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REVIEW 3 major objections 5 minor 63 references

Non-Relativistic Anisotropic Magnetoresistance with Collinear and Non-Collinear Magnetic Order

T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Magnetic order alone can produce anisotropic magnetoresistance, with no spin-orbit coupling required.

desk verdict The intrinsic symmetry-based claim is real and the MnN calculation is convincing, but the extrinsic impurity mechanism as written is not a scattering calculation and needs major revision. read the letter →

arxiv 2506.22115 v2 pith:ZACBXWME submitted 2025-06-27 cond-mat.mtrl-sci

Philipp Ritzinger , Ondřej Sedláček , Jakub Železný , Karel Výborný This is my paper · ORCID
classification cond-mat.mtrl-sci
keywords anisotropicmagnetoresistancespin-orbitcouplingmagneticsublatticesantiferromagneticorderFermisurfaceanisotropyBoltzmanntransporttheorynon-collinearmagnetismsymmetryanalysis
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

This paper claims that anisotropic magnetoresistance--the dependence of resistivity on the direction of magnetic order--can appear without spin-orbit coupling whenever the magnetic order involves more than one magnetic sublattice. The mechanism is a lowering of the real-space symmetry of the conductivity tensor by the magnetic order itself, which makes the Fermi surface direction-dependent. The authors demonstrate the effect in tight-binding models of kagome and triangular lattices, in density-functional calculations of the collinear antiferromagnet MnN (where the anisotropy is about 17 percent), and in the non-collinear antiferromagnet Mn3Sn under moment tilting. They also show an extrinsic version caused by spin-dependent scattering from magnetic impurities. If the claim holds, magnetoresistive materials can be designed using light elements and strong magnetic order rather than heavy atoms with strong spin-orbit coupling.

What carries the argument

The load-bearing identity is Eq. (8), which in the relaxation-time approximation writes the longitudinal conductivity as $\sigma_{ii}\propto\int_{\rm FS}\sum_n v_{n,i}(\mathbf{k})^2\,dk$. The central object is the real-space symmetry group of the magnetic configuration: Neumann's principle restricts the allowed form of the conductivity tensor, and AMR appears exactly when magnetic order breaks the rotational symmetries (90° in cubic MnN; 60° and 120° around $z$ in kagome-type order) that would otherwise enforce isotropic diagonal conductivity. For the extrinsic mechanism the machinery is Fermi's golden rule with a spin-impurity scattering operator, which makes the scattering rate $\Gamma_{n,\mathbf{k}}$ direction-dependent on the Fermi surface.

What would settle it

Measure the longitudinal resistivity of a single-domain MnN crystal along [100] and [001] as a function of temperature and magnetic-field history; if the anisotropy fails to follow the orientation of the A-type antiferromagnetic planes or persists above the ordering temperature, the spontaneous-AMR claim is refuted. Equivalently, replace the constant relaxation time in Eq. (8) with a momentum-dependent scattering rate obtained from first-principles electron-phonon or impurity calculations; if the 17 percent anisotropy changes sign or falls below a few percent, the quantitative claim is not robust.

Watch

Extended reading notes

Core claim

The central discovery is that in crystals with several magnetic sublattices, magnetic ordering alone can lower the real-space symmetry of the conductivity tensor in the non-relativistic limit. In a single-sublattice ferromagnet, a rigid spin rotation is a symmetry of the Hamiltonian without spin-orbit coupling, so rotating all moments cannot change the conductivity; but when symmetry operations map one sublattice onto another, the magnetic order can break rotational symmetries of the nonmagnetic lattice. With isotropic scattering, the longitudinal conductivity becomes an integral over the Fermi surface of squared Fermi velocities (Eq. 8), so the broken rotations show up as different conductivities along inequivalent directions. The paper supports this with a collinear A-type antiferromagnet, MnN, for which DFT gives $\sigma_{xx}/\sigma_{zz} - 1 \approx 17\%$; with kagome- and triangular-lattice models where tilting moments breaks the 60° and 120° rotations and induces anisotropy; and with Mn3Sn, where the same tilting logic explains rotated Fermi surfaces and non-saturating transverse AMR. It also establishes a separate extrinsic mechanism: magnetic impurities aligned by a weak field scatter electrons with a spin-dependent rate, producing AMR even when the host magnetic order is symmetry-isotropic.

Load-bearing premise

The quantitative intrinsic AMR values, including the 17 percent for MnN, assume a constant and isotropic relaxation time in the Boltzmann equation, so the entire anisotropy is attributed to Fermi-surface shape; if real scattering is momentum- or band-dependent, the magnitude and even the sign of the effect could change.

Editorial extensions

If this is right

  • MnN should show spontaneous non-relativistic AMR of about 17 percent, comparable in size to spin-orbit-driven AMR, with spin-orbit coupling changing the result only mildly.
  • In kagome-type antiferromagnets, an applied field or strain that tilts the moments breaks the 60° and 120° rotational symmetries and acts as a control knob for the conductivity anisotropy.
  • Mn3Sn should display field-tunable non-relativistic AMR through moment tilting, consistent with the non-saturating transverse AMR measured up to 9 T.
  • Magnetic impurities aligned by a weak field can produce extrinsic AMR even in configurations whose intrinsic conductivity is isotropic, through a two-fold modulation of the scattering rate on the Fermi surface.
  • A symmetry-based scan of known magnetic structures identifies 280 candidate materials for non-relativistic AMR.

Reading between the lines

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

  • If the constant-relaxation-time result survives full scattering calculations, the same symmetry argument should apply to other transport coefficients, so non-relativistic magnetic-order-induced anisotropies could appear in thermoelectric, optical, and thermal responses of the same materials.
  • The tilting-based mechanism suggests a magneto-mechanical transducer concept: strain or pressure that tilts magnetic moments would produce a resistance change without any heavy-element spin-orbit coupling, potentially interesting for sensors.
  • The intrinsic and extrinsic channels should be separable experimentally by frequency dependence: the intrinsic contribution is frequency-independent while the impurity-driven contribution scales as $1/\omega$, so THz or optical measurements could disentangle them.
  • If verified in MnN, the effect implies that antiferromagnetic spintronics does not need to rely on spin-orbit coupling for magnetoresistive readout, which would broaden the available materials beyond heavy-element compounds.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper proposes that anisotropic magnetoresistance (AMR) can arise without spin-orbit coupling when magnetic order with multiple sublattices lowers the real-space symmetry of the crystal. It combines symmetry analysis based on Neumann's principle with tight-binding transport calculations, Boltzmann theory in the relaxation-time approximation, and DFT plasma-frequency calculations. The intrinsic mechanism is studied in MnN, in kagome and triangular lattice models, and in a symmetry-based discussion of Mn3Sn; the extrinsic mechanism is studied through spin-dependent scattering from magnetic impurities. The central claim is that both intrinsic Fermi-surface anisotropy and extrinsic spin-dependent impurity scattering can produce non-relativistic AMR, and the paper also reports a symmetry-based screen of MAGNDATA entries that yields 280 putative candidate materials.

Significance. If the intrinsic claim holds, the paper significantly broadens the conceptual scope of AMR beyond the conventional spin-orbit-coupling mechanism and connects it to the growing field of non-collinear and multi-sublattice magnets, which is of clear interest for antiferromagnetic spintronics. The symmetry analysis is clean and provides a useful organizing framework, and the MnN DFT plasma-frequency calculation is an independent quantitative anchor for the intrinsic effect. The proposed database screening also has practical value for materials discovery. However, the extrinsic scattering calculation contains a serious formal problem that affects one of the two advertised mechanisms, and the Mn3Sn case is argued by symmetry analogy rather than by an explicit transport calculation, so the full set of claims is not yet supported.

major comments (3)
  1. [Sec. IV, Eq. (10)] The impurity operator defined in Sec. IV as M = S_i ⊗ 1_{N×N}, with 1_{N×N} the identity in the N-atom unit cell, is translationally invariant on the lattice period rather than a local potential. For Bloch states normalized over the crystal, the matrix element in Eq. (10) is therefore diagonal in crystal momentum up to reciprocal-lattice vectors; when combined with the (1 − cos θ_{vv'}) factor in Eq. (9), this yields a vanishing relaxation rate for non-degenerate bands. Consequently, the finite scattering rates and the resulting AMR reported in Table I and Fig. 8 do not follow for a dilute magnetic impurity. A local impurity at site R0 would instead require M = S_i ⊗ P_{R0}, whose Bloch matrix element carries the phase e^{−i(k−k′)·R0}. If the identity operator is intended to represent a uniform spin-dependent field, it should be included in the band Hamiltonian rather than in the scattering rate. Because the abstract explicitly advertises spin-dependent impurity scattering as one of the two mechanisms, this flaw affects a load-bearing part of the central claim.
  2. [Sec. III D] The Mn3Sn discussion does not contain a transport calculation. The paper confirms the symmetry lowering with the Symmetr code and illustrates Fermi surfaces only conceptually in Fig. 6; no tight-binding or DFT conductivity calculation for Mn3Sn is presented, and the connection to the toy-model results is analogical. The abstract nevertheless lists Mn3Sn as a case study supporting the findings. This overstates the available support; either a real calculation should be added or the Mn3Sn claim should be framed as a symmetry-based prediction rather than a demonstrated case study.
  3. [Sec. III A, Eq. (8)] The quantitative 17% AMR for MnN is obtained from Eq. (8), which assumes a constant, isotropic relaxation time. If the true scattering rate is momentum- or band-dependent, the anisotropy magnitude and even its sign could change, and the paper provides no estimate of this uncertainty. Since the abstract emphasizes that the effect may reach significant magnitudes, the authors should either compute or bound the effect of momentum-dependent scattering or explicitly present the 17% as the constant-τ estimate rather than as a predicted material value.
minor comments (5)
  1. [Sec. IV] The sentence 'assuming magnetic impurities pointing ini-direction' appears to be garbled; it should presumably read 'pointing in the x-direction' or 'in a given direction'.
  2. [Sec. III B] The 280 candidate materials are only referenced as 'detailed in the Supplementary Material'; without the supplementary list, the screening result cannot be verified from the main text. The manuscript should either include the list or clearly state that it is available in a separate file.
  3. [Sec. III A] The DFT calculation for MnN should specify the exchange-correlation functional, basis-set parameters, and the exact lattice structure used. The phrase 'perfectly cubic structure' followed later by a/c = 0.4256/0.4189 nm for the distorted case is confusing and should be clarified.
  4. [Appendix A, Eq. (A1)] In Eq. (A1), the symbol c_{m,n} is described as 'the index of the n-th harmonic' but it is a coefficient in the expansion; the wording should be corrected.
  5. [Sec. III D] The sentence 'We will examine scattering on such defects in the next section' promises a calculation for Mn3Sn, but the next section treats only a toy-model kagome lattice; the cross-reference should be adjusted.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the AMR predictions are computed from stated TB/DFT models, not imported from or fitted to the target anisotropies.

full rationale

The paper's central quantities are obtained by direct first-principles and model calculations that do not assume the effect they claim. The MnN intrinsic AMR (Sec. III A) follows from LAPW plasma-frequency tensors computed for the stated cubic and distorted structures, fed into Eq. (8); neither the plasma frequencies nor the resulting 17% ratio is fitted to AMR data. The kagome/triangular intrinsic AMR (Sec. III C) is a forward tight-binding Boltzmann calculation with stated hopping, exchange, and Fermi-energy parameters; the observed Fermi-surface anisotropy is an output, not an input. The Mn3Sn discussion is a symmetry analysis of the same tight-binding model plus literature comparison, and the extrinsic AMR (Sec. IV) is a Fermi's Golden Rule calculation with the stated impurity operator. Self-references (Refs. 2, 27, 32, 33, 37, 39) provide the Hamiltonian form, the non-relativistic symmetry framework, and the Boltzmann/Fermi's Golden Rule equations, but none of these citations supplies the numerical AMR values or the Fermi-surface anisotropies; each is either an explicitly stated model assumption or an algorithmic/reproducible tool such as the Symmetr code. The constant isotropic relaxation-time approximation (Eq. 8) is a controlled assumption about scattering, not a circular identification of the target anisotropy. A separate, non-circular correctness concern could be raised about the translationally invariant impurity operator M = S_i ⊗ 1_{N×N} in Sec. IV, which is not a site-localized potential; this affects the physical interpretation of the extrinsic calculation but does not make the derivation circular.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The central claim does not require many invented quantities; the main cost is the set of model parameters and idealized scattering assumptions. No new particles or fields are introduced.

free parameters (5)
  • Tight-binding hopping amplitude t = not stated (treated as unit energy)
    The kagome and triangular model band structures and Fermi surfaces depend on t, but its value is not given in the text.
  • Exchange coupling J = not stated
    Together with t it sets the spin-split band structure; no value is specified.
  • Fermi energy EF = 0 and 0.1 (in units of t) used in figures
    The intrinsic AMR is energy-dependent (Fig. 5b), so the reported anisotropies depend on the chosen filling.
  • Tilting angle alpha = 0, 24, 36, 60, 120, 240 degrees (illustrative)
    Field-induced tilts are imposed by hand; no model for how a magnetic field or strain produces a given alpha is provided.
  • Impurity spin orientation and density = x or y orientation; density N_scat unspecified
    Extrinsic AMR results are qualitative and depend on the impurity direction and concentration.
assumptions (6)
  • domain assumption Boltzmann transport equation with delta-function Fermi-surface integration (Eq. 6) describes longitudinal conductivity in these systems.
    Used throughout Secs. III and IV without derivation; assumes coherent quasiparticles and neglects vertex corrections.
  • domain assumption Constant, isotropic relaxation time in the intrinsic AMR calculations (RTA, Sec. II A, Eq. 8).
    Central to the quantitative intrinsic AMR; momentum-dependent scattering is not treated.
  • domain assumption Without SOC, spin and orbital degrees of freedom decouple, so global spin rotations do not affect the conductivity tensor.
    Used in Sec. I to distinguish the two forms of AMR and to argue that only non-rigid manipulations matter.
  • standard math Neumann's principle: response tensors must be invariant under the symmetry group of the magnetic configuration (Sec. II B).
    Basis of the symmetry analysis and the 280-candidate screening.
  • domain assumption The MAGNDATA crystal and magnetic structures used in the candidate search are correct and representative.
    The 280 candidates are identified solely by symmetry analysis applied to database entries, without electronic-structure checks.
  • domain assumption Magnetic impurities in systems like Mn3Sn can be aligned by a weak field without disturbing the host order.
    Needed for the extrinsic AMR mechanism; supported only by references to antiferromagnetic salts and alloys, not by a calculation for Mn3Sn.

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Cite this review

Pith. "Pith review of Non-Relativistic Anisotropic Magnetoresistance with Collinear and Non-Collinear Magnetic Order." pith.science (2026). https://pith.science/paper/ZACBXWME

@misc{pith2026250622115,
  author       = {Pith},
  title        = {Pith review of: Non-Relativistic Anisotropic Magnetoresistance with Collinear and Non-Collinear Magnetic Order},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZACBXWME}},
  note         = {Machine review of arXiv:2506.22115}
}
abstract

Anisotropic magnetoresistance (AMR) arises from symmetry lowering of the conductivity tensor induced by magnetic order. In simple ferromagnets, AMR is a relativistic effect, relying on spin-orbit interaction (SOC). Here, we demonstrate that a comparable symmetry lowering can also occur in a non-relativistic limit. Using tight-binding models, density functional theory calculations, and Boltzmann transport theory, we investigate systems with multiple magnetic sublattices, including both collinear and non-collinear antiferromagnets, as well as ferrimagnetic configurations. We show that AMR and related anisotropies can emerge purely from magnetic order, without the need for SOC, and may reach significant magnitudes. The findings are supported by case studies on toy-model lattices and real materials such as MnN, Mn$_3$Sn, and are further interpreted using a symmetry analysis based on Neumann's principle. Material candidates that exhibit non-relativistic anisotropic magnetoresistance are identified by symmetry analysis applied to entries in the MAGNDATA database.

Figures

Figures reproduced from arXiv: 2506.22115 by the authors.

Figure 1
Figure 1. FIG. 1. (a) A square lattice without magnetic order exhibits [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Schematic illustration of (a) the kagome lattice and [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 4
Figure 4. FIG. 4. Illustration of the rotation of the moments B (coun [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figures from the paper (3 more)
Figure 3
Figure 3. Figure 3: FIG. 3. Results for two compensated magnetic configuration [PITH_FULL_IMAGE:figures/full_fig_p006_3.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Illustration of symmetry breaking through in [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]
Figure 8
Figure 8. Figure 8: FIG. 8. Kagome lattice with magnetic impurity. Scattering [PITH_FULL_IMAGE:figures/full_fig_p008_8.png]

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