[Paper Review] Overheated Topological Hall Effect

Liang Wu, Yujun Zhang|arXiv (Cornell University)|Dec 24, 2018

Topological Materials and Phenomena4 citations

TL;DR

This paper demonstrates that the topological Hall effect (THE) signal—commonly used to infer skyrmions—can be mimicked by the superposition of two anomalous Hall effect (AHE) components with opposite signs. Using empirical numerical modeling, the authors show that finely tuned AHE contributions can produce THE-like bumps/dips, challenging the validity of relying solely on Hall signals to confirm skyrmionic textures.

ABSTRACT

The topological Hall effect (THE) originates from the real-space Berry phase that an electron gains when its spin follows the spatially varying non-trivial magnetization textures, such as skyrmions. Such topologically protected magnetization textures can provide great potential for information storage and processing. Since directly imaging the skyrmions or detecting the magnetic diffraction of skyrmion lattice are significantly more challenging than conducting Hall measurements, THE has been widely used to attest the presence of skyrmions. However, the key feature of THE, namely the bump/dip in the Hall signal is not sufficient proof of THE. Here, we use empirical numerical modeling to demonstrate all possible THE-like signals that two anomalous Hall effect (AHE) signals with opposite signs can superpose. Besides the reproduction of many published results by the numerical model, we propose an exotic {\lq THE q} could, in principle, emerge with finely tuned two-channel AHE. The importance of the scrupulous re-examination of the THE observed in experiments cannot be exaggerated.

Motivation & Objective

• To challenge the assumption that a Hall signal bump/dip is definitive evidence of the topological Hall effect (THE).
• To investigate whether the THE signal can be reproduced by other physical mechanisms, particularly the superposition of two anomalous Hall effects (AHE).
• To assess the reliability of using Hall measurements as a primary diagnostic tool for identifying skyrmions in magnetic materials.
• To propose that the observed THE-like signals in experiments may not originate from real-space Berry phase due to skyrmions, but from competing AHE contributions.
• To advocate for a rigorous re-evaluation of experimental THE data using numerical modeling to avoid false attribution of topological signatures.

Proposed method

• Employed empirical numerical modeling to simulate Hall resistivity responses under various magnetic texture and transport conditions.
• Modeled two distinct AHE contributions with opposite signs, varying their relative amplitudes and temperature dependencies.
• Used the superposition of these two AHE signals to reproduce Hall signal features resembling the topological Hall effect (e.g., bumps and dips).
• Validated the model against published experimental results showing apparent THE signals in various materials.
• Explored parameter space to identify conditions under which the AHE superposition produces signals indistinguishable from true THE.
• Applied the model to demonstrate the theoretical possibility of an exotic 'THE' arising purely from tuned AHE components, without topological spin textures.

Experimental results

Research questions

• RQ1 Can the characteristic bump/dip feature in Hall measurements be reproduced without the presence of skyrmions or topological spin textures?
• RQ2 To what extent can the superposition of two anomalous Hall effects with opposite signs mimic the topological Hall effect?
• RQ3 What parameter ranges allow AHE contributions to produce Hall signals indistinguishable from those attributed to the topological Hall effect?
• RQ4 How robust is the current experimental practice of identifying skyrmions based solely on Hall effect signatures?
• RQ5 Under what conditions could an apparent THE signal be a false positive due to competing AHE mechanisms?

Key findings

• The numerical model successfully reproduces a wide range of published Hall effect data that were previously interpreted as evidence of the topological Hall effect.
• The superposition of two AHE signals with opposite signs can generate Hall signal features—such as bumps and dips—that closely resemble the topological Hall effect.
• An exotic 'THE' signal can, in principle, emerge from finely tuned two-channel AHE, even in the absence of skyrmions or non-trivial Berry curvature.
• The study demonstrates that the hallmark bump/dip in Hall measurements is not sufficient evidence for the presence of topologically protected spin textures.
• The findings underscore the critical need for complementary experimental techniques—such as direct imaging or magnetic diffraction—to confirm skyrmion existence.
• The authors conclude that the current reliance on Hall measurements alone to identify skyrmions is highly susceptible to misinterpretation due to AHE artifacts.