🔬 materials science

Weyl Magnons in the Non-Coplanar Antiferromagnet MnTe $_2$

This study establishes MnTe $_2$ as a tunable Weyl magnon material by combining experimental spectroscopy and theoretical modeling to demonstrate how its non-coplanar antiferromagnetic order hosts symmetry-protected topological nodal lines that transform into Weyl magnons under an external magnetic field.

Original authors: Ahmed E. Fahmy, Archibald J. Williams, Yufei Li, Thuc T. Mai, Kevin F. Garrity, Matthew B. Stone, Mohammed J. Karaki, Sara Haravifard, Angela R. Hight Walker, Rolando Valdés Aguilar, Joshua E. Goldber

Published 2026-02-20

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Ahmed E. Fahmy, Archibald J. Williams, Yufei Li, Thuc T. Mai, Kevin F. Garrity, Matthew B. Stone, Mohammed J. Karaki, Sara Haravifard, Angela R. Hight Walker, Rolando Valdés Aguilar, Joshua E. Goldberger, Yuan-Ming Lu

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 bustling city where the traffic isn't made of cars, but of tiny, invisible waves of energy called magnons. In most magnetic materials, these waves move in predictable, boring lanes. But in a special material called MnTe₂, scientists have discovered that these waves can do something magical: they can travel along "highways" that are protected by the laws of physics, and they can even turn into exotic particles called Weyl magnons when you tweak the environment.

Here is the story of this discovery, broken down into simple concepts.

1. The City and the Traffic (Magnons)

Think of a magnet as a city grid. The "cars" driving through this city are magnons. These aren't physical cars; they are ripples in the magnetic alignment of atoms. Just like electrons in a wire carry electricity, magnons carry spin (a type of angular momentum) without carrying any electric charge. This makes them perfect for building future computers that use less energy and generate less heat.

2. The "Non-Coplanar" Twist

Most magnets are like a flat sheet of paper; all the atoms line up in a single plane. But MnTe₂ is different. It's non-coplanar, meaning the atoms are arranged in a 3D, twisted, pyramid-like structure.

The Analogy: Imagine a group of dancers. In a normal magnet, they all face the same direction (like a choir). In MnTe₂, they are doing a complex, 3D dance where some face up, some down, and some sideways, forming a twisted knot. This twisted dance breaks the usual rules of symmetry, creating a unique playground for the magnons.

3. The Protected Highways (Nodal Lines)

In this twisted city, the scientists found that the magnons don't just move in straight lines. They travel along nodal lines.

The Analogy: Imagine a roller coaster track that forms a perfect, unbreakable loop in the sky. No matter how the wind blows (or how defects in the material try to stop them), the magnons can't fall off this track. These tracks are "protected" by the symmetry of the material's structure. If you try to push the magnon off the track, the laws of physics force it back on. This makes the transport of energy incredibly efficient and robust.

4. The Magic Switch: Turning on the Magnetic Field

The most exciting part of the paper is what happens when you apply an external magnetic field.

The Analogy: Think of the nodal line as a closed loop of a rubber band. When you apply a magnetic field, it's like pinching that rubber band in the middle. The loop breaks, and the two ends pull apart, creating two separate points.
The Result: These two points are called Weyl points. In the world of quantum physics, these are like "monopoles" or magical sources and sinks of energy flow. They are the bosonic (magnon) version of the famous "Weyl fermions" found in electronic materials.

5. How They Found It (The Detective Work)

The scientists didn't just guess; they used a multi-tool approach to prove this:

Neutron Scattering (The X-Ray Vision): They shot neutrons (tiny particles) at the crystal. When the neutrons hit the magnons, they bounced off in specific patterns. By looking at these patterns, they could "see" the energy bands and the nodal lines, just like an X-ray reveals a broken bone.
Raman Spectroscopy (The Musical Tuner): They shined a laser on the material and listened to the light that bounced back. The "notes" (frequencies) the material sang changed when they applied a magnetic field, confirming that the twisted dance of the atoms was indeed breaking apart into Weyl points.
Computer Modeling (The Simulation): They built a digital twin of the material on a computer. When they simulated the magnetic field, the digital magnons behaved exactly like the real ones, confirming the existence of the Weyl points.

6. Why This Matters

Why should you care about invisible waves in a crystal?

The "Traffic Jam" Solution: Because these magnons are protected by topology, they don't get stuck or scattered by impurities in the material. They flow smoothly, like a car on a maglev train that never hits a bump.
Future Tech: This discovery opens the door to magnonics—a new type of computing that uses spin waves instead of electricity. This could lead to super-fast, ultra-low-power devices that don't overheat.
The "Weyl" Connection: It proves that the strange, topological physics usually reserved for electrons can also happen with bosons (particles like magnons). It's like finding out that the same laws of gravity that make planets orbit also apply to a specific type of dance step.

Summary

In short, the researchers found a magnetic material (MnTe₂) where energy waves naturally travel on protected, unbreakable loops. By applying a magnetic field, they can snap these loops into two distinct, exotic points (Weyl magnons). This is a major step toward building the next generation of energy-efficient, topological computers.

1. Problem Statement

Topological magnons—bosonic quasiparticles with non-trivial band topology—are promising candidates for low-dissipation spin transport and novel magnonic devices. While Weyl electrons (fermions) have been extensively studied, and Weyl magnons have been theoretically predicted, experimental evidence for Weyl magnons has been lacking.

The primary challenges in realizing Weyl magnons are:

Symmetry Constraints: In many magnetic systems, combined inversion ( $I$ ) and effective time-reversal ( $\bar{T}$ ) symmetries force the Berry curvature to vanish, prohibiting Weyl points.
Material Complexity: Identifying materials with the specific non-coplanar magnetic ordering required to break these symmetries and host topological features is difficult.
Lack of Unified Framework: There was a need for a unified theoretical and experimental approach to identify, model, and verify topological features across diverse magnetic materials.

This paper aims to experimentally confirm the existence of Weyl magnons and topological nodal lines in a specific material, MnTe $_2$ , and demonstrate their tunability via external magnetic fields.

2. Methodology

The authors employed a multi-faceted approach combining symmetry analysis, advanced spectroscopy, and theoretical modeling:

Symmetry-Based Topology Indicators:
- Utilized Band Representation (BR) analysis to determine the topological nature of magnon bands based on the magnetic space group (MSG) $Pa\bar{3}$ .
- Identified that the non-coplanar antiferromagnetic order breaks effective time-reversal symmetry, allowing for topological features.
- Predicted that applying an external magnetic field along a low-symmetry direction would reduce the symmetry to subgroup $P\bar{1}$ , inducing Weyl points from pre-existing nodal lines.
Experimental Techniques:
- Inelastic Neutron Scattering (INS): Performed at 5 K on high-quality single crystals using the SEQUOIA spectrometer (Oak Ridge National Lab) to map the full magnon dispersion relations in reciprocal space.
- Magneto-Raman Spectroscopy: Conducted at NIST (1.6 K) in both Faraday ( $k \parallel B$ ) and Voigt ( $k \perp B$ ) configurations to probe zone-center magnons and their splitting under magnetic fields.
- Crystal Growth: Grown cm-sized single crystals of MnTe $_2$ via the Bridgman method with Te self-flux.
Theoretical Modeling:
- Linear Spin Wave Theory (LSWT): Constructed a microscopic spin Hamiltonian including Heisenberg exchange ( $J_{1-5}$ ), Dzyaloshinsky-Moriya Interaction (DMI) to stabilize non-coplanarity, and Zeeman terms.
- Fitting: Parameters were fitted to reproduce both the INS dispersion and the field-dependent Raman splitting.
- Topological Calculations: Calculated Chern numbers, Berry phases, and Symmetry Indicators (SI) to confirm the presence of Weyl points and nodal lines.

3. Key Contributions

First Experimental Confirmation of Weyl Magnons: This work provides the first direct experimental evidence of Weyl magnons in a bulk magnetic material.
Discovery of Tunable Topology: Demonstrates that MnTe $_2$ hosts symmetry-protected nodal lines in zero field, which gap out into tunable Weyl magnons upon the application of a magnetic field.
Unified Framework Validation: Successfully integrated symmetry-based topological indicators with experimental data (INS and Raman) to validate a theoretical prediction of topological magnons in a non-coplanar antiferromagnet.
Direct Topological Signatures: Observed the characteristic pseudo-spin winding of scattering intensity around nodal lines, a direct signature of non-trivial topology.

4. Key Results

A. Crystal and Magnetic Structure

MnTe $_2$ crystallizes in the cubic pyrite structure ( $Pa\bar{3}$ ).
Below the Néel temperature ( $T_N \approx 87$ K), Mn $^{2+}$ moments ( $S=5/2$ ) order into a non-coplanar antiferromagnetic structure with four sublattices pointing along different local $[111]$ directions, resulting in zero net magnetization.
This non-coplanar order breaks effective time-reversal symmetry ( $\bar{T}$ ), a prerequisite for Weyl magnons.

B. Zero-Field Topology: Nodal Lines

INS Data: Revealed magnon dispersions consistent with the predicted band representations.
Nodal Lines: Symmetry analysis and LSWT calculations confirmed the existence of nodal lines on the $k_i = 0$ planes (glide-symmetric planes).
Experimental Signature: The authors observed a sinusoidal winding of INS intensity around these nodal lines in momentum space. This "winding" behavior, where intensity patterns reverse above and below the nodal energy, confirms the non-trivial Berry phase ( $\pi$ ) associated with the nodal lines.

C. Field-Induced Topology: Weyl Magnons

Symmetry Breaking: Applying a magnetic field (e.g., 14 T along $[0, 1, 6]$ ) reduces the symmetry to $P\bar{1}$ .
Gap Opening & Weyl Points: The nodal lines gap out, and the band crossing points evolve into isolated Weyl points (linear band crossings) in 3D momentum space.
Symmetry Indicators (SI): Calculated SI values for the middle band gap ( $Z_2 \times Z_4$ ) confirmed the topological nature of the gap, predicting an even number of Weyl points.
Chern Numbers: Numerical calculations showed non-zero Chern numbers ( $C = \pm 1$ ) on high-symmetry planes, consistent with the presence of Weyl monopoles.
Raman Confirmation: The triply degenerate $\Gamma$ -point magnon (3.5 meV) split into three distinct modes under the magnetic field, matching the LSWT prediction for the $P\bar{1}$ symmetry.

D. Spin Hamiltonian

The fitted Hamiltonian (Table 2) revealed dominant nearest-neighbor Heisenberg exchange ( $J_1 \approx 0.59$ meV) and finite DMI ( $D \approx 0.09$ meV), which stabilizes the non-coplanar structure.
The model accurately reproduced the INS spectra and the field-induced splitting of Raman modes.

5. Significance

Bosonic Analogue to Weyl Fermions: MnTe $_2$ is established as a direct bosonic analog to electronic Weyl semimetals, bridging the gap between electronic and magnonic topological physics.
Tunability: The ability to create, shift, or annihilate Weyl magnons via external magnetic fields offers a high degree of control over topological bosonic quasiparticles, which is crucial for device applications.
Future Applications: This discovery paves the way for:
- Thermal Hall Effect: Observing anomalous thermal Hall transport driven by the Berry curvature of Weyl magnons.
- Magnonic Devices: Developing chiral spin-wave waveguides, unidirectional magnon diodes, and logic elements based on topological protection.
- Material Discovery: Validating the symmetry-based algorithm as a powerful tool for discovering new topological magnetic materials.

In conclusion, this work provides a comprehensive experimental and theoretical demonstration of Weyl magnons in MnTe $_2$ , highlighting the critical interplay between non-coplanar magnetic order and band topology.