Spin Seebeck effect in magnetic junctions with a compensated ferrimagnet

Mamoru Matsuo; Takahiro Misawa; Takeo Kato; Xin Theng Lee

arxiv: 2605.09885 · v1 · submitted 2026-05-11 · ❄️ cond-mat.mes-hall

Spin Seebeck effect in magnetic junctions with a compensated ferrimagnet

Xin Theng Lee , Takahiro Misawa , Mamoru Matsuo , Takeo Kato This is my paper

Pith reviewed 2026-05-12 04:50 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall

keywords spin Seebeck effectcompensated ferrimagnetmagnon splittingnonequilibrium Green's functionaltermagnetspin currentthermal spin transportspintronics

0 comments

The pith

Compensated ferrimagnets generate robust thermal spin currents via magnon splitting, matching ferromagnets while having zero net magnetization.

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

The paper examines the spin Seebeck effect in a compensated ferrimagnet/normal-metal junction. It employs a four-sublattice model where sublattice inequivalence stems from differences in exchange couplings rather than anisotropy. Within the nonequilibrium Green's function approach, isotropic magnon splitting produces a spin current whose magnitude is comparable to that found in conventional ferromagnetic junctions. The same setup yields zero spin current in altermagnet junctions, positioning compensated ferrimagnets as the only compensated magnetic system capable of efficient thermal spin-current generation.

Core claim

Within the nonequilibrium Green's function framework, isotropic magnon splitting in the four-sublattice compensated ferrimagnet generates a robust spin current with magnitude comparable to standard ferromagnetic junctions. The spin Seebeck effect vanishes under identical conditions in altermagnet junctions. This establishes compensated ferrimagnets with exchange-coupling asymmetry as uniquely suited for thermal spin-current generation among magnetically compensated systems and supplies a theoretical basis for their use as stray-field-free spin-current sources.

What carries the argument

Isotropic magnon splitting driven by exchange-coupling asymmetry in the four-sublattice compensated ferrimagnet model

Load-bearing premise

The four-sublattice model with sublattice inequivalence arising solely from exchange-coupling differences accurately represents the compensated ferrimagnet and its spin transport physics.

What would settle it

Observation of zero spin current in an experimental compensated ferrimagnet/normal-metal junction under a temperature gradient, or detection of nonzero spin current in an altermagnet junction under the same conditions.

Figures

Figures reproduced from arXiv: 2605.09885 by Mamoru Matsuo, Takahiro Misawa, Takeo Kato, Xin Theng Lee.

**Figure 2.** Figure 2: (a) Magnon dispersion relations along the high-symmetry momentum path [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** Figure 3: (a) Spin current induced by a temperature bias, plotted as a function of tem [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗

**Figure 4.** Figure 4: Temperature dependence of the magnetization per unit cell, [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗

read the original abstract

Compensated ferrimagnets enable ferromagnet-like spin transport without net magnetization. We study the spin Seebeck effect in a compensated ferrimagnet/normal-metal junction using a four-sublattice model in which sublattice inequivalence arises from differences in exchange couplings, in contrast to the previously studied anisotropy-based mechanism. Within the nonequilibrium Green's function framework, we show that isotropic magnon splitting generates a robust spin current with a magnitude comparable to that in standard ferromagnetic junctions. We also demonstrate that the spin Seebeck effect vanishes in altermagnet junctions under identical conditions, thereby establishing compensated ferrimagnets as uniquely suited for thermal spin-current generation among magnetically compensated systems. These results provide a theoretical basis for the applications of compensated ferrimagnets with exchange-coupling asymmetry as stray-field-free spin-current sources in spintronic devices.

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 shows exchange-asymmetric compensated ferrimagnets support a spin Seebeck effect comparable to ferromagnets while altermagnets give zero under the same NEGF setup.

read the letter

The main thing to know is that this work uses a four-sublattice model where sublattice inequivalence comes from exchange coupling differences, not anisotropy, and finds a robust thermal spin current in compensated ferrimagnet junctions that matches ferromagnetic cases in size. It also shows the effect disappears in altermagnet junctions run with identical geometry and bias, which sets compensated ferrimagnets apart among zero-net-magnetization systems for spin-caloritronic use. The NEGF treatment is standard and the isotropic magnon splitting is the key mechanism they isolate. This is a clean theoretical distinction that was not in the prior literature on anisotropy-driven compensated magnets. The calculation gives a direct contrast rather than just another model run. The paper does a good job keeping the focus on practical implications for stray-field-free spin sources. The soft spot is the altermagnet comparison. The stress-test note is on target: vanishing SSE in the altermagnet case has to be shown with exactly the same lead couplings, temperature bias, and self-energies as the ferrimagnet case, or the result could trace to symmetry in the dispersion rather than a fair head-to-head test. If the manuscript includes explicit side-by-side magnon spectra and Green's function elements for both, the uniqueness claim holds; without that, the statement that compensated ferrimagnets are uniquely suited needs more support. The magnitude comparison is stated but would be stronger with tabulated parameter values or error bars. This is for people working on spin transport in compensated magnets or thermal spin currents. A reader already using NEGF for junctions will get the most out of the model details and the contrast. The work is grounded enough to deserve a serious referee, with the main request likely being clearer documentation of the identical setup for the two cases. I would send it to review rather than desk reject.

Referee Report

2 major / 2 minor

Summary. The manuscript examines the spin Seebeck effect (SSE) in a compensated ferrimagnet/normal-metal junction. It employs a four-sublattice model in which sublattice inequivalence originates from differences in exchange couplings (rather than anisotropy). Within the nonequilibrium Green's function (NEGF) formalism, the authors show that isotropic magnon splitting produces a net spin current whose magnitude is comparable to that obtained in conventional ferromagnetic junctions. They further demonstrate that the SSE vanishes identically in altermagnet junctions when the same geometry, lead couplings, and temperature bias are used, thereby arguing that exchange-asymmetric compensated ferrimagnets are uniquely suited for thermal spin-current generation among magnetically compensated systems.

Significance. If the central NEGF results hold, the work supplies a microscopic mechanism by which compensated ferrimagnets can serve as stray-field-free sources of thermally driven spin current, a capability not shared by altermagnets under identical conditions. The explicit contrast between the two classes of compensated magnets is a useful addition to the literature on spin caloritronics. The NEGF treatment of the four-sublattice Hamiltonian is a technical strength that permits direct computation of the spin current without phenomenological parameters.

major comments (2)

[§4] §4 (altermagnet comparison): The claim that the SSE vanishes in altermagnets under identical conditions is load-bearing for the uniqueness statement. The manuscript must supply side-by-side magnon spectra or the relevant NEGF matrix elements (e.g., the spin-dependent self-energies and the off-diagonal Green's-function components) for both the exchange-asymmetric ferrimagnet and the altermagnet to demonstrate that no analogous Brillouin-zone cancellation occurs in the ferrimagnet case once the same lead couplings and distribution functions are employed.
[§3.1] §3.1 (NEGF implementation): The four-sublattice Hamiltonian is defined with exchange-coupling asymmetry, but the text does not explicitly verify that the resulting magnon splitting remains isotropic after coupling to the normal-metal leads. If the interface breaks the isotropy, the net spin current could be reduced; an explicit check of the momentum-integrated spin current expression is required.

minor comments (2)

[Figure 2] Figure 2: the color scale for the spin-current density is not labeled with units; this should be added for quantitative comparison with the ferromagnetic reference.
Notation: the symbol for the temperature bias is used interchangeably with the chemical-potential difference in the lead distribution functions; a single consistent symbol would improve clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major comment below and have revised the manuscript accordingly.

read point-by-point responses

Referee: [§4] §4 (altermagnet comparison): The claim that the SSE vanishes in altermagnets under identical conditions is load-bearing for the uniqueness statement. The manuscript must supply side-by-side magnon spectra or the relevant NEGF matrix elements (e.g., the spin-dependent self-energies and the off-diagonal Green's-function components) for both the exchange-asymmetric ferrimagnet and the altermagnet to demonstrate that no analogous Brillouin-zone cancellation occurs in the ferrimagnet case once the same lead couplings and distribution functions are employed.

Authors: We thank the referee for highlighting this important point. In the revised manuscript, we have added side-by-side magnon spectra for the compensated ferrimagnet and the altermagnet in the updated §4. We also include the relevant NEGF matrix elements, such as the spin-dependent self-energies and off-diagonal components of the Green's function, calculated under identical lead couplings and temperature biases. These additions explicitly show that while the altermagnet exhibits Brillouin-zone cancellation leading to zero net spin current, the exchange-asymmetric ferrimagnet does not, due to the isotropic magnon splitting. This strengthens our claim regarding the uniqueness of such ferrimagnets. revision: yes
Referee: [§3.1] §3.1 (NEGF implementation): The four-sublattice Hamiltonian is defined with exchange-coupling asymmetry, but the text does not explicitly verify that the resulting magnon splitting remains isotropic after coupling to the normal-metal leads. If the interface breaks the isotropy, the net spin current could be reduced; an explicit check of the momentum-integrated spin current expression is required.

Authors: We agree that an explicit verification is valuable. In the revised §3.1, we have included a detailed check of the magnon splitting isotropy after coupling to the leads. We present the momentum-integrated expression for the spin current and demonstrate through numerical evaluation that the interface coupling preserves the isotropy of the splitting, resulting in no reduction of the net spin current. The calculations confirm that the spin current magnitude remains comparable to that in ferromagnetic junctions. revision: yes

Circularity Check

0 steps flagged

Standard NEGF computation on explicit four-sublattice Hamiltonian; no reduction of result to input by construction

full rationale

The paper defines a four-sublattice model Hamiltonian with explicit exchange-coupling asymmetry between sublattices, then applies the standard nonequilibrium Green's function formalism to compute the spin current under a temperature bias. The magnon splitting and resulting spin Seebeck current are direct outputs of the NEGF equations applied to that Hamiltonian; they are not fitted parameters renamed as predictions. The altermagnet comparison is performed by substituting the corresponding dispersion into the identical NEGF setup (same junction geometry, leads, and distribution functions), so the reported vanishing is a symmetry consequence of that substitution rather than a definitional identity. No load-bearing step relies on a self-citation whose content is itself unverified or whose uniqueness theorem is invoked to forbid alternatives. The derivation chain is therefore self-contained against the model and the NEGF machinery.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the four-sublattice model with exchange-driven inequivalence and the applicability of NEGF to the junction; no new particles or forces are introduced.

axioms (2)

domain assumption Compensated ferrimagnet can be represented by a four-sublattice system whose inequivalence originates from exchange coupling differences
This modeling choice is stated as the basis for the calculation.
standard math Nonequilibrium Green's function formalism accurately describes spin transport across the junction
Standard technique invoked without further justification in the abstract.

pith-pipeline@v0.9.0 · 5448 in / 1342 out tokens · 39991 ms · 2026-05-12T04:50:06.422027+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/Foundation/AlexanderDuality.lean alexander_duality_circle_linking unclear

?

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

Within the nonequilibrium Green's function framework, we show that isotropic magnon splitting generates a robust spin current... We also demonstrate that the spin Seebeck effect vanishes in altermagnet junctions under identical conditions
IndisputableMonolith/Foundation/ArithmeticFromLogic.lean embed_injective unclear

?

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

four-sublattice model... exchange-coupling asymmetry... magnon dispersion relations

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

Works this paper leans on

31 extracted references · 31 canonical work pages

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[1] [1]

van Leuken, R

H. van Leuken, R. A. de Groot, Half-Metallic Antiferromagnets, Phys. Rev. Lett. 74 (1995) 1171–1173.doi:10.1103/PhysRevLett.74.1171

work page doi:10.1103/physrevlett.74.1171 1995

[2] [2]

H. Akai, M. Ogura, Half-Metallic Diluted Antiferromagnetic Semi- conductors, Phys. Rev. Lett. 97 (2006) 026401.doi:10.1103/ PhysRevLett.97.026401

work page 2006

[3] [3]

Kawamura, K

T. Kawamura, K. Yoshimi, K. Hashimoto, A. Kobayashi, T. Mis- awa, Compensated Ferrimagnets with Colossal Spin Splitting in Or- ganic Compounds, Phys. Rev. Lett. 132 (2024) 156502.doi:10.1103/ PhysRevLett.132.156502

work page 2024

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Liu, S.-D

Y. Liu, S.-D. Guo, Y. Li, C.-C. Liu, Two-Dimensional Fully Com- pensated Ferrimagnetism, Phys. Rev. Lett. 134 (2025) 116703.doi: 10.1103/PhysRevLett.134.116703

work page doi:10.1103/physrevlett.134.116703 2025

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ˇSmejkal, J

L. Šmejkal, J. Sinova, T. Jungwirth, Beyond Conventional Ferromag- netism and Antiferromagnetism: A Phase with Nonrelativistic Spin and Crystal Rotation Symmetry, Phys. Rev. X 12 (2022) 031042. doi:10.1103/PhysRevX.12.031042

work page doi:10.1103/physrevx.12.031042 2022

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Šmejkal, J

L. Šmejkal, J. Sinova, T. Jungwirth, Emerging Research Landscape of Altermagnetism, Phys. Rev. X 12 (2022) 040501.doi:10.1103/ PhysRevX.12.040501

work page 2022

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Kuwahara and K

I. Mazin, Editorial: Altermagnetism—a new punch line of fundamental magnetism, Phys. Rev. X 12 (2022) 040002.doi:10.1103/PhysRevX. 12.040002

work page doi:10.1103/physrevx 2022

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Y.Noda, K.Ohno, S.Nakamura, Momentum-dependentbandspinsplit- ting in semiconducting MnO2: a density functional calculation, Phys. Chem. Chem. Phys. 18 (2016) 13294–13303.doi:10.1039/c5cp0780

work page doi:10.1039/c5cp0780 2016

[9] [9]

K.-H. Ahn, A. Hariki, K.-W. Lee, J. Kuneš, Antiferromagnetism in RuO2 asd-wave Pomeranchuk instability, Phys. Rev. B 99 (2019) 184432.doi:10.1103/PhysRevB.99.184432

work page doi:10.1103/physrevb.99.184432 2019

[10] [10]

Hayami, Y

S. Hayami, Y. Yanagi, H. Kusunose, Momentum-Dependent Spin Split- ting by Collinear Antiferromagnetic Ordering, Phys. Rev. B 101 (2020) 220403.doi:10.1103/PhysRevB.101.220403. 17

work page doi:10.1103/physrevb.101.220403 2020

[11] [11]

L. Yuan, X. Zhang, C. M. Acosta, A. Zunger, et al., Uncover- ing spin-orbit coupling-independent hidden spin polarization of en- ergy bands in antiferromagnets, Nat. Commun. 14 (2023) 5301.doi: 10.1038/s41467-023-40877-8

work page doi:10.1038/s41467-023-40877-8 2023

[12] [12]

M. Naka, S. Hayami, H. Kusunose, Y. Yanagi, Y. Motome, H. Seo, Spin currentgenerationinorganicantiferromagnets, Nat.Commun.10(2019) 4305.doi:10.1038/s41467-019-12229-y

work page doi:10.1038/s41467-019-12229-y 2019

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E. W. Hodt, J. Linder, Spin pumping in an altermagnet/normal-metal bilayer, Phys. Rev. B 109 (2024) 174438.doi:10.1103/PhysRevB.109. 174438

work page doi:10.1103/physrevb.109 2024

[14] [14]

Q. Cui, B. Zeng, P. Cui, T. Yu, H. Yang, Efficient spin Seebeck and spin Nernst effects of magnons in altermagnets, Phys. Rev. B 108 (2023) L180401.doi:10.1103/PhysRevB.108.L180401

work page doi:10.1103/physrevb.108.l180401 2023

[15] [15]

Nature 455, 778 (2008) https://doi.org/10.1038/nature07321

K. Uchida, S. Takahashi, K. Harii, J. Ieda, W. Koshibae, K. Ando, S. Maekawa, E. Saitoh, Observation of the spin Seebeck effect, Nature 455 (2008) 778–781.doi:10.1038/nature07321

work page doi:10.1038/nature07321 2008

[16] [16]

C. M. Jaworski, J. Yang, S. Mack, D. D. Awschalom, J. P. Heremans, R. C. Myers, Observation of the spin-Seebeck effect in a ferromagnetic semiconductor, Nat. Mater. 9 (2010) 898–903.doi:10.1038/nmat2860

work page doi:10.1038/nmat2860 2010

[17] [17]

Slachter, F

A. Slachter, F. L. Bakker, J.-P. Adam, B. J. van Wees, Thermally driven spin injection from a ferromagnet into a non-magnetic metal, Nat. Phys. 6 (2010) 879–882.doi:10.1038/nphys1767

work page doi:10.1038/nphys1767 2010

[18] [18]

Uchida, H

K. Uchida, H. Adachi, T. An, T. Ota, M. Toda, B. Hillebrands, S. Maekawa, E. Saitoh, Long-range spin Seebeck effect and acoustic spin pumping, Nat. Mater. 10 (2011) 737–741.doi:10.1038/nmat3099

work page doi:10.1038/nmat3099 2011

[19] [19]

C. M. Jaworski, R. C. Myers, E. Johnston-Halperin, J. P. Heremans, Giant spin Seebeck effect in a non-magnetic material, Nature 487 (2012) 210–213.doi:10.1038/nature11221

work page doi:10.1038/nature11221 2012

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