🔬 mesoscale physics

Altermagnetism in quasicrystals

This paper theoretically demonstrates that quasicrystals can host exotic altermagnetic orders, specifically predicting stable $g$ -wave and $i$ -wave phases in octagonal and dodecagonal structures that exhibit unique anisotropic spin-splittings and nodal patterns distinct from those found in periodic crystals.

Original authors: Rui Chen, Bin Zhou, Dong-Hui Xu

Published 2026-05-29

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CC BY 4.0

Original authors: Rui Chen, Bin Zhou, Dong-Hui Xu

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a world where magnets usually come in two flavors: Ferromagnets (like your fridge magnets, where all the tiny internal arrows point the same way) and Antiferromagnets (where the arrows point in opposite directions, canceling each other out so the whole thing has no magnetic pull).

Recently, scientists discovered a "third flavor" called Altermagnets. These are tricky hybrids. Like antiferromagnets, their internal arrows cancel out perfectly (zero net magnetism), but like ferromagnets, they still manage to split their electrons into two different energy groups based on their spin. It's a bit like a dance floor where everyone is paired up perfectly (no net movement), but the couples are dancing in two completely different styles that never mix.

Until now, scientists thought this special dance could only happen in periodic crystals—materials with a repeating, wallpaper-like pattern. They believed the rules of the dance required a specific, repeating grid.

The Big Twist: The Quasicrystal
This paper introduces a new venue for this dance: Quasicrystals.

Think of a periodic crystal like a tiled floor made of identical squares. It repeats perfectly. A quasicrystal is more like a complex, beautiful mosaic (like the intricate patterns in a mosque or a Penrose tiling). It has order and symmetry, but it never repeats. You can't slide the pattern over and have it match up exactly. For a long time, scientists thought these messy, non-repeating patterns were too chaotic to support organized magnetic states.

The Discovery
The authors, Rui Chen, Bin Zhou, and Dong-Hui Xu, propose that these non-repeating mosaics are actually perfect stages for a new kind of altermagnetism that periodic crystals can't do.

Here is how they explain it using simple analogies:

The Octagonal Dance (The "g-wave"):
They looked at an octagonal quasicrystal (an 8-sided pattern). In a normal crystal, you can only have 2, 3, 4, or 6-fold symmetries. You can't have an 8-fold repeating pattern. But in this quasicrystal, the pattern rotates in 8 directions.
The authors found that the electrons in this material can form a "g-wave" pattern. Imagine a flower with 8 petals. The magnetic properties of the electrons change as you rotate around the center, creating a pattern that repeats every 45 degrees. This is a "g-wave" because it has 8-fold symmetry.
The Dodecagonal Dance (The "i-wave"):
They also looked at a 12-sided (dodecagonal) pattern. Here, the electrons form an "i-wave," which is like a flower with 12 petals. This is even more complex and impossible to achieve in standard, repeating crystals.

How They Know It's Real (The "Magic Mirror")
The paper uses a theoretical tool called "Mean-Field Theory" (think of it as a super-accurate simulation) to prove these states are stable. They found that while the material looks like it has no overall magnetism, it actually has a hidden rule: Time-Reversal + Rotation.

The Analogy: Imagine a spinning top. If you reverse time (make it spin backward) and rotate the room by 45 degrees (for the 8-sided one), the system looks exactly the same. This "magic mirror" symmetry is what protects the special electron splitting.

How to See It (The "Double-Tip Microscope")
The paper suggests two ways to spot this in the real world:

The Spectral Camera (ARPES): This is like taking a photo of the electrons' energy. In a normal magnet, the photo looks the same for "spin-up" and "spin-down" electrons. In this new altermagnet, the photo would show a split, with the "spin-up" electrons looking like an 8-petaled flower and the "spin-down" electrons looking like a rotated version of that flower.
The Double-Tip Microscope (STM): Imagine using two tiny needles (like a pair of tweezers) to touch the material from different angles. The paper predicts that if you send an electric current through these needles, the current will flow differently depending on the angle you hold them. It's like a road that is wide and easy to drive on in some directions, but narrow and bumpy in others, creating a distinct "eight-pointed star" pattern of resistance.

The Conclusion
The paper claims that quasicrystals are not just chaotic messes; they are a versatile playground for creating exotic magnetic states that are impossible in standard crystals. By using the unique, non-repeating symmetries of quasicrystals (like 8-fold or 12-fold), nature can host these "g-wave" and "i-wave" altermagnets.

The authors suggest that while finding these in solid materials is hard, we might be able to simulate them in the lab using ultra-cold atoms or special light patterns, giving us a new way to design magnetic materials for the future.

Technical Summary: Altermagnetism in Quasicrystals

Problem Statement
Altermagnetism is a recently identified class of magnetic materials characterized by a collinear, zero-net-magnetization spin structure (typical of antiferromagnets) combined with spin-split electronic bands (typical of ferromagnets). This phenomenon arises from the breaking of combined time-reversal and spatial symmetries (e.g., inversion or translation), which are preserved in conventional antiferromagnets. To date, research on altermagnetism has been confined to periodic crystals, where the existence of altermagnetic phases relies on specific crystal rotational symmetries (such as four-fold or six-fold) compatible with translational periodicity. This constraint fundamentally forbids altermagnets with higher-order rotational symmetries (e.g., 8-fold or 12-fold) that are incompatible with periodicity. Concurrently, while quasicrystals were historically presumed to support only disordered, spin-glass-like states due to geometric frustration, recent experimental observations have confirmed long-range magnetic order in true icosahedral quasicrystals. However, the potential for quasicrystals to host exotic altermagnetic orders protected by their unique, non-periodic rotational symmetries remains unexplored.

Methodology
The authors employ a theoretical framework combining symmetry analysis and self-consistent mean-field theory to investigate altermagnetism in aperiodic systems.

Models: The study utilizes minimal $t-J$ $t - J$ -like models for two specific quasicrystalline tilings:
1. Ammann-Beenker (AB) tiling: An octagonal quasicrystal composed of square and rhombus tiles, possessing global $C_8$ rotational symmetry. The model involves two orbitals per site (e.g., $\{d_{xy}, d_{x^2-y^2}\}$ ) connected by $C_8$ rotation, with angular-dependent hopping textures.
2. Stampfli tiling: A dodecagonal quasicrystal composed of squares, regular triangles, and rhombuses, possessing global $C_{12}$ rotational symmetry. The model utilizes $f$ -orbitals ( $f_x(x^2-3y^2)$ and $f_y(3x^2-y^2)$ ) with analogous hopping textures.
Hamiltonian: The total Hamiltonian includes a kinetic term with orbital-dependent hopping matrices and a ferromagnetic Heisenberg-like combined spin-orbital interaction term.
Calculation: The interaction term is decoupled via a mean-field approximation. The authors perform self-consistent calculations to determine site-resolved local charge density and magnetization, allowing for spatially inhomogeneous ordering without presupposing translational symmetry.
Analysis: The study analyzes the resulting spectral functions via Fourier projection (since crystal momentum is not a good quantum number in quasicrystals) and calculates spin-resolved transport properties using a two-terminal setup modeled with scanning tunneling microscopy (STM) tips and the Landauer-Büttiker formalism.

Key Contributions and Results
The paper demonstrates that quasicrystals can host stable altermagnetic phases with symmetries inaccessible in periodic crystals:

Emergence of Stable Phases: In the AB-tiling octagonal quasicrystal, a stable $g$ -wave altermagnetic phase emerges at strong interaction coupling ( $J$ ). Similarly, the Stampfli-tiling dodecagonal quasicrystal supports a stable $i$ -wave altermagnetic phase.
Symmetry Protection: These phases are protected by composite symmetries that combine spatial rotation with time reversal:
- The octagonal phase preserves $C_8\mathcal{T}$ symmetry.
- The dodecagonal phase preserves $C_{12}\mathcal{T}$ symmetry.
- Crucially, while the individual magnetic order breaks the pure rotational symmetry ( $C_8$ or $C_{12}$ ) and time-reversal symmetry ( $\mathcal{T}$ ), their combination remains intact, preventing the system from becoming a trivial ferromagnet or a conventional antiferromagnet with degenerate bands.
Spectral Signatures: The spectral functions exhibit distinct anisotropic spin splittings.
- For the $g$ -wave phase, the spin-resolved spectral difference ( $A_\uparrow - A_\downarrow$ ) transforms antisymmetrically under $C_8$ rotation, resulting in an eight-fold nodal structure where the splitting vanishes along lines defined by $\theta = \pi/8 + n\pi/4$ .
- For the $i$ -wave phase, a twelve-fold nodal structure is observed, with the splitting vanishing under $C_{12}$ rotation.
Transport Anisotropy: The study predicts that spin conductance in these systems will exhibit strong anisotropy reflecting the underlying symmetry. The difference in spin-up and spin-down conductance ( $\sigma_\uparrow - \sigma_\downarrow$ ) changes sign under the respective $C_8$ or $C_{12}$ rotations, vanishing along the same nodal lines as the spectral function.

Significance and Claims
The authors claim to establish quasicrystals as a versatile platform for realizing unconventional altermagnetic orders that transcend the constraints of translational periodicity. By uniting the frontiers of altermagnetism and quasicrystal physics, the work demonstrates that the rich, higher-fold rotational symmetries of quasicrystals can stabilize altermagnetic states (specifically $g$ -wave and $i$ -wave) that are forbidden in periodic lattices.

The paper proposes that these phases can be experimentally identified through:

Spin-resolved Angle-Resolved Photoemission Spectroscopy (spin-ARPES): To visualize the momentum-space nodal structures.
Double-tip Scanning Tunneling Microscopy (STM): To probe the anisotropic spin conductance and non-local transport correlations.

The authors acknowledge that resolving these nodal structures in solid-state quasicrystals presents significant experimental challenges with current techniques. However, they suggest that candidate materials (such as transition-metal quasicrystals like Au-In-Eu systems) and highly tunable platforms (such as optical quasicrystals for ultracold atoms or moiré quasicrystals) offer viable routes for future verification. The work provides a theoretical framework and specific symmetry-based signatures for identifying altermagnetism beyond periodic systems.

Technical Summary: Altermagnetism in Quasicrystals

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