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Reversible intrinsic-extrinsic crossover of the anomalous Hall effect in PrAlSi via Al/Si ratio tuning

This study demonstrates that reversible tuning of the Al/Si ratio in PrAlSi single crystals acts as a chemical knob to drive a unique intrinsic-extrinsic-intrinsic crossover of the anomalous Hall effect, primarily by modulating the Fermi level and carrier mobility.

Original authors: Huiyang Yang, Xiaohua Luo, Hongwei You, Wei Ren, Yuntao Gao, Changcai Chen, Zhishuo Zhang, Chunsheng Fang, Shengcan Ma

Published 2026-10-14

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CC BY 4.0

Original authors: Huiyang Yang, Xiaohua Luo, Hongwei You, Wei Ren, Yuntao Gao, Changcai Chen, Zhishuo Zhang, Chunsheng Fang, Shengcan Ma

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

In the hidden world of certain magnetic crystals, electrons do not simply flow like water in a pipe; they twist and turn in ways that create their own internal magnetic fields. This phenomenon, known as the anomalous Hall effect, is a signature of materials where the paths of electrons are shaped by the very geometry of the atomic lattice. Scientists have long known that this effect can arise from two different sources. One source is built into the material's structure, a fundamental property of its electronic landscape that acts like a permanent, internal compass. The other source comes from imperfections, where electrons bounce off random defects in the crystal, a process that can sometimes amplify the signal to enormous sizes. The challenge for researchers has been to find a way to switch between these two behaviors within the same material, to see how the fundamental structure and the messy reality of imperfections compete and cooperate. Understanding this balance is crucial for developing new types of electronics that rely on the flow of spin rather than just charge, potentially leading to faster and more efficient computing devices.

A team of researchers in China has now demonstrated that they can reversibly switch between these two regimes in a single crystal by making tiny, precise adjustments to its chemical recipe. Working with a compound called PrAlSi, which is made of praseodymium, aluminum, and silicon, the scientists grew high-quality crystals and carefully varied the ratio of aluminum to silicon. They did not change the elements themselves, but rather shifted the balance slightly, creating a series of samples where the amount of silicon ranged from being slightly low to slightly high. This subtle chemical tuning acted like a dial, allowing them to move the material back and forth between a state dominated by structural imperfections and a state dominated by the crystal's intrinsic geometry.

The results revealed a dramatic, non-linear journey. When the researchers measured the strength of the anomalous Hall effect across their different samples, they found it did not simply go up or down. Instead, it rose to a massive peak and then fell back down, forming a distinct arch. In the middle of their series, a sample with a nearly balanced ratio of aluminum to silicon produced a giant signal, measuring 1413 units of conductivity. This massive value was driven by the extrinsic mechanism, where electrons scattering off the crystal's disorder created a huge response. However, as they moved away from this middle ground toward either aluminum-rich or silicon-rich compositions, the signal dropped significantly, settling at much lower values of 170 and 164 units respectively. In these outer samples, the behavior was no longer dominated by disorder but by the intrinsic, built-in properties of the material's electronic structure.

What makes this discovery particularly striking is how the researchers ruled out the idea that simple disorder was the only factor at play. If the effect were purely about how messy the crystal was, one would expect the signal to get weaker as the material became more disordered. Yet, the data showed a more complex picture. The sample with the highest signal was actually the cleanest and most mobile, while the samples with lower signals had more disorder but still retained a strong, intrinsic signal that did not vanish. The researchers found that changing the aluminum-to-silicon ratio did something more profound than just adding defects; it shifted the energy level where the electrons live, effectively changing the type of charge carriers from positive to negative and altering how they moved through the crystal. This shift in the electronic landscape was the primary driver, while the disorder played a secondary role.

By mapping out these changes, the team established that the material can be tuned to reveal its fundamental topological nature or to amplify its response through disorder, all within the same non-magnetic crystal structure. The intermediate sample, with its giant signal, acted as a peak where the extrinsic effects were maximized, while the samples on either side revealed the underlying, intrinsic behavior that is often hidden by such noise. This work provides a clear, reversible method for controlling the anomalous Hall effect, showing that by simply adjusting the chemical balance, scientists can switch a material between two distinct physical regimes. It offers a new tool for exploring the deep connection between the arrangement of atoms and the behavior of electrons, proving that the path to understanding these quantum materials lies not just in finding perfect crystals, but in understanding how to tune the imperfect ones.

Technical Summary: Reversible Intrinsic–Extrinsic Crossover of the Anomalous Hall Effect in PrAlSi via Al/Si Ratio Tuning

Problem Statement
The anomalous Hall effect (AHE) in magnetic Weyl semimetals arises from two distinct microscopic origins: an intrinsic contribution driven by the Berry curvature of topological band structures and extrinsic contributions mediated by disorder (skew scattering and side jump). A critical challenge in the field is that when extrinsic skew scattering dominates, it produces a "giant" anomalous Hall conductivity (AHC) that far exceeds intrinsic limits, effectively masking the underlying topological Berry contribution. Consequently, it is difficult to assess the topological origin of the AHE based on magnitude alone. While previous strategies to tune AHE have relied on hetero-element doping or hydrostatic pressure, these approaches often result in unidirectional crossovers or are entangled with magnetic texture changes. The authors identify a need for a tunable platform where subtle compositional variations can reversibly switch the AHE mechanism between intrinsic and extrinsic regimes within a single material system.

Methodology
The study employs the self-flux method to grow high-quality single crystals of off-stoichiometric PrAlSi. By varying the nominal molar ratios of Pr, Al, and Si (specifically adjusting the Al/Si ratio), the authors synthesized a series of crystals spanning a narrow silicon variation.

Sample Characterization: Phase purity and crystal structure were verified using powder X-ray diffraction (XRD) and energy-dispersive X-ray spectroscopy (EDS). The study focuses on the single-phase noncentrosymmetric $I4_1md$ (LaPtSi-type) structure, excluding samples that formed centrosymmetric impurities.
Transport and Magnetic Measurements: Temperature-dependent magnetization, isothermal magnetization hysteresis, longitudinal resistivity, and Hall effect measurements were conducted using a Quantum Design PPMS.
Data Analysis: The Hall resistivity was decomposed using a two-band model for multi-carrier samples and a single-band model for others. The anomalous Hall conductivity ( $\sigma_{AHE}$ ) was extracted and analyzed via Karplus–Luttinger (KL) plots ( $\rho_{xy}^A$ vs. $\rho_{xx}^2 M$ ) and scaling with saturation magnetization ( $M_S$ ) to distinguish between intrinsic (Berry curvature) and extrinsic (skew scattering) mechanisms.

Key Results
The authors investigated four specific compositions (A1–A4) with Al/Si ratios ranging from ~1.05 to ~0.75. The study reveals a pronounced, non-monotonic evolution of the AHC and a reversible crossover of the AHE mechanism:

Non-Monotonic AHC Evolution: The AHC exhibits an "arch" behavior across the series:
- A1 (Si-poor, Al/Si ~1.05): $\sigma_{AHC} \approx 170 \, \Omega^{-1}\text{cm}^{-1}$ .
- A2 (Intermediate, PrAl $_{0.90}$ Si $_{0.94}$ , Al/Si ~0.96): $\sigma_{AHC} \approx 1413 \, \Omega^{-1}\text{cm}^{-1}$ (Giant peak).
- A3 (Si-rich, Al/Si ~0.88): $\sigma_{AHC} \approx 507 \, \Omega^{-1}\text{cm}^{-1}$ .
- A4 (Si-rich, Al/Si ~0.75): $\sigma_{AHC} \approx 164 \, \Omega^{-1}\text{cm}^{-1}$ .
Mechanism Crossover:
- Intermediate Composition (A2): This sample exhibits high carrier mobility and multi-carrier transport (coexisting electron and hole pockets). The giant AHC is dominated by extrinsic skew scattering, evidenced by the failure of the data to collapse onto a linear KL plot and the scaling of $\sigma_{AHE}$ deviating from a simple linear dependence on $M_S$ .
- Off-Stoichiometric Compositions (A1, A3, A4): Deviating from the intermediate ratio suppresses carrier mobility and shifts the transport regime to single-carrier dominance (hole-like for A1, electron-like for A3/A4). In these regimes, the AHE is intrinsically dominated by Berry curvature. This is confirmed by the linear scaling of $\sigma_{AHE}$ with $M_S$ and the collapse of KL plots, with AHC values falling within or near the theoretical intrinsic limit (~400 $\Omega^{-1}\text{cm}^{-1}$ ).
Carrier Type Reversal: The Al/Si ratio tuning drives a continuous reversal of the dominant carrier type from hole-dominated (A1) to multi-carrier (A2) to electron-dominated (A3/A4). This indicates that the compositional change acts primarily as a Fermi-level engineering tool via band filling, rather than merely altering disorder strength.
Role of Disorder: While off-stoichiometry introduces chemical disorder (Al/Si anti-site defects) that reduces mobility, the study demonstrates that disorder alone does not dictate the AHE mechanism. The enhancement of AHC in A3 compared to A1 (despite lower mobility) contradicts a pure disorder-dose model, confirming that Fermi-level shifting and the resulting changes in the Berry-curvature-weighted bands are the dominant factors.

Significance and Claims
The paper claims to demonstrate a reversible intrinsic–extrinsic–intrinsic crossover of the AHE within a single material platform (PrAlSi) solely through off-stoichiometric tuning of the Al/Si ratio.

Tunability: The Al/Si ratio serves as a "chemical knob" that primarily modulates the Fermi level via compositional band filling. This allows for the systematic suppression of the extrinsic skew-scattering channel to unveil the intrinsic Berry-curvature contribution, and vice versa.
Decoupling: The results establish a decoupling between carrier mobility and the AHE mechanism, showing that the crossover is governed by the position of the Fermi level relative to topological features (multi-carrier windows) rather than just the density of scattering centers.
Platform Utility: Off-stoichiometric PrAlSi is positioned as a tunable platform for exploring the interplay between composition and topology, offering a distinct alternative to hetero-doping or pressure-induced tuning, which often lack reversibility or are limited by phase boundaries.

The authors conclude that subtle compositional variations can reversibly switch the AHE mechanism, providing a controlled method to access both giant extrinsic signals and intrinsic topological responses in magnetic Weyl semimetals.

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