Spin-ice microstate reconstruction

Reconstructing the states of 2,178 nanomagnets from magnetic images too blurry to resolve any one.

2,178 islands

Fit residual (measured minus fitted field) at 30.3 mT, at saturation, on the same pixels and colour scale: the baseline fit leaves 101 µT rms with strong edge artifacts; the joint fit leaves 20 µT rms. This saturated frame shows the clearest difference; mid-reversal residuals drop less. — Measured data · fit residual at 30.3 mT (saturation) · baseline fit 101 → joint fit 20 µT rms · residual maps computed from the campaign's records (the baseline and joint fits of preprint Fig. 7). This saturated frame shows the clearest difference; on the same pixels, mid-reversal residuals drop less (e.g. 40 → 38 µT rms at 17.25 mT).

2,178nanomagnet islands in the array

~700 nmsensor standoff; islands ~180 nm wide

~12campaigns and sessions over ~2 months

The problem

Artificial spin ice is a patterned array of nanomagnets, each a two-state Ising spin. A diamond (NV) imager ~700 nm away, with 500 nm pixels, suppresses single-island field detail ~10⁴–10⁵‑fold; about 12 parameters are uncertain.

What we did

Over ~2 months, researchers and collaborative agents ran about a dozen campaigns and sessions, building the physics model piece by piece. The final joint fit (each island flips at most once) was the team's earlier idea; agents later proposed it independently.

Result

To our knowledge, the first reconstruction of an artificial spin ice's Ising microstate from diffraction-limited magnetic imaging: each island's reversal across a 27-frame field sweep, now part of a forthcoming study.

Keep in mind

On current synthetic tests ~2.7% of island states come out wrong (5.6% in a noisier sweep; the preprint's 'under 2%' used an earlier benchmark); on real data, similarly good fits disagree on up to a third of islands mid-reversal.

In the preprint

Sec. IV.F, “Artificial spin-ice (ASI) magnetization reconstruction,” and Fig. 7 of arXiv:2610.17193 describe the campaign and its checks in more detail.

Fig. 7 of the preprint, full size — Fig. 7 of the preprint: (b) the reconstructed microstate at 17.2 mT (the enlarged region, chosen for visibility, holds more reversed islands than the 6% array average); (c) the measured field and the fields of the baseline and joint fits at 16.8, 17.2 and 30.3 mT; (d) their residuals; (e) line cuts. Panel (a), an SEM image, is omitted here. Click to enlarge.

Data: Measured data (confocal NV magnetic images, 27-frame field sweep)
Models (as stated in the preprint): Claude Sonnet 4.5, Sonnet 5, Opus 4.8, Opus 5, Fable 5 (several campaigns and sessions)
PhysKit versions (as stated in the preprint): 0.3.0, 0.4.0, 0.6.0, earlier versions
Where: Sec. IV.F, Fig. 7

We list the versions the preprint reports so readers can trace each result to its tools, not as a recommendation: for new work, use the latest release.