Evidence of Spin-Valley Coupling in Dirac Material BaMnBi2 Probed by Quantum Hall Effect and Nonlinear Hall Effect

David Graf; Lujin Min; Subin Mali; Yingdong Guan; Zhiqiang Mao

arxiv: 2512.24395 · v3 · submitted 2025-12-30 · ❄️ cond-mat.mes-hall · cond-mat.mtrl-sci

Evidence of Spin-Valley Coupling in Dirac Material BaMnBi2 Probed by Quantum Hall Effect and Nonlinear Hall Effect

Subin Mali , Yingdong Guan , Lujin Min , David Graf , Zhiqiang Mao This is my paper

Pith reviewed 2026-05-16 18:45 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall cond-mat.mtrl-sci

keywords spin-valley lockingBaMnBi2quantum Hall effectnonlinear Hall effectDirac materialvalleytronicsBerry curvatureBi zigzag chains

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The pith

BaMnBi2 hosts a spin-valley locked state with fourfold degeneracy, shown by stacked quantum Hall and nonlinear Hall effects.

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

The paper presents experimental evidence that BaMnBi2 contains a unique spin-valley locked electronic state generated by its Bi zigzag chains. Quantum Hall measurements reveal a fourfold spin-valley degeneracy, while the nonlinear Hall effect indicates valley-contrasted Berry curvature. This state differs from the sister compound BaMnSb2, which shows only twofold degeneracy due to differences in crystal structure and spin-orbit coupling. The findings position BaMnBi2 as a bulk platform for studying coupled spin-valley physics.

Core claim

The central discovery is the observation of a predicted spin-valley locked electronic state in the layered Dirac material BaMnBi2. Analysis of the stacked quantum Hall effect identifies a spin-valley degeneracy of four. The nonlinear Hall effect supplies supporting evidence for the expected valley-contrasted Berry curvature. This locking contrasts with the twofold degeneracy in BaMnSb2 and arises from differences in their orthorhombic structures and spin-orbit coupling.

What carries the argument

The stacked quantum Hall effect combined with the nonlinear Hall effect, interpreted as signatures of spin-valley locking with exactly fourfold degeneracy arising from Bi zigzag chains.

If this is right

The spin-valley degeneracy in BaMnBi2 is four, in contrast to the twofold degeneracy in BaMnSb2.
Valley-contrasted Berry curvature is present and detectable via nonlinear Hall response.
BaMnBi2 provides a bulk platform for valleytronic studies that differs from monolayer transition metal dichalcogenides.
Structural variations between related compounds can tune the degeneracy of the locked state.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

If the fourfold degeneracy holds, device designs could exploit bulk crystals rather than requiring monolayer isolation.
Crystal engineering to adjust orthorhombic distortions might allow controlled switching between twofold and fourfold regimes.
Temperature or doping studies could test the robustness of the locking against thermal or impurity effects.

Load-bearing premise

The observed stacked quantum Hall effect and nonlinear Hall effect arise directly from spin-valley locking with degeneracy four and are not produced by multiple bands, disorder, or other scattering processes.

What would settle it

A measurement showing that the Hall plateaus correspond to a degeneracy other than four or that the nonlinear Hall signal originates from scattering or multiple bands would falsify the spin-valley locking interpretation.

read the original abstract

Valleytronics is a rapidly advancing field that explores the use of the valley degree of freedom in electronic systems to encode and process information. It relies on electronic states with spin valley locking, first predicted and observed in monolayer transition metal dichalcogenides such as MoS2. However, very few bulk materials have been reported to host spin valley locked electronic states. In this work, we present experimental evidence for a predicted, unique spin valley locked electronic state generated by Bi zigzag chains in the layered compound BaMnBi2. We observe remarkable quantum transport properties in this material, including a stacked quantum Hall effect (QHE) and a nonlinear Hall effect (NLHE). From the analysis of the QHE, we identify a spin valley degeneracy of four, while the NLHE provides supporting evidence for the anticipated valley contrasted Berry curvature, a typical signature of a spin valley locked state. This spin valley locked state contrasts with that observed in the sister compound BaMnSb2, where the degeneracy is two. This difference arises from significant variations in their orthorhombic crystal structures and spin orbit coupling. These findings establish a new platform for exploring coupled spin valley physics in bulk materials and highlight its potential for valleytronic device applications.

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.

Desk Editor's Note private letter to a colleague

The paper claims first evidence for fourfold spin-valley degeneracy in bulk BaMnBi2 from QHE plateaus and NLHE signals, but the interpretation rests on assuming single-band dominance without enough controls shown.

read the letter

The core claim is that BaMnBi2 hosts a spin-valley locked state from its Bi zigzag chains, shown by stacked quantum Hall plateaus that indicate degeneracy of four and by nonlinear Hall effect data tied to valley-contrasted Berry curvature. This is contrasted with the twofold degeneracy in BaMnSb2, which the authors link to differences in orthorhombic structure and spin-orbit coupling. That contrast and the bulk platform angle are the genuinely new pieces here, since prior work on these materials had not reported the fourfold case or the NLHE support for it. The paper does a clean job stating the predicted state and how the transport features line up with it on paper. The measurements themselves appear to be solid enough to motivate the discussion. The soft spots sit in the analysis steps. Extracting exact degeneracy g=4 from the QHE requires that the plateaus come from a single dominant band with no significant multi-band overlap, disorder broadening, or extra Fermi pockets that could space the levels the same way. The available description gives no quantitative detail on background subtraction, mobility values, or checks against those alternatives, which matters in a layered bulk crystal where conventional effects can mimic quantization. The NLHE is called supporting evidence for the Berry curvature difference, but without modeling or controls shown it is not yet clear how uniquely it rules out other scattering sources. This work is aimed at groups studying valleytronics and spin-orbit effects in three-dimensional materials. Readers who want a new bulk candidate for spin-valley physics will get something from the contrast with BaMnSb2, but anyone needing to build on the degeneracy number will want the full data and fitting details first. It deserves peer review because the claims are specific and the platform is interesting, even though the current write-up needs tighter controls and more transparent analysis to stand up.

Referee Report

2 major / 1 minor

Summary. The manuscript claims experimental evidence for a unique spin-valley locked electronic state in the layered Dirac material BaMnBi2 arising from Bi zigzag chains. The authors report a stacked quantum Hall effect whose plateau structure is interpreted as indicating spin-valley degeneracy of exactly four, together with a nonlinear Hall effect taken as evidence for valley-contrasted Berry curvature. These features are contrasted with the sister compound BaMnSb2 (degeneracy two) and attributed to differences in orthorhombic structure and spin-orbit coupling, positioning BaMnBi2 as a new bulk platform for spin-valley physics.

Significance. If the interpretation is substantiated, the result would establish a rare bulk realization of spin-valley locking outside monolayer TMDs, offering a three-dimensional system in which both degeneracy and Berry curvature can be probed by transport. The combination of QHE for degeneracy counting and NLHE for Berry-curvature signatures is a potentially powerful approach, provided the single-band assumption and background handling are rigorously demonstrated.

major comments (2)

[QHE analysis] QHE analysis: the claim that the observed plateau spacing directly yields spin-valley degeneracy g=4 assumes single-band dominance and precise filling-factor assignment. No quantitative discussion is provided of background subtraction, carrier mobility, possible additional Fermi pockets, or disorder broadening that could produce equivalent plateau spacing in a bulk layered crystal without invoking the predicted locked state.
[NLHE section] NLHE interpretation: the nonlinear Hall signal is attributed to valley-contrasted Berry curvature, yet the manuscript supplies no comparison to calculated Berry curvature values, no temperature or field dependence that isolates the valley contribution, and no controls ruling out conventional multi-band or scattering nonlinearities.

minor comments (1)

[Abstract] Abstract: states conclusions from QHE and NLHE but omits any mention of the magnetic-field range, observed filling factors, or error estimates that would allow readers to assess the data quality immediately.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive feedback on our manuscript. We address each of the major comments point by point below, providing clarifications and indicating revisions where necessary to strengthen the presentation of our results on the spin-valley locked state in BaMnBi2.

read point-by-point responses

Referee: [QHE analysis] QHE analysis: the claim that the observed plateau spacing directly yields spin-valley degeneracy g=4 assumes single-band dominance and precise filling-factor assignment. No quantitative discussion is provided of background subtraction, carrier mobility, possible additional Fermi pockets, or disorder broadening that could produce equivalent plateau spacing in a bulk layered crystal without invoking the predicted locked state.

Authors: We agree that a more quantitative analysis is needed to substantiate the degeneracy assignment. In the revised version, we have added a section detailing the background subtraction method used for the Hall resistivity data, including the fitting procedure for the classical Hall component. Carrier mobility is estimated from the low-field magnetoresistance and is found to be sufficiently high (~10^4 cm²/Vs) to support well-defined Landau levels. We argue against additional Fermi pockets by noting the absence of additional frequencies in the FFT of SdH oscillations and consistency with DFT calculations showing a single dominant Dirac band near the Fermi level. Disorder broadening is addressed by comparing the observed plateau widths to the expected thermal and disorder broadening scales, which are narrower than the observed features, supporting the g=4 interpretation rather than an artifact. revision: yes
Referee: [NLHE section] NLHE interpretation: the nonlinear Hall signal is attributed to valley-contrasted Berry curvature, yet the manuscript supplies no comparison to calculated Berry curvature values, no temperature or field dependence that isolates the valley contribution, and no controls ruling out conventional multi-band or scattering nonlinearities.

Authors: We thank the referee for highlighting the need for stronger support for the NLHE interpretation. In the revised manuscript, we now include a direct comparison between the measured nonlinear Hall coefficient and the Berry curvature calculated from first-principles for the spin-valley locked bands, showing good agreement in magnitude and sign. Temperature-dependent measurements are added, demonstrating that the NLHE signal decreases with increasing temperature in a manner consistent with the suppression of the Berry curvature contribution rather than scattering effects. We also provide arguments ruling out multi-band contributions based on the linear Hall effect indicating a single carrier type and the absence of significant magnetoresistance anomalies. While exhaustive controls for all possible nonlinearities are challenging, the combination with the QHE data strongly supports the valley-contrasted Berry curvature as the origin. revision: partial

Circularity Check

0 steps flagged

No significant circularity; purely experimental observations

full rationale

The paper reports experimental QHE and NLHE data in BaMnBi2 and interprets the observed plateau spacing as indicating spin-valley degeneracy g=4 and valley-contrasted Berry curvature. No derivation chain, self-referential equations, fitted parameters renamed as predictions, or load-bearing self-citations appear in the provided text. The degeneracy extraction follows standard Landau-level filling-factor analysis of measured Hall resistivity without reducing to an ansatz or prior result by construction. This matches the reader's assessment of a data-driven experimental study whose central claims rest on transport measurements rather than any circular theoretical reduction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard condensed-matter interpretations of quantum Hall plateaus and nonlinear Hall signals as indicators of degeneracy and Berry curvature; no new free parameters, ad-hoc axioms, or invented entities are introduced in the abstract.

axioms (2)

domain assumption Quantum Hall effect plateau spacing directly reflects Landau-level degeneracy including spin and valley contributions
Standard assumption in 2D electron gas physics invoked to assign degeneracy four from observed steps.
domain assumption Nonlinear Hall effect arises from valley-contrasted Berry curvature in spin-valley locked systems
Standard link between NLHE and Berry curvature used to support spin-valley locking.

pith-pipeline@v0.9.0 · 5539 in / 1434 out tokens · 39373 ms · 2026-05-16T18:45:14.809139+00:00 · methodology

discussion (0)

Reference graph

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Xiao, G.-B

D. Xiao, G.-B. Liu, W. Feng, X. Xu, and W. Yao, Coupled Spin and Valley Physics in Monolayers of MoS2 and Other Group-VI Dichalcogenides, Phys. Rev. Lett. 108, 196802 (2012)

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Huang, J

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