🔬 mesoscale physics

Topological magnons in a collinear altermagnet

This paper proposes a honeycomb lattice model of collinear altermagnets that hosts Weyl and nodal-line magnons without Dzyaloshinskii-Moriya interaction, characterized by chirality and topological invariants, which give rise to observable phenomena such as the magnon spin Nernst effect and a topology-induced differential gyromagnetic ratio detectable via the Einstein-de Haas effect.

Original authors: Meng-Han Zhang, Lu Xiao, Dao-Xin Yao

Published 2026-09-03

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CC BY 4.0

Original authors: Meng-Han Zhang, Lu Xiao, Dao-Xin Yao

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

In the microscopic world of magnets, tiny waves of spin, known as magnons, carry information and energy. For decades, scientists have understood how these waves behave in standard magnets and even in anti-magnets, where opposing spins cancel each other out. However, a newer class of magnetic materials, called altermagnets, has recently emerged as a fascinating middle ground. These materials possess a unique internal order where the spins are arranged in a specific, alternating pattern that cancels out the overall magnetic pull, much like a standard anti-magnet, yet they still exhibit properties usually reserved for magnets with a strong net force. This unusual combination allows them to split energy levels for particles moving in different directions without needing the heavy, relativistic effects that usually complicate such behavior. Understanding how waves move through these materials is crucial because it could lead to new ways of processing information that consume far less energy than current technology, potentially revolutionizing how we build computers and sensors.

Researchers have now proposed a theoretical model showing how these special magnetic waves can become "topological" within a honeycomb lattice structure, a pattern resembling a sheet of chicken wire. In this study, the scientists constructed a model of an altermagnet where the connections between atoms are slightly uneven. By breaking the symmetry of these connections, they discovered that the magnetic waves naturally organize themselves into two distinct, exotic forms: one where the waves meet at specific points in their energy landscape, known as Weyl points, and another where they form continuous lines of contact. Crucially, this happens without the need for a specific type of interaction called the Dzyaloshinskii-Moriya interaction, which usually requires complex atomic forces to create similar effects. Instead, the researchers found that simply adjusting the strength of the bonds between atoms in the honeycomb pattern was enough to generate these complex, topological structures.

The study reveals that these magnetic waves carry a property called chirality, which can be thought of as a handedness, distinguishing them as either left-handed or right-handed. In this model, the left-handed and right-handed waves travel along the edges of the material in opposite directions, creating a one-way street for energy that is immune to backscattering from impurities or defects. The researchers calculated that if you heat one side of this material, these chiral waves will flow across to the other side, creating a measurable spin current. This phenomenon, known as the magnon spin Nernst effect, suggests that the material could act as a highly efficient pump for spin information, driven purely by temperature differences.

Furthermore, the team explored how these waves interact with the physical rotation of the material itself. Because the waves carry angular momentum, their movement can exert a tiny mechanical torque on the material. The researchers calculated a specific ratio that describes how the material's magnetic moment changes in response to temperature, a relationship that can be detected through a phenomenon called the Einstein-de Haas effect. Their simulations show that this effect produces a distinct signal, particularly at optimal temperatures, which could serve as a fingerprint to prove the existence of these topological magnetic waves. The findings suggest that by tuning the atomic bonds in these materials, scientists could create stable, high-performance devices for spin-based electronics that are robust against external disturbances and do not rely on the heavy relativistic effects found in other systems.

The work also highlights that these theoretical models could be tested in various experimental setups beyond traditional solid-state crystals. Because the model does not require complex relativistic interactions, it could be simulated using ultracold atoms trapped in light lattices, atoms on surfaces observed with scanning tunneling microscopes, or even specialized electrical circuits. This versatility means that the principles discovered here could be verified and utilized in a wide range of future technologies, offering a new pathway to manipulate spin currents with precision. The study ultimately provides a foundational framework for understanding how symmetry breaking in magnetic lattices can generate complex, topological behaviors, paving the way for the next generation of magnonic devices.

Technical Summary: Topological Magnons in a Collinear Altermagnet

Problem Statement
Conventional antiferromagnets often exhibit pairwise magnons with opposite chiralities that remain degenerate, hindering the generation of pure spin currents mediated by magnons due to the inability to separate spin states. While spin-orbit coupling (SOC) and the Dzyaloshinskii-Moriya interaction (DMI) have been utilized to induce chiral magnetic properties and spin textures, their efficiency can be limited by specific lattice geometries and the inherent constraints of relativistic spin-splitting phases. The authors address the need for a mechanism to realize topological magnons with symmetry-compensated zero net magnetization in collinear altermagnets without relying on SOC or DMI. Specifically, the paper investigates how symmetry-breaking in exchange couplings can lift Kramers degeneracy and generate topological magnon states (Weyl and nodal-line magnons) that exhibit unique transport properties and mechanical responses, despite the presence of magnon pairs with opposite chiralities.

Methodology
The authors construct a theoretical Heisenberg model on a honeycomb lattice featuring Néel order. The Hamiltonian includes nearest-neighbor coupling ( $J_1$ ) and three distinct types of next-nearest-neighbor (NNN) couplings ( $J_2, J'_2 \pm \delta, J''_2$ ). The breaking of sublattice symmetry via these NNN couplings is proposed as the mechanism to generate altermagnetic magnon bands.

The study employs the following theoretical frameworks:

Holstein-Primakoff Transformation: Spins are mapped to bosonic operators to describe magnetic excitations.
Bogoliubov-de Gennes (BdG) Formalism: The system is analyzed using a generalized BdG equation with a Nambu spinor basis to handle particle-hole symmetry. A para-unitary transformation is applied to diagonalize the Hamiltonian and obtain the magnon energy spectra.
Topological Invariants: The authors calculate the Berry curvature and Berry connection using the BdG inner product. They define a $Z_2$ topological invariant for Kramers pairs of bands and analyze the Chern number.
Semiclassical Transport: The magnon spin Nernst effect and angular momentum are derived using semiclassical equations of motion, incorporating the Berry curvature as an effective magnetic field in momentum space.
Numerical Simulation: The authors calculate phase diagrams, density of states (DOS), edge mode spectra for finite ribbons (zigzag and armchair terminations), and temperature-dependent differential gyromagnetic ratios.

Key Contributions and Results

Model Realization without SOC/DMI: The paper demonstrates that Weyl magnons and nodal-line magnons can be realized in a collinear altermagnet solely by breaking the symmetry of second-nearest-neighbor exchange couplings. This avoids the need for DMI or significant SOC.
Topological Phases:
- Nodal-Line Magnons: In the absence of the symmetry-breaking parameter $\delta$ , the system hosts symmetry-protected nodal lines centered at time-reversal-invariant momenta (TRIM). These are characterized by a non-trivial $Z_2$ invariant ( $\nu_n = 1$ ).
- Weyl Magnons: Introducing a finite $\delta$ splits the nodal lines into pairs of Weyl points with opposite chiralities located along high-symmetry axes. The $J''_2$ term acts as a mass term, generating a topological gap $\Delta_{W\chi}$ via the operator $M = \sigma_0^+ \otimes (M(k)\sigma_0)$ , thereby creating a Weyl semimetal structure.
Chirality and Spin Accumulation: The model exhibits chiral splitting where left- and right-hand magnons form pairs with opposite chiralities. However, the non-relativistic spin splitting lifts the Kramers degeneracy, allowing for anisotropic spin accumulation on chiral edge states and enabling the separation of spin states that is typically hindered in conventional antiferromagnets.
Magnon Spin Nernst Effect (MSNE): The presence of non-zero Berry curvature induces a magnon spin Nernst effect. When a longitudinal temperature gradient is applied, magnon currents flow in the transverse direction. The conductivity depends on the temperature and the symmetry-breaking parameter $\delta$ .
Einstein-de Haas (EdH) Effect: The authors calculate the differential gyromagnetic ratios ( $\gamma^*_{self}$ and $\gamma^*_{edge}$ ) induced purely by the topology of the magnons. They find that the accumulation of topological angular momentum (from both self-rotation and edge currents) leads to a measurable mechanical rotation (EdH effect), particularly showing a peak response in an optimal temperature zone.
Edge States: The study identifies robust chiral edge modes in finite ribbon geometries. The nature of these modes (degeneracy and dispersion) depends on the edge termination (zigzag vs. armchair) and the specific topological phase (Weyl vs. nodal-line).

Significance and Claims
The paper claims to provide a fundamental framework for understanding and manipulating topological magnons in collinear altermagnets without the reliance on relativistic effects like SOC or DMI. The primary significance lies in:

New Mechanism for Spin Transport: By utilizing non-relativistic symmetry breaking, the model offers a pathway to generate pure spin currents and spin accumulation with low energy consumption, potentially improving the quality of magnet-superconductor and magnet-semiconductor heterostructures for quantum computation.
Mechanical Detection of Topology: The calculation of the differential gyromagnetic ratio suggests that the Einstein-de Haas effect can serve as a sensitive probe for the chiral splitting and topological nature of altermagnetic magnons, linking band topology directly to macroscopic mechanical effects.
Experimental Feasibility: The authors note that because the model does not require SOC, it can be more easily implemented in simulators such as atomic spins on surfaces (via STM), ultracold atoms in optical lattices, Rydberg atoms, and topolectrical circuits.
Device Potential: The robustness of these topological magnons against impurities and external fields positions them as building blocks for next-generation magnonic devices.

The authors conclude that while the low-energy edge states share similarities with honeycomb antiferromagnets, the interplay between collinear altermagnetism and non-trivial bulk topology creates unique magnon currents and topological responses, including the lifting of Kramers degeneracy and the emergence of high-energy chiral edge transport.

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