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Field-induced topological Hall effect and butterfly-shaped magnetoresistance in the centrosymmetric antiferromagnet EuAuAs

This study reveals that the centrosymmetric antiferromagnet EuAuAs exhibits a field-induced topological Hall effect and butterfly-shaped magnetoresistance in its antiferromagnetic state, driven by finite scalar spin chirality and magnetic domain evolution.

Original authors: Yu Zhang, Junfa Lin, Huan Wang, Kun Han, Yiting Wang, Xue Dong, Zhenfeng Guan, Shengdi Xi, Tian-Long Xia

Published 2026-06-30

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CC BY 4.0

Original authors: Yu Zhang, Junfa Lin, Huan Wang, Kun Han, Yiting Wang, Xue Dong, Zhenfeng Guan, Shengdi Xi, Tian-Long Xia

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 crystal called EuAuAs as a tiny, perfectly organized city built from atoms. In this city, the "residents" are electrons (the electricity carriers) and "magnetic spins" (tiny internal compasses attached to the atoms). Usually, in a city like this, the compasses point in opposite directions, canceling each other out, making the material an antiferromagnet (a magnetic material that doesn't act like a magnet to the outside world).

This paper is like a detective story where scientists investigated what happens to the traffic (electricity) in this city when they apply an external magnetic field (a giant, invisible hand pushing on the compasses).

Here is the breakdown of their findings using simple analogies:

1. The City Layout and the "Cold Snap"

The scientists grew perfect, stick-shaped crystals of EuAuAs. They found that when the city gets very cold (below about 6 Kelvin, which is just a few degrees above absolute zero), the magnetic compasses of the residents suddenly lock into a specific pattern. This is the antiferromagnetic transition. It's like the whole city suddenly deciding to stand in perfect, alternating rows.

2. The "Butterfly" Traffic Jam (Magnetoresistance)

When the scientists sent electricity through the city, they noticed something strange about the traffic flow when they applied a magnetic field.

The Phenomenon: They observed a "butterfly-shaped" pattern in how the electricity resisted the flow. Imagine drawing a butterfly on a graph: as the magnetic field increases, the resistance goes down, then up, then down again, creating two wings.
The Direction Matters: This butterfly shape was very strong when the magnetic field was pushed from the top (along the c-axis) but disappeared when pushed from the side.
The Cause: The scientists believe this is caused by magnetic domains (neighborhoods where compasses agree) and domain walls (the fences between them). When the magnetic field pushes, these fences get stuck or "pin" in place, like a traffic jam caused by a stalled car. As the field changes, the fences move, creating that unique butterfly shape in the data.

3. The "Topological Hall Effect" (The Invisible Detour)

This is the most exciting discovery. Usually, if you drive straight down a road, you go straight. But in this material, under specific conditions (cold temperature, field from the side), the electrons started taking a detour.

The Analogy: Imagine the electrons are cars driving through a neighborhood where the compasses of the atoms are arranged in a twisted, 3D spiral (a "non-coplanar" spin texture). Even though there is no actual magnetic field pushing the cars sideways, the twisted arrangement of the compasses acts like a hidden, invisible magnetic field.
The Result: This "hidden field" forces the electrons to curve off their path, creating a voltage on the side of the road. This is called the Topological Hall Effect.
The "Scalar Spin Chirality": The scientists explain that this happens because the magnetic compasses form a specific 3D twist (like a screw or a corkscrew) that has a property called "chirality." It's like a right-handed screw vs. a left-handed screw. This twist creates the invisible field that pushes the electrons sideways.

4. The "Flip-Flop" Moment

When the scientists increased the magnetic field from the side, they saw a sudden jump in magnetization (a metamagnetic transition). It's like a sudden shift in the city's mood where the compasses suddenly reorient themselves.

Right at this moment, the "Topological Hall Effect" (the sideways voltage) appeared, peaked, and then flipped its sign (went from positive to negative) before disappearing.
This suggests that the "invisible detour" for the electrons only exists while the magnetic compasses are in that specific, twisted, transitional state. Once the compasses are fully aligned by the strong field, the twist disappears, and the electrons go straight again.

Summary

In short, the paper shows that in this specific crystal (EuAuAs):

Cold temperatures make the magnetic atoms line up in a specific pattern.
Magnetic fields cause the boundaries between magnetic neighborhoods to get stuck, creating a butterfly-shaped resistance in the electricity.
Twisted magnetic patterns created by the field act like an invisible magnetic force, forcing electrons to take a detour, creating a Topological Hall Effect.

The scientists conclude that the way these magnetic textures (the twists and turns of the compasses) interact with the moving electrons is the key to understanding how electricity flows through this material. They didn't propose any new gadgets or medical uses; they simply mapped out these fascinating physical behaviors.

Technical Summary: Field-induced topological Hall effect and butterfly-shaped magnetoresistance in the centrosymmetric antiferromagnet EuAuAs

Problem Statement
While the coupling between magnetic and electronic degrees of freedom in magnetic materials is known to generate complex transport phenomena, the specific mechanisms driving the topological Hall effect (THE) and magnetoresistance (MR) in centrosymmetric antiferromagnets remain an active area of investigation. Unlike noncentrosymmetric systems where Dzyaloshinskii–Moriya interaction (DMI) stabilizes skyrmions, centrosymmetric materials lack this intrinsic symmetry breaking, yet they can still exhibit topological spin textures. The EuTX family (T = transition metal, X = pnictogen) offers a fertile platform for studying these phenomena, but a detailed understanding of the magnetism and transport properties of EuAuAs, specifically its relation to magnetic textures, was previously unclear.

Methodology
The authors synthesized high-quality single crystals of EuAuAs using a bismuth flux method. The structural quality was verified via powder and single-crystal X-ray diffraction (XRD), confirming the hexagonal ZrBeSi-type structure (space group $P6_3/mmc$ ). Magnetic properties were characterized using a Quantum Design MPMS-3 system, measuring zero-field-cooled (ZFC) and field-cooled (FC) susceptibility, as well as field-dependent magnetization ( $M(H)$ ) curves with fields applied parallel to the $ab$-plane ( $H \parallel ab$ ) and the $c$ -axis ( $H \parallel c$ ). Electrical transport measurements were conducted on a Quantum Design PPMS-14 T system. Hall resistivity ( $\rho_{xz}$ ) and longitudinal resistivity ( $\rho_{xx}$ ) were measured with current along the $c$ -axis ( $I \parallel c$ ) and magnetic fields applied along $ab$, as well as configurations with $H \parallel c$ and $I \parallel ab$ . Angular-dependent MR measurements were performed by rotating the magnetic field from the $c$ -axis toward the $ab$-plane.

Key Results

Crystal Structure and Resistivity: EuAuAs crystallizes in a layered structure with alternating magnetic Eu layers and nonmagnetic Au–As layers. Resistivity measurements indicate metallic behavior. A strong electronic anisotropy is observed, with longitudinal resistivity along the $c$ -axis ( $\rho_{zz}$ ) being significantly larger than that in the $ab$-plane ( $\rho_{xx}$ ).
Magnetic Properties: Magnetic susceptibility measurements reveal antiferromagnetic (AFM) transitions at $T_N \approx 5.7$ $T_{N} \approx 5.7$ K ( $H \parallel ab$ $H ∥ ab$ ) and $T_N \approx 6.3$ $T_{N} \approx 6.3$ K ( $H \parallel c$ $H ∥ c$ ). The Curie-Weiss fitting yields positive Weiss temperatures, suggesting ferromagnetic interactions in the paramagnetic regime.
- For $H \parallel ab$ , the $M(H)$ curves exhibit a distinct metamagnetic transition at approximately 0.5 T ( $H_t^{ab}$ ) and a small hysteresis loop below 0.6 T.
- For $H \parallel c$ , the $M(H)$ curves are smooth with no metamagnetic transition or hysteresis.
- Saturation magnetization is reached at $\sim$ 2.5 T ( $H \parallel ab$ ) and $\sim$ 3.5 T ( $H \parallel c$ ), with values close to the theoretical moment of $7.0 \mu_B$ /Eu, indicating easy-plane anisotropy.
Topological Hall Effect (THE): A pronounced THE is observed in the AFM state with $H \parallel ab$ $H ∥ ab$ and $I \parallel c$ $I ∥ c$ . By separating the total Hall resistivity into normal, anomalous, and topological components, the authors extracted a topological Hall resistivity ( $\rho_{xz}^T$ $ρ_{x z}^{T}$ ) that peaks at $\sim$ $\sim$ 0.32 $\mu\Omega$ $μ Ω$ cm at 1.1 T.
- The $\rho_{xz}^T$ signal exhibits a sign reversal (from positive to negative) as the field increases, vanishing near the saturation field ( $H_s^{ab} \approx 3.35$ T).
- The signal is confined to temperatures below $T_N$ and fields below $H_s^{ab}$ , correlating with the metamagnetic transition region.
Magnetoresistance (MR):
- For $H \parallel ab$ and $I \parallel c$ , a weak butterfly-shaped negative MR is observed at low temperatures, peaking near the metamagnetic transition field.
- For $H \parallel c$ and $I \parallel ab$ , a pronounced butterfly-shaped hysteresis in MR is observed, which is absent in the $M(H)$ curves. This hysteresis is strongly angle-dependent, diminishing as the field rotates from the $c$ -axis to the $ab$-plane.

Interpretation and Mechanisms
The authors attribute the observed THE to a finite scalar spin chirality (SSC) arising from field-induced noncoplanar spin textures. Since EuAuAs is centrosymmetric, the formation of these textures is likely driven by the metamagnetic transition and competition between anisotropic magnetic configurations rather than bulk DMI. The sign reversal of the THE is interpreted as a reconstruction of the noncoplanar AFM state.

The butterfly-shaped MR, particularly the hysteresis observed for $H \parallel c$ where no metamagnetic transition is seen in magnetization, is linked to the evolution of antiferromagnetic domains and domain-wall pinning. The strong angular dependence of the MR suggests that these domain dynamics are governed by the system's magnetic anisotropy.

Significance
This work provides a systematic investigation of the interplay between magnetic textures and electronic transport in the centrosymmetric antiferromagnet EuAuAs. The key contributions include:

Identification of THE in a Centrosymmetric AFM: Demonstrating that field-induced noncoplanar spin textures can generate a significant THE in a centrosymmetric system without bulk DMI.
Correlation of Transport and Magnetic Transitions: Establishing a direct link between the metamagnetic transition, the sign-reversing THE, and the low-field MR anomalies.
Insight into Domain Dynamics: Revealing that butterfly-shaped MR hysteresis can serve as a sensitive probe for AFM domain evolution and pinning, even when magnetization curves appear smooth.

The results suggest that field-induced spin textures and magnetic domain dynamics play a critical role in the magnetotransport properties of EuAuAs, offering new insights into the physics of centrosymmetric antiferromagnets.

1. The City Layout and the "Cold Snap"

2. The "Butterfly" Traffic Jam (Magnetoresistance)

3. The "Topological Hall Effect" (The Invisible Detour)

4. The "Flip-Flop" Moment

Summary

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