🔬 mesoscale physics

Higher-order Hall response arises from octupole order and scalar spin chirality in a noncollinear antiferromagnet

By using specific magnetic field orientations to disentangle different electronic contributions, the researchers demonstrate that the anomalous Hall effect in noncollinear antiferromagnets arises from distinct mechanisms, specifically octupole order and scalar spin chirality.

Original authors: Adithya Rajan, Tom G. Saunderson, Fabian R. Lux, Rocío Yanes Díaz, Hasan M. Abdullah, Arnab Bose, Beatrice Bednarz, Jun-Young Kim, Dongwook Go, Tetsuya Hajiri, Gokaran Shukla, Olena Gomonay, Yugui Yao

Published 2026-02-10

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CC BY 4.0

Original authors: Adithya Rajan, Tom G. Saunderson, Fabian R. Lux, Rocío Yanes Díaz, Hasan M. Abdullah, Arnab Bose, Beatrice Bednarz, Jun-Young Kim, Dongwook Go, Tetsuya Hajiri, Gokaran Shukla, Olena Gomonay, Yugui Yao, Wanxiang Feng, Hidefumi Asano, Udo Schwingenschlögl, Luis López-Díaz, Jairo Sinova, Gerhard Jakob, Yuriy Mokrousov, Aurélien Manchon, Mathias Kläui

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 you are at a massive, crowded dance floor. Usually, in a "normal" crowd (like a standard magnet), everyone is either facing one direction or facing the opposite direction. If you try to push through the crowd, you feel a predictable resistance based on which way the "mass" of the crowd is leaning.

This paper is about a very strange, "non-collinear" dance floor—specifically in a material called Mn3NiCuN. In this dance, the dancers (the electrons/spins) aren't just facing North or South; they are arranged in complex, beautiful geometric patterns, like a spinning kaleidoscope.

Here is the breakdown of what the scientists discovered, using everyday analogies:

1. The "Ghost" Magnet (The Octupole Order)

In a standard magnet, you have a "Dipole"—think of it like a single giant arrow pointing North. If you move a magnet, that arrow moves, and you feel it.

But in this material, the "arrows" are arranged in such a complex way that if you look at the whole crowd, the net direction is zero. It’s like having 100 people: 50 are facing North and 50 are facing South. To a casual observer, the crowd isn't "going" anywhere.

However, the researchers discovered a "Higher-Order" effect called an Octupole.

The Analogy: Imagine the dancers aren't just facing directions; they are performing a complex synchronized routine where they lean in specific, multi-directional ways. Even though the crowd isn't "moving" in one direction, the pattern of their leaning creates a hidden force.
The Discovery: By tilting the magnetic field sideways (in-plane) rather than just pushing from the top, the scientists were able to "trip" this hidden pattern, proving that this "ghostly" octupole force exists and can actually push electricity around.

2. The "Swirl" Effect (Scalar Spin Chirality)

The researchers also found a second, even weirder phenomenon at low magnetic fields. They call it Scalar Spin Chirality, but you can think of it as "The Whirlpool Effect."

The Analogy: Imagine the dancers are usually in a flat, 2D pattern on the floor. But when you nudge them with a small magnetic field, they don't just turn; they start to tilt up and down, creating tiny, swirling whirlpools in the crowd.
The Discovery: These tiny "whirlpools" create a secondary push on the electrons. This is a "Topological" effect, meaning the electricity isn't just being pushed by a magnet; it's being pushed by the shape of the swirl itself.

3. Why does this matter? (The Spintronics Revolution)

Right now, our computers use electricity (the flow of electrons) to process information. This generates heat and uses a lot of energy. The next frontier is Spintronics, which uses the "spin" (the direction the electron is facing) instead of just the charge.

The Problem: Most current spintronic materials are like heavy, clunky magnets that are hard to control and get hot.

The Solution: This paper shows that we can use these "non-collinear" materials—which have almost no net magnetism—to control electricity using these complex "octupole" and "whirlpool" patterns. Because these patterns are built into the very geometry of the material, they offer a way to create ultra-fast, tiny, and incredibly efficient electronic components that work in ways we previously thought were impossible.

Summary in a Nutshell:

The scientists found that even when a material appears to have no magnetic "pull," it possesses hidden, complex geometric patterns (Octupoles) and tiny swirling motions (Chirality) that can be used to steer electricity. It’s like discovering that a seemingly still crowd of people actually has a secret, powerful way of moving energy just by the way they dance.

Technical Summary: Higher-order Hall response arises from octupole order and scalar spin chirality in a noncollinear antiferromagnet

1. Problem Statement

In noncollinear antiferromagnets (NC-AFMs), a transverse electrical response known as the Anomalous Hall Effect (AHE) is observed despite the absence of significant net magnetization. While it has been established that the weak magnetic dipole moment in these materials cannot account for the magnitude of the observed AHE, the microscopic origin of this phenomenon has remained elusive.

The fundamental difficulty in identifying the mechanism lies in conventional measurement geometries. Most studies apply a magnetic field perpendicular to the plane of electrical measurement, which entangles the signal from the conventional magnetic dipole (magnetization) with any novel higher-order contributions. Consequently, it has been difficult to distinguish whether the AHE arises from magnetization, Berry curvature related to complex magnetic orders, or topological effects.

2. Methodology

The researchers investigated the NC-AFM compound $\text{Mn}_3\text{Ni}_{0.35}\text{Cu}_{0.65}\text{N}$ (Mn3NiCuN) using a multi-disciplinary approach:

Experimental Transport Measurements: The team grew 20 nm thin films of Mn3NiCuN on MgO (111) substrates. Crucially, they moved beyond perpendicular field geometries by performing magnetotransport measurements in in-plane magnetic field configurations. By sweeping the field within the (111) kagome plane along different crystallographic directions, they were able to suppress the conventional dipole-driven AHE signal.
Symmetry Analysis: Using representation theory, the authors derived the irreducible representations of the crystal structure to predict how different magnetic order parameters (dipole, octupole, and chirality) should respond to field rotation.
First-Principles Calculations: Density Functional Theory (DFT) was employed using the FLEUR code to calculate Berry curvature and the evolution of the octupole vector ( $\vec{Q}_{T1g}$ ).
Atomistic Spin Dynamics: They utilized Landau-Lifshitz-Gilbert (LLG) simulations to model how spin textures reorient under in-plane fields and to calculate the resulting scalar spin chirality.

3. Key Contributions

The paper provides a comprehensive framework for decomposing the Hall response in NC-AFMs into three distinct components:

Dipole Contribution ( $\vec{M}_{T1g}$ ): The conventional AHE proportional to net magnetization (minimal in this system).
Octupole Contribution ( $\vec{Q}_{T1g}$ ): A higher-order magnetic order arising from the coplanar 120° spin arrangement in the kagome plane.
Scalar Spin Chirality (SSC) Contribution: A topological Hall-like effect (THE) arising from noncoplanar spin textures ( $\vec{S}_i \cdot (\vec{S}_j \times \vec{S}_k)$ ).

4. Results

Isolation of Octupole Order: The in-plane field measurements successfully isolated a purely octupole-driven Hall response. Unlike the dipole-driven AHE (which vanishes when the field and current are coplanar), the octupole-driven AHE remains finite and exhibits a characteristic three-fold (120°) angular symmetry as the field is rotated in-plane.
Discovery of Low-Field Chirality: At low magnetic fields, the researchers observed an additional Hall-like signal that follows a Gaussian-like shape and changes sign with field polarity. This was identified as a Topological Hall Effect (THE) driven by scalar spin chirality. This occurs when the magnetic field forces the spins to rotate out of their coplanar orientation, creating noncoplanar textures.
Validation of Coexisting Orders: The experimental data (showing 120° periodicity for both the octupole and SSC components) matched the theoretical predictions and simulations. The results confirm that octupole order, dipole moments, and chirality coexist and dominate in different magnetic field regimes.

5. Significance

This work represents a paradigm shift in the study of antiferromagnetic spintronics. It demonstrates that NC-AFMs possess a much richer landscape of magnetic order parameters than conventional ferromagnets or collinear antiferromagnets.

By providing a method to disentangle these complex orders through specific field geometries, the study establishes a roadmap for identifying and controlling unconventional magnetic moments. This capability is essential for the development of next-generation spintronic devices that utilize the high-speed dynamics and robustness of antiferromagnets, moving beyond simple magnetization-based logic to more complex, higher-order magnetic information processing.