diff ref struct Rietveld refinement for the Mac · powder diffraction with X-rays, synchrotron and neutrons · started October 2026

Inference for magnetic structures, with MAGNDATA as the family and the test bed

Inference for magnetic structures, with MAGNDATA as the family and the test bed discussed

I04 · an idea of the seed-place, on its way to the core.

Said
2026-10-16, Josu
Status
discussed
Home
core (where it migrates)
Needs
none

The idea

A derivative of the Bayesian inference before refinement (L286): extend the approach to the analysis of magnetic structures, with their symmetry treated thoroughly in the superspace formalism. The Bilbao Crystallographic Server's magnetic structures database could be a massive source of data for it.

Assessment

What MAGNDATA is, checked on its pages on 16 October 2026. "More than 2000 published commensurate and incommensurate magnetic structures" (its front page), each as an .mcif file: the commensurate ones in a Shubnikov group in the BNS setting, the incommensurate ones in a magnetic superspace group, the symmetry applied to the moments and the positions alike (Gallego et al. 2016, J. Appl. Cryst. 49, parts I and II). A paper of May 2026 counts 2241 commensurate entries as of June 2026 (arXiv 2605.16230). The whole database is downloadable after registering a user account (its "How to download" page). Its files are read by FullProf, JANA2006, ISODISTORT, ISOCIF, VESTA and Jmol. It holds models, not patterns: there is no diffraction data in it, so nothing in MAGNDATA can be re-refined. That fixes what it can be here.

What it can be, then: two things, both exact fits to L286.

  • The family's prior. L286's first weakness was the prior over the candidate models, and MAGNDATA is the measured prior for the magnetic case: given a parent group and a propagation vector, which irreps and which epikernels are realised, how often, with which moment directions. A paper of 14 October 2026 that uses it as a benchmark reports that 91 % of the entries it analysed (1083) are compatible with a single-irrep Landau theory, 96 % of those have the propagation vector at a high-symmetry point, and 61 % have \(\mathbf{k} \neq 0\) (arXiv 2601.01617; numbers read from the paper, not recomputed). That is the prior in one sentence: one irrep, almost always, and the candidate list is the finite set k-SUBGROUPSMAG already enumerates. Two thousand entries is the right size for a hierarchical model with counts per (parent group, \(\mathbf{k}\), irrep); it is not the size for a network, as L286 said of the double perovskites.
  • The test bed. Every entry is a solved structure. From each, the core can compute the neutron powder pattern it would give on a stated instrument, add the noise, and ask the inference to find the published model among the candidates of k-SUBGROUPSMAG. Two thousand real cases with known answers is the calibration test L286 demands (does a 90 % region hold the truth 90 % of the time; is the published model the one with the evidence), run at the scale no single family allows. The ambiguities MAGNDATA's authors flag (several models that fit equally, moment directions not determined by powder data) become the cases where the inference must say "undetermined" and not pick.

What exists elsewhere, checked by search on 16 October 2026. On the data side, equivariant networks trained on MAGNDATA predict the magnetic order from the atomic structure alone: Merker et al. 2022 (iScience) classify the order and the propagation vector, right on over 70 % of magnetic cases; the Magnetic Structure Network of May 2026 predicts commensurate and incommensurate structures from the coordinates, with no symmetry input (arXiv 2605.16230). Neither uses diffraction data: they are priors, not inference, and they give no evidence for one model against another. On the inference side, BLAND (Lesniewski et al. 2016, J. Appl. Cryst. 49, 2201) refines crystal and magnetic structures by Markov-chain Monte Carlo over a \(\chi^2\) likelihood, with the magnetic components as free parameters and a uniform prior; ANDiE (ORNL, 2022) steers a neutron diffractometer by Bayesian inference and uses a Bayes factor once, on the order parameter's temperature dependence. The practice itself is representation analysis (BasIreps, SARAh, ISODISTORT, k-SUBGROUPSMAG) followed by trial refinements of each candidate, in FullProf (Rodríguez-Carvajal, González-Platas and Katcho 2025, Acta Cryst. B81, 302, which calls the field "lacking standardization") and in GSAS-II, with simulated annealing where the start is unknown. No program found compares the candidates by their evidence, with a prior learned from the published structures, and says which are undetermined by the data. That gap is the same one L286 found for the nuclear case, and it is wider here, because the candidate list is finite and enumerated and the ambiguities are the daily problem.

The cost is larger than L286's. The core has no magnetic scattering: magnetic structures are "later" by L012 and the brief's scope. Before any inference the core needs, each with its test against FullProf's magnetic runs: the magnetic form factors; the magnetic structure factor and the powder intensity with the perpendicular projection of the moment; the propagation vector and the satellites; the moments described by a Shubnikov group (.mcif read and written, the 1651 groups generated and checked as the 230 were); and, for Josu's "thorough" symmetry, the irreps of the little group and the basis vectors (the magnetic analogue of the mode decomposition of L263, which the core computes without tables). The superspace description of the incommensurate structures is a layer above that, which Jana2020 has and FullProf has in part (its 2025 paper's keywords). Only then does the inference of L286 apply, and then it applies almost unchanged: the candidates are the epikernels, the amplitudes are the basis-vector coefficients, the equivalent solutions are the domains, the nuisances are the same.

Honest numbers for the data. MAGNDATA is massive against a family (L286's double perovskites: 47 materials) and small against what the word "data" means elsewhere. Its entries are not independent samples: they are what people measured, published and the curators entered, with the fashions of the field in them. The prior learned from it is a prior over what has been found, which is exactly what a refiner's experience is, made explicit and countable; it must be said so.

Proposal

Not before L286's toy has passed its calibration test on the nuclear case, since this inherits every risk of L286 and adds the physics. Then:

  • Step 1. Register with MAGNDATA, download it, and measure the prior: the counts per parent group, \(\mathbf{k}\), irrep and epikernel, the moment directions, the fraction of entries whose authors flag an ambiguity. A finding entry in the log, with the numbers. No code in the core.
  • Step 2. The core's magnetic layer, in the order above and under the gate rule (L037): form factors, structure factors, propagation vectors, Shubnikov groups and .mcif, each against FullProf's magnetic tutorials (manuals/fullprof/ holds NdNi-HTO's magnetic phase already, L053).
  • Step 3. The test bed: one hundred MAGNDATA entries, patterns simulated on D2B's and D20's resolution, the candidates from k-SUBGROUPSMAG, the inference of L286 run on each, the recovery and the calibration counted. Published as a finding with its failures.
  • Step 4. The incommensurate case, in superspace, only if step 3 holds. Where it lives: drs-infer (L286, I02's first engine), with the magnetic layer in the core.

For Josu to decide

  • Whether magnetic structures move from "later" (L012) into the plan at all, and in which version: this is the first idea that asks it.
  • Whether step 1, the measured prior, is done now as a study (a week, no code) or waits for the nuclear toy.
  • Whether the superspace description is required from the start or follows the commensurate case.
  • Whether to approach the Bilbao server's group (the same university) about the download and the statistics before publishing anything measured on their database.

The idea's log

  • 2026-10-16 · said

    Said by Josu in the ideas chat: extend the Bayesian inference of L286 to magnetic structures, with superspace symmetry, using the Bilbao server's magnetic structures database as a massive data source.

  • 2026-10-16 · discussion

    Assessed with MAGNDATA's pages and the literature: the database holds models, not patterns, so it is the measured prior and the test bed, not data to refine; 91 % single-irrep in a 2026 analysis; no program compares magnetic candidates by evidence; the core has no magnetic scattering yet, which is the real cost. L298