating field of research. Bohr conjectured that it is impossible to spin filter an electron beam or, using Bohr words, “to observe the spin of the electron, separated fully from its orbital momentum, by means of experiments based on the concept of classical particle trajectories”[1]. However, the principle seems to be violated by theoretical calculations [2,3]. One of the most convincing proposals for free electron polarization is a multipolar Wien filter. But the fields involved are typically very large [2] while multipolar Wien filters in microscopy are still rare. The device, together with the diffractive elements, is called as “q‐filter” where q hints at the topologic charge of the field. The objective lens of the microscope provides a very large field with the potentiality of introducing a spin‐orbit coupling, we performed spin‐multislice simulations [4], where a Bessel beam was propagated through the objective lens (modeled as a Glaser field) in order to quantify the degree of spin polarization. We will discuss in particular that the spin‐orbit conversion in the pre‐ and post‐field can be understood in terms of the q‐filter. Fig 1 a shows on the left a scheme of the objective lens and of the electron wavefunction (blue) passing through it. A schematic “Bohmian” trajectory is indicated by a curve. The image also features arrows indicating the classical spin orientation along the curve for an initial state with spin |↑> along the optic axis. The fig 1b indicates the multislice calculated evolution of the wavefunction. While the expectation value of the spin operator S has components < S x >=< S y > =0 we can track the expectation of the x,y vector P=(S.r,S.t) (with r being the in plane position versor and t its orthogonal in plane versor). The result is shown in fig 2. P represents a sort of local in plane projection of the spin operator. To a good degree of approximation here |P| is equal to the rate of conversion from |↑> to |↓>. The results indicates a net, typically weak , increase of P as an effect of the objective lens . The overall final wavefunction is described in Fig 3 as a non‐separable spin‐orbital angular momentum state. The multislice results are in quantitative agreement with ray tracing calculations, confirming the reliability of both methods in this case. However, the multislice approach enables us to use less classical states like Laguerre Gauss beams, to explore possible advantages and more quantum physical effects.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 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".