This experimental study develops a fabrication route for a three-dimensional pyrochlore artificial spin ice made from physically separated permalloy nanomagnets at four heights. Two-photon lithography prints a polymer scaffold; controlled pyrolysis on a hemispherical decoupling base reduces its dimensions to about one third; thin-film deposition forms the tilted magnetic islands. Magnetic force microscopy identifies single-domain, s-, and vortex states, supported by micromagnetic simulations. A point-dipole model predicts equal Type I and Type II vertex energies near 35° and a preference for T

What happens when a flat array of tiny magnets grows into the third dimension?

This paper makes a new kind of magnetic scaffold: separate nanomagnets, tilted and lifted to four heights. Explore the geometry, discover its energy landscape, and shrink a structure into the nanoscale.

Separate structures. Collective possibilities.

Artificial spin ice is an array of tiny magnets whose interactions depend on how they are arranged. Here, the authors lift the familiar square pattern into a pyrochlore-inspired 3D architecture.

heights, one array

The stadium-shaped magnetic caps sit at four heights and tilt by ±45°. Two unit cells vertically keep every cap exposed from above.

Why keep them separate? The nanomagnets exchange information through magnetic stray fields. Their geometry can tune these dipolar interactions without magnetic junctions joining the elements.

≈250 × 650 nm Typical lateral dimensions after shrinking.

Original 3D model from the authors’ research dataset, CC BY 4.0. Colors and lighting adapted, coordinate-axis annotations omitted, viewing controls added. Geometry represents the design, not a microscopy measurement.

The supplementary movie reveals how the differently oriented caps form the 3D array. Authors’ original geometry movie, resized and transcoded from the research dataset (CC BY 4.0).

Change the angle. Change the rules.

Four magnets meet around an empty center. In the ideal single-domain model, “two in, two out” has two distinct arrangements. Their relative energy changes when you tilt the geometry.

Find the ice angle

Can you make the two ice-rule energies meet?

Point-dipole model · Methods 7.8 / Figure S10. Each magnet is represented by one moment. Energies omit the common dimensional prefactor. This explores ideal vertex interactions.

At ≈35.3°, Type I and Type II become equally favorable. The fabricated 45° geometry favors Type II in this model. A flip can create a three-in/one-out ice-rule defect.

Build big. Make it small.

Two-photon lithography gives control over the 3D architecture. Pyrolysis then reduces the dimensions to about one-third, before evaporation adds the magnetic material.

A scaffold written by light

A Nanoscribe GT2 writes the IP-Dip polymer in 3D. Precise piezo-mode lines make smooth sloped platforms; faster galvo-mode woodpiles create their supports.

A shared hemispherical decoupling base and an additional cylindrical foot let the structure contract while remaining attached to the substrate. This preserves the geometry as the polymer shrinks.

Illustrative geometry, based on Sections 3 and 7.1–7.3. Shrinking animation represents the approximate linear size reduction, not real-time heating. Silver caps represent the deposited magnetic layer.

Authors’ supplementary diagram and scanning electron micrograph from the research dataset, CC BY 4.0; resized for display.

One shape. Several magnetic lives.

A magnet need not point uniformly in one direction. The paper’s magnetic force microscopy reveals single-domain, s- and vortex-like states in the 30 nm-thick nanomagnets.

A shared direction

Opposing, roughly symmetric contrast at the two ends suggests a uniform single-domain state. The magnet behaves approximately like one magnetic moment.

For 250 × 650 nm nanomagnets, reducing thickness below ≈7 nm favors a single-domain state. At 200 × 650 nm, the simulated transition is ≈21 nm. Shape and thickness help choose the magnetic texture.

Figure 3 crops, resized from Berchialla et al., CC BY 4.0. The colored outlines and magnetic-state schematics are the authors’ originals. MFM contrast is interpreted with micromagnetic simulations; the schematic arrows are not direct vector measurements.

A third dimension. A richer state space.

The achievement is a fabricated and characterized 3D architecture of disconnected nanomagnets. It opens a route toward designer dipolar spin systems, studies of emergent magnetic charges, and magnetic states that could support neuromorphic computing.

Tune the interactions

Change orientation, spacing and size to explore magnetic energy landscapes unavailable in natural spin crystals.

Resolve the states

MFM identifies multiple textures. For the thinner XPEEM samples, the magnetic configuration could not yet be reliably determined.

Explore collective behavior

Single-domain nanomagnets would bring the array closer to an ideal dipolar spin-ice system. Computation remains a future direction.

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, Laura J. Heyderman

Small Structures (2026) · DOI: 10.1002/sstr.70593. Paper and research-dataset material used under Creative Commons Attribution 4.0. Source figures are cropped/resized; the 3D model is recolored and relit; the supplementary movie is resized/transcoded. The graphical abstract is an AI-generated conceptual illustration. Interactive applets explain the paper’s geometry and models.

Research, made explorable.