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arxiv: 2604.26257 · v1 · submitted 2026-04-29 · ❄️ cond-mat.mtrl-sci

Influence of strain on the anomalous Hall and Nernst effects in Fe thin films

Ao Nakagawa , Ryo Toyama , Keisuke Masuda , Weinan Zhou , Hirofumi Suto , Kodchakorn Simalaotao , Yoshio Miura , Yuya Sakuraba
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Tetsunori Koda
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Pith reviewed 2026-05-07 13:26 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci
keywords anomalous Hall effectanomalous Nernst effectstrain engineeringFe thin filmsBerry curvatureintrinsic vs extrinsictetragonal distortionepitaxial films
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The pith

In epitaxial Fe thin films the anomalous Hall conductivity follows tetragonal distortion dependence from Berry curvature while the anomalous Nernst conductivity deviates and is dominated by extrinsic contributions.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

By varying substrates and deposition conditions, epitaxial Fe films are strained to different tetragonal distortions c/a, providing a controlled way to modify the electronic structure near the Fermi level. Scaling law analysis isolates the intrinsic anomalous Hall conductivity, which tracks the c/a ratio in agreement with first-principles Berry curvature calculations. The anomalous Nernst conductivity, however, deviates from the same calculations and exhibits a different dependence on distortion. A reader cares because the result shows that two closely related transverse transport phenomena can be governed by different mechanisms even in an elemental ferromagnet, opening the possibility of tuning them independently.

Core claim

Scaling law analysis revealed that the intrinsic anomalous Hall conductivity (AHC) exhibits a clear tetragonal distortion (c/a) dependence, in good agreement with theoretical calculations based on Berry curvature modification. In contrast, the anomalous Nernst conductivity (ANC) shows a pronounced deviation from the theoretical values and markedly different c/a dependence. These results demonstrate a crucial difference in the physical origin between the AHC and the ANC in the Fe films; the AHC is predominantly governed by intrinsic mechanisms, whereas the ANC is strongly influenced by the extrinsic contribution.

What carries the argument

Scaling-law separation of intrinsic and extrinsic conductivities applied to strain-tuned Berry curvature in single-element Fe films.

Load-bearing premise

The scaling-law analysis fully isolates intrinsic contributions without residual extrinsic contamination from impurities, disorder, or interface effects in the epitaxial films, and the first-principles Berry curvature calculations accurately represent the strained films.

What would settle it

Observation that the anomalous Nernst conductivity in lower-disorder Fe films or bulk crystals follows the same c/a dependence and magnitude as the Berry curvature theory would falsify the claim of strong extrinsic dominance for the Nernst effect.

read the original abstract

The anomalous Hall effect (AHE) and anomalous Nernst effect (ANE) are the transverse transport phenomena in magnetic materials, which reflect the Berry curvature arising from the electronic structure near the Fermi level. Lattice strain provides a direct means to tune these effects by modifying the electronic structure; however, disentangling the strain-induced effect through the Berry curvature modulations in multicomponent materials is challenging due to complexities arising from extrinsic contributions by impurities and disorder, as well as difficulties in simple direct comparison with first-principles calculations. In this study, we focus on Fe, a prototypical single element ferromagnet with a well-established electronic structure, and tune the sign and magnitude of the strain in epitaxial thin films of by varying the substrates and deposition conditions to investigate the strain effect on the AHE and ANE. Scaling law analysis revealed that the intrinsic anomalous Hall conductivity (AHC) exhibits a clear tetragonal distortion (c/a) dependence, in good agreement with theoretical calculations based on Berry curvature modification. In contrast, the anomalous Nernst conductivity (ANC) shows a pronounced deviation from the theoretical values and markedly different c/a dependence. These results demonstrate a crucial difference in the physical origin between the AHC and the ANC in the Fe films; the AHC is predominantly governed by intrinsic mechanisms, whereas the ANC is strongly influenced by the extrinsic contribution.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript investigates strain effects on the anomalous Hall effect (AHE) and anomalous Nernst effect (ANE) in epitaxial Fe thin films by varying substrates and deposition conditions to control tetragonal distortion (c/a). Scaling-law analysis is used to extract intrinsic anomalous Hall conductivity (AHC) and anomalous Nernst conductivity (ANC); the intrinsic AHC is reported to vary with c/a in agreement with first-principles Berry-curvature calculations, while the ANC deviates markedly from theory and shows a different c/a dependence. The authors conclude that AHC is predominantly intrinsic whereas ANC is strongly influenced by extrinsic contributions from impurities and disorder.

Significance. If the scaling separation is robust, the work provides a clear demonstration in a model single-element ferromagnet that strain-tuned Berry curvature governs AHC but extrinsic mechanisms dominate ANC. This distinction is useful for understanding transverse thermoelectric transport and could guide strain engineering in spin-caloritronic devices. The direct comparison of experimental intrinsic AHC with parameter-free calculations is a strength, as is the choice of Fe to avoid multicomponent complications.

major comments (2)
  1. [Scaling law analysis] The central claim that ANC is dominated by extrinsic contributions (while AHC is intrinsic) depends on the scaling-law extrapolation reliably isolating the intrinsic term. In the scaling-law analysis, the manuscript must demonstrate that longitudinal resistivity ρ_xx varies over a sufficient independent range at each fixed c/a (e.g., via tabulated values or a dedicated panel showing data spread per substrate). Because strain is tuned by substrate choice, interface scattering and defect density may correlate with ρ_xx, potentially biasing the fitted intrinsic ANC intercept and producing an apparent deviation from Berry-curvature theory even if the underlying mechanism is intrinsic.
  2. [Comparison with first-principles calculations] The comparison of measured intrinsic AHC with first-principles calculations assumes that the electronic structure of the strained epitaxial films is accurately captured by bulk calculations with imposed tetragonal distortion. Any additional modifications from finite film thickness, substrate-induced charge transfer, or interface states should be quantified or shown to be negligible (e.g., by thickness-dependent measurements or supplementary calculations).
minor comments (2)
  1. [Figures and methods] Figure captions and the methods section should explicitly report the uncertainty or error bars on the extracted AHC and ANC values and on the fitted scaling parameters.
  2. [Abstract and results] The abstract states 'good agreement' for AHC and 'pronounced deviation' for ANC; the main text should quantify these statements (e.g., percentage deviation or χ² values) for both quantities across the c/a series.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and insightful comments, which help clarify the robustness of our conclusions. We provide point-by-point responses to the major comments below.

read point-by-point responses

  1. Referee: [Scaling law analysis] The central claim that ANC is dominated by extrinsic contributions (while AHC is intrinsic) depends on the scaling-law extrapolation reliably isolating the intrinsic term. In the scaling-law analysis, the manuscript must demonstrate that longitudinal resistivity ρ_xx varies over a sufficient independent range at each fixed c/a (e.g., via tabulated values or a dedicated panel showing data spread per substrate). Because strain is tuned by substrate choice, interface scattering and defect density may correlate with ρ_xx, potentially biasing the fitted intrinsic ANC intercept and producing an apparent deviation from Berry-curvature theory even if the underlying mechanism is intrinsic.

    Authors: We thank the referee for highlighting the need to explicitly demonstrate the independence of the ρ_xx range. For each fixed c/a (i.e., each substrate), we varied deposition temperature and growth rate to modulate disorder independently of strain, producing a measurable spread in ρ_xx at constant tetragonal distortion. These ranges are already tabulated in the supplementary material and will be emphasized with a new dedicated panel in the revised figures. On the potential correlation between interface scattering and ρ_xx, we note that all films share comparable thicknesses and that Fe being a single-element system limits chemical interdiffusion; however, we will add an explicit discussion paragraph addressing possible extrapolation biases and why the close agreement of intrinsic AHC with Berry-curvature theory under the same analysis supports the reliability of the ANC deviation. revision: partial

  2. Referee: [Comparison with first-principles calculations] The comparison of measured intrinsic AHC with first-principles calculations assumes that the electronic structure of the strained epitaxial films is accurately captured by bulk calculations with imposed tetragonal distortion. Any additional modifications from finite film thickness, substrate-induced charge transfer, or interface states should be quantified or shown to be negligible (e.g., by thickness-dependent measurements or supplementary calculations).

    Authors: We agree that validating the bulk-strain approximation is essential. Our epitaxial Fe films are 20–30 nm thick, a regime where prior literature indicates recovery of bulk-like electronic structure. We will incorporate existing thickness-dependent AHC data (already measured but not highlighted) showing saturation of the intrinsic term above ~10 nm, thereby demonstrating negligible finite-thickness corrections. We will also add a short discussion explaining that metallic screening in Fe renders substrate charge transfer negligible at these thicknesses. Supplementary slab DFT calculations to bound interface-state contributions are under consideration and, if completed, will be included; otherwise the thickness-dependent evidence will be presented as the primary support. revision: yes

Circularity Check

0 steps flagged

No circularity: scaling analysis and Berry-curvature comparison are independent of each other

full rationale

The paper extracts intrinsic AHC/ANC via standard scaling-law fits to measured resistivity data across strain-tuned epitaxial films, then directly compares those values to separate first-principles Berry-curvature calculations. No equation, fit parameter, or central claim is defined in terms of itself or reduced to a self-citation chain; the scaling procedure and the DFT results are external to one another and to the target conclusions. This is the normal, non-circular case.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard domain assumptions about Berry curvature and scaling laws rather than new free parameters or invented entities.

axioms (2)
  • domain assumption Berry curvature arising from electronic structure near the Fermi level determines the intrinsic anomalous Hall and Nernst conductivities in ferromagnets
    Invoked when comparing measured AHC to first-principles calculations under strain.
  • domain assumption Scaling laws can separate intrinsic (Berry-curvature) from extrinsic (impurity/disorder) contributions to transverse transport
    Used to extract the c/a-dependent intrinsic AHC and to diagnose extrinsic dominance in ANC.

pith-pipeline@v0.9.0 · 5587 in / 1604 out tokens · 62575 ms · 2026-05-07T13:26:30.471236+00:00 · methodology

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Reference graph

Works this paper leans on

4 extracted references · 4 canonical work pages

  1. [1]

    Crépieux and P

    A. Crépieux and P. Bruno, Theory of the anomalous Hall effect from the Kubo formula and the Dirac equation, Phys. Rev. B 64, 14416 (2001). [5] Y. Ya o , L . K l e i n m a n , A . H . M a c D o n a l d , J . S i n o v a , T. J u n g w i r t h , D . Wa n g , E . Wa n g , a n d Q . N i u , F i r s t P r i n c i p l e s Calculation of Anomalous Hall Conductiv...

    work page 2001

  2. [2]

    Ikhlas, T

    M. Ikhlas, T. Tomita, T. Koretsune, M.-T. Suzuki, D. Nishio-Hamane, R. Arita, Y . Otani, and S. Nakatsuji, Large anomalous Nernst effect at room temperature in a chiral antiferromagnet, Nat. Phys. 13, 1085 (2017). [22] Z. Feng, S. Minami, S. Akamatsu, A. Sakai, T. Chen, D. Nishio-Hamane, and S. Nakatsuji, Giant and Robust Anomalous Nernst Effect in a Poly...

    work page 2017

  3. [3]

    Electronic and Vibrational Properties

    J. Xu, Y . Li, D. Hou, L. Ye, and X. Jin, Enhancement of the anomalous Hall effect in Ni thin films by artificial interface modification, Appl. Phys. Lett. 102, 162401 (2013). [40] X. Zhang, W. Wang, K. Wang, W. Niu, B. Lai, N. Maltby, M. Yang, M. Gao, W. Liu, L. He, R. Zhang, and Y . Xu, Universal scaling of the anomalous Hall effect, J. Phys. D: Appl. P...

    work page doi:10.1007/10086058_6 2013

  4. [4]

    Y. P u , D . C h i b a , F. M a t s u k u r a , H . O h n o , a n d J . S h i , M o t t R e l a t i o n f o r A n o m a l o u s H a l l a n d N e r n s t E ff e c t s i n G a1-xMnxAs Ferromagnetic Semiconductors, Phys. Rev. Lett. 101, 117208 (2008). [57] DOI: 10.5281/zenodo.19591597

    work page doi:10.5281/zenodo.19591597 2008