Anomalous and Topological Hall Effects in Antiferromagnetic EuSn2As2 Nanostructures

This study investigates magnetotransport in exfoliated $\mathrm{EuSn_{2}As_{2}}$ nanostructures, revealing that the canted antiferromagnetic state induces an anomalous Hall effect while chiral spin textures give rise to a topological Hall effect, suggesting these phenomena are characteristic features of magnetic 3D topological insulators.

The Gist

Imagine you have a tiny, magical sandwich made of layers of atoms. This isn't just any sandwich; it's a magnetic topological insulator called EuSn₂As₂. Think of it as a high-tech highway for electrons, but with a twist: the road is made of magnets, and the traffic rules change depending on how you tilt the compass.

Scientists took this material, peeled off incredibly thin slices (like peeling layers of an onion), and studied how electricity flows through them. Here is what they found, explained in everyday terms:

1. The "Traffic Jam" that Disappears (Negative Magnetoresistance)

Usually, when you put a magnet near a wire, it makes it harder for electricity to flow (like adding a speed bump). But in this material, below a certain cold temperature (about -249°C), doing the exact opposite happens: the electricity flows better when you apply a magnetic field.

• The Analogy: Imagine a crowded dance floor where everyone is spinning in different directions, bumping into each other (this is the "antiferromagnetic" state). It's chaotic and slow. When you apply a strong magnetic field, it's like a DJ shouting, "Everyone face North!" Suddenly, everyone lines up perfectly. The crowd stops bumping into each other, and the "traffic" (electricity) zooms through smoothly.
• The Catch: The scientists found that you have to push harder to get everyone to line up if you try to make them face "up" (perpendicular to the layers) compared to making them face "sideways" (along the layers).

2. The "S-Shaped" Curve (Multi-Band Transport)

When the scientists measured the "Hall Effect" (a sideways voltage that tells us what kind of particles are moving), they didn't get a straight line. They got an S-shaped curve.

• The Analogy: Imagine a highway with two lanes. One lane is full of heavy trucks (holes), and the other has a few speedy sports cars (electrons). At low speeds, the trucks dominate. But as you speed up, the sports cars start to matter more, changing the shape of the traffic flow. This "S-shape" told the scientists that two different types of charge carriers were working together in this material.

3. The Big Discovery: The "Ghost" Turn (Topological Hall Effect)

This is the most exciting part. The scientists saw a tiny, extra "bump" in the sideways voltage that couldn't be explained by the trucks or the sports cars alone. It was a Topological Hall Effect.

• The Analogy: Imagine driving on a straight road, but suddenly the road has a hidden, invisible spiral twist in the air. Even though the road looks straight from above, your car gets pushed sideways because of the invisible twist.
• What's causing the twist? The scientists believe the magnetic atoms inside the material aren't just pointing up or down. They are forming chiral spin textures.
  • Think of these as tiny, swirling tornadoes or spirals of magnetism that exist in the material.
  • When electrons fly past these invisible tornadoes, the tornadoes "twist" the electrons, pushing them sideways. This creates the extra voltage signal.

4. Why Does This Matter?

For a long time, scientists thought these swirling magnetic tornadoes (called skyrmions or chiral textures) were rare and only found in very specific, exotic materials.

• The "Aha!" Moment: This paper suggests that these swirling textures might be a common feature in a whole family of magnetic materials (like EuSn₂As₂ and its cousin MnBi₂Te₄).
• The Future: If these "magnetic tornadoes" are everywhere in these materials, it opens up a new way to build super-fast, super-efficient computers. We could potentially use these tiny spirals to store data or process information in ways that current electronics can't.

Summary

In short, the scientists peeled back layers of a magnetic crystal and discovered that:

1. Magnetic fields make electricity flow faster in this material.
2. Two types of particles are sharing the road.
3. Hidden magnetic tornadoes inside the material are twisting the electricity, creating a special signal called the Topological Hall Effect.

This discovery suggests that these "magnetic tornadoes" might be a standard feature in the next generation of quantum computers, rather than a rare curiosity.

Technical Summary

1. Problem Statement

Intrinsic magnetic topological insulators (TIs), such as EuSn2As2, are of significant interest for realizing exotic quantum phases like axion insulators and quantum anomalous Hall (QAH) states. While EuSn2As2 is theoretically predicted to be a strong TI in its paramagnetic phase and an axion insulator in its antiferromagnetic (AFM) phase, experimental understanding of its transport properties in the nanostructure regime remains incomplete.

Key open questions include:

• How do magnetic textures (e.g., domain walls, chiral spin structures) influence magnetotransport in exfoliated EuSn2As2 nanostructures?
• Can a Topological Hall Effect (THE) be observed in this material, which would imply the existence of real-space chiral spin textures (similar to those found in MnBi2Te4)?
• How do contact effects and multi-band transport complicate the interpretation of Hall data in these heavily p-doped systems?

2. Methodology

The authors investigated the magnetotransport properties of mechanically exfoliated EuSn2As2 nanostructures with thicknesses ranging from 60 nm to 140 nm.

• Sample Preparation: Single crystals were grown via stoichiometric melt cooling. Flakes were exfoliated using scotch tape and transferred to Si/SiO2 substrates. Contacts were fabricated using electron-beam or optical lithography (Hall bar geometry) with Ti/Au metallization.
• Measurement Setup: Transport measurements were performed in a Quantum Design Dynacool cryostat (up to 14 T) with a single-axis rotator to vary the magnetic field angle ($\theta$) from out-of-plane (OOP, $0^\circ$) to in-plane (IP, $90^\circ$).
• Data Analysis Strategy:
  • Longitudinal Resistance ($R_{xx}$): Analyzed for magnetoresistance (MR) behavior and saturation fields.
  • Hall Effect ($R_{xy}$): Decomposed into three components:
    1. Ordinary Hall Effect (OHE): Extracted from high-field linear slopes to determine carrier density and mobility.
    2. Anomalous Hall Effect (AHE): Proportional to net magnetization.
    3. Topological Hall Effect (THE): Extracted by subtracting the OHE and the scaled AHE (proportional to magnetization) from the total Hall signal.
  • Modeling: A two-band model was used to fit the non-linear Hall response observed at high fields, accounting for the coexistence of majority holes and minority electrons.

3. Key Results

A. Magnetoresistance (MR) and Magnetic Phase

• Negative MR: Below the Néel temperature ($T_N \approx 24$ K), a negative MR with a "dome" shape was observed. This is attributed to the canted antiferromagnetic (CAF) state of the easy-plane AFM.
• Anisotropy: The saturation field ($H_s$) depends on the field orientation:
  • Out-of-plane ($H_c^s$): $\approx 4.9$ T.
  • In-plane ($H_{ab}^s$): $\approx 3.6$ T.
  • This confirms an easy-plane AFM structure with a small anisotropy energy ($K_u \approx 1.7 \times 10^5$ J/m$^3$).
• Low-Field Peak: A narrow peak in MR was observed at low fields ($\sim 0.12$ T) only when the field was tilted toward the in-plane direction. This is attributed to the alignment of antiferromagnetic domains, distinct from standard weak localization.

B. Carrier Properties

• Multi-band Transport: The Hall resistivity curves exhibited an "S-shape" at high fields, indicating multi-band transport.
• Carrier Density: The material is heavily p-doped (hole-dominated). Calculated carrier densities were $\sim 10^{20} - 10^{21}$ cm$^{-3}$, consistent with bulk crystals but varying slightly due to contact invasiveness.
• Mobility: Average mobilities were calculated to be between 17 and 39 cm$^2$/(V s), indicating a disordered system.

C. Hall Effect Decomposition (The Core Discovery)

The study successfully isolated two distinct magnetic contributions to the transverse resistance:

1. Anomalous Hall Effect (AHE): A contribution proportional to the net magnetization induced by the external field. This component saturates above $H_s$.
2. Topological Hall Effect (THE): A non-linear, non-magnetization-proportional contribution.
   • Signature: A distinct peak appears in the residual Hall signal below the saturation field ($H_s$) and vanishes above it.
   • Temperature Dependence: The THE amplitude decreases with increasing temperature and vanishes near $T_N$.
   • Hysteresis: The THE peak shows no hysteresis, distinguishing it from standard AHE.

4. Interpretation and Mechanisms

The presence of a non-zero THE implies the existence of real-space chiral spin textures in EuSn2As2. The authors propose three potential origins for these textures:

1. Helical Spin Textures: A helical state developing along the c-axis under an external field, creating a "tripod" spin structure felt by electrons.
2. Antiferromagnetic Domain Walls: Uniaxial domain walls acting as sources of spin chirality (similar to observations in EuAl$_2$Si$_2$).
3. Magnetic Skyrmions: Possible emergence due to Dzyaloshinskii-Moriya interactions (DMI) at the interfaces of the nanostructures.

5. Significance and Conclusion

• First Evidence in EuSn2As2: This work provides the first experimental evidence of a Topological Hall Effect in EuSn2As2 nanostructures, confirming the presence of chiral magnetic textures.
• Generalization to Magnetic TIs: The observation of THE in EuSn2As2, alongside similar findings in MnBi$_2$Te$_4$ and EuIn$_2$As$_2$, suggests that chiral spin textures may be a universal characteristic of layered magnetic 3D topological insulators with A-type antiferromagnetic order.
• Implications for QAH: Understanding these magnetic textures is crucial for the development and tuning of the Quantum Anomalous Hall effect, as domain walls and chiral textures can disrupt perfect quantization or serve as platforms for new topological phases.
• Methodological Insight: The study highlights the critical importance of separating multi-band transport effects and contact artifacts when analyzing Hall data in disordered, heavily doped topological materials.

In summary, the paper establishes EuSn2As2 as a robust platform for studying chiral spin textures in magnetic topological insulators, bridging the gap between theoretical predictions of axion electrodynamics and experimental transport signatures.