Enhanced transverse electron transport via disordered composite formation

Transverse electron transport in magnetic materials - manifested in effects such as the anomalous Hall and Nernst effects - holds promise for spintronic and thermoelectric applications. While recent advances have focused on enhancing such transport through topological single crystals via intrinsic mechanisms linked to Berry curvature, practical limitations remain due to their mechanical fragility and narrow material scope. Here, we demonstrate a distinct approach for transverse transport enhancement based on composite formation. Using both theoretical modeling and experiments, we show that disordered mixtures of two ferromagnetic materials can exhibit significantly stronger transverse electron deflection than either constituent alone. This enhancement originates from meandering electron pathways created by the disordered mixture of two materials and does not rely on long-range crystalline order. The identified requirements for this mechanism can be broadly satisfied across different material systems, offering a universal and tunable strategy to engineer large transverse responses in structurally robust platforms.

💡 Research Summary

The paper introduces a fundamentally new route to boost transverse electron transport (TT) – the anomalous Hall effect (AHE) and anomalous Nernst effect (ANE) – by forming disordered composites of two ferromagnetic materials rather than relying on intrinsic Berry‑curvature mechanisms or conventional extrinsic scattering. The authors first develop a two‑dimensional square‑lattice network model in which each lattice site is randomly assigned to material A or material B. Each site carries a conductance tensor Gαij that contains a symmetric part (related to longitudinal conductivity γxx) and an antisymmetric part (related to transverse conductivity γyx). By imposing Hall‑type boundary conditions and averaging over many random realizations, they compute the effective transverse conductivity γ̄yx as a function of the volume fraction P(B).

A striking non‑monotonic dependence emerges: when material A has a lower longitudinal conductivity (γ(A)xx < γ(B)xx) but a higher transverse conductivity (γ(A)yx > γ(B)yx), the composite’s average γ̄yx can exceed the values of both pure constituents. This “enhancement condition” is rooted in the formation of meandering current paths. In configurations where high‑γxx domains (material B) form a continuous matrix and low‑γxx islands (material A) are embedded, the current preferentially stays within the high‑γxx matrix, making large‑scale “side‑jumps” around the islands. These jumps are macroscopic (tens of nanometers), far larger than atomic‑scale side‑jump scattering, and they are biased to one side, producing a net Hall voltage larger than the sum of the parts. Simulations of homogeneous mixtures, stripe‑like patterns, and island‑type patterns confirm that only the latter generate a substantial boost, while random networks almost always contain island‑type features, making the effect generic under the stated condition.

To validate the theory, the authors fabricate Fe₉₂․₅Si₅B₂․₅ metallic glass, a simple ferromagnet that can be partially crystallized into α‑Fe by annealing. By varying the annealing temperature (Ta), they tune the fraction and morphology of the crystalline phase. At low Ta the sample is fully amorphous (low σxx, high σyx); at high Ta it is fully crystalline (high σxx, low σyx). At an intermediate Ta ≈ 723 K, transmission electron microscopy reveals isolated crystalline islands within an amorphous matrix, precisely the geometry required for the predicted enhancement. Electrical measurements at 300 K show σxx ≈ 8.3 × 10³ S cm⁻¹ and |σyx| ≈ 467 S cm⁻¹ for the amorphous state, and σxx ≈ 15.6 × 10³ S cm⁻¹, |σyx| ≈ 155 S cm⁻¹ for the fully crystalline state. The mixed sample at Ta = 723 K exhibits |σyx| ≈ 780 S cm⁻¹—a five‑fold increase over the crystalline reference—and an anomalous Hall angle of 6.7 %, surpassing that of well‑known topological ferromagnets such as Fe₃Ga or Fe₃Al.

Thermoelectric measurements reveal a similar boost in the ANE. The anomalous Nernst coefficient S_yx reaches 2.67 µV K⁻¹ (or 3.69 µV K⁻¹ for a shorter anneal), and the anomalous Nernst conductivity α_yx peaks at 3.37 A (m·K)⁻¹ (or 4.94 A (m·K)⁻¹), values comparable to or exceeding those of intrinsic Berry‑curvature materials like Co₂MnGa and Fe₃Ga. The temperature dependence of σxx and σyx mirrors the microstructural evolution: the strongest enhancement coincides with the regime where σxx switches rapidly from the crystalline to the amorphous value, i.e., when the meandering paths are most pronounced.

The authors also discuss alternative explanations. If the intrinsic Berry‑curvature mechanism dominated, σyx would be independent of σxx, which is not observed; instead σyx varies non‑monotonically while σxx changes monotonically, supporting the composite‑induced mechanism. Moreover, the side‑jump length in this system is set by the island size (tens of nanometers), far larger than the atomic‑scale side‑jump in conventional extrinsic AHE, explaining the magnitude of the effect.

In summary, the work demonstrates that a simple physical mixture of two ferromagnets—one with low longitudinal but high transverse conductivity, the other with the opposite traits—can generate a transverse response that exceeds either component. This strategy does not require delicate band‑structure engineering, is compatible with robust, easily processed materials, and can be applied across a wide range of magnetic alloys, oxides, or layered compounds. It opens a new design paradigm for spintronic and thermoelectric devices where large Hall or Nernst signals are desired without sacrificing mechanical stability or manufacturability.