Berry curvature induced giant anomalous and spin texture driven Hall responses in the layered kagome antiferromagnet GdTi3Bi4

This study reports the synthesis and characterization of the layered kagome antiferromagnet GdTi3Bi4, revealing a colossal anomalous Hall effect driven by Berry curvature and f-electron contributions, alongside a spin-cluster-like glassy phase that generates spin-texture-driven Hall responses.

The Gist

Imagine a microscopic city built from layers of a special, honeycomb-like material called a kagome lattice. In this city, tiny magnetic particles (spins) act like citizens who usually stand in perfect, opposing rows (an antiferromagnet). Now, imagine a new type of city, GdTi3Bi4, where these citizens are not just standing still; they are dancing in complex, swirling patterns when you apply a magnetic field.

This paper is about discovering that this specific material is a "super-city" for electricity, capable of generating two massive, unusual electrical currents simultaneously. Here is the breakdown using simple analogies:

1. The Material: A Layered Sandwich

Think of GdTi3Bi4 as a stack of pancakes.

• The Pancakes: Each layer is a "kagome" lattice (a pattern of triangles and hexagons, like a woven basket).
• The Filling: Between these layers are chains of Gadolinium (Gd) atoms.
• The Magic: Because the layers are held together weakly (like a stack of sticky notes), you could theoretically peel them apart into ultra-thin sheets. This makes them perfect for future tiny electronic devices.

2. The Dance: Spins and Magnetic Transitions

When the scientists cooled this material down to near absolute zero and applied a magnetic field, the magnetic "citizens" didn't just line up; they went through a dramatic transformation.

• The Metamagnetic Transitions: Imagine a crowd of people suddenly shifting from a calm queue to a chaotic mosh pit, and then back to a different organized formation. The material did this three times as the magnetic field increased.
• The "Glassy" State: At one specific point (around 3.4 Tesla), the spins got stuck in a confused, frozen state, like traffic in a gridlock. The scientists call this a "spin-cluster glass." It's a state where the spins are frustrated and can't decide which way to point, creating a messy, swirling texture.

3. The Two Giant Hall Effects (The Main Discovery)

Usually, when you push electricity through a magnet, it gets pushed slightly to the side. This is the Hall Effect. In this material, the scientists found two different reasons why the electricity gets pushed sideways, and both are huge.

Effect A: The "Berry Curvature" Highway (Momentum Space)

• The Analogy: Imagine driving a car on a road that looks flat but is actually a hidden rollercoaster. Even if you try to drive straight, the shape of the road (the "Berry curvature") forces your car to turn.
• In the Material: The electrons moving through the kagome lattice are traveling on these "rollercoaster" paths created by the material's quantum geometry. This creates a massive Anomalous Hall Effect.
• The Result: The material generates a colossal electrical signal (conductivity) just from this internal road shape. It's like the electrons are being pushed by an invisible, giant hand.

Effect B: The "Spin Texture" Whirlpool (Real Space)

• The Analogy: Imagine a river flowing through a forest. If the trees (spins) are arranged in a perfect grid, the water flows straight. But if the trees form a giant, swirling whirlpool (a skyrmion or spin texture), the water gets caught in the spin and diverted sideways.
• In the Material: The "glassy" state mentioned earlier creates these tiny, swirling whirlpools of magnetic spins. As electrons flow past these whirlpools, they get kicked sideways.
• The Result: This creates a second, distinct electrical signal called the Topological Hall Effect.

4. Why This Matters

Most materials show either the "rollercoaster road" effect or the "whirlpool" effect, but rarely both at the same time, and certainly not with such giant strength.

• The "Dual Engine": GdTi3Bi4 is unique because it has both engines running at full power.
• The Potential: Because this material is layered (like a stack of paper), we might be able to peel off single sheets and use them in future electronics.
• The Application: This could lead to super-sensitive magnetic sensors (like a compass that can see the tiniest magnetic fields) or new types of spintronic devices that use the "spin" of electrons rather than just their charge to store and process data.

Summary

The researchers discovered a new magnetic material that acts like a quantum traffic director. It forces electricity to take two different, massive detours at the same time: one because the "road" it travels on is curved (Berry curvature), and another because the "scenery" (magnetic spins) is swirling like a whirlpool. This dual ability makes it a superstar candidate for the next generation of high-speed, low-energy electronics.

Technical Summary

1. Problem Statement

Layered kagome magnets are emerging as critical platforms for exploring Berry curvature engineering and unconventional transport phenomena. However, materials that simultaneously exhibit robust dual Hall responses—integrating both a large intrinsic anomalous Hall effect (AHE) driven by momentum-space Berry curvature and a significant topological Hall effect (THE) driven by real-space non-collinear spin textures (e.g., skyrmions)—remain rare. The specific material GdTi3Bi4, a van der Waals-like layered antiferromagnet with a kagome lattice, has shown complex magnetic phase diagrams and magnetization plateaus, but a comprehensive understanding of its transport mechanisms, particularly the coexistence of giant AHE and spin-texture-driven Hall effects, was lacking.

2. Methodology

The authors employed a multi-faceted approach combining experimental synthesis, characterization, and theoretical modeling:

• Synthesis: High-quality single crystals of GdTi3Bi4 were grown using the flux method with Bismuth as the flux.
• Structural Characterization: X-ray diffraction (XRD), Scanning Electron Microscopy (SEM), Energy Dispersive X-ray (EDX), and Laue diffraction confirmed the orthorhombic crystal structure ($Fmmm$ space group), high crystallinity, and stoichiometry.
• Magnetic Measurements:
  • DC Magnetization: Zero-field-cooled (ZFC) and field-cooled (FC) measurements to determine magnetic ordering temperatures ($T_N$) and field-induced metamagnetic transitions (MMT).
  • AC Susceptibility: Frequency-dependent measurements to probe spin dynamics and identify glassy states or spin clusters.
  • Hysteresis Analysis: Examination of thermal and field hysteresis to characterize the order of phase transitions.
• Electrical Transport:
  • Resistivity & Magnetoresistance (MR): Four-probe measurements to analyze metallic behavior and MR jumps.
  • Hall Effect: Systematic decomposition of Hall resistivity ($\rho_{yx}$) into ordinary ($\rho_{yx}^o$), anomalous ($\rho_{yx}^A$), and topological/spin-texture ($\rho_{yx}^T$) components.
  • Scaling Analysis: Application of the Tian-Ye-Jin (TYJ) model to separate extrinsic (skew scattering) and intrinsic (Berry curvature) contributions to the Anomalous Hall Conductivity (AHC).
• Theoretical Calculations: First-principles Density Functional Theory (DFT) calculations (using VASP) with Maximally Localized Wannier Functions to compute band structures and intrinsic AHC, including the effects of Coulomb interaction ($U$) on Gd $f$-electrons.

3. Key Results

A. Magnetic Properties and Phase Transitions

• Antiferromagnetic Ordering: The system orders antiferromagnetically at $T_N \approx 14.2$ K, with a secondary spin reorientation at $T_{N2} \approx 13.2$ K.
• Metamagnetic Transitions (MMT): Under a magnetic field along the easy axis ($c$-axis), the system exhibits two distinct first-order phase transitions at $H_{C1} \approx 1.7$ T and $H_{C2} \approx 3.4$ T, characterized by narrow hysteresis loops and thermal hysteresis.
• Glassy Spin Dynamics: AC susceptibility measurements at $H_{C2}$ revealed a frequency-dependent peak shift at low temperatures ($T_f \approx 3.5$ K). Scaling analysis yielded a spin relaxation time $\tau_0 \approx 4.21 \times 10^{-8}$ s, indicative of a field-induced spin-cluster glassy phase or nanoscale spin textures, rather than a canonical spin glass.

B. Transport Phenomena

• Giant Anomalous Hall Effect (AHE): At 2 K, GdTi3Bi4 exhibits a colossal anomalous Hall conductivity of $\sigma_{xy}^A \approx 8.6(7) \times 10^3 \, \Omega^{-1} \text{cm}^{-1}$.
  • Mechanism: Scaling analysis using the TYJ model revealed that the AHE arises from a coexistence of skew scattering (extrinsic, $\sigma_{xy,sk}^A \approx 1.06 \times 10^4 \, \Omega^{-1} \text{cm}^{-1}$) and intrinsic Berry curvature ($\sigma_{xy,in}^A \approx -2.3 \times 10^3 \, \Omega^{-1} \text{cm}^{-1}$).
  • Origin: The intrinsic contribution is attributed to flat bands near the Fermi level derived from the Ti kagome lattice and enhanced by Gd $f$-electron magnetic effects.
• Spin-Texture Driven Hall Response: A significant additional Hall resistivity ($\rho_{yx}^T$) of up to $0.12 \, \mu\Omega \cdot \text{cm}$ was observed near the second metamagnetic transition ($H_{C2}$). This value is comparable to or larger than those in known skyrmionic systems (e.g., MnSi, MnP), confirming the presence of non-trivial real-space spin textures.
• Magnetoresistance (MR): The system shows giant magnetoresistance jumps (~26% increase at $H_{C1}$ and ~27% decrease at $H_{C2}$), analogous to Giant Magnetoresistance (GMR) in multilayers, driven by the reorientation of magnetic moments between adjacent layers.

C. Theoretical Insights

• DFT calculations confirmed the presence of flat bands near the Fermi level.
• While standard DFT underestimated the intrinsic AHC compared to experimental values (likely due to challenges in modeling $f$-electron correlations and complex non-collinear magnetic phases), the calculations confirmed that Gd $f$-electrons play a crucial role in amplifying the Hall response.
• Varying the Coulomb interaction parameter ($U$) showed that increasing $U$ shifts flat bands away from the Fermi level, reducing the AHC, highlighting the sensitivity of the transport properties to electronic correlations.

4. Key Contributions

1. Discovery of Dual Hall Response: The paper identifies GdTi3Bi4 as a rare layered kagome antiferromagnet that simultaneously hosts a giant anomalous Hall conductivity (momentum-space Berry curvature) and a large topological Hall resistivity (real-space spin textures).
2. Characterization of Glassy Spin Textures: It provides strong evidence for a field-induced, non-equilibrium glassy magnetic state with slow spin dynamics ($\tau_0 \sim 10^{-8}$ s) and nanoscale spin clusters near 3.4 T, distinct from conventional spin glasses.
3. Mechanistic Decomposition: The study successfully deconvolutes the Hall signal into extrinsic (skew scattering) and intrinsic (Berry curvature) components, demonstrating that both mechanisms contribute significantly to the colossal AHE.
4. Material Benchmarking: It establishes GdTi3Bi4 as a benchmark material for layered magnetic systems, offering a platform for exfoliation and device integration in spintronics.

5. Significance

This work significantly advances the field of topological quantum materials and spintronics by:

• Validating the "Dual Hall" Concept: It demonstrates that a single material can effectively utilize both momentum-space and real-space Berry curvature effects, offering a versatile platform for studying the interplay between electronic topology and magnetic texture.
• Enabling Low-Dimensional Spintronics: As a van der Waals material, GdTi3Bi4 can be exfoliated into atomically thin sheets, making it a prime candidate for next-generation spin-orbit torque devices, Hall sensors, and spintronic logic gates.
• Guiding Material Design: The findings suggest that tuning the interplay between kagome lattice geometry, $f$-electron magnetism, and magnetic frustration can lead to materials with tunable, giant Hall responses, paving the way for "smart" materials with exotic, controllable transport properties.