🔬 materials science

Origin of the large topological Hall effect in the EuCd $_2$ Sb $_2$ antiferromagnet

This study attributes the large topological Hall effect in the antiferromagnet EuCd $_2$ Sb $_2$ to three distinct mechanisms: Weyl states generated by $C_3$ symmetry breaking below the Néel temperature, Weyl states induced by strong spin fluctuations above it, and real-space Berry curvature arising from scalar spin chirality within antiferromagnetic domain walls.

Original authors: Faheem Gul, Orest Pavlosiuk, Tetiana Romanova, Dariusz Kaczorowski, Piotr Wiśniewski

Published 2026-02-24

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CC BY 4.0

Original authors: Faheem Gul, Orest Pavlosiuk, Tetiana Romanova, Dariusz Kaczorowski, Piotr Wiśniewski

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 driving a car through a city. Usually, if you turn the steering wheel (apply a magnetic field), the car turns. But in some special, exotic cities, the roads themselves seem to have a hidden "twist" or "spin" that pushes the car sideways, even if you didn't turn the wheel. This sideways push is called the Topological Hall Effect.

This paper is a detective story about a specific material, EuCd₂Sb₂ (a crystal made of Europium, Cadmium, and Antimony), where scientists discovered a massive version of this sideways push. They wanted to figure out: What is causing this giant twist?

Here is the story of their investigation, broken down into simple concepts.

1. The Setting: A Magnetic Dance Floor

The material acts like a dance floor for electrons (the tiny particles that carry electricity).

The Temperature: At room temperature, the electrons are chaotic. But when you cool the material down to about -266°C (7.4 Kelvin), the atoms start to organize. They form a specific pattern called an Antiferromagnet.
The Analogy: Imagine a line of dancers. In a normal magnet, they all face the same way. In this "Antiferromagnet," they stand in pairs: one faces North, the next faces South, the next North, and so on. They are perfectly balanced, canceling each other out.

2. The Mystery: The "Ghost" Force

When the scientists applied a magnetic field to this organized dance floor, they expected the electrons to flow straight. Instead, they saw a huge, unexpected sideways force (the Topological Hall Effect). It was so strong that it couldn't be explained by the usual rules of magnetism.

They realized there were three different "ghosts" (mechanisms) pushing the electrons sideways, and these ghosts appeared at different times and places.

Ghost #1: The Broken Symmetry (Below the freezing point)

The Scene: When the material is cold (below 7.4 K), the dancers are in their strict North-South pattern.
The Trick: The material has a specific symmetry (like a perfect triangle). But because the magnetic field is applied, this symmetry is broken.
The Result: This breaking creates "traffic jams" in the electron's energy map called Dirac points. When you push with a magnetic field, these traffic jams split into two separate "Weyl nodes."
The Analogy: Imagine a roundabout where traffic flows smoothly. Suddenly, a barrier appears, splitting the roundabout into two separate loops. Electrons taking these new loops get a "boost" of energy that pushes them sideways. This is the Momentum-Space Berry Curvature.

Ghost #2: The Spin Fluctuations (Above the freezing point)

The Scene: Even when the material is slightly warmer (above 7.4 K), the dancers aren't perfectly still. They are jittering and shaking (spin fluctuations).
The Trick: Even though the dancers aren't in a perfect pattern, their jittering is so strong and coordinated that they temporarily create those same "Weyl nodes" mentioned above.
The Result: The electrons still get that sideways push, even though the material isn't fully "frozen" into its magnetic order yet. It's like the dancers are shaking so hard they accidentally create the same traffic jams as the organized group.

Ghost #3: The Border Patrol (Inside the walls)

The Scene: In the cold material, the "North-South" dancers don't form one giant perfect block. They form small islands (domains) of North-South patterns. Where these islands meet, there are borders called Domain Walls.
The Trick: At these borders, the dancers don't just flip from North to South instantly. They twist and turn in a spiral to get from one side to the other. This twisting is called Spin Chirality.
The Result: This spiral twist acts like a real-world curve in the road. As electrons drive through this spiral, they get pushed sideways. This is the Real-Space Berry Curvature.
The Clue: The scientists noticed a tiny "bump" in their data at a specific magnetic field strength. This bump happened exactly when the magnetic field was strong enough to make these domain walls twist the most.

3. The Investigation Tools

To solve this, the scientists used three main tools:

Measuring Resistance: They saw how hard it was for electricity to flow. They found that the resistance spiked at specific magnetic fields, matching the "twisting" of the dancers.
Measuring Heat Capacity: They heated the crystal and measured how much energy it took. This confirmed that the magnetic ordering happens exactly at 7.4 K and that the atoms are behaving like the expected Europium ions.
The Hall Effect: They measured the sideways voltage. By mathematically subtracting the "normal" sideways push, they isolated the "Topological" (exotic) push.

4. The Conclusion: A Three-Part Mystery

The paper concludes that the giant Topological Hall Effect in EuCd₂Sb₂ isn't caused by just one thing. It's a team effort:

Below 7.4 K: The effect comes from Weyl nodes created by breaking the crystal's symmetry (Ghost #1) AND the spiral twisting at the borders of magnetic islands (Ghost #3).
Above 7.4 K: The effect comes from Weyl nodes created by the jittering of the atoms (Ghost #2).

Why Does This Matter?

Think of this material as a new kind of "super-highway" for electrons. If we can control these "ghost forces" (the Berry curvature), we might be able to build computers that are faster, use less energy, and are more secure. This paper helps us understand the traffic rules of these exotic highways, showing us that sometimes the road twists because of the terrain (symmetry breaking), sometimes because of the weather (fluctuations), and sometimes because of the construction zones (domain walls).

In short: EuCd₂Sb₂ is a magnetic chameleon that uses three different tricks to push electricity sideways, and the scientists finally figured out all three.

1. Problem Statement

The study addresses the microscopic origin of the large Topological Hall Effect (THE) observed in the antiferromagnetic (AFM) semimetal EuCd $_2$ Sb $_2$ . While the THE is generally attributed to Berry curvature in momentum space (from Weyl/Dirac points) or real space (from spin chirality), the specific mechanisms driving the effect in EuCd $_2$ Sb $_2$ remained ambiguous. Previous studies on this compound and its isostructural relatives (e.g., EuCd $_2$ As $_2$ , EuZn $_2$ Sb $_2$ ) offered conflicting or incomplete explanations, particularly regarding:

The nature of anomalies in Hall resistivity ( $\rho_{xy}$ ) and magnetoresistance (MR) that evolve with temperature and magnetic field.
The distinction between contributions arising from the AFM state (below $T_N$ ) and the paramagnetic state (above $T_N$ ).
The specific role of symmetry breaking, spin fluctuations, and domain wall physics in generating the observed Berry curvature.

2. Methodology

The authors conducted a comprehensive experimental investigation on high-quality single crystals of EuCd $_2$ Sb $_2$ grown via the Sn-flux method. The study employed a multi-faceted approach:

Structural & Compositional Characterization: Energy-dispersive X-ray (EDX) spectroscopy and single-crystal X-ray diffraction confirmed the stoichiometry (Eu:Cd:Sb $\approx$ 1:2:2) and trigonal crystal structure ( $P\bar{3}m1$ space group).
Magnetic Measurements: Magnetization ( $M$ ) and magnetic susceptibility ( $\chi$ ) were measured using a Quantum Design MPMS-XL to determine the Néel temperature ( $T_N$ ), magnetic anisotropy, and saturation fields ( $H_s$ ).
Thermodynamic Measurements: Heat capacity ( $C_p$ ) was measured using a relaxation method to calculate magnetic entropy and confirm the ground state of Eu $^{2+}$ ions.
Transport Measurements: Longitudinal and transverse magnetoresistance (LMR and TMR) and Hall resistivity ( $\rho_{xy}$ ) were measured in magnetic fields up to 9 T across a temperature range of 2–150 K.
Data Analysis:
- Decomposition of Hall resistivity into ordinary ( $\rho^o_{xy}$ ), conventional anomalous ( $\rho^{CA}_{xy}$ ), and topological ( $\rho^T_{xy}$ ) components.
- Scaling analysis of topological Hall conductivity ( $\sigma^T_{xy}$ ) versus longitudinal conductivity ( $\sigma_{xx}$ ) to distinguish intrinsic vs. extrinsic mechanisms.
- Correlation of transport anomalies with magnetization data to identify critical field points (e.g., $H_s/\sqrt{2}$ ).

3. Key Results

A. Magnetic and Thermodynamic Properties

Néel Temperature: Confirmed $T_N = 7.4$ K, consistent with previous reports.
Magnetic State: The system exhibits an A-type antiferromagnetic order with moments aligned ferromagnetically within the $ab$-plane and antiferromagnetically stacked along the $c$ -axis.
Entropy: Magnetic entropy ( $S_{mag}$ ) saturates at $\approx 16.6$ J mol $^{-1}$ K $^{-1}$ near 35 K, close to the theoretical value for Eu $^{2+}$ ( $R \ln 8 \approx 17.3$ J mol $^{-1}$ K $^{-1}$ ), confirming the divalent state.
Phonons: Heat capacity analysis indicates acoustic phonon modes dominate the lattice specific heat.

B. Magnetoresistance (MR)

Anomalies: Distinct peaks in both TMR and LMR were observed below $T_N$ , occurring near the field $H \approx H_s/\sqrt{2}$ (where $H_s$ is the saturation field).
Sign: Large negative MR was observed at 8 K (up to -31% in LMR), attributed to the chiral magnetic anomaly associated with Weyl points.
Comparison: The MR behavior differs significantly from semiconducting analogs (like EuZn $_2$ P $_2$ ) which show colossal negative MR due to magnetic polarons; EuCd $_2$ Sb $_2$ behaves as a semimetal with higher carrier density ( $n_H \approx 2.3 \times 10^{19}$ cm $^{-3}$ ).

C. Topological Hall Effect (THE)

Extraction: The topological Hall resistivity ( $\rho^T_{xy}$ ) was successfully extracted by subtracting the ordinary and conventional anomalous components.
Three Distinct Mechanisms: The study identifies three distinct sources of Berry curvature driving the THE:
1. Below $T_N$ (Symmetry Breaking): The breaking of $C_3$ rotational symmetry in the AFM state opens a band gap, creating Dirac points. Upon applying a magnetic field, these split into Weyl nodes, generating large momentum-space Berry curvature.
2. Below $T_N$ (Real Space): Small "humps" in $\rho^T_{xy}$ and TMR align precisely with the field $H_s/\sqrt{2}$ . These are attributed to scalar spin chirality developing within antiferromagnetic domain walls where local non-coplanar spin textures emerge. This generates a real-space Berry curvature.
3. Above $T_N$ (Spin Fluctuations): A broad THE anomaly persists above the ordering temperature. This is attributed to Weyl states induced by strong short-range spin fluctuations, which create transient Berry curvature even in the paramagnetic phase.

D. Scaling Behavior

The scaling of $\sigma^T_{xy}$ vs. $\sigma_{xx}$ suggests an intrinsic mechanism (Berry curvature dominated) rather than an extrinsic one (skew scattering), although the system sits near the border of the two regimes.
The Hall angle ( $\theta_H$ ) reaches a maximum of 2.6% at 6 K, which is smaller than in pure Weyl semimetals but comparable to other Eu-based 1:2:2 systems.

4. Significance and Contributions

Mechanistic Clarity: The paper resolves the origin of the large THE in EuCd $_2$ Sb $_2$ by distinguishing between momentum-space (Weyl nodes) and real-space (spin chirality in domain walls) contributions, and by identifying the persistence of Weyl states via spin fluctuations above $T_N$ .
Universal Insight: The identification of the $H_s/\sqrt{2}$ anomaly as a signature of scalar spin chirality in domain walls provides a new diagnostic tool for studying AFM systems with similar structures (e.g., EuZn $_2$ Sb $_2$ , EuCd $_2$ As $_2$ ).
Material Characterization: It provides the first comprehensive single-crystal characterization of EuCd $_2$ Sb $_2$ , including precise heat capacity and transport data, correcting previous inconsistencies in the literature regarding Curie-Weiss temperatures and field-dependent anomalies.
Topological Physics: The work reinforces the concept that antiferromagnetic semimetals can host robust topological transport phenomena driven by both symmetry breaking and dynamic spin fluctuations, expanding the landscape of candidate materials for topological spintronics.

Conclusion

The authors conclude that the large Topological Hall Effect in EuCd $_2$ Sb $_2$ is a multi-faceted phenomenon. It arises from Weyl nodes generated by $C_3$ symmetry breaking in the AFM state, scalar spin chirality within domain walls at specific field ratios, and fluctuation-induced Weyl states in the paramagnetic phase. This comprehensive understanding highlights the complex interplay between magnetic order, crystal symmetry, and electronic topology in rare-earth pnictides.