Scientists have made a new material that is both a quasicrystal and antiferromagnetic — a combination never seen before.

Quasicrystals are a special kind of solid. Unlike normal crystals, whose atoms are arranged in repeating patterns, quasicrystals have patterns that never exactly repeat but which still have an overall order. While regular crystals have left-right symmetries, quasicrystals have unusual rotational ones.

For decades, scientists wondered if certain kinds of magnetism, but especially antiferromagnetism, could exist in these strange materials. In all materials the electrons have a property called spin. It’s as if a small magnet is embedded inside each electron. The spin denotes the direction of this magnet’s magnetic field. In ferromagnets, the spins are aligned in a common direction, so the materials are attracted to magnets. In antiferromagnetic materials, the electron spins line up in alternating directions, so their effects cancel out.

While antiferromagnetism is common in regular crystals, it’s thus far never been observed in a true quasicrystal.

The new study is the first to show clear evidence of antiferromagnetic order in a real, three-dimensional quasicrystal — one made of gold, indium, and europium. The findings were published in Nature Physics on April 14.

The team confirmed such a material is real by carefully measuring how its atoms and spins are arranged and by observing how it behaves at low temperatures. Their work shows that even in the weird world of quasicrystals, complex magnetic order is possible, opening the door to new discoveries and technologies.

The scientists created a new alloy with the formula Au₅₆In_28.5Eu_15.5. This means in 1,000 atoms’ worth of the material, 560 will be gold, 285 will be indium, and 155 will be europium. The composition tells us that the scientists were going for a particularly precise combination of these elements — which they could have known in one of two ways. It might have been trial-and-error*, but that makes research very expensive, or the scientists had reasons to expect antiferromagnetic order would appear in this material.

They did. Specifically, the team focused on Au₅₆In_28.5Eu_15.5 because of its (i) unique positive Curie-Weiss temperature and (ii) rare-earth content, and (iii) because its structural features matched the theoretical criteria for stable antiferromagnetic order. Previous studies focused on quasicrystals containing rare-earth elements because they often have strong magnetic interactions. However, these compounds typically displayed a negative Curie-Weiss temperature, indicating dominant antiferromagnetic interactions but resulting only in disordered magnetic states.

A positive Curie-Weiss temperature indicates dominant ferromagnetic interactions. In this case, however, it also suggested a unique balance of magnetic forces that could potentially stabilise antiferromagnetic order rather than spin-glass behaviour. Studies on approximant crystals — periodic structures closely related to quasicrystals — had also shown that both ferromagnetic and antiferromagnetic orders are stabilised only when the Curie-Weiss temperature is positive. In contrast, a negative temperature led to spin-glass states.

The scientists of the new study noticed that the Au-In-Eu quasicrystal fit into the positive Curie-Weiss temperature category, making it a promising candidate to have antiferromagnetic order.

For added measure, by slightly altering the composition, e.g. adding an impurity to increase the electron-per-atom ratio, the scientists could make the antiferromagnetic phase disappear, to be replaced by spin-glass behaviour. This sensitivity to electron concentration further hinted that the composition of the alloy was at a sweet spot for stabilising antiferromagnetism.

Finally, the team had also recently discovered ferromagnetic order in some similar gold-based quasicrystals with rare-earth elements. The success encouraged them to explore the magnetic properties of new compositions, especially those with unusual Curie-Weiss temperatures.

The Au-In-Eu quasicrystal is also a Tsai-type icosahedral quasicrystal, meaning it features a highly symmetric atomic arrangement. Theoretical work has suggested that such structures could support antiferromagnetic order in the right conditions, especially if the atoms occupied specific sites in the lattice.

To make the alloy, the scientists used a technique called arc-melting, where highly pure metals are melted together using an electric arc, then quickly cooled to form the solid quasicrystal. To ensure the mixture was even, the team melted and flipped the sample several times.

Then they used X-ray and electron diffraction to check the atomic arrangement. These techniques passed X-rays and electrons through the material. A detector on the other side picked up the radiation scattered by the material’s atoms and used it to recreate their arrangement. The patterns showed the material was a primitive icosahedral quasicrystal, a structure with 20-sided symmetry and no repeating units.

The team also confirmed special arrangement of atoms by the way the diffraction patterns followed mathematical rules that are special to quasicrystals. Team members also used a magnetometer to track how much the material was magnetised when exposed to a magnetic field, from temperatures as low as 0.4 K to up to 300 K. Finally they also measured the material’s specific heat, i.e. the amount of heat energy it took to raise its temperature by 1º C. This reading can show signs of magnetic transitions.

To confirm how the spins inside the material were arranged, the team used neutron diffraction. Neutrons are adept at passing through materials and are sensitive to both atoms’ positions and magnetic order. By comparing patterns at temperatures above and below the suspected transition point, they could spot the appearance of new peaks that signal magnetic order.

This way, the team reported that at 6.5 K, the magnetisation curve showed a sharp change, known as a cusp. This is a classic sign of an antiferromagnetic transition, where the material suddenly changes from being unordered to having a regular up-and-down pattern of spins. The specific heat also showed a sharp peak at this temperature, confirming something dramatic was happening inside the material.

The scientists also reported that there was no sign of spin-glass behaviour — where the spins are pointing in random directions but unchanging — which is common in other magnetic quasicrystals.

Below 6.5 K, new peaks appeared in the neutron diffraction data, evidence that the spins inside the material were lining up in the regular but alternating pattern characteristic of antiferromagnetic order. The peaks were also sharp and well-defined, showing the order was long-range, meaning they were there throughout the material and not confined to small patches.

The team also experimented by adding a small amount of tin to the alloy, which changed the balance of electrons. This little change caused the material to lose its antiferromagnetic order and become a spin glass instead, showing how delicate the balance is between different magnetic states in quasicrystals.

The findings are important because this is the first time scientists have observed antiferromagnetic order in a real, three-dimensional quasicrystal, settling a long-standing debate. They also open up a new field of study, of quasiperiodic antiferromagnets, and suggest that by carefully tuning the composition, scientists may be able to find yet other types of magnetic order in quasicrystals.

“The present discovery will stimulate both experimental and theoretical efforts to elucidate not only its unique magnetic structure but also the intrinsic properties of the quasiperiodic order parameter,” the scientists wrote in their paper. “Another exciting aspect of magnetically ordered quasicrystals is their potential for new applications such as functional materials in spintronics” — which use electron spins to store and process information in ultra-fast computers of the future.

* Which is not the same as serendipity.

Featured image credit: Nature Physics volume 21, pages 974–979 (2025).

There’s a concept in quantum mechanics, and also in parts of classical mechanics, called the Berry phase. Say you’re walking around a mountain. You start off along a path and follow it all the way until you’re back to the point where you started. You’re at the same point, sure, but you’re probably facing a different direction now. The Berry phase works something like this. Say you’ve got a bunch of electrons that you’re manipulating using a magnetic field. As you vary the field in continuous increments, the electrons will respond continuously in some way. But as you vary the field through a cycle of changes and bring it back to the original setting, the electrons won’t exactly be at their original configuration as well. Or they will be in addition to some change. This ‘additional change’ is called the Berry phase.

Reading about the Kancha Gachibowli forest brought the Berry phase to mind. Yesterday, India’s new Chief Justice, B.R. Gavai, faced Telangana state with a choice: “between restoring the forest or having the Chief Secretary and [half a dozen] officials in prison,” per The Hindu. The latter people are being held responsible for attempting to divert mostly moderately and densely forested land to a planned campus for information technology companies. The court had no sympathy for Telangana counsel Abhishek Manu Singhvi’s argument that the state’s efforts had been good-intentioned. The principle reason: the state hasn’t been able to explain the fact that it organised a phalanx of bulldozers to bring down 104 acres of old trees during an extended weekend, when the courts were closed, leaving the felling’s opponents without access to legal recourse. A few telling passages from The Hindu:

The State had previously denied the land was a forest. The claim, it said, that the area was forest land had sprung up only after developmental activities commenced following the allotment of the land to the Telangana Industrial Infrastructure Corporation. Mr. Singhvi submitted that the processes regarding the allotment had been on since March 2024. He said the intention of the State was bona fide.

…

Mr. Singhvi maintained that “thousands” of trees were not cut. “We have seen the photographs,” Chief Justice Gavai responded.

Mr. Singhvi submitted that not a leaf has been moved on the site after the apex court ordered everything to be stopped on April 16. The State was complying with the court’s direction in letter and spirit. A huge afforestation programme was underway in the area.

Amicus curiae, senior advocate K. Parameshwar, drew the attention of the court to a finding in a Forest Survey of India report, which was forwarded to the Central Empowered Committee, that out of the 104 acres cut in two nights, over 60% had been moderately and heavily dense forest.

It’s worthwhile these days to treat the concept of afforestation as a yellow flag at best and a despicable idea at worst. In the last decade it has evolved regressively into a sort of olive branch offered up alongside casual excuses to divert forested land for non-forest uses, often in open defiance of India’s existing forest protection laws — which sadly have been increasingly enfeebled by the environment ministry. That the state is now afforesting the area is little consolation because the trees that have already been cut represent a greater ecological loss than that can be recouped by young plants anytime in the near future. We may have come full circle since the state first felled the trees but we bear the burden of an additional change as well.

In fact, this could be more like magnetic hysteresis than the Berry phase depending on the mode of afforestation. Quantum systems are said to have acquired a Berry phase when they undergo a reversible process in which entropy doesn’t increase*. But entropy, the amount of disorder, has indeed increased. We’ve lost energy. We’ve lost old trees and their ecosystem services. We’ve lost a sustainable carbon store. We’ve learnt that the Telangana government is willing to act in bad faith. We’ve learnt that our forest protection laws continue to not work. Why, we’ve been reminded that the Supreme Court remains the country’s last democratic institution, perhaps short of Parliamentary majority, prepared to measure the loss of green cover by the precepts of sustainable development. Every Supreme Court decision to stall a project that entails deforestation has been met with cheers in the conservation and environmental justice communities but each such verdict also serves a reminder that we remain at the mercy of the last line of defence. If someday the Supreme Court also yields, or is let down by Parliament passing a law that makes a mockery of protecting trees, we are only left with protest — like the brave students of the University of Hyderabad mounted to bring the Kancha Gachibowli issue to the whole country’s attention.

When you apply a magnetic field over a ferromagnet, like a block of iron, it becomes magnetised. If you remove the magnetic field, the block stays magnetised to some degree. This phenomenon is called remanence. Future attempts to magnetise and demagnetise the block will have to work against the remanence, causing the block to lose energy over time as heat. This macroscopic feature is called magnetic hysteresis**: it’s irreversible, dissipative, disorderly, and vexatious. Much like the state of Telangana, it claims to find value in the context of computers (disk drives in particular), and much like the trees of Kancha Gachibowli, there’s nothing a ferromagnet can do about it.

* I’ve used entropy here with reference to a quantum adiabatic process. In a thermodynamic adiabatic process, entropy isn’t produced only if the process is also reversible.

** The term ‘hysteresis’ comes from the Greek ‘hústeros’, meaning ‘later’. This is a reference to the shape of the curve on a graph with the strength of the magnetic field H on one axis and the magnetisation M on the other. As the H curve rises and falls, the M curve starts to fall behind. The seemingly closely related ‘hysteria’ comes from the Greek ‘hustéra’, for ‘womb’, and is thus unrelated. However, the well-known Cornell University physicist James P. Sethna wrote sometime before 1995:

There seems to be no etymological link between hysteresis and either hysterical (fr. L hystericus of the womb) or history (fr. Gk, inquiry, history, fr. histor, istor knowing, learned). This is too bad, as there are scientific connections to both words. (There is no link, scientific or etymological, to histolysis, the breakdown of bodily tissues, or to blood.) … Many hysteretic systems make screeching noises as they respond to their external load (hence, the natural connection with hysteria).

‘Hysteria’ has of course rightly fallen out of favour both within and without clinical contexts.