Discovery of a large magnetic nonlinear Hall effect in an altermagnet

Cheng Song; Feng Pan; Hua Bai; Jiankun Dai; Junwei Liu; Lei Han; Maciej Sawicki; Ruiyue Chu; Shixuan Liang; Xiaokang Li

REVIEW 3 major objections 5 minor 1 cited by

Discovery of a large magnetic nonlinear Hall effect in an altermagnet

T0 review · 3 major / 5 minor · reviewed 2026-08-08 · deepseek-v4-flash

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Pith's one-line read This paper claims that the altermagnet Mn5Si3 exhibits a large, non-analytic Hall conductivity term that grows as the square of the applied magnetic field, produced by chiral next-nearest-neighbor hopping.

desk verdict Solid experimental evidence for a new sgn(H)H² Hall term in Mn5Si3, paired with a theoretical mechanism that needs its full derivation to be credible. read the letter →

arxiv 2502.04920 v2 pith:FI76V36R submitted 2025-02-07 cond-mat.mtrl-sci

Lei Han , Xizhi Fu , Cheng Song , Yuxiang Zhu , Xiaokang Li , Zengwei Zhu , Hua Bai , Ruiyue Chu

show 5 more authors

Jiankun Dai Shixuan Liang Maciej Sawicki Junwei Liu Feng Pan

This is my paper · ORCID

classification cond-mat.mtrl-sci

keywords magneticnonlinearHalleffectaltermagnetMn5Si3BerrycurvatureHaldane-likehoppingnon-analyticconductivityhighfieldchiralnext-nearest-neighbor

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper reports a new transport phenomenon, the magnetic nonlinear Hall effect (MNLHE), in which the Hall conductivity grows quadratically with the applied magnetic field rather than with the electric field. The central claim is that in the altermagnet Mn5Si3 thin film, the DC Hall conductivity contains a non-analytic term $\mathrm{sgn}(H)\,\sigma_2 H^2$ that changes sign when the field is reversed. The quadratic term is traced to chiral next-nearest-neighbor hopping that acquires both an exchange energy and Haldane-like flux phases from the field-driven canted moment, producing an $m^2$ term in the Hamiltonian that opens a Berry-curvature gap. If the claim is correct, MNLHE gives a direct transport fingerprint for altermagnetism and a response that does not saturate up to 60 T.

What carries the argument

The central object is the chiral next-nearest-neighbor hopping term $-t_2 e^{i\Phi}\sum_i (\mathbf{m}_i\cdot\boldsymbol{\sigma})$ in a two-dimensional hexagonal tight-binding model of Mn5Si3. The two independent Haldane-like phases $\Phi_1,\Phi_2$ are odd functions of the canted moment $\mathbf{m}$, so to first order they are linear in $m$; combined with the linear exchange energy, the hopping term yields an $m^2\tau_z$ mass term in the two-band Hamiltonian (Eqs. 1\textendash 2). That mass opens the Dirac-cone gap in the alternating-spin-split bands and generates the Berry curvature whose occupied-state integral gives $\sigma_2 H^2$; the sign functions in the final fit (Eq. 3) encode the 180\degree{} switching of $\mathbf{m}$ and $\mathbf{N}$ under field reversal.

What would settle it

Measure the canted moment $m(H)$ directly over the same field range used for Hall transport and check whether the fitted coefficient $\sigma_2$ scales as $m(H)^2$ while $m(H)$ remains linear in $H$; if it does not, the $\Phi \propto m$ mechanism is wrong. A second check is to search for the non-analytic $\mathrm{sgn}(H)\sigma_2 H^2$ term in an unstrained collinear Mn5Si3 crystal, where symmetry forbids the spontaneous canted moment: its presence there, or its absence when a nonzero $m$ exists, would falsify the symmetry-based account.

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Extended reading notes

Core claim

At 93 K in the altermagnetic phase of a strained 100-nm Mn5Si3(0001) film, the perpendicular-field Hall conductivity up to roughly 60 T cannot be fitted by the analytic linear form $\sigma_1 H$. It requires the non-analytic expression $\sigma_H \simeq \mathrm{sgn}(H)\,\sigma_0 + \sigma_1 H + \mathrm{sgn}(H)\,\sigma_2 H^2$, where both sign functions reflect the 180\degree{} switching of the magnetic structure under field reversal. Control measurements show the quadratic term is absent in the paramagnetic phase, in a ferromagnetic Mn$_{5+\delta}$Si$_{3-\delta}$ film, and in the non-collinear antiferromagnetic phase, and the temperature dependence of $\sigma_2$ matches a tight-binding model. In that model, next-nearest-neighbor hopping through magnetic atoms acquires an $m$-dependent exchange energy and an $m$-dependent Haldane-like phase, so the two contributions combine into an $m^2\tau_z$ gap term; the gap opens a Berry curvature that integrates to the $H^2$ Hall response.

Load-bearing premise

The derivation assumes the Haldane-like hopping phases $\Phi_1$ and $\Phi_2$ are odd functions of the canted moment $\mathbf{m}$, so to first order they are proportional to $m$; if that proportionality vanishes or becomes nonlinear, the $m^2$ term in the Hamiltonian\textemdash and with it the quadratic-in-$H$ Hall response\textemdash disappears.

Editorial extensions

If this is right

A quadratic, sign-reversing Hall term becomes a transport fingerprint that separates the altermagnetic phase of Mn5Si3 from its paramagnetic, ferromagnetic-control, and non-collinear antiferromagnetic phases.
Because the quadratic response is unsaturated up to 60 T, DC Hall measurement in Mn5Si3 can serve as a pulsed high-field sensor.
The mechanism generalizes to any magnetic material with alternating-sign Berry curvature and a small switchable canted moment; the paper explicitly names MnTe and CrSb as candidates.
The non-analytic $\mathrm{sgn}(H)H^2$ term cannot be captured by any smooth power-series expansion of the Hall conductivity in $H$, so standard field-expansion analyses would miss it.
The temperature dependence of $\sigma_2$ tracks the Fermi\textendash Dirac occupation, making the effect a probe of band occupation near the crystal-symmetry-paired spin-valley-locked points.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

An intrinsic Berry-curvature mechanism implies analogous quadratic-in-field terms should appear in other Berry-curvature-weighted responses of the same films, such as the anomalous Nernst and thermal Hall coefficients; the paper does not report those measurements.
The linear dependence of the hopping phases $\Phi_1,\Phi_2$ on $m$ is assumed rather than quantitatively derived; ab initio calculation of the phases as a function of canting angle would either confirm the $H^2$ law or reveal a different field exponent.
Because $\sigma_2$ depends on the Fermi\textendash Dirac occupation near the crystal-symmetry-paired spin-valley-locked bands, electrostatic gating or doping of Mn5Si3 should tune the magnitude and sign of the quadratic term, providing a controllable experimental test.
In unstrained collinear Mn5Si3, where symmetry forbids a spontaneous canted moment, the non-analytic $\mathrm{sgn}(H)$ signature should disappear; testing this would isolate the role of the canted moment from the role of the N\'eel vector.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Lei Han et al. report a Hall conductivity term in the altermagnet Mn5Si3 that grows as sgn(H)H², which they call magnetic nonlinear Hall effect. The experimental work is the strongest part of the paper. The quadratic term appears only in the altermagnetic phase, disappears in the paramagnetic phase, is absent in ferromagnetic and noncollinear antiferromagnetic control samples, and reproduces on a second film. The derivative of σ_H with respect to H shows a clear linear region at high field, and the authors demonstrate that an analytic H³ fit fails, which supports the non-analytic sgn(H)H² form. That is a genuinely new observation, and the control matrix is about as thorough as one could ask for in a single paper.

The theory is the soft spot. The central mechanism posits that NNN hopping acquires a Haldane-like phase Φ that is an odd function of the canted moment m, so that to first order Φ ∝ m. Combined with the exchange-energy term also proportional to m, this yields an m²τ_z term that opens a gap and produces the H² Hall response. But the derivation of the m² term is not shown in the main text; it is deferred to SI Notes S2 and S3, which are not included in the preprint. The stress-test note is right that the sign change is subtle: m → -m leaves m² invariant, so the sign of σ₂ under field reversal must come from a step involving the Néel vector or the chirality of the flux phases. The main text's sketch, 'Φ∝m so e^{iΦ}m ≃ m + iαm²', does not by itself explain why the coefficient of τ_z changes sign when H, m, and N all reverse. The authors need to write down the Hermitian sum over NNN bonds and show the sign structure explicitly. This is an addressable gap, but until it is filled, the mechanism is a conjecture rather than a derivation. There are also no error bars on the fitted σ₂ values, and the temperature dependence is compared after the fact rather than predicted from independent inputs.

Overall, the experimental result deserves to be published and will attract attention. The theory may survive once the SI is examined, but as it stands the mechanism is under-verified. I would send this to a good referee, with the explicit instruction to request the full derivation in the SI and to check the sign-reversal argument. The paper is likely to be an important data point for altermagnet transport, independent of whether the Haldane-style mechanism holds in detail.

Referee Report

3 major / 5 minor

Summary. The paper reports Hall conductivity measurements on strained Mn5Si3 thin films in the altermagnetic phase under pulsed magnetic fields up to about 60 T. It claims the observation of a magnetic nonlinear Hall effect (MNLHE) with a non-analytic contribution sgn(H)σ2H^2 that is quadratic in field and changes sign upon field reversal. The claim is supported by temperature-dependent measurements in the altermagnetic phase, control measurements in the paramagnetic, ferromagnetic, and noncollinear antiferromagnetic phases of related samples, and a second Mn5Si3 sample. The authors propose a tight-binding mechanism in which chiral next-nearest-neighbor hopping through magnetic atoms acquires both an exchange-energy term proportional to m and a Haldane-like flux phase also proportional to m, producing an m^2τ_z term that opens a Berry-curvature gap and yields the H^2 dependence. The non-analytic sign change is attributed to 180° switching of the magnetic structure under field reversal.

Significance. If the central claim holds, the paper identifies a qualitatively new Hall effect—one whose quadratic term is non-analytic in magnetic field—and provides a transport fingerprint for altermagnetic Mn5Si3 with potential high-field sensing applications. The experimental design is strong in several respects: the effect appears only in the altermagnetic phase, is reproduced on a second sample, is absent when the field is parallel to the current, and the authors explicitly exclude a simple ferromagnetic-moment explanation through control experiments on ferromagnetic Mn5+δSi3−δ. The high R² values for the fitting function are also encouraging. However, the theoretical derivation of the m^2 term and of the sign-reversing σ2H^2 contribution is only sketched and is deferred to Supplementary Notes that are not included in the preprint, and the experimental determination of the non-analytic form lacks explicit error bars and quantitative model comparison. The significance of the result therefore depends on completing both of these points.

major comments (3)

[Chiral next-nearest-neighbor hopping mechanism, Eqs. (1)–(3)]
[Experimental observation, Fig. 2b and Extended Data Fig. 3]
[Temperature dependence, Fig. 4e]

minor comments (5)

[Main text, altermagnet introduction]
[Chiral NNN hopping mechanism]
[Figure 3 caption and main text]
[Extended Data Fig. 9]
[Main text, experimental observation]

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the quadratic-field Hall term is an experimental observable, and the chiral-hopping model is a proposed explanation rather than a fitted tautology.

full rationale

The experimental Hall conductivity is fit to sgn(H)σ0 + σ1H + sgn(H)σ2H2, and the paper constructs a separate tight-binding model to explain that form. The H2 dependence is traced to an m2 term: the NNN hopping exchange energy is linear in the canted moment m, the Haldane-like hopping phase Φ is argued by symmetry to be odd in m (hence linear to leading order), and the product yields m2; since m is independently calculated to grow linearly with H (Note S1, Extended Data Fig. 2), the model reproduces the quadratic-in-H gap and Berry-curvature contribution. This is a mechanism proposed to match data, not a definition of σ2 in terms of the fitted coefficient. The non-analytic sgn(H) factors are likewise not derived from the m2 gap alone; the paper explicitly attributes them to the experimentally established 180° switching of N and m under field reversal (states I–IV), an independent input grounded in magnetization, AHE, and prior published work. The main text defers the key algebraic steps to SI Notes S2/S3 and compares the temperature trend of σ2 after the fact, but a deferred or post-hoc comparison is a completeness and verifiability concern, not a circular reduction. The self-citations (refs 37, 49) support the sample's altermagnetic state and switching behavior through external experimental publications and are corroborated by independent refs 38 and 43; they do not force the central result. No equation is defined in terms of the target quantity, and no fitted parameter is renamed as an independent prediction.

Assumptions & free parameters 2 free parameters · 4 assumptions · 1 invented entities

The central claim depends on a small number of fitted or assumed quantities: the experimental σ2 coefficient, the linearity of the canted moment in H, and the linear-in-m hopping phases. The canted moment's field dependence is computed from prior DFT exchange parameters, but the hopping phase linearity is an ad hoc model element.

free parameters (2)

σ2 (quadratic Hall coefficient) = temperature dependent, not given
The coefficient of the sgn(H)H^2 term is extracted by fitting the experimental Hall conductivity with Eq. (3). It is the central quantity whose H^2 dependence is claimed.
Haldane-like phase proportionality constants = not specified
The model assumes Φ1 and Φ2 are linearly proportional to m, with coefficients not derived from first principles; they are chosen so the model yields m^2 dependence.

assumptions (4)

domain assumption The 2D hexagonal tight-binding model with A/B sites and four magnetic sites captures the essential symmetries of Mn5Si3.
Used to build the Hamiltonian in the mechanism section; the model is a simplification of the real crystal structure.
domain assumption The canted moment m increases linearly with H under strong fields.
The H^2 dependence of Hall conductivity follows from m^2; this linearity is shown by atomic spin simulations in Extended Data Fig. 2 rather than derived from the transport data.
ad hoc to paper Φ1 and Φ2 are odd functions of m, and to first order linearly proportional to m.
This assumption is stated in the main text with a proof deferred to the SI, and it is essential for obtaining the m^2 term that produces σ2H^2.
domain assumption The magnetic structure undergoes 180-degree switching when the field reverses, producing the sgn(H) factors.
The non-analytic sign functions in Eq. (3) rely on this observed switching behavior of the Néel vector and canted moment.

invented entities (1)

m-dependent Haldane-like chiral flux phases on NNN hopping
purpose: To produce a correction to the hopping that is linear in m, so that together with the exchange energy it yields an m^2 term and thus a quadratic Hall response.
No independent measurement of these phases is offered; they are introduced in the model to explain the observed H^2 dependence.

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Pith. "Pith review of Discovery of a large magnetic nonlinear Hall effect in an altermagnet." pith.science (2026). https://pith.science/paper/FI76V36R

@misc{pith2026250204920,
  author       = {Pith},
  title        = {Pith review of: Discovery of a large magnetic nonlinear Hall effect in an altermagnet},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FI76V36R}},
  note         = {Machine review of arXiv:2502.04920}
}

read the original abstract

Since Edwin Halls groundbreaking discovery of the Hall effect in 1879, magnetism, spin, and quantization have been expanding the scope of Hall effects, continuously driving transformative progress in science and technology. Among them, the latest nonlinear Hall effect (NLHE), where longitudinal electric field tunes quantum geometry to generate nonlinear Hall voltage, attracts wide attention as a sensitive probe of topological phases across a wide range of materials. Here, we report a new Hall effect member: the magnetic nonlinear Hall effect (MNLHE), characterized by a quadratic Hall conductivity dependence on magnetic field, rather than electric field as in NLHE. This finding relies on an altermagnet, Mn5Si3 thin film, whose alternating-sign Berry curvatures ensure higher-order MNLHE clearly distinguishable from the first-order anomalous Hall effect. The observed quadratic dependence originates from chiral next-nearest-neighbor hopping processes that acquire magnetic-exchange-driven Zeeman energies and Haldane-like chiral flux phases. Remarkably, this MNLHE is non-analytic, as reversing the magnetic field flips the alternating spin-splitting bands and reverses the hopping chirality, which is absent in traditional NLHE. Beyond offering a distinctive transport fingerprint for altermagnet Mn5Si3 thin film, this MNLHE is large and unsaturated up to 60 T, providing opportunities for pulsed high-field sensing technologies in both fundamental researches and engineering applications.

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Works this paper leans on

1 extracted references · 1 canonical work pages · cited by 1 Pith paper

[1]

Scaling Behavior of Magnetoresistance and Hall Resistivity in Altermagnet CrSb

Remarkably, Eq. (1-2) is very similar with the Hamiltonian of graphene, except for the m2τz term. This m2τz term opens the gap of the Dirac cones for the emergence of additional Berry curvature under 14 magnetic field, which gives the final form of Hall conductivity as following Eq. (3): 𝜎𝐻 ≅ sgn(𝐻) 𝜎0 + 𝜎1𝐻 + sgn(𝐻) 𝜎2𝐻2 (3) The sign functions in the Eq....

work page Pith review arXiv 1980

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[1] [1]

Scaling Behavior of Magnetoresistance and Hall Resistivity in Altermagnet CrSb

Remarkably, Eq. (1-2) is very similar with the Hamiltonian of graphene, except for the m2τz term. This m2τz term opens the gap of the Dirac cones for the emergence of additional Berry curvature under 14 magnetic field, which gives the final form of Hall conductivity as following Eq. (3): 𝜎𝐻 ≅ sgn(𝐻) 𝜎0 + 𝜎1𝐻 + sgn(𝐻) 𝜎2𝐻2 (3) The sign functions in the Eq....

work page Pith review arXiv 1980