arxiv: 2605.10747 · v1 · submitted 2026-05-11 · ❄️ cond-mat.mes-hall

Recognition: 2 theorem links

· Lean Theorem

Theory of Spin-splitter Magnetoresistance in Altermagnets

Tim Kokkeler , Vitaly N. Golovach , F. Sebastian Bergeret

Authors on Pith no claims yet

Pith reviewed 2026-05-12 04:07 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall

keywords altermagnetismspin-splitter magnetoresistanceangle-dependent magnetoresistancecollinear magnetismNéel vectorspin-Hall magnetoresistanceferromagnetic insulator

0 comments

The pith

Spin-splitter magnetoresistance in metallic altermagnets depends only on the relative angle between magnetization and Néel vector, shows opposite-sign longitudinal response, and has proportional longitudinal and transverse signals.

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

The paper develops a transport theory for angle-dependent magnetoresistance at interfaces between metallic altermagnets and ferromagnetic insulators. It shows that the spin-splitter magnetoresistance arises from the altermagnet's characteristic spin splitting and coupling to the insulator's magnetization. This produces three clear distinctions from conventional spin-Hall magnetoresistance in compensated magnets that rely on spin-orbit coupling. The resistance changes depend solely on the relative orientation of the two magnetic vectors. The longitudinal signal has the opposite sign, and the longitudinal and transverse signals are directly proportional to each other. These features supply a direct transport-based test for collinear altermagnetic order.

Core claim

In a metallic altermagnet interfaced with a ferromagnetic insulator the angle-dependent magnetoresistance takes the form of spin-splitter magnetoresistance generated by the exchange coupling between the altermagnet's spin-split bands and the insulator magnetization. This resistance depends only on the relative angle between the ferromagnetic magnetization and the altermagnetic Néel vector, produces a longitudinal response of opposite sign to that found in spin-Hall magnetoresistance, and yields longitudinal and transverse components that are directly proportional.

What carries the argument

Spin-splitter magnetoresistance (SSMR) at the altermagnet-ferromagnetic insulator interface, arising from the altermagnet's spin splitting and its exchange coupling to the adjacent magnetization.

If this is right

SSMR provides an unambiguous transport signature for identifying collinear altermagnetism in metallic systems.
The longitudinal component of the angle-dependent magnetoresistance has the opposite sign to the conventional spin-Hall case.
Longitudinal and transverse angle-dependent magnetoresistance signals are directly proportional under SSMR but not under spin-Hall magnetoresistance.
The resistance depends solely on the relative orientation of the ferromagnetic magnetization and the altermagnetic Néel vector.

Where Pith is reading between the lines

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

Transport measurements alone could serve as a practical method to confirm altermagnetic order in metallic samples.
The predicted proportionality and sign reversal offer concrete experimental checks that can be performed on bilayer devices.
Similar distinctions may appear in other hybrid structures that combine altermagnets with insulating magnets.
Real-device interface disorder could reduce the visibility of the predicted signatures.

Load-bearing premise

The interface transport is governed by the altermagnet's spin splitting and its coupling to the ferromagnet without confounding contributions from spin-orbit coupling or disorder that could produce similar angular dependencies.

What would settle it

Observation of a longitudinal angle-dependent magnetoresistance signal with the same sign as in conventional spin-Hall magnetoresistance, or absence of direct proportionality between longitudinal and transverse signals, in an altermagnet-ferromagnetic insulator structure would contradict the predicted distinctions.

Figures

Figures reproduced from arXiv: 2605.10747 by F. Sebastian Bergeret, Tim Kokkeler, Vitaly N. Golovach.

**Figure 3.** Figure 3: FIG. 3. The angle ( [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

read the original abstract

We develop a theory of angle-dependent magnetoresistance (ADMR) in metallic altermagnets coupled to ferromagnetic insulators and establish criteria that distinguish them from conventional compensated magnets with spin-orbit coupling. We show that the spin-splitter magnetoresistance (SSMR) reported by H. Chen et al. [Adv. Mater. 37, 2507764 (2025)] constitutes a smoking-gun signature of collinear altermagnetism in metallic systems. In contrast to spin-Hall magnetoresistance (SMR), SSMR exhibits three key distinctions: it depends solely on the relative orientation between the ferromagnetic magnetization and the altermagnetic N\'eel vector, yields a longitudinal ADMR response of opposite sign, and features a direct proportionality between longitudinal and transverse ADMR signals, absent in SMR. These results provide a clear route to unambiguously identify altermagnets in transport.

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

This paper gives a clean symmetry derivation that turns SSMR into a set of three testable distinctions from ordinary SMR, making it a practical way to flag collinear altermagnets in transport.

read the letter

Colleague, the main point is that this work shows how the spin-splitter magnetoresistance seen in the Chen experiment follows directly from altermagnetic symmetry and carries three built-in features that set it apart from standard spin-Hall magnetoresistance. The authors build a transport model at the metallic altermagnet–ferromagnetic insulator interface using only the allowed spin-splitter terms. From the resulting conductivity tensor they extract the angular dependence that depends solely on the relative angle between the ferromagnet magnetization and the altermagnet Néel vector, produces a longitudinal ADMR of opposite sign, and gives a direct proportionality between the longitudinal and transverse signals. These three distinctions are new relative to the prior experimental report and do not require additional fitting parameters or extra spin-orbit terms in the ideal case. The derivation is straightforward and the stress-test confirms there are no internal inconsistencies in the tensor construction or the final ADMR formulas. The model is grounded in symmetry, which is the right starting point for this kind of claim. The main limitation is the ideal-interface assumption. Real samples will include some disorder or stray spin-orbit contributions that could soften or mimic the predicted distinctions, so the smoking-gun status will still need careful experimental control of interface quality. That is a standard caveat rather than a fatal gap. The paper is aimed at people working on altermagnetic and antiferromagnetic spintronics who need concrete transport criteria. A reader who wants a falsifiable protocol to identify altermagnets in metals will get something directly usable. It deserves peer review because the distinctions are specific, the symmetry argument is solid, and the claims can be checked against new data.

Referee Report

0 major / 2 minor

Summary. The manuscript develops a symmetry-based transport theory for angle-dependent magnetoresistance (ADMR) at the interface between a metallic altermagnet and a ferromagnetic insulator. It derives the angular dependence of the spin-splitter magnetoresistance (SSMR) and establishes three distinguishing criteria from conventional spin-Hall magnetoresistance (SMR): sole dependence on the relative orientation of the ferromagnetic magnetization and altermagnetic Néel vector, opposite sign in the longitudinal ADMR response, and direct proportionality between longitudinal and transverse ADMR signals. These features are presented as smoking-gun signatures for identifying collinear altermagnetism in metallic systems.

Significance. If the central derivations hold, the work provides a clear, falsifiable route to distinguish altermagnets from compensated magnets with spin-orbit coupling via transport measurements, directly addressing recent experimental reports of SSMR. The symmetry-based construction of the conductivity tensor yields parameter-free angular dependencies in the ideal limit, offering strong predictive power without fitted parameters.

minor comments (2)

The abstract and introduction would benefit from a brief explicit statement of the key assumptions in the interface transport model (e.g., absence of additional SOC or disorder terms) to make the scope of the distinctions immediately clear to readers.
Notation for the Néel vector and magnetization directions should be standardized across figures and equations to avoid any ambiguity in the angular dependence plots.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of our manuscript, including the recognition that our symmetry-based theory provides clear, falsifiable criteria to distinguish spin-splitter magnetoresistance in altermagnets from conventional spin-Hall magnetoresistance. We appreciate the recommendation for minor revision.

Circularity Check

0 steps flagged

No significant circularity; derivation is forward from model to signatures

full rationale

The manuscript constructs a symmetry-based transport model for the metallic altermagnet/ferromagnetic-insulator interface and derives the angular dependence of the conductivity tensor from spin-splitter scattering terms. The three claimed distinctions (sole dependence on relative M/N orientation, opposite-sign longitudinal ADMR, and direct longitudinal-transverse proportionality) emerge directly as consequences of that tensor without any fitted parameters, self-referential definitions, or load-bearing self-citations. The reference to Chen et al. is an external experimental report being interpreted, not an internal premise. No step reduces by construction to its own inputs; the central results are independent predictions of the chosen Hamiltonian and scattering assumptions.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Based solely on the abstract, no explicit free parameters, axioms, or invented entities are stated; the theory relies on standard assumptions of collinear altermagnetic order and interfacial coupling in condensed-matter transport models.

pith-pipeline@v0.9.0 · 5459 in / 1251 out tokens · 27108 ms · 2026-05-12T04:07:45.718270+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

We compute the longitudinal and transverse resistances... ρ_L = σ^{-1} + Δρ_L and ρ_T = T_yz / T_xy Δρ_L with Δρ_L containing tanh(L_y / 2 l_s∥) and sin²φ terms
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

For d-wave altermagnets, the charge and spin current densities... j_k = σ/e (∂_k μ + 1/2 N_a T_kj ∂_j μ_s^a)

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

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