The researchers fabricate a disconnected three-dimensional artificial spin ice inspired by the pyrochlore lattice, using two-photon lithography, pyrolysis and magnetic thin-film deposition to place tilted nanomagnets at four heights. Magnetic force microscopy identifies single-domain, s- and vortex states; micromagnetic calculations explain how dimensions influence these textures, and a point-dipole calculation shows how tilt changes vertex energy ordering. Synchrotron imaging improves structural visibility but does not reliably determine the magnetic configuration. Uniform single-domain array

✦ 3D ARTIFICIAL SPIN ICE

Four magnets. One local rule. A surprising number of ways to belong.

Researchers print, shrink, and coat a scaffold to lift separate nanomagnets into three dimensions. Explore the geometry—and the magnetic possibilities it opens.

01 / THE LOCAL RULE

Can you keep the vertex balanced?

Each magnet can point toward the meeting point, or away. In ideal spin ice, the low-energy rule is two in, two out. Flip one and see what changes.

Balanced · two in, two out

An ice-rule state. Two inward arrows balance two outward arrows. Now try flipping just one magnet.

Two flips can take you to a new balanced state.

Why spin ice is so cool

Each pair of magnets has a preferred arrangement—but geometry prevents every pair from being satisfied at once. Physicists call this frustration . Instead of one obvious answer, many low-energy arrangements can coexist. Breaking the rule creates a defect that behaves like an effective magnetic charge : a collective property of the magnets, rather than an isolated fundamental pole.

This playground assumes each magnet acts as one uniform arrow. The paper fabricated and imaged a 3D architecture with richer magnetic textures; motion of these charge-like defects is a future direction.

02 / GEOMETRY CHOOSES THE ENERGY

Tilt the magnets. Change the rules.

Being “two in, two out” is only part of the story. The angle between magnets changes their interactions—and decides which balanced arrangements have the lowest energy.

Six equal-energy possibilities

At 35.3°, the six balanced arrangements have the same interaction energy.

The paper’s fabricated magnets are tilted at 45° . Its point-dipole calculation favors Type II states at this angle. The ideal tetrahedral angle of about 35.3° restores equal energies. These curves are calculated for four ideal dipoles, not measured energies of the fabricated sample.

Each ideal magnet is represented by a magnetic dipole: a direction and a strength, concentrated at one point. We add the interaction of all six pairs using the paper’s point-dipole expression (Section 7.8).

The four dipoles lie at equal distance R from the vertex, with alternating positive and negative elevation θ. Values are in units of μ₀m² / (4πR³). Lower values mean lower interaction energy. Here ΔE = EII − EI.

03 / FROM POLYMER TO METAMATERIAL

Print big. Shrink small. Add magnets.

How do you arrange separate magnets hundreds of nanometers across at four different heights? Start with a larger structure that a laser can write—and shrink it.

Print the 3D polymer scaffold

A laser writes sloped platforms and strong supporting columns on a hemispherical base. The platforms put future magnets at four different heights.

The tiny base has a big job.

Silicon stays the same size during heating; the polymer shrinks. A hemisphere on a short cylindrical foot mechanically separates the scaffold from its substrate so the top can shrink uniformly while staying attached.

Separate magnets, three dimensions.

The final magnetic platforms are about 250 × 650 nm , with the lowest magnets at least 650 nm above the flat top of the decoupling structure. The four-level layout keeps magnets from overlapping when viewed from above.

© 2026 The Authors · CC BY 4.0 · Figures cropped and resized from the paper.

04 / THE MAGNETS HAVE AN INNER LIFE

A magnet can be more than one arrow.

The playground treats a magnet as a single direction. In the fabricated sample, magnetic force microscopy revealed a mixture of magnetic textures inside the 30 nm-thick magnets.

One collective direction

Inside a single-domain magnet, the magnetization points mostly the same way. That lets us represent the whole magnet as one arrow—the building block of the ice-rule model.

Magnetic force microscopy detected single-domain, S-shaped, and circulating vortex states in the 30 nm-thick fabricated magnets.

WHAT WAS SIMULATED

Thinner magnets favor one direction.

Micromagnetic simulations predict a preference for a single-domain state below about 7 nm thickness for a 250 × 650 nm magnet. Reducing the width to 200 nm shifts that crossover to about 21 nm . Shape and size therefore help select which magnetic states are available.

The researchers also used X-ray photoemission electron microscopy. Conductive coatings and normal-incidence illumination improved structural imaging; magnetic contrast under field reversal did not reliably identify the configuration. The measured texture evidence shown here comes from magnetic force microscopy.

AN ARCHITECTURE FOR NEW QUESTIONS

Geometry becomes a magnetic design tool.

Physically separated magnets in three dimensions offer new ways to tune interactions, connectivity, and magnetic states. That makes this architecture a platform for studying frustrated magnetism—and a possible route toward future computing systems inspired by networks of neurons.

This paper advances fabrication and characterization. Neuromorphic computing and charge-like defect dynamics are directions for future investigation.

SOURCE & CREDITS

Pyrochlore Artificial Spin Ice: Advances in Fabrication and Characterization of a 3D Magnetic Metamaterial

Luca Berchialla, Arjen van den Berg, Gavin M. Macauley, Evangelos Golias, Yuran Niu, Tianyue Wang, Armin Kleibert, Sam Ladak, and Laura J. Heyderman. Small Structures 7, e70593 (2026) · DOI: 10.1002/sstr.70593.

Paper and reproduced figures © 2026 The Authors, licensed under Creative Commons Attribution 4.0. Figures are cropped and resized. Interactive vertex and scaffold views are conceptual reconstructions; magnetic textures are illustrative. The graphical abstract is an AI-generated conceptual illustration informed by Figures 1–2.