The Magnetism That Learns to Dance on Forbidden Tiles
29 May 2026, Yanjiang
A quasicrystal’s never-repeating tiling hosts altermagnetic spin order with exotic eightfold symmetry, merging magnetic and geometric impossibilities.
What if the most intricate magnetic order known to physics could bloom in a crystal with no repeating pattern at all? Imagine a wallpaper whose design never quite repeats, yet still fills the room with perfect, coherent logic — a pattern that mathematicians once dismissed as impossible, until it was found forged in an alloy of aluminium and manganese, and its discoverer won a Nobel Prize. Now imagine that this impossible wallpaper can host a magnetic state that is itself a kind of oxymoron: a material with the zero-net-magnetisation modesty of an antiferromagnet, yet with electron bands that split according to spin as forcefully as any common iron magnet. That state is called altermagnetism, it was discovered only a few years ago, and a team of physicists has just shown that it can thrive in the most unlikely of homes — a quasicrystal — where it exhibits patterns of spin with an exotic, eightfold or twelvefold symmetry never seen before.
The work comes from a collaboration led by Dong-Hui Xu at Chongqing University, with Rui Chen at Hubei University and Bin Zhou. Their theoretical study, posted as a preprint (arXiv:2507.18408), is not just a demonstration that “altermagnet plus quasicrystal” is possible. It is an invitation to rethink what magnetic order actually needs: not a neat, repeating grid of atoms, but simply a set of rotational symmetries that can be combined with time reversal in a harmonious, global way. And it proposes an experiment — a two‑tip scanning tunnelling microscope — that could, perhaps one day, detect the signature eight‑pointed star of this new magnetic phase in an actual laboratory.
The unexpected geometry of magnets
To appreciate the surprise, you first need to understand that altermagnetism itself overturned a long‑standing categorical divide. Magnets came in two flavours. Ferromagnets are the familiar ones: their electron spins all point the same way, producing a macroscopic field; the electronic bands are spin‑split, so spin‑up and spin‑down electrons experience different energies. Antiferromagnets, by contrast, have alternating spins that cancel out perfectly — zero net magnetisation — and their bands are spin‑degenerate: no energetic difference between a spin‑up and a spin‑down electron at the same momentum. The two categories seemed as separate as the ocean and the desert, linked only by a spin‑flip transition that turned one into the other when the material was heated above its Néel temperature.
Altermagnetism, identified in 2022, inhabits a strange middle ground. It is collinear like an antiferromagnet, with moments on different sublattices pointing exactly opposite, so the total magnetisation remains zero. Yet its electronic bands are strongly spin‑split, a feature usually reserved for ferromagnets. How is that possible? The trick is that the crystal lattice itself provides a twist: when you rotate the crystal by a specific angle — say 90 degrees — the up‑spin and down‑spin sublattices swap, but time reversal is also required to restore the original configuration. The combined symmetry (rotation plus time reversal) protects the spin splitting even while the net moment vanishes. In ordinary periodic crystals, this principle restricts the allowed rotational symmetries: you can have d‑wave altermagnetism (four‑fold) or i‑wave (twelve‑fold nodal lines), but the mathematics of periodicity forbids other angles, like five‑fold, eight‑fold, or the full twelve‑fold rotational symmetry itself. The menu of possible altermagnetic orders is finite and rather small.
Quasicrystals: order without repetition
Quasicrystals laugh at such restrictions. When Dan Shechtman discovered an aluminium‑manganese alloy in the early 1980s whose electron diffraction pattern exhibited five‑fold rotational symmetry — a forbidden symmetry in any periodic crystal — the initial reaction from the scientific establishment was incredulity, famously encapsulated by a senior colleague handing him a textbook and telling him to read it again. But the data were unambiguous, and the 2011 Nobel Prize in Chemistry vindicated what the atoms had been quietly doing all along: order can exist without translation. The internal structure of a quasicrystal is as precise and long‑range as any crystal’s, but it never repeats. Instead, it can be generated from two or more primitive tiles — squares and rhombuses, for instance — arranged according to matching rules that create a pattern with, say, eight‑fold or twelve‑fold rotational symmetry, yet no unit cell ever repeats exactly.
A perfect octagonal quasicrystal, like the AB‑tiling studied by Chen, Xu, and Zhou, consists of squares and 45° rhombuses that fill the plane in a dizzying, never‑repeating mosaic. At each site one can place two electron orbitals, linked by a 45° rotation, so that the entire electronic structure inherits a global eight‑fold rotational symmetry. Add electron‑electron interactions, and something remarkable can happen: the electrons spontaneously organise their spins into a pattern that respects a combined eight‑fold‑rotation‑and‑time‑reversal symmetry, denoted C₈T. The resulting magnetic order is an exotic g‑wave altermagnet: the spin splitting in momentum space varies as the real part of a complex function with an eight‑fold angular dependence, looking like an eight‑pointed flower. A similar story plays out on a dodecagonal quasicrystal, the Stampfli tiling, where the relevant symmetry is C₁₂T and the predicted order is an i‑wave altermagnet with twelve‑fold nodal lines.
The team’s numerical experiments, carried out using self‑consistent mean‑field theory on clusters of several hundred sites, reveal stable altermagnetic ground states for realistic interaction strengths. They compute the spectral density — a map of the electronic states available at each momentum — and find that, in the magnetically ordered phase, the spin‑up and spin‑down spectral weights differ dramatically. For strong enough coupling, the difference traces out a crisp pattern of eight (or twelve) bright and dark rays, alternating in angle. The prediction is robust: the altermagnetisation survives over a wide range of electron fillings, provided the interaction exceeds a critical threshold.
The compass‑rose in a two‑tip experiment
Such abstract pictures are all very well, but a new magnetic phase must eventually be seen. Here the paper makes a creative leap. It proposes a two‑tip scanning tunnelling microscope as a direct probe of altermagnetic order in quasicrystals. In a standard STM, a single sharp metal tip hovers over the surface, allowing electrons to tunnel from the tip into the sample; by measuring the resulting current, one can map the local density of states. A two‑tip setup, by contrast, can do something far richer: electrons can be injected by one tip and collected by the other, and by analysing the spin of the collected current one can measure transport properties that depend on the direction of propagation relative to the magnetic order. The crucial idea is that an unpolarised current injected into the quasicrystal will, after traversing the altermagnetic order, emerge with a net spin polarisation that varies with the angle between the two tips. In the octagonal case, the spin conductance should exhibit an eight‑fold modulation — twice the signal in certain directions, suppressed in others — directly reflecting the g‑wave symmetry.
Achieving quantum coherence between two independent tunnelling tips remains a formidable experimental challenge, as recent work on coincidence two‑tip spectroscopy has shown (Su et al., arXiv:2507.17532). The calculation by Chen and colleagues is a first step: they computed the spin conductance within a simplified orbital model, essentially asking the quasicrystal what spin bias it would produce if one could perfectly inject and collect electrons at two idealised points. Whether the clean eightfold pattern survives a full transport calculation that couples the two tips to the quasicrystal’s correlated ground state is a question that remains open.
The deeper symmetry beneath
None of this diminishes the conceptual advance. The real contribution of the work is to demonstrate that altermagnetism can exist beyond the strictures of periodicity, and that the only essential ingredient is a set of combined rotation‑time‑reversal symmetries that the electrons spontaneously break — or, more precisely, that they respect in a subtle, compensated manner. Quasicrystals, with their forbidden rotational angles, provide a vast new landscape for magnetic order. Instead of just d‑wave and g‑wave, one can imagine a whole hierarchy of altermagnetic patterns corresponding to any polygonal tiling: a ten‑fold decagonal quasicrystal might host a spin‑split pattern with twenty nodes, and so on. The interplay between the topological properties of the aperiodic lattice and the magnetic order could also give rise to novel edge states or pumping phenomena, a direction the authors briefly point towards.
Magnetism, that most ancient of condensed‑matter phenomena, keeps revealing fresh layers. First came the simple ferromagnet and antiferromagnet. Then the non‑collinear antiferromagnet, with its spiralling textures. Then the topological magnet, whose winding numbers protect edge modes. Now altermagnetism, and now altermagnetism in quasicrystals. Each step has been not a replacement of what came before, but a broadening of the palette — a demonstration that the universe of possible magnetic orders is far richer than our textbooks had assumed.
What the work ultimately shows us is that the mathematics of forbidden symmetry, long thought to be a curiosity of crystallography, can become a playground for new magnetic states. The marriage of quasicrystals and altermagnetism is not just a union of two exotic topics; it is a demonstration that symmetry, not periodicity, is the deeper organising principle of magnetic order. The question is no longer whether altermagnetism can exist without a unit cell — we now know it can — but how far the principle can be pushed, and whether the signatures predicted by theorists can be coaxed into the light of an experimenter’s laboratory.
We are left not with a finished product, but with a tantalising new set of questions. Can we grow real octagonal quasicrystals with local moments that interact strongly enough to realise a g‑wave state? Can we build a two‑tip STM sensitive enough to detect the eight‑fold spin asymmetry? The journey from a mathematical tiling pattern on a theorist’s blackboard to a working magnetic device may be long, but it has just gained a beautiful new starting point. And it reminds us, once again, that the most interesting things in nature often happen where the rule books say they cannot.
— Yanjiang
Yanjiang is an online editor of LoomSci.com.
References
- Rui Chen et al., Altermagnetism in quasicrystals, arXiv:2507.18408
- Su et al., Coincidence double-tip scanning tunneling spectroscopy, arXiv:2507.17532