Symmetry, microscopy and spectroscopy signatures of altermagnetism

Hikaru Watanabe; Jairo Sinova; Libor Smejkal; Qihang Liu; Rafael M. Fernandes; Satoru Nakatsuji; Shuichi Murakami; Tomas Jungwirth

Symmetry, microscopy and spectroscopy signatures of altermagnetism

T0 review · 0 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Altermagnetism is a collinear compensated magnetic phase whose spin-group symmetries produce d-, g-, or i-wave spin splitting and symmetry-protected nodal surfaces without spin-orbit coupling.

desk verdict Solid, authoritative review of altermagnetism; no new results, but the synthesis is honest and the classification concern doesn't undercut it. read the letter →

arxiv 2506.22860 v1 pith:LXR24HLC submitted 2025-06-28 cond-mat.mtrl-sci

Tomas Jungwirth , Jairo Sinova , Rafael M. Fernandes , Qihang Liu , Hikaru Watanabe , Shuichi Murakami , Satoru Nakatsuji , Libor Smejkal This is my paper

classification cond-mat.mtrl-sci

keywords altermagnetismspingroupscompensatedmagnetssplittingnodalsurfacesanomalousHalleffectspin-resolvedphotoemissionhigher-partial-wavedensity

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 review argues that altermagnetism is a distinct magnetic phase of matter, not a variant of ferromagnetism or Neel antiferromagnetism. In an altermagnet, the spins are collinear and fully compensated, so there is no net magnetization, yet the electronic structure is spin-split and time-reversal-broken because the opposite-spin sublattices are related by rotations that combine a real-space rotation with a spin flip. The paper shows how this phase is defined by spin-group symmetries, realized microscopically as a ferroic order of d-, g-, or i-wave components of atomic spin densities, and observable in spin-resolved photoemission as alternating-sign spin splitting with symmetry-protected nodal surfaces. If correct, altermagnetism gives compensated magnets the spintronic advantages of ferromagnets without stray fields, and connects magnetically ordered matter to unconventional superconductivity and topological band structures.

What carries the argument

The central object is the spin group, the symmetry group of a magnetic crystal when spin-orbit coupling is neglected, in which spin-space rotations ($C_2$, $SO(2)$, $T$) and real-space operations ($E$, $G$, $H$) are paired independently. Altermagnetism is delineated by spin groups of the form $Z_2^{C_2T}\ltimes SO(2)\times([E\parallel H]+[C_2\parallel G-H])$. This machinery determines whether and at which momenta the non-relativistic band structure can be spin split, protects the nodal surfaces, and separates the spin-ordering physics from spin-orbit-coupling effects, which are instead described by magnetic groups.

What would settle it

Compute or measure the non-relativistic spin-resolved band structure of an altermagnetic candidate such as MnTe or CrSb with the Neel vector in the magnetic easy plane: the prediction is spin-degenerate nodal planes crossing the zone center. Observing a spin splitting on those nodal planes, in a calculation with spin-orbit coupling turned off or in a low-spin-orbit material where the splitting cannot be attributed to spin-orbit coupling, would falsify the spin-group assignment.

Watch

Extended reading notes

Core claim

Altermagnetism is defined as a collinear, fully compensated magnetic order in which opposite-spin sublattices are connected by a rotation in real space combined with a two-fold spin rotation, not by translation or inversion. Because the real-space and spin-space transformations differ, the compensating nature (zero net magnetization) coexists with an even-parity, time-reversal-breaking spin splitting of the non-relativistic bands: the spin-up and spin-down energy iso-surfaces are equally sized but anisotropically distorted and mutually rotated, intersecting at 2, 4, or 6 symmetry-protected nodal surfaces for d-, g-, or i-wave order. Microscopically, this is a ferroic order of higher-partial-wave (d, g, i) components of the atomic spin density, which can exist with or without atomic dipole moments. The paper reviews how these signatures appear in ARPES, X-ray dichroism, magnetotransport, and in spin-orbit coupling and topological effects.

Load-bearing premise

The classification assumes that spin-orbit coupling is weak enough that a non-relativistic electronic structure with separate spin-up and spin-down channels is a valid starting point, so that the spin-group symmetries determine the magnetic phase; if spin-orbit coupling were strong, the nodal structure and the phase labels would change.

Editorial extensions

If this is right

In altermagnets, spin-up and spin-down bands are split without spin-orbit coupling and intersect at 2, 4, or 6 symmetry-protected nodal surfaces in the Brillouin zone.
Altermagnetic order generates time-reversal-broken responses such as the anomalous Hall effect even though the net magnetization is zero.
Spin-orbit coupling can lift the nodal degeneracies, producing Berry-curvature hot spots, Weyl points, and topological spin-Chern insulators.
Altermagnetism can occur in insulators, semiconductors, metals, and strongly correlated Mott insulators, with distinct signatures in ARPES, X-ray magnetic circular dichroism, and transport.
Altermagnets combine the scalability of compensated magnets with the well-separated spin-up and spin-down channels of ferromagnets, opening routes to spintronic, multiferroic, and superconducting hybrid devices.

Reading between the lines

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

Beyond the paper: if the spin-group classification is correct, many already-known collinear compounds may need to be reclassified as altermagnets, and magnetic-structure databases can be screened for the defining spin-group form to expand the candidate list.
Beyond the paper: the symmetry-protected nodal surfaces should survive as approximate degeneracies in materials with weak spin-orbit coupling, so low-spin-orbit altermagnets are the cleanest testbeds and the most device-relevant for nodal physics.
Beyond the paper: the same logic of pairing independent spin-space and real-space symmetries may extend to other orders, such as p-wave antialtermagnetism and odd-parity spin textures, suggesting a broader family of spin-symmetry-enriched magnetic phases awaiting classification.
Beyond the paper: in heavy-element altermagnets where spin-orbit coupling is not negligible, the non-relativistic spin-group labels may fail, and the observable test would be a deviation from the predicted nodal structure that grows with atomic number.

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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

Colleague,

This paper is a review, not a research claim, and the reader's UNVERDICTED verdict is the right one. There are no new derivations, data, or predictions. What you get is a synthesis of the altermagnetism field by the people who named it, covering symmetry, microscopic ordering, and spectroscopic signatures, with a strong bibliography.

It does what a good review should. The exposition of the spin-group formalism is clear and careful, and the authors explicitly separate the non-relativistic spin-order physics from spin-orbit coupling. They acknowledge the RuO2 controversy openly, including the null muon and neutron results, and note the magnetic order's fragility. The comparison with non-collinear compensated magnets, p-wave magnets, and conventional Néel antiferromagnets is useful for placing altermagnetism in a broader taxonomy. Credit is also due for covering recent ARPES work on MnTe, CrSb, and KV2Se2O.

The main soft spot is the same one the stress-test flags: the abstract's d/g/i-wave characterization rests on the classification of 10 non-trivial spin Laue groups, which is cited to prior work rather than re-derived. But I don't think this is as vulnerable as it sounds. The review cites the independent spin-group enumeration papers by Liu et al., Jiang et al., Chen et al., and Xiao et al., so the 10-group count is not only the authors' own claim. In a review, citing the original derivation is exactly what you'd expect. A reader who wants the derivation should go to those papers; asking this review to re-do the enumeration is asking for a research paper.

The heavier caveat is structural: the review is written mostly from the authors' own framework, and the field's language ('altermagnetism') was coined by them. That is not a fatal flaw, and the authors are transparent about it, but it means the review is not an impartial map. The zero-spin-orbit assumption is stated and then SOC is treated as a perturbation, which is defensible for the materials discussed.

Bottom line: this is a competent, honest, and genuinely useful review by the leading people in the field. It deserves a serious referee for a review venue, and it will be a standard citation for anyone entering altermagnetism. Just don't ask it to be a research paper.

Referee Report

0 major / 6 minor

Summary. This review article provides a comprehensive account of the symmetry, microscopy, and spectroscopy signatures of altermagnetism, which the authors define as a collinear compensated magnetic phase with even-parity higher-angular-momentum (d, g, or i-wave) anisotropy. The paper begins with the research context in spintronics and unconventional ordering, then introduces the spin-group formalism in which altermagnetic spin groups take the form [E||H]+[C2||G−H], with G−H containing only rotation operations and no inversion or pure translation. It reviews the microscopic realization of altermagnetism in specific materials (rutile oxides, MnTe, CrSb, KV2Se2O, Lieb-lattice systems, and insulating perovskites), the resulting non-relativistic band structures with symmetry-enforced nodal surfaces, the effects of spin-orbit coupling and topology, and a comparison with ferromagnets, conventional antiferromagnets, and non-collinear compensated magnets.

Significance. If the claims hold, this review is a timely and valuable synthesis of a rapidly developing field. Its strengths are the clear presentation of the spin-group classification, the careful distinction between spin-ordering and spin-orbit-coupling effects, the comprehensive referencing of experimental work (ARPES, XMCD, anomalous Hall and Nernst effects, NMR, Raman), and the explicit acknowledgment of unresolved controversies, most notably the debated magnetic order in RuO2. The paper is a review, not a primary research article, and it does not re-derive the central classification; instead it cites the original literature, including independent spin-space-group enumerations. The authors' balanced treatment of candidate materials and their signatures gives the review credibility. I consider the central claims defensible, with only local presentation issues remaining.

minor comments (6)

[D] The classification of altermagnets into 10 non-trivial P-symmetric spin point groups (spin Laue groups) is load-bearing for the review's central definition of altermagnetism, but it is cited only to Ref. 1. Since the abstract's d/g/i-wave characterization rests on the exhaustiveness of this enumeration, the authors should either include a table of the 10 groups with their nodal-surface counts or explicitly state that the enumeration is independently confirmed by the spin-space-group classifications of Refs. 148, 150, and 152.
[C] The chemical formulas for the layered altermagnets are inconsistent: Sec. C introduces KV2Se2 and RbV2Te2, whereas Sec. D and Fig. 5 use KV2Se2O and RbV2Te2. Please harmonize the formulas.
[A] The compound referred to as VNb3S6 in Secs. A and D is V1/3NbS2 in the cited references (Refs. 92 and 237); please correct the formula to match the experimental literature.
[B] In the sentence 'The symmetries of the collinear spin-only group ZC2T2⋉SO(2) effectively act in the momentum space as the P-symmetry,' the mechanism is not spelled out; a brief explanation that the C2T operation combined with a spin-space rotation about the collinearity axis enforces Eσ(k)=Eσ(−k) would help readers.
[D] There are several typos and formatting artifacts, including 'Néel antiferromagntism' in the abstract, 'Hamiltonain' in Sec. B, and the garbled citation string '10 spin Laue 1 (37/442 point1/space141) groups' in Sec. D; these should be corrected.
[C] In the sentence on Ba2CaOsO6, the citation '180' appears twice consecutively ('Ba2CaOsO6180,192'); remove the duplicate.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the review synthesizes parameter-free spin-group classifications and independent experimental signatures; self-citations are not load-bearing reductions.

full rationale

This manuscript is a review rather than a derivation; the central characterization of altermagnetism (collinear compensated, even-parity higher-partial-wave spin order with alternating spin polarization) is presented as a synthesis of prior published classification work and independent experimental reports. The abstract's d/g/i-wave taxonomy rests on the spin-point-group enumeration in Sec. D, cited to Ref. [1]; that enumeration is a parameter-free group-theoretic result (zero-SOC spin groups of the form [E||H]+[C2||G-H]) and has been independently reproduced in later spin-space-group classifications (Refs. [148,150,152]), so the self-citation constitutes real evidence rather than an unverified premise. The experimental signatures (ARPES spin splitting in MnTe, CrSb, KV2Se2O; NMR; neutron diffraction) come largely from independent groups, and the review explicitly flags the RuO2 magnetic-order controversy and the need for further experimental confirmation. No equation or fitted parameter is renamed as a prediction; the definitions and the reported spectral consequences are tied by the spin-group symmetry argument, not by construction in the sense of a fitted input. The only mild concern is the heavy reliance on the authors' own prior papers for nomenclature and classification, but because the underlying classification is externally checkable and the existence of the phase is supported by independent experiments, this does not amount to circularity. Accordingly, no circular step is identified and the circularity score is 0.

Assumptions & free parameters 0 free parameters · 3 assumptions · 1 invented entities

The review introduces no new free parameters or ad hoc entities. It relies on the spin-group formalism and the non-relativistic approximation as foundational assumptions, and on the concept of altermagnetism which has independent experimental support.

assumptions (3)

domain assumption The spin-group formalism is a valid symmetry framework for describing the electronic structure of magnets with negligible spin-orbit coupling.
The review relies on this formalism to define altermagnetism and distinguish it from other phases; e.g., Sec. B.
domain assumption The non-relativistic limit, with spin-orbit coupling treated as a perturbation, is a valid starting point for the electronic structure of the reviewed materials.
The nodal structure and spin splitting are discussed in the zero-SOC limit, with SOC effects added later (Sec. D).
standard math Standard quantum mechanical many-body theory of electrons in crystals (Bloch theorem, exchange interaction) underlies the ordering mechanism.
The ordering mechanism is attributed to exchange interaction; this is a standard assumption in condensed matter physics.

invented entities (1)

Altermagnetism independent evidence
purpose: Classify a collinear compensated magnetic phase with alternating spin polarization in momentum space.
The review cites experimental signatures (ARPES spin splitting, anomalous Hall effect, XMCD) that provide falsifiable evidence, though the phase concept was introduced by the authors' prior work.

how reviews work

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Cite this review

Pith. "Pith review of Symmetry, microscopy and spectroscopy signatures of altermagnetism." pith.science (2026). https://pith.science/paper/LXR24HLC

@misc{pith2026250622860,
  author       = {Pith},
  title        = {Pith review of: Symmetry, microscopy and spectroscopy signatures of altermagnetism},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LXR24HLC}},
  note         = {Machine review of arXiv:2506.22860}
}

read the original abstract

Altermagnetism is a collinear compensated magnetically-ordered phase with a d, g or i-wave anisotropy and alternating spin polarization of the electronic structure in the position and momentum space. Its recent discovery was in part motivated by the research of compensated magnets towards highly scalable spintronic technologies. Simultaneously, altermagnetism shares the anisotropic higher-partial-wave nature of ordering with unconventional superfluid phases which have been at the forefront of research for the past several decades. These examples illustrate the interest in altermagnetism from a broad range of science and technology perspectives. After summarizing the diverse research context, we turn the focus of this review to the symmetry, microscopy and spectroscopy signatures of altermagnetism. We start from the description of spontaneously broken and retained symmetries which delineate the compensated altermagnetic ordering as a distinct magnetic phase. Next we focus on microscopic signatures and ordering mechanism of the altermagnetic phase. We highlight crystal-structure realizations of a characteristic ferroic order of anisotropic higher-partial-wave components of atomic-scale spin densities in altermagnets, ranging from weakly-interacting metals to strongly correlated insulators. The symmetry and microscopy signatures of altermagnetism are directly reflected in spin-dependent electronic spectra and responses. We review salient band-structure features originating from the altermagnetic ordering, and from its interplay with spin-orbit coupling and topological phenomena. Throughout the review we compare altermagnetism to traditional ferromagnetism and Neel antiferromagntism, and to the currently intensely explored magnetic phases with non-collinear symmetry-protected compensated spin orders. We accompany the theoretical discussions by references to relevant experiments.

Figures

Figures reproduced from arXiv: 2506.22860 by the authors.

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

**Figure 4.** FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗

Figures from the paper (2 more)

**Figure 5.** Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]

**Figure 7.** Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]

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Forward citations

Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Nanoscale Imaging of Strain-Controlled Altermagnetic Domains in {\alpha}-MnTe
cond-mat.mtrl-sci 2026-07 conditional novelty 7.0 of 10

In alpha-MnTe, compression makes magnetic domains grow by merging, and unloading leaves them fragmented in a different, metastable pattern, so the material remembers the strain history.
Impact of strong electronic correlations on altermagnets: the case of NiS2
cond-mat.str-el 2025-12 conditional novelty 6.0 of 10

In the metallic altermagnet NiS2, dynamic correlations renormalize the altermagnetic spin splitting in a band- and energy-dependent way and give spin-up and spin-down quasiparticles markedly different lifetimes.
Orbital altermagnetism on the kagome lattice and possible application to $A$V$_3$Sb$_5$
cond-mat.str-el 2025-09 conditional novelty 6.0 of 10

On an odd-sublattice kagome lattice, non-uniform collinear orbital moments from CDW/loop-current order can form a d-wave altermagnet with spin-split bands, as possibly realized in AV3Sb5.
Altermagnetism and Superconductivity: A Short Historical Review
cond-mat.supr-con 2025-10 conditional novelty 4.0 of 10

A historical review unifies electronic liquid-crystal phases, multipole expansions, and altermagnetism under nonrelativistic spin-momentum locking, and surveys the resulting unconventional superconductivity.

Reference graph

Works this paper leans on

239 extracted references · 41 canonical work pages · cited by 4 Pith papers

[1]

, author Sinova, J

author S mejkal, L. , author Sinova, J. & author Jungwirth, T. title Beyond Conventional Ferromagnetism and Antiferromagnetism: A Phase with Nonrelativistic Spin and Crystal Rotation Symmetry . journal Physical Review X volume 12 , pages 031042 ( year 2022 ). ://link.aps.org/doi/10.1103/PhysRevX.12.031042. 2105.05820

arXiv 2022
[2]

, author Sinova, J

author S mejkal, L. , author Sinova, J. & author Jungwirth, T. title Emerging Research Landscape of Altermagnetism . journal Physical Review X volume 12 , pages 040501 ( year 2022 ). ://arxiv.org/abs/2204.10844 https://link.aps.org/doi/10.1103/PhysRevX.12.040501. 2204.10844

arXiv 2022
[3]

, author Gonz \' a lez-Hern \' a ndez, R

author S mejkal, L. , author Gonz \' a lez-Hern \' a ndez, R. , author Jungwirth, T. & author Sinova, J. title Crystal time-reversal symmetry breaking and spontaneous Hall effect in collinear antiferromagnets . journal Science Advances volume 6 , pages eaaz8809 ( year 2020 ). ://www.science.org/doi/10.1126/sciadv.aaz8809. 1901.00445

arXiv 2020
[4]

, author Gonz \' a lez-Hern \' a ndez, R

author Mazin, I. , author Gonz \' a lez-Hern \' a ndez, R. & author S mejkal, L. title Induced Monolayer Altermagnetism in MnP(S,Se) _3 and FeSe pages 1--11 ( year 2023 ). ://arxiv.org/abs/2309.02355. 2309.02355

arXiv 2023
[5]

, author Brataas, A

author Brekke, B. , author Brataas, A. & author Sudb , A. title Two-dimensional altermagnets: Superconductivity in a minimal microscopic model . journal Physical Review B volume 108 , pages 224421 ( year 2023 ). ://arxiv.org/abs/2308.08606 https://link.aps.org/doi/10.1103/PhysRevB.108.224421. 2308.08606

arXiv 2023
[6]

author Antonenko, D. S. , author Fernandes, R. M. & author Venderbos, J. W. F. title Mirror Chern Bands and Weyl Nodal Loops in Altermagnets . journal Physical Review Letters volume 134 , pages 096703 ( year 2025 ). ://link.aps.org/doi/10.1103/PhysRevLett.134.096703

doi:10.1103/physrevlett.134.096703 2025
[7]

& author Franz, M

author Kaushal, N. & author Franz, M. title Altermagnetism in modified Lieb lattice Hubbard model . journal Arxiv Preprint ( year 2024 ). ://arxiv.org/abs/2412.16421. 2412.16421

arXiv 2024
[8]

author Jungwirth, T. et al. title Altermagnetism: an unconventional spin-ordered phase of matter . journal ArXiv 2411.00717 ( year 2024 ). ://arxiv.org/abs/2411.00717. 2411.00717

arXiv 2024

Show all 239 references

[9]

author Mazin, I. I. title Notes on altermagnetism and superconductivity ( year 2022 ). ://arxiv.org/abs/2203.05000. 2203.05000

2022 arXiv
[10]

author Beenakker, C. W. J. & author Vakhtel, T. title Phase-shifted Andreev levels in an altermagnet Josephson junction . journal Physical Review B volume 108 , pages 075425 ( year 2023 ). ://arxiv.org/abs/2306.16300 http://dx.doi.org/10.1103/PhysRevB.108.075425 https://link.a...

2023 arXiv
[11]

& author Liu, C.-C

author Li, Y.-X. & author Liu, C.-C. title Majorana corner modes and tunable patterns in an altermagnet heterostructure . journal Physical Review B volume 108 , pages 205410 ( year 2023 ). ://link.aps.org/doi/10.1103/PhysRevB.108.205410

2023 doi
[12]

, author Zhuang, Z.-Y

author Zhu, D. , author Zhuang, Z.-Y. , author Wu, Z. & author Yan, Z. title Topological superconductivity in two-dimensional altermagnetic metals . journal Physical Review B volume 108 , pages 184505 ( year 2023 ). ://arxiv.org/abs/2305.10479 https://link.aps.org/doi/10.1103/...

2023 arXiv
[13]

, author Naka, M

author Sumita, S. , author Naka, M. & author Seo, H. title Fulde-Ferrell-Larkin-Ovchinnikov state induced by antiferromagnetic order in k-type organic conductors . journal Physical Review Research volume 5 , pages 043171 ( year 2023 ). ://link.aps.org/doi/10.1103/PhysRevResear...

2023 arXiv
[14]

author Ghorashi, S. A. A. , author Hughes, T. L. & author Cano, J. title Altermagnetic Routes to Majorana Modes in Zero Net Magnetization . journal Physical Review Letters volume 133 , pages 106601 ( year 2024 ). ://link.aps.org/doi/10.1103/PhysRevLett.133.106601

2024 doi
[15]

title Andreev reflection at the altermagnet-superconductor interface

author Papaj, M. title Andreev reflection at the altermagnet-superconductor interface . journal Physical Review B volume 108 , pages 1--7 ( year 2023 ). ://arxiv.org/abs/2305.03856 https://link.aps.org/doi/10.1103/PhysRevB.108.L060508. 2305.03856

2023 arXiv
[16]

author Wei, M. et al. title Gapless superconducting state and mirage gap in altermagnets . journal Physical Review B volume 109 , pages L201404 ( year 2023 ). ://arxiv.org/abs/2308.00248 https://link.aps.org/doi/10.1103/PhysRevB.109.L201404. 2308.00248

2023 arXiv
[17]

& author Sun, Q.-F

author Cheng, Q. & author Sun, Q.-F. title Orientation-dependent Josephson effect in spin-singlet superconductor/altermagnet/spin-triplet superconductor junctions . journal Physical Review B volume 109 , pages 024517 ( year 2024 ). ://arxiv.org/abs/2402.02810 https://link.aps....

2024 arXiv
[18]

, author Brekke, B

author M land, K. , author Brekke, B. & author Sudb , A. title Many-body effects on superconductivity mediated by double-magnon processes in altermagnets . journal Physical Review B volume 109 , pages 134515 ( year 2024 ). ://arxiv.org/abs/2402.14061 http://dx.doi.org/10.1103/...

2024 arXiv
[19]

author Zhao, Y. et al. title Hybrid-order topology in unconventional magnets of Eu-based Zintl compounds with surface-dependent quantum geometry . journal Physical Review B volume 110 , pages 205111 ( year 2024 ). ://arxiv.org/abs/2403.06304 https://link.aps.org/doi/10.1103/Ph...

2024 arXiv
[20]

& author Black-Schaffer, A

author Chakraborty, D. & author Black-Schaffer, A. M. title Zero-field finite-momentum and field-induced superconductivity in altermagnets . journal Physical Review B volume 110 , pages L060508 ( year 2024 ). ://link.aps.org/doi/10.1103/PhysRevB.110.L060508

2024 doi
[21]

& author Scheurer, M

author Banerjee, S. & author Scheurer, M. S. title Altermagnetic superconducting diode effect . journal Physical Review B volume 110 , pages 024503 ( year 2024 ). ://arxiv.org/abs/2402.14071 http://dx.doi.org/10.1103/PhysRevB.110.024503 https://link.aps.org/doi/10.1103/PhysRev...

2024 arXiv
[22]

author Jeschke, H. O. , author Shimizu, M. & author Mazin, I. I. title CuAg(SO4)2: A doubly strongly correlated altermagnetic three-dimensional analog of the parent compounds of high- <math> . journal Physical Review B volume 109 , pages L220412 ( year 2024 ). ://arxiv.org/abs...

2024 arXiv
[23]

author Verbeek, X. H. , author Urru, A. & author Spaldin, N. A. title Hidden orders and (anti-)magnetoelectric effects in Cr2O3 and Fe2O3 . journal Physical Review Research volume 5 , pages L042018 ( year 2023 ). ://link.aps.org/doi/10.1103/PhysRevResearch.5.L042018

2023 doi
[24]

, author Liu, Z.-X

author Guo, P.-J. , author Liu, Z.-X. & author Lu, Z.-Y. title Quantum anomalous hall effect in collinear antiferromagnetism . journal npj Computational Materials volume 9 , pages 70 ( year 2023 ). ://www.nature.com/articles/s41524-023-01025-4

2023
[25]

, author Gu, Y

author Guo, P.-J. , author Gu, Y. , author Gao, Z.-F. & author Lu, Z.-Y. title Altermagnetic ferroelectric LiFe2F6 and spin-triplet excitonic insulator phase ( year 2023 ). ://arxiv.org/abs/2312.13911. 2312.13911

2023 arXiv
[26]

, author Fiebig, M

author Bernardini, F. , author Fiebig, M. & author Cano, A. title Ruddlesden–Popper and perovskite phases as a material platform for altermagnetism . journal Journal of Applied Physics volume 137 ( year 2025 ). ://pubs.aip.org/jap/article/137/10/103903/3339285/Ruddlesden-Poppe...

2025
[27]

author Zyuzin, A. A. title Magnetoelectric effect in superconductors with d-wave magnetization . journal Physical Review B volume 109 , pages L220505 ( year 2024 ). ://link.aps.org/doi/10.1103/PhysRevB.109.L220505

2024 doi
[28]

& author Knolle, J

author Sim, G. & author Knolle, J. title Pair Density Waves and Supercurrent Diode Effect in Altermagnets pages 1--9 ( year 2024 ). ://arxiv.org/abs/2407.01513. 2407.01513

2024 arXiv
[29]

& author Black-Schaffer, A

author Chakraborty, D. & author Black-Schaffer, A. M. title Constraints on superconducting pairing in altermagnets ( year 2024 ). ://arxiv.org/abs/2408.03999. 2408.03999

2024 arXiv
[30]

, author Matsyshyn, O

author Hu, J.-X. , author Matsyshyn, O. & author Song, J. C. W. title Nonlinear Superconducting Magnetoelectric Effect . journal Physical Review Letters volume 134 , pages 026001 ( year 2025 ). ://link.aps.org/doi/10.1103/PhysRevLett.134.026001

2025 doi
[31]

author Shick, A. B. , author Khmelevskyi, S. , author Mryasov, O. N. , author Wunderlich, J. & author Jungwirth, T. title Spin-orbit coupling induced anisotropy effects in bimetallic antiferromagnets: A route towards antiferromagnetic spintronics . journal Physical Review B vo...

2010 arXiv
[32]

author Park, B. G. et al. title A spin-valve-like magnetoresistance of an antiferromagnet-based tunnel junction . journal Nature Materials volume 10 , pages 347--351 ( year 2011 )

2011
[33]

author Marti, X. et al. title Room-temperature antiferromagnetic memory resistor . journal Nature Materials volume 13 , pages 367--374 ( year 2014 ). ://www.nature.com/articles/nmat3861. 0402594

2014
[34]

author Z elezn \' y , J. et al. title Relativistic N \' e el-order fields induced by electrical current in antiferromagnets . journal Physical Review Letters volume 113 , pages 157201 ( year 2014 ). 1410.8296

2014 arXiv
[35]

author Wadley, P. et al. title Electrical switching of an antiferromagnet . journal Science volume 351 , pages 587--590 ( year 2016 ). 1503.03765

2016 arXiv
[36]

, author Marti, X

author Jungwirth, T. , author Marti, X. , author Wadley, P. & author Wunderlich, J. title Antiferromagnetic spintronics . journal Nature Nanotechnology volume 11 , pages 231--241 ( year 2016 ). ://www.nature.com/articles/nnano.2016.18. 1606.04284

2016 arXiv
[37]

author Wadley, P. et al. title Current polarity-dependent manipulation of antiferromagnetic domains . journal Nature Nanotechnology volume 13 , pages 362--365 ( year 2018 ). ://www.nature.com/articles/s41565-018-0079-1. arXiv:1711.05146

2018 arXiv
[38]

author Manchon, A. et al. title Current-induced spin-orbit torques in ferromagnetic and antiferromagnetic systems . journal Reviews of Modern Physics volume 91 , pages 035004 ( year 2019 ). ://link.aps.org/doi/10.1103/RevModPhys.91.035004. 1801.09636

2019 arXiv
[39]

author Olejn \' i k, K. et al. title Terahertz electrical writing speed in an antiferromagnetic memory . journal Science Advances volume 4 , pages eaar3566 ( year 2018 ). ://advances.sciencemag.org/lookup/doi/10.1126/sciadv.aar3566 https://www.science.org/doi/10.1126/sciadv.aa...

2018 arXiv
[40]

& author Nagaosa, N

author Shindou, R. & author Nagaosa, N. title Orbital Ferromagnetism and Anomalous Hall Effect in Antiferromagnets on the Distorted fcc Lattice . journal Physical Review Letters volume 87 , pages 116801 ( year 2001 ). ://link.aps.org/doi/10.1103/PhysRevLett.87.116801. 0108322

2001 doi
[41]

& author Bruno, P

author Metalidis, G. & author Bruno, P. title Topological Hall effect studied in simple models . journal Physical Review B volume 74 , pages 045327 ( year 2006 ). ://link.aps.org/doi/10.1103/PhysRevB.74.045327

2006 doi
[42]

& author Batista, C

author Martin, I. & author Batista, C. D. title Itinerant electron-driven chiral magnetic ordering and spontaneous quantum hall effect in triangular lattice models . journal Physical Review Letters volume 101 , pages 156402 ( year 2008 ). ://journals.aps.org/prl/abstract/10.11...

2008 doi
[43]

, author Niu, Q

author Chen, H. , author Niu, Q. & author Macdonald, A. H. title Anomalous hall effect arising from noncollinear antiferromagnetism . journal Physical Review Letters volume 112 , pages 017205 ( year 2014 ). 1309.4041

2014 arXiv
[44]

& author Felser, C

author K \" u bler, J. & author Felser, C. title Non-collinear antiferromagnets and the anomalous Hall effect . journal Epl volume 108 , pages 67001 ( year 2014 ). 1410.5985

2014 arXiv
[45]

, author Nakatsuji, S

author Machida, Y. , author Nakatsuji, S. , author Onoda, S. , author Tayama, T. & author Sakakibara, T. title Time-reversal symmetry breaking and spontaneous Hall effect without magnetic dipole order . journal Nature volume 463 , pages 210--213 ( year 2010 )

2010
[46]

, author Kiyohara, N

author Nakatsuji, S. , author Kiyohara, N. & author Higo, T. title Large anomalous Hall effect in a non-collinear antiferromagnet at room temperature . journal Nature volume 527 , pages 212--215 ( year 2015 ). ://www.nature.com/articles/nature15723

2015
[47]

, author Tomita, T

author Kiyohara, N. , author Tomita, T. & author Nakatsuji, S. title Giant Anomalous Hall Effect in the Chiral Antiferromagnet Mn3Ge . journal Physical Review Applied volume 5 , pages 064009 ( year 2016 ). 1511.04619

2016 arXiv
[48]

author Nayak, A. K. et al. title Large anomalous Hall effect driven by a nonvanishing Berry curvature in the noncolinear antiferromagnet Mn 3 Ge . journal Science Advances volume 2 , pages e1501870--e1501870 ( year 2016 ). ://www.science.org/doi/10.1126/sciadv.1501870. 1511.03128

2016 arXiv
[49]

author Liu, Z. Q. et al. title Electrical switching of the topological anomalous Hall effect in a non-collinear antiferromagnet above room temperature . journal Nature Electronics volume 1 , pages 172--177 ( year 2018 ). ://www.nature.com/articles/s41928-018-0040-1

2018
[50]

author Xu, L. et al. title Finite-temperature violation of the anomalous transverse Wiedemann-Franz law . journal Science Advances volume 6 , pages eaaz3522 ( year 2020 )

2020
[51]

author Takagi, H. et al. title Spontaneous topological Hall effect induced by non-coplanar antiferromagnetic order in intercalated van der Waals materials . journal Nature Physics volume 19 , pages 961--968 ( year 2023 ). ://www.nature.com/articles/s41567-023-02017-3

2023
[52]

author Ikhlas, M. et al. title Large anomalous Nernst effect at room temperature in a chiral antiferromagnet . journal Nature Physics volume 13 , pages 1085--1090 ( year 2017 ). ://www.nature.com/doifinder/10.1038/nphys4181. 1710.00062

2017 arXiv
[53]

author Li, X. et al. title Anomalous Nernst and Righi-Leduc Effects in Mn3Sn: Berry Curvature and Entropy Flow . journal Physical Review Letters volume 119 , pages 056601 ( year 2017 ). ://link.aps.org/doi/10.1103/PhysRevLett.119.056601. 1612.06128

2017 arXiv
[54]

author Higo, T. et al. title Large magneto-optical Kerr effect and imaging of magnetic octupole domains in an antiferromagnetic metal . journal Nature Photonics volume 12 , pages 73--78 ( year 2018 ). ://www.nature.com/articles/s41566-017-0086-z. 1805.06758

2018 arXiv
[55]

, author Kanda, N

author Matsuda, T. , author Kanda, N. , author Higo, T. & author Matsunaga, R. title Room-temperature terahertz anomalous Hall effect in Weyl antiferromagnet Mn3Sn thin films . journal Nature Communications volume 11 , pages 909 ( year 2020 ). ://dx.doi.org/10.1038/s41467-020-14690-6

2020 doi
[56]

author Feng, W. et al. title Topological magneto-optical effects and their quantization in noncoplanar antiferromagnets . journal Nature Communications volume 11 , pages 118 ( year 2020 ). ://arxiv.org/pdf/1811.05803.pdf https://www.nature.com/articles/s41467-019-13968-8 http:...

2020 arXiv
[57]

author Kimata, M. et al. title X-ray study of ferroic octupole order producing anomalous Hall effect . journal Nature Communications volume 12 , pages 5582 ( year 2021 ). ://dx.doi.org/10.1038/s41467-021-25834-7 https://www.nature.com/articles/s41467-021-25834-7

2021 doi
[58]

author Sakamoto, S. et al. title Observation of spontaneous x-ray magnetic circular dichroism in a chiral antiferromagnet . journal Physical Review B volume 104 , pages 134431 ( year 2021 ). ://link.aps.org/doi/10.1103/PhysRevB.104.134431

2021 doi
[59]

, author Zhang, Y

author Z elezn \' y , J. , author Zhang, Y. , author Felser, C. & author Yan, B. title Spin-Polarized Current in Noncollinear Antiferromagnets . journal Physical Review Letters volume 119 , pages 187204 ( year 2017 ). https://link.aps.org/doi/10.1103/PhysRevLett.119.187204 htt...

2017 arXiv
[60]

, author Z elezn \' y , J

author Zhang, Y. , author Z elezn \' y , J. , author Sun, Y. , author van den Brink, J. & author Yan, B. title Spin Hall effect emerging from a noncollinear magnetic lattice without spin–orbit coupling . journal New Journal of Physics volume 20 , pages 073028 ( year 2018 ). :/...

2018 arXiv
[61]

author Kimata, M. et al. title Magnetic and magnetic inverse spin Hall effects in a non-collinear antiferromagnet . journal Nature volume 565 , pages 627--630 ( year 2019 ). ://doi.org/10.1038/s41586-018-0853-0 http://www.nature.com/articles/s41586-018-0853-0

2019 doi
[62]

author Hu, S. et al. title Efficient perpendicular magnetization switching by a magnetic spin Hall effect in a noncollinear antiferromagnet . journal Nature Communications volume 13 , pages 4447 ( year 2022 ). ://www.nature.com/articles/s41467-022-32179-2

2022
[63]

author Tsai, H. et al. title Electrical manipulation of a topological antiferromagnetic state . journal Nature volume 580 , pages 608--613 ( year 2020 ). ://www.nature.com/articles/s41586-020-2211-2

2020
[64]

author Takeuchi, Y. et al. title Chiral-spin rotation of non-collinear antiferromagnet by spin–orbit torque . journal Nature Materials volume 20 , pages 1364--1370 ( year 2021 ). ://www.nature.com/articles/s41563-021-01005-3 http://www.nature.com/articles/s41563-021-01005-3

2021
[65]

author Higo, T. et al. title Perpendicular full switching of chiral antiferromagnetic order by current . journal Nature volume 607 , pages 474--479 ( year 2022 ). ://www.nature.com/articles/s41586-022-04864-1

2022
[66]

author Pal, B. et al. title Setting of the magnetic structure of chiral kagome antiferromagnets by a seeded spin-orbit torque . journal Science Advances volume 8 , pages eabo5930 ( year 2022 ). ://www.science.org/doi/10.1126/sciadv.abo5930

2022 doi
[67]

author Chen, X. et al. title Octupole-driven magnetoresistance in an antiferromagnetic tunnel junction . journal Nature volume 613 , pages 490--495 ( year 2023 ). ://doi.org/10.1038/s41586-022-05463-w https://www.nature.com/articles/s41586-022-05463-w

2023 doi
[68]

author Qin, P. et al. title Room-temperature magnetoresistance in an all-antiferromagnetic tunnel junction . journal Nature volume 613 , pages 485--489 ( year 2023 ). ://doi.org/10.1038/s41586-022-05461-y https://www.nature.com/articles/s41586-022-05461-y

2023 doi
[69]

& author Arita, R

author Nakatsuji, S. & author Arita, R. title Topological Magnets: Functions Based on Berry Phase and Multipoles . journal Annual Review of Condensed Matter Physics volume 13 ( year 2022 )

2022
[70]

author Wu, M. et al. title Current-driven fast magnetic octupole domain-wall motion in noncollinear antiferromagnets . journal Nature Communications volume 15 , pages 4305 ( year 2024 ). ://www.nature.com/articles/s41467-024-48440-9

2024
[71]

author Kuroda, K. et al. title Evidence for magnetic Weyl fermions in a correlated metal . journal Nature Materials volume 16 , pages 1090--1095 ( year 2017 ). ://arxiv.org/abs/1710.06167 http://www.nature.com/doifinder/10.1038/nmat4987. 1710.06167

2017 arXiv
[72]

author Chen, T. et al. title Anomalous transport due to Weyl fermions in the chiral antiferromagnets Mn3X, X = Sn, Ge . journal Nature Communications volume 12 , pages 572 ( year 2021 ). ://dx.doi.org/10.1038/s41467-020-20838-1 http://www.nature.com/articles/s41467-020-20838-1...

2021 arXiv
[73]

, author MacDonald, A

author S mejkal, L. , author MacDonald, A. H. , author Sinova, J. , author Nakatsuji, S. & author Jungwirth, T. title Anomalous Hall antiferromagnets . journal Nature Reviews Materials volume 7 , pages 482--496 ( year 2022 ). ://arxiv.org/abs/2107.03321 https://www.nature.com/...

2022 arXiv
[74]

author Rimmler, B. H. , author Pal, B. & author Parkin, S. S. P. title Non-collinear antiferromagnetic spintronics . journal Nature Reviews Materials pages 1--19 ( year 2024 ). ://www.nature.com/articles/s41578-024-00706-w

2024
[75]

, author Yoon, J.-Y

author Han, J. , author Yoon, J.-Y. , author Ohno, H. & author Fukami, S. title Unconventional responses in non-collinear antiferromagnets . journal Newton volume 1 , pages 100012 ( year 2025 ). ://linkinghub.elsevier.com/retrieve/pii/S2950636025000040

2025
[76]

author Lee, T. Y. et al. title World-most energy-efficient MRAM technology for non-volatile RAM applications . In booktitle 2022 International Electron Devices Meeting (IEDM) , pages 10.7.1--10.7.4 ( publisher IEEE , year 2022 ). ://ieeexplore.ieee.org/document/10019430/

2022
[77]

author Ambrosi, E. et al. title Low voltage (1.8 V) and high endurance (1M) 1-Selector/1-STT-MRAM with ultra-low (1 ppb) read disturb for high density embedded memory arrays . In booktitle 2023 International Electron Devices Meeting (IEDM) , pages 1--4 ( publisher IEEE , year ...

2023
[78]

type Tech

title IRDS 2023 update: Beyond CMOS and Emerging Materials Integration . type Tech. Rep. ( year 2023 ). ://irds.ieee.org/images/files/pdf/2023/2023IRDS_BC.pdf

2023
[79]

author Samanta, K. et al. title Crystal Hall and crystal magneto-optical effect in thin films of SrRuO3 . journal Journal of Applied Physics volume 127 , pages 213904 ( year 2020 ). ://doi.org/10.1063/5.0005017 http://aip.scitation.org/doi/10.1063/5.0005017

2020 doi
[80]

author Gonz \' a lez-Hern \' a ndez, R. et al. title Efficient Electrical Spin Splitter Based on Nonrelativistic Collinear Antiferromagnetism . journal Physical Review Letters volume 126 , pages 127701 ( year 2021 ). ://arxiv.org/abs/2002.07073 https://link.aps.org/doi/10.1103...

2021 arXiv
[81]

, author Feng, W

author Zhou, X. , author Feng, W. , author Yang, X. , author Guo, G. Y. & author Yao, Y. title Crystal chirality magneto-optical effects in collinear antiferromagnets . journal Physical Review B volume 104 , pages 1--8 ( year 2021 )

2021
[82]

author Feng, Z. et al. title An anomalous Hall effect in altermagnetic ruthenium dioxide . journal Nature Electronics volume 5 , pages 735--743 ( year 2022 ). ://arxiv.org/abs/2002.08712 https://www.nature.com/articles/s41928-022-00866-z. 2002.08712

2022 arXiv
[83]

author Reichlova, H. et al. title Observation of a spontaneous anomalous Hall response in the Mn5Si3 d-wave altermagnet candidate . journal Nature Communications volume 15 , pages 4961 ( year 2024 ). ://arxiv.org/abs/2012.15651 https://www.nature.com/articles/s41467-024-48493-...

2024 arXiv
[84]

, author Hellenes, A

author S mejkal, L. , author Hellenes, A. B. , author Gonz \' a lez-Hern \' a ndez, R. , author Sinova, J. & author Jungwirth, T. title Giant and Tunneling Magnetoresistance in Unconventional Collinear Antiferromagnets with Nonrelativistic Spin-Momentum Coupling . journal Phys...

2022 arXiv
[85]

, author Zhang, S.-H

author Shao, D.-F. , author Zhang, S.-H. , author Li, M. , author Eom, C.-B. & author Tsymbal, E. Y. title Spin-neutral currents for spintronics . journal Nature Communications volume 12 , pages 7061 ( year 2021 ). ://doi.org/10.1038/s41467-021-26915-3 https://www.nature.com/a...

2021 arXiv
[86]

author Gonzalez Betancourt , R. D. et al. title Spontaneous Anomalous Hall Effect Arising from an Unconventional Compensated Magnetic Phase in a Semiconductor . journal Physical Review Letters volume 130 , pages 036702 ( year 2023 ). ://arxiv.org/abs/2112.06805v1 https://link....

2023 arXiv
[87]

author Tschirner, T. et al. title Saturation of the anomalous Hall effect at high magnetic fields in altermagnetic RuO2 . journal APL Materials volume 11 , pages 101103 ( year 2023 ). ://arxiv.org/abs/2309.00568 https://pubs.aip.org/apm/article/11/10/101103/2913994/Saturation-...

2023 arXiv
[88]

author Wang, M. et al. title Emergent zero-field anomalous Hall effect in a reconstructed rutile antiferromagnetic metal . journal Nature Communications volume 14 , pages 8240 ( year 2023 ). ://www.nature.com/articles/s41467-023-43962-0

2023
[89]

author Jiang, Y.-Y. et al. title Prediction of Giant Tunneling Magnetoresistance in RuO2/TiO2/RuO2 (110) Antiferromagnetic Tunnel Junctions . journal Physical Review B volume 108 , pages 174439 ( year 2023 ). ://arxiv.org/abs/2309.02634v1 https://link.aps.org/doi/10.1103/PhysR...

2023 arXiv
[90]

author Shao, D.-F. et al. title N \' e el Spin Currents in Antiferromagnets . journal Physical Review Letters volume 130 , pages 216702 ( year 2023 ). ://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.216702 https://link.aps.org/doi/10.1103/PhysRevLett.130.216702

2023 doi
[91]

, author Zhu, Y

author Cui, Q. , author Zhu, Y. , author Yao, X. , author Cui, P. & author Yang, H. title Giant spin-Hall and tunneling magnetoresistance effects based on a two-dimensional nonrelativistic antiferromagnetic metal . journal Physical Review B volume 108 , pages 024410 ( year 202...

2023 doi
[92]

author Ray, M. K. et al. title Zero-field Hall effect emerging from a non-Fermi liquid in a collinear antiferromagnet V1/3NbS2 . journal Nature Communications volume 16 , pages 3532 ( year 2025 ). ://www.nature.com/articles/s41467-025-58476-0

2025
[93]

author Takagi, R. et al. title Spontaneous Hall effect induced by collinear antiferromagnetic order at room temperature . journal Nature Materials volume 24 , pages 63--68 ( year 2025 ). ://www.nature.com/articles/s41563-024-02058-w

2025
[94]

, author Jiang, Y.-Y

author Samanta, K. , author Jiang, Y.-Y. , author Paudel, T. R. , author Shao, D.-F. & author Tsymbal, E. Y. title Tunneling magnetoresistance in magnetic tunnel junctions with a single ferromagnetic electrode . journal Physical Review B volume 109 , pages 174407 ( year 2023 )...

2023 arXiv
[95]

author Chi, B. et al. title Crystal-facet-oriented altermagnets for detecting ferromagnetic and antiferromagnetic states by giant tunneling magnetoresistance . journal Physical Review Applied volume 21 , pages 034038 ( year 2024 ). ://arxiv.org/abs/2309.09561 http://arxiv.org/...

2024 arXiv
[96]

author Hariki, A. et al. title X-Ray Magnetic Circular Dichroism in Altermagnetic -MnTe . journal Physical Review Letters volume 132 , pages 176701 ( year 2024 ). ://arxiv.org/abs/2305.03588 https://link.aps.org/doi/10.1103/PhysRevLett.132.176701. 2305.03588

2024 arXiv
[97]

author Amin, O. J. et al. title Nanoscale imaging and control of altermagnetism in MnTe . journal Nature volume 636 , pages 348--353 ( year 2024 ). ://www.nature.com/articles/s41586-024-08234-x https://arxiv.org/abs/2405.02409v1 http://arxiv.org/abs/2405.02409. 2405.02409

2024 arXiv
[98]

author Yamamoto, R. et al. title Altermagnetic nanotextures revealed in bulk MnTe . journal Arxiv Preprint pages 1--12 ( year 2025 ). ://arxiv.org/abs/2502.18597. 2502.18597

2025 arXiv
[99]

author Han, L. et al. title Electrical 180° switching of N \' e el vector in spin-splitting antiferromagnet . journal Science Advances volume 10 , pages eadn0479 ( year 2024 ). ://www.science.org/doi/10.1126/sciadv.adn0479

2024 doi
[100]

author Kluczyk, K. P. et al. title Coexistence of anomalous Hall effect and weak magnetization in a nominally collinear antiferromagnet MnTe . journal Physical Review B volume 110 , pages 155201 ( year 2024 ). ://link.aps.org/doi/10.1103/PhysRevB.110.155201

2024 doi
[101]

author Badura, A. et al. title Observation of the anomalous Nernst effect in altermagnetic candidate Mn5Si3 . journal Nat. Commun. in press, ArXiv 2403.12929 ( year 2024 ). ://arxiv.org/abs/2403.12929v1 http://arxiv.org/abs/2403.12929. 2403.12929

2024
[102]

author Han, L. et al. title Nonvolatile anomalous Nernst effect in Mn5Si3 with a collinear N \' e el vector . journal Physical Review Applied volume 23 , pages 044066 ( year 2025 ). ://arxiv.org/abs/2403.13427 https://link.aps.org/doi/10.1103/PhysRevApplied.23.044066. 2403.13427

2025 arXiv
[103]

author Zhou, X. et al. title Crystal Thermal Transport in Altermagnetic RuO2 . journal Physical Review Letters volume 132 , pages 056701 ( year 2024 ). ://arxiv.org/abs/2305.01410 https://link.aps.org/doi/10.1103/PhysRevLett.132.056701. 2305.01410

2024 arXiv
[104]

, author Nomoto, T

author Tanaka, K. , author Nomoto, T. & author Arita, R. title First-principles study of the tunnel magnetoresistance effect with Cr-doped <math> <msub> <mi>RuO</mi> <mn>2</mn> </msub> </math> electrode . journal Physical Review B volume 110 , pages 064433 ( year 2024 ). ://li...

2024 doi
[105]

, author Hamaguchi, Y

author Kunitomi, N. , author Hamaguchi, Y. & author Anzai, S. title Neutron diffraction study on manganese telluride . journal Journal de Physique volume 25 , pages 568--574 ( year 1964 ). ://www.edpsciences.org/10.1051/jphys:01964002505056800

1964 doi
[106]

author Lovesey, S. W. , author Khalyavin, D. D. & author van der Laan, G. title Templates for magnetic symmetry and altermagnetism in hexagonal MnTe . journal Physical Review B volume 108 , pages 174437 ( year 2023 ). ://arxiv.org/abs/2309.04282 https://link.aps.org/doi/10.110...

2023 arXiv
[107]

author Mazin, I. I. title Altermagnetism in MnTe: Origin, predicted manifestations, and routes to detwinning . journal Physical Review B volume 107 , pages L100418 ( year 2023 ). ://arxiv.org/abs/2301.08573 http://dx.doi.org/10.1103/PhysRevB.107.L100418 https://link.aps.org/do...

2023 arXiv
[108]

author Krempask \' y , J. et al. title Altermagnetic lifting of Kramers spin degeneracy . journal Nature volume 626 , pages 517--522 ( year 2024 ). ://doi.org/10.1038/s41586-023-06907-7 https://www.nature.com/articles/s41586-023-06907-7 http://arxiv.org/abs/2308.10681. 2308.10681

2024 arXiv
[109]

author Lee, S. S. et al. title Broken Kramers Degeneracy in Altermagnetic MnTe . journal Physical Review Letters volume 132 , pages 036702 ( year 2024 ). ://arxiv.org/abs/2308.11180v1 http://arxiv.org/abs/2308.11180 https://link.aps.org/doi/10.1103/PhysRevLett.132.036702. 2308.11180

2024 arXiv
[110]

author Osumi, T. et al. title Observation of a giant band splitting in altermagnetic MnTe . journal Physical Review B volume 109 , pages 115102 ( year 2024 ). ://arxiv.org/abs/2308.10117v1 http://arxiv.org/abs/2308.10117 https://link.aps.org/doi/10.1103/PhysRevB.109.115102. 2308.10117

2024 arXiv
[111]

author Hajlaoui, M. et al. title Temperature Dependence of Relativistic Valence Band Splitting Induced by an Altermagnetic Phase Transition . journal Advanced Materials volume 36 , pages 2314076 ( year 2024 ). ://onlinelibrary.wiley.com/doi/10.1002/adma.202314076

2024 doi
[112]

& author Ohno, H

author Dietl, T. & author Ohno, H. title Dilute ferromagnetic semiconductors: Physics and spintronic structures . journal Reviews of Modern Physics volume 86 , pages 187--251 ( year 2014 ). ://link.aps.org/doi/10.1103/RevModPhys.86.187. 1307.3429

2014 arXiv
[113]

author Jungwirth, T. et al. title Spin-dependent phenomena and device concepts explored in (Ga,Mn)As . journal Reviews of Modern Physics volume 86 , pages 855--896 ( year 2014 ). ://link.aps.org/doi/10.1103/RevModPhys.86.855. 1310.1944

2014 arXiv
[114]

& author Spaldin, N

author Ramesh, R. & author Spaldin, N. A. title Multiferroics: progress and prospects in thin films . journal Nature Materials volume 6 , pages 21--29 ( year 2007 ). ://www.worldscientific.com/doi/abs/10.1142/9789814287005_0003 http://www.nature.com/articles/nmat1805. arXiv:10...

2007 arXiv
[115]

author Kim, S.-J. et al. title Observation of the Anomalous Hall Effect in a Layered Polar Semiconductor . journal Advanced Science volume 11 ( year 2024 ). ://arxiv.org/abs/2307.03541 https://onlinelibrary.wiley.com/doi/10.1002/advs.202307306. 2307.03541

2024 arXiv
[116]

author Gu, M. et al. title Ferroelectric switchable altermagnetism . journal Physical Review Letters volume 134 , pages 106802 ( year 2024 ). ://arxiv.org/abs/2411.14216 https://link.aps.org/doi/10.1103/PhysRevLett.134.106802. 2411.14216

2024 arXiv
[117]

title Altermagnetic multiferroics and altermagnetoelectric effect ( year 2024 )

author S mejkal, L. title Altermagnetic multiferroics and altermagnetoelectric effect ( year 2024 ). ://arxiv.org/abs/2411.19928. 2411.19928

2024 arXiv
[118]

author Bai, L. et al. title Altermagnetism: Exploring New Frontiers in Magnetism and Spintronics . journal Advanced Functional Materials pages 1--49 ( year 2024 ). ://onlinelibrary.wiley.com/doi/10.1002/adfm.202409327 http://arxiv.org/abs/2406.02123. 2406.02123

2024 arXiv
[119]

, author Dai, X

author Liu, Q. , author Dai, X. & author Bl \" u gel, S. title Different facets of unconventional magnetism . journal Nature Physics volume 21 , pages 329--331 ( year 2025 ). ://www.nature.com/articles/s41567-024-02750-3

2025
[120]

author Song, C. et al. title Altermagnets as a new class of functional materials . journal Nature Reviews Materials ( year 2025 ). ://www.nature.com/articles/s41578-025-00779-1

2025
[121]

, author Li, J

author Liu, P. , author Li, J. , author Han, J. , author Wan, X. & author Liu, Q. title Spin-Group Symmetry in Magnetic Materials with Negligible Spin-Orbit Coupling . journal Physical Review X volume 12 , pages 21016 ( year 2022 ). ://arxiv.org/abs/2103.15723 https://link.aps...

2022 arXiv
[122]

author Litvin, D. B. & author Opechowski, W. title Spin groups . journal Physica volume 76 , pages 538--554 ( year 1974 ). https://linkinghub.elsevier.com/retrieve/pii/0031891474901578 https://www.sciencedirect.com/science/article/abs/pii/0031891474901578?via

1974
[123]

author Litvin, D. B. title Spin point groups . journal Acta Crystallographica Section A volume 33 , pages 279--287 ( year 1977 ). ://scripts.iucr.org/cgi-bin/paper?S0567739477000709 https://scripts.iucr.org/cgi-bin/paper?S0567739477000709

1977
[124]

author Andreev, A. F. & author Marchenko, V. title Symmetry and the macroscopic dynamics of magnetic materials . journal Uspekhi Fizicheskih Nauk volume 130 , pages 39 ( year 1980 )

1980
[125]

& author Grishchuk, I

author Andreev, A. & author Grishchuk, I. title Spin nematics . journal Sov. Phys. JETP volume 60 , pages 267 ( year 1984 )

1984
[126]

author Gor'kov, L. P. & author Sokol, A. title Nontrivial magnetic order: Localized versus itinerant systems . journal Physical Review Letters volume 69 , pages 2586--2589 ( year 1992 ). ://link.aps.org/doi/10.1103/PhysRevLett.69.2586

1992 doi
[127]

author Leggett, A. J. title Nobel Lecture: Superfluid He3 : the early days as seen by a theorist . journal Reviews of Modern Physics volume 76 , pages 999 ( year 2004 ). ://www.nobelprize.org/uploads/2018/06/leggett-lecture.pdf https://link.aps.org/doi/10.1103/RevModPhys.76.999

2004 doi
[128]

& author Moore, J

author Moessner, R. & author Moore, J. E. title Topological Phases of Matter ( publisher Cambridge University Press , year 2021 ). ://www.cambridge.org/core/product/identifier/9781316226308/type/book

2021
[129]

title Relativistic Quantum Mechanics ( publisher Cambridge University Press , address Cambridge , year 1998 ), edition 1 edn

author Strange, P. title Relativistic Quantum Mechanics ( publisher Cambridge University Press , address Cambridge , year 1998 ), edition 1 edn. ://books.google.de/books?id=sdVrBM2w0OwC&printsec=frontcover&dq=Relativistic+quantum+mechanics&hl=en&sa=X&ved=0ahUKEwjvitehpeniAhVus...

1998
[130]

title Spin—Orbit Coupling Effects in Two-Dimensional Electron and Hole Systems , vol

author Winkler, R. title Spin—Orbit Coupling Effects in Two-Dimensional Electron and Hole Systems , vol. volume 191 of series Springer Tracts in Modern Physics ( publisher Springer Berlin Heidelberg , address Berlin, Heidelberg , year 2003 ). ://link.springer.com/10.1007/b1358...

2003 doi
[131]

& author Lifshitz, E

author Landau, L. & author Lifshitz, E. title Electrodynamics of Continuous Media, vol. 8 of Course of Theoretical Physics ( publisher Pergamon Press, Oxford , year 1965 ), edition 2nd edn

1965
[132]

, author Valenzuela, S

author Sinova, J. , author Valenzuela, S. O. , author Wunderlich, J. , author Back, C. H. & author Jungwirth, T. title Spin Hall effects . journal Reviews of Modern Physics volume 87 , pages 1213--1260 ( year 2015 ). ://link.aps.org/doi/10.1103/RevModPhys.87.1213

2015 doi
[133]

, author Sinova, J

author Nagaosa, N. , author Sinova, J. , author Onoda, S. , author MacDonald, A. H. & author Ong, N. P. title Anomalous Hall effect . journal Reviews of Modern Physics volume 82 , pages 1539--1592 ( year 2010 ). ://link.aps.org/doi/10.1103/RevModPhys.82.1539. 0904.4154

2010 arXiv
[134]

& editor Molenkamp, L

editor Franz, M. & editor Molenkamp, L. (eds.) title Contemporary Concepts of Condensed Matter Science, vol. 6 - Topological Insulators ( publisher Elsevier , year 2013 )

2013
[135]

& author Yokoyama, T

author Murakami, S. & author Yokoyama, T. title Quantum spin Hall effect and topological insulators , vol. volume 1 ( publisher Oxford University Press , year 2017 ). ://academic.oup.com/book/27906/chapter/203910964

2017
[136]

author Bradlyn, B. et al. title Topological quantum chemistry . journal Nature volume 547 , pages 298--305 ( year 2017 ). ://dx.doi.org/10.1038/nature23268 http://www.nature.com/articles/nature23268 https://www.nature.com/articles/nature23268. 1703.02050

2017 arXiv
[137]

author Armitage, N. P. , author Mele, E. J. & author Vishwanath, A. title Weyl and Dirac semimetals in three-dimensional solids . journal Reviews of Modern Physics volume 90 , pages 015001 ( year 2018 ). ://link.aps.org/doi/10.1103/RevModPhys.90.015001. 1705.01111

2018 arXiv
[138]

author Elcoro, L. et al. title Magnetic Topological Quantum Chemistry . journal Nature Communications volume 12 , pages 5965 ( year 2021 ). ://dx.doi.org/10.1038/s41467-021-26241-8 https://www.nature.com/articles/s41467-021-26241-8 http://www.cryst.ehu. http://arxiv.org/abs/20...

2021 arXiv
[139]

author Mazin, I. I. , author Koepernik, K. , author Johannes, M. D. , author Gonz \' a lez-Hern \' a ndez, R. & author S mejkal, L. title Prediction of unconventional magnetism in doped FeSb 2 . journal Proceedings of the National Academy of Sciences volume 118 , pages e210892...

2021 arXiv
[140]

author S mejkal, L. et al. title Chiral magnons in altermagnetic RuO2 . journal Physical Review Letters volume 131 , pages 256703 ( year 2023 ). ://link.aps.org/doi/10.1103/PhysRevLett.131.256703

2023 doi
[141]

author Chen, X. et al. title Unconventional magnons in collinear magnets dictated by spin space groups . journal Nature volume 640 , pages 349--354 ( year 2025 ). ://www.nature.com/articles/s41586-025-08715-7

2025
[143]

author Hellenes, A. B. , author Jungwirth, T. , author Sinova, J. & author S mejkal, L. title Exchange spin-orbit coupling and unconventional p-wave magnetism . journal Arxiv Preprint ( year 2023 ). ://arxiv.org/abs/2309.01607v1. 2309.01607v1

2023 arXiv
[144]

author McClarty, P. A. & author Rau, J. G. title Landau Theory of Altermagnetism . journal Physical Review Letters volume 132 , pages 176702 ( year 2023 ). ://link.aps.org/doi/10.1103/PhysRevLett.132.176702 http://arxiv.org/abs/2308.04484. 2308.04484

2023 arXiv
[145]

, author S mejkal, L

author Smolyanyuk, A. , author S mejkal, L. & author Mazin, I. I. title A tool to check whether a symmetry-compensated collinear magnetic material is antiferro- or altermagnetic . journal SciPost Physics Codebases volume 30 , pages 1--16 ( year 2024 ). ://scipost.org/10.21468/...

2024 arXiv
[146]

author Shinohara, K. et al. title Algorithm for spin symmetry operation search . journal Acta Crystallographica Section A Foundations and Advances volume 80 , pages 94--103 ( year 2024 ). ://scripts.iucr.org/cgi-bin/paper?S2053273323009257

2024
[147]

, author Shinohara, K

author Watanabe, H. , author Shinohara, K. , author Nomoto, T. , author Togo, A. & author Arita, R. title Symmetry analysis with spin crystallographic groups: Disentangling effects free of spin-orbit coupling in emergent electromagnetism . journal Physical Review B volume 109 ...

2024 doi
[148]

author Jiang, Y. et al. title Enumeration of Spin-Space Groups: Toward a Complete Description of Symmetries of Magnetic Orders . journal Physical Review X volume 14 , pages 1--25 ( year 2024 ). ://arxiv.org/abs/2307.10371 https://link.aps.org/doi/10.1103/PhysRevX.14.031039. 2307.10371

2024 arXiv
[149]

, author Li, J

author Zhu, H. , author Li, J. , author Chen, X. , author Yu, Y. & author Liu, Q. title Magnetic geometry induced quantum geometry and nonlinear transports . journal Nature Communications volume 16 , pages 4882 ( year 2025 ). ://www.nature.com/articles/s41467-025-60128-2

2025
[150]

author Chen, X. et al. title Enumeration and Representation Theory of Spin Space Groups . journal Physical Review X volume 14 , pages 031038 ( year 2024 ). ://arxiv.org/abs/2307.10369 https://link.aps.org/doi/10.1103/PhysRevX.14.031038. 2307.10369

2024 arXiv
[151]

, author Corticelli, A

author Schiff, H. , author Corticelli, A. , author Guerreiro, A. , author Romh \' a nyi, J. & author McClarty, P. title The Spin Point Groups and their Representations . journal ArXiv 2307.12784 ( year 2023 ). ://arxiv.org/abs/2307.12784. 2307.12784

2023 arXiv
[152]

, author Zhao, J

author Xiao, Z. , author Zhao, J. , author Li, Y. , author Shindou, R. & author Song, Z.-D. title Spin Space Groups: Full Classification and Applications . journal Physical Review X volume 14 , pages 031037 ( year 2024 ). ://link.aps.org/doi/10.1103/PhysRevX.14.031037

2024 doi
[153]

author Litvin, D. B. title Magnetic Group Tables ( year 2013 ). ://www.iucr.org/publ/978-0-9553602-2-0

2013
[154]

://www.cryst.ehu.es/magndata/

title MAGNDATA: A Collection of magnetic structures with portable cif-type files . ://www.cryst.ehu.es/magndata/
[155]

title Magnetism and Local Molecular Field

author N \' e el, L. title Magnetism and Local Molecular Field . journal Science volume 174 , pages 985--992 ( year 1971 ). ://www.ncbi.nlm.nih.gov/pubmed/17757022 http://www.sciencemag.org/cgi/doi/10.1126/science.174.4013.985

1971
[156]

author Reimers, S. et al. title Direct observation of altermagnetic band splitting in CrSb thin films . journal Nature Communications volume 15 , pages 2116 ( year 2024 ). ://www.nature.com/articles/s41467-024-46476-5 http://arxiv.org/abs/2310.17280. 2310.17280

2024 arXiv
[157]

author Berlijn, T. et al. title Itinerant Antiferromagnetism in RuO2 . journal Physical Review Letters volume 118 , pages 077201 ( year 2017 ). ://link.aps.org/doi/10.1103/PhysRevLett.118.077201. 1612.09589

2017 arXiv
[158]

author Zhu, Z. H. et al. title Anomalous Antiferromagnetism in Metallic RuO2 Determined by Resonant X-ray Scattering . journal Physical Review Letters volume 122 , pages 017202 ( year 2019 ). ://arxiv.org/abs/1806.02036 http://dx.doi.org/10.1103/PhysRevLett.122.017202 https://...

2019 arXiv
[159]

author Lovesey, S. W. , author Khalyavin, D. D. & author van der Laan, G. title Magnetic properties of RuO2 and charge-magnetic interference in Bragg diffraction of circularly polarized x-rays . journal Physical Review B volume 105 , pages 014403 ( year 2022 ). ://link.aps.org...

2022 doi
[160]

author Occhialini, C. A. et al. title Local electronic structure of rutile RuO2 . journal Physical Review Research volume 3 , pages 033214 ( year 2021 ). ://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.3.033214. 2108.06256

2021 arXiv
[161]

author Bose, A. et al. title Tilted spin current generated by the collinear antiferromagnet ruthenium dioxide . journal Nature Electronics volume 5 , pages 267--274 ( year 2022 ). ://arxiv.org/abs/2108.09150 https://www.nature.com/articles/s41928-022-00758-2 https://www.nature...

2022 arXiv
[162]

author Bai, H. et al. title Observation of Spin Splitting Torque in a Collinear Antiferromagnet RuO2 . journal Physical Review Letters volume 128 , pages 197202 ( year 2022 ). ://arxiv.org/abs/2109.05933 https://link.aps.org/doi/10.1103/PhysRevLett.128.197202. 2109.05933

2022 arXiv
[163]

author Karube, S. et al. title Observation of Spin-Splitter Torque in Collinear Antiferromagnetic RuO2 . journal Physical Review Letters volume 129 , pages 137201 ( year 2022 ). ://doi.org/10.1103/PhysRevLett.129.137201 https://link.aps.org/doi/10.1103/PhysRevLett.129.137201. ...

2022 arXiv
[164]

author Lovesey, S. W. , author Khalyavin, D. D. & author van der Laan, G. title Magnetic structure of RuO2 in view of altermagnetism . journal Physical Review B volume 108 , pages L121103 ( year 2023 ). ://link.aps.org/doi/10.1103/PhysRevB.108.L121103

2023 doi
[165]

author Liu, Y. et al. title Inverse Altermagnetic Spin Splitting Effect‐Induced Terahertz Emission in RuO2 . journal Advanced Optical Materials volume 11 , pages 1--7 ( year 2023 ). ://onlinelibrary.wiley.com/doi/10.1002/adom.202300177

2023 doi
[166]

author Fedchenko, O. et al. title Observation of time-reversal symmetry breaking in the band structure of altermagnetic RuO 2 . journal Science Advances volume 10 , pages 31 ( year 2024 ). ://www.science.org http://arxiv.org/abs/2306.02170 https://www.science.org/doi/10.1126/s...

2024 arXiv
[167]

, author Mazin, I

author Smolyanyuk, A. , author Mazin, I. I. , author Garcia-Gassull, L. & author Valent \' i , R. title Fragility of the magnetic order in the prototypical altermagnet RuO _2 . journal Physical Review B volume 109 , pages 134424 ( year 2024 ). ://arxiv.org/abs/2310.06909 https...

2024 arXiv
[168]

author Lin, Z. et al. title Observation of Giant Spin Splitting and d-wave Spin Texture in Room Temperature Altermagnet RuO2 . journal Arxiv Preprint ( year 2024 ). ://arxiv.org/abs/2402.04995. 2402.04995

2024 arXiv
[169]

author Ke ler, P. et al. title Absence of magnetic order in RuO _2 : insights from SR spectroscopy and neutron diffraction . journal Arxiv Preprint ( year 2024 ). ://arxiv.org/abs/2405.10820. 2405.10820

2024 arXiv
[170]

, author Zhang, Z

author Li, Z. , author Zhang, Z. , author Lu, X. & author Xu, Y. title Spin Splitting in Altermagnetic RuO2 Enables Field-free Spin-Orbit Torque Switching via Dominant Out-of-Plane Spin Polarization . journal Arxiv Preprint ( year 2024 ). ://arxiv.org/abs/2407.07447. 2407.07447

2024 arXiv
[171]

author Wenzel, M. et al. title Fermi-liquid behavior of nonaltermagnetic RuO2 . journal Physical Review B volume 111 , pages L041115 ( year 2025 ). ://link.aps.org/doi/10.1103/PhysRevB.111.L041115

2025 doi
[172]

author Jeong, S. G. et al. title Altermagnetic Polar Metallic phase in Ultra-Thin Epitaxially-Strained RuO2 Films . journal Arxiv Preprint pages 1--15 ( year 2024 ). ://arxiv.org/abs/2405.05838. 2405.05838

2024 arXiv
[173]

author Hiraishi, M. et al. title Nonmagnetic Ground State in RuO2 Revealed by Muon Spin Rotation . journal Physical Review Letters volume 132 , pages 166702 ( year 2024 ). ://arxiv.org/abs/2403.10028 https://link.aps.org/doi/10.1103/PhysRevLett.132.166702. 2403.10028

2024 arXiv
[174]

, author Ohno, K

author Noda, Y. , author Ohno, K. & author Nakamura, S. title Momentum-dependent band spin splitting in semiconducting MnO2 : a density functional calculation . journal Physical Chemistry Chemical Physics volume 18 , pages 13294--13303 ( year 2016 ). ://xlink.rsc.org/?DOI=C5CP07806G

2016
[175]

, author Yanagi, Y

author Hayami, S. , author Yanagi, Y. & author Kusunose, H. title Momentum-Dependent Spin Splitting by Collinear Antiferromagnetic Ordering . journal Journal of the Physical Society of Japan volume 88 , pages 123702 ( year 2019 ). ://journals.jps.jp/doi/10.7566/JPSJ.88.123702....

2019 arXiv
[176]

, author Wang, Z

author Yuan, L.-D. , author Wang, Z. , author Luo, J.-W. , author Rashba, E. I. & author Zunger, A. title Giant momentum-dependent spin splitting in centrosymmetric low-Z antiferromagnets . journal Physical Review B volume 102 , pages 014422 ( year 2020 ). ://arxiv.org/pdf/191...

2020 arXiv
[177]

& author Spaldin, N

author Bhowal, S. & author Spaldin, N. A. title Ferroically Ordered Magnetic Octupoles in d-Wave Altermagnets . journal Physical Review X volume 14 , pages 011019 ( year 2024 ). ://link.aps.org/doi/10.1103/PhysRevX.14.011019

2024 doi
[178]

author Jiang, B. et al. title A metallic room-temperature d-wave altermagnet . journal Nature Physics ( year 2025 ). ://www.nature.com/articles/s41567-025-02822-y

2025
[179]

author Zhu, Y.-P. et al. title Observation of plaid-like spin splitting in a noncoplanar antiferromagnet . journal Nature volume 626 , pages 523--528 ( year 2024 ). https://www.nature.com/articles/s41586-024-07023-w https://arxiv.org/abs/2303.04549v2 2303.04549

2024 arXiv
[180]

author Jaeschke-Ubiergo, R. et al. title Atomic Altermagnetism . journal Arxiv Preprint ( year 2025 ). ://arxiv.org/pdf/2503.10797. 2503.10797

2025 arXiv
[181]

author Grzybowski, M. J. et al. title Wurtzite vs . rock-salt MnSe epitaxy: electronic and altermagnetic properties . journal Nanoscale volume 16 , pages 6259--6267 ( year 2024 ). ://xlink.rsc.org/?DOI=D3NR04798A

2024
[182]

& author Ohgushi, K

author Aoyama, T. & author Ohgushi, K. title Piezomagnetic Properties in Altermagnetic MnTe . journal Physical Review Materials volume 8 , pages L041402 ( year 2023 ). ://arxiv.org/abs/2305.14786 https://link.aps.org/doi/10.1103/PhysRevMaterials.8.L041402. 2305.14786

2023 arXiv
[183]

author Yang, G. et al. title Three-dimensional mapping of the altermagnetic spin splitting in CrSb . journal Nature Communications volume 16 , pages 1442 ( year 2025 ). ://arxiv.org/abs/2405.12575 https://www.nature.com/articles/s41467-025-56647-7. 2405.12575

2025 arXiv
[184]

author Ding, J. et al. title Large Band Splitting in g-Wave Altermagnet CrSb . journal Physical Review Letters volume 133 , pages 206401 ( year 2024 ). .Rev.Lett.133,206401(2024) https://link.aps.org/doi/10.1103/PhysRevLett.133.206401. 2405.12687

2024 arXiv
[185]

author Li, C. et al. title Topological Weyl Altermagnetism in CrSb . journal ArXiv 2405.14777 ( year 2024 ). ://arxiv.org/abs/2405.14777v1 http://arxiv.org/abs/2405.14777. 2405.14777

2024 arXiv
[186]

author Lu, W. et al. title Observation of surface Fermi arcs in altermagnetic Weyl semimetal CrSb . journal ArXiv 2407.13497 ( year 2024 ). ://arxiv.org/abs/2407.13497. 2407.13497

2024 arXiv
[187]

author Zeng, M. et al. title Observation of Spin Splitting in Room‐Temperature Metallic Antiferromagnet CrSb . journal Advanced Science volume 11 , pages 2406529 ( year 2024 ). ://arxiv.org/abs/2405.12679v1 http://arxiv.org/abs/2405.12679 https://onlinelibrary.wiley.com/doi/10...

2024 arXiv
[188]

author Dale, N. et al. title Non-relativistic spin splitting above and below the Fermi level in a g -wave altermagnet ( year 2024 ). ://arxiv.org/abs/2411.18761. 2411.18761

2024
[189]

, author Ozeki, M

author Liu, Z. , author Ozeki, M. , author Asai, S. , author Itoh, S. & author Masuda, T. title Chiral-Split Magnon in Altermagnetic MnTe . journal Physical Review Letters volume 133 , pages 156702 ( year 2024 ). ://arxiv.org/abs/2408.16490. 2408.16490

2024 arXiv
[190]

author Zhang, F. et al. title Crystal-symmetry-paired spin–valley locking in a layered room-temperature metallic altermagnet candidate . journal Nature Physics volume 21 , pages 760--767 ( year 2025 ). ://www.nature.com/articles/s41567-025-02864-2

2025
[191]

author Wei, C. C. et al. title La2 O3Mn2Se2: A correlated insulating layered d -wave altermagnet . journal Physical Review Materials volume 9 , pages 24402 ( year 2025 ). ://doi.org/10.1103/PhysRevMaterials.9.024402

2025 doi
[192]

author Maharaj, D. D. et al. title Octupolar versus N \' e el Order in Cubic 5d2 Double Perovskites . journal Physical Review Letters volume 124 , pages 87206 ( year 2020 ). ://doi.org/10.1103/PhysRevLett.124.087206. 1909.03113

2020 arXiv
[193]

, author Gonz \' a lez Hern \' a ndez , R

author Chakraborty, A. , author Gonz \' a lez Hern \' a ndez , R. , author S mejkal, L. & author Sinova, J. title Strain-induced phase transition from antiferromagnet to altermagnet . journal Physical Review B volume 109 , pages 144421 ( year 2024 ). ://arxiv.org/abs/2402.0015...

2024 arXiv
[194]

, author Yu, J

author Liu, Y. , author Yu, J. & author Liu, C.-C. title Twisted Magnetic Van der Waals Bilayers: An Ideal Platform for Altermagnetism . journal Physical Review Letters volume 133 , pages 206702 ( year 2024 ). ://arxiv.org/abs/2404.17146 https://link.aps.org/doi/10.1103/PhysRe...

2024 arXiv
[195]

, author Mook, A

author Leeb, V. , author Mook, A. , author S mejkal, L. & author Knolle, J. title Spontaneous Formation of Altermagnetism from Orbital Ordering . journal Physical Review Letters volume 132 , pages 236701 ( year 2024 ). ://arxiv.org/abs/2312.10839 https://journals.aps.org/prl/a...

2024 arXiv
[196]

author Fernandes, R. M. , author de Carvalho, V. S. , author Birol, T. & author Pereira, R. G. title Topological transition from nodal to nodeless Zeeman splitting in altermagnets . journal Physical Review B volume 109 , pages 024404 ( year 2024 ). ://arxiv.org/abs/2307.12380 ...

2024 arXiv
[197]

, author Suri, D

author Das, S. , author Suri, D. & author Soori, A. title Transport across junctions of altermagnets with normal metals and ferromagnets . journal Journal of Physics: Condensed Matter volume 35 , pages 435302 ( year 2023 ). ://arxiv.org/abs/2305.06680 http://dx.doi.org/10.1088...

2023 arXiv
[198]

author Maier, T. A. & author Okamoto, S. title Weak-coupling theory of neutron scattering as a probe of altermagnetism . journal Physical Review B volume 108 , pages L100402 ( year 2023 ). ://arxiv.org/abs/2307.03793 http://dx.doi.org/10.1103/PhysRevB.108.L100402 https://link....

2023 arXiv
[199]

, author Haddad, S

author Sato, T. , author Haddad, S. , author Fulga, I. C. , author Assaad, F. F. & author van den Brink, J. title Altermagnetic Anomalous Hall Effect Emerging from Electronic Correlations . journal Physical Review Letters volume 133 , pages 086503 ( year 2024 ). ://link.aps.or...

2024 doi
[200]

, author Kreisel, A

author Roig, M. , author Kreisel, A. , author Yu, Y. , author Andersen, B. M. & author Agterberg, D. F. title Minimal models for altermagnetism . journal Physical Review B volume 110 , pages 144412 ( year 2024 ). ://arxiv.org/abs/2402.15616v2 http://arxiv.org/abs/2402.15616 ht...

2024 arXiv
[201]

, author Vadnais, S

author Bose, A. , author Vadnais, S. & author Paramekanti, A. title Altermagnetism and superconductivity in a multiorbital t-J model . journal Physical Review B volume 110 , pages 205120 ( year 2024 ). ://arxiv.org/abs/2403.17050 https://link.aps.org/doi/10.1103/PhysRevB.110.2...

2024 arXiv
[202]

& author Valent \' i , R

author Ferrari, F. & author Valent \' i , R. title Altermagnetism on the Shastry-Sutherland lattice . journal Physical Review B volume 110 , pages 205140 ( year 2024 ). ://arxiv.org/abs/2408.00841 https://link.aps.org/doi/10.1103/PhysRevB.110.205140. 2408.00841

2024 arXiv
[203]

, author Saxena, S

author Rooj, S. , author Saxena, S. & author Ganguli, N. title Altermagnetism in the orthorhombic Pnm structure through group theory and DFT calculations . journal Physical Review B volume 111 , pages 014434 ( year 2025 ). ://arxiv.org/abs/2406.06232 https://link.aps.org/doi/1...

2025 arXiv
[204]

& author Goodenough, J

author T \" o pfer, J. & author Goodenough, J. title LaMnO3+ Revisited . journal Journal of Solid State Chemistry volume 130 , pages 117--128 ( year 1997 ). ://linkinghub.elsevier.com/retrieve/pii/S002245969797287X

1997
[205]

author Matl, P. et al. title Hall effect of the colossal magnetoresistance manganite La1-xCaxMnO3 . journal Physical Review B volume 57 , pages 10248--10251 ( year 1998 ). ://link.aps.org/doi/10.1103/PhysRevB.57.10248

1998 doi
[206]

author Zhou, J. et al. title Predicted Quantum Topological Hall Effect and Noncoplanar Antiferromagnetism in K0.5RhO2 . journal Physical Review Letters volume 116 , pages 256601 ( year 2016 ). 1602.08553

2016 arXiv
[207]

, author Romero, A

author L \' o pez-Moreno, S. , author Romero, A. H. , author Mej \' i a-L \' o pez, J. , author Mu \ n oz, A. & author Roshchin, I. V. title First-principles study of electronic, vibrational, elastic, and magnetic properties of FeF2 as a function of pressure . journal Physical...

2012 doi
[208]

, author Romero, A

author L \' o pez-Moreno, S. , author Romero, A. H. , author Mej \' i a-L \' o pez, J. & author Mu \ n oz, A. title First-principles study of pressure-induced structural phase transitions in MnF 2 . journal Physical Chemistry Chemical Physics volume 18 , pages 33250--33263 ( y...

2016
[209]

, author Hariki, A

author Ahn, K.-H. , author Hariki, A. , author Lee, K.-W. & author Kune s , J. title Antiferromagnetism in RuO2 as d-wave Pomeranchuk instability . journal Physical Review B volume 99 , pages 184432 ( year 2019 ). ://link.aps.org/doi/10.1103/PhysRevB.99.184432. 1902.04436

2019 arXiv
[210]

author Naka, M. et al. title Spin current generation in organic antiferromagnets . journal Nature Communications volume 10 , pages 4305 ( year 2019 ). ://dx.doi.org/10.1038/s41467-019-12229-y http://www.nature.com/articles/s41467-019-12229-y https://doi.org/10.1038/s41467-019-...

2019 arXiv
[211]

author Guo, Y. et al. title Spin-split collinear antiferromagnets: A large-scale ab-initio study . journal Materials Today Physics volume 32 , pages 100991 ( year 2023 ). ://linkinghub.elsevier.com/retrieve/pii/S2542529323000275. 2207.07592

2023 arXiv
[212]

author Ma, H.-Y. et al. title Multifunctional antiferromagnetic materials with giant piezomagnetism and noncollinear spin current . journal Nature Communications volume 12 , pages 2846 ( year 2021 ). ://doi.org/10.1038/s41467-021-23127-7 http://www.nature.com/articles/s41467-0...

2021 arXiv
[213]

author Egorov, S. A. & author Evarestov, R. A. title Colossal Spin Splitting in the Monolayer of the Collinear Antiferromagnet MnF2 . journal Journal of Physical Chemistry Letters volume 12 , pages 2363--2369 ( year 2021 ). ://pubs.acs.org/doi/10.1021/acs.jpclett.1c00282

2021 doi
[214]

, author Wang, D

author Chen, X. , author Wang, D. , author Li, L. & author Sanyal, B. title Giant spin-splitting and tunable spin-momentum locked transport in room temperature collinear antiferromagnetic semimetallic CrO monolayer . journal Applied Physics Letters volume 123 ( year 2023 ). :/...

2023
[215]

& author Olsen, T

author S dequist, J. & author Olsen, T. title Two-dimensional altermagnets from high throughput computational screening: Symmetry requirements, chiral magnons, and spin-orbit effects . journal Applied Physics Letters volume 124 , pages 1--7 ( year 2024 ). ://arxiv.org/abs/2401...

2024 arXiv
[216]

author Zhu, Y. et al. title Multipiezo Effect in Altermagnetic V 2 SeTeO Monolayer . journal Nano Letters volume 24 , pages 472--478 ( year 2024 ). ://pubs.acs.org/doi/10.1021/acs.nanolett.3c04330

2024 doi
[217]

author Kramers, H. A. title Th \' e orie g \' e n \' e rale de la rotation paramagn \' e tique dans les cristaux. journal Proc. Amsterdam Acad. volume 33 ( year 1930 ). ://www.dwc.knaw.nl/DL/publications/PU00015981.pdf

1930
[218]

title Ueber die Operation der Zeitumkehr in der Quantenmechanik

author Wigner, E. title Ueber die Operation der Zeitumkehr in der Quantenmechanik . journal Nachrichten von der Gesellschaft der Wissenschaften zu G \" o ttingen, Mathematisch-Physikalische Klasse volume 1932 , pages 546--559 ( year 1932 ). ://www.digizeitschriften.de/dms/img/...

1932
[219]

, author Zhou, Q

author Tang, P. , author Zhou, Q. , author Xu, G. & author Zhang, S.-C. title Dirac fermions in an antiferromagnetic semimetal . journal Nature Physics volume 12 , pages 1100--1104 ( year 2016 ). ://www.nature.com/articles/nphys3839. 1603.08060

2016 arXiv
[220]

, author Z elezn \' y , J

author S mejkal, L. , author Z elezn \' y , J. , author Sinova, J. & author Jungwirth, T. title Electric Control of Dirac Quasiparticles by Spin-Orbit Torque in an Antiferromagnet . journal Physical Review Letters volume 118 , pages 106402 ( year 2017 ). ://link.aps.org/doi/10...

2017 arXiv
[221]

, author Mokrousov, Y

author S mejkal, L. , author Mokrousov, Y. , author Yan, B. & author MacDonald, A. H. title Topological antiferromagnetic spintronics . journal Nature Physics volume 14 , pages 242--251 ( year 2018 ). ://arxiv.org/abs/1706.00670 http://www.nature.com/articles/s41567-018-0064-5...

2018 arXiv
[222]

, author Sukhachov, P

author Brekke, B. , author Sukhachov, P. , author Giil, H. G. , author Brataas, A. & author Linder, J. title Minimal Models and Transport Properties of Unconventional p-Wave Magnets . journal Physical Review Letters volume 133 , pages 236703 ( year 2024 ). ://arxiv.org/abs/240...

2024 arXiv
[223]

title Topological insulators and superconductors based on p-wave magnets: Electrical control and detection of a domain wall

author Ezawa, M. title Topological insulators and superconductors based on p-wave magnets: Electrical control and detection of a domain wall . journal Physical Review B volume 110 , pages 165429 ( year 2024 ). ://journals.aps.org/prb/abstract/10.1103/PhysRevB.110.165429 https:...

2024 doi
[224]

, author dos Santos, F

author Sivianes, J. , author dos Santos, F. J. & author Iba \ n ez-Azpiroz, J. title Optical signatures of spin symmetries in unconventional magnets ( year 2024 ). ://arxiv.org/abs/2406.19842. 2406.19842

2024
[225]

author Chakraborty, A. et al. title Highly Efficient Non-relativistic Edelstein effect in p-wave magnets . journal Nat. Commun. in press, ArXiv 2411.16378 ( year 2024 ). ://arxiv.org/abs/2411.16378. 2411.16378

2024 arXiv
[226]

author Hellenes, A. B. , author Tomas, J. , author Jairo Sinova & author Libor Smejkal . title Unconventional B-type magnetism . journal Unpublished
[227]

author Yu, Y. et al. title Odd-parity Magnetism Driven by Antiferromagnetic Exchange ( year 2025 ). ://arxiv.org/abs/2501.02057. 2501.02057

2025 arXiv
[228]

, author Sattigeri, R

author Fakhredine, A. , author Sattigeri, R. M. , author Cuono, G. & author Autieri, C. title Interplay between altermagnetism and nonsymmorphic symmetries generating large anomalous Hall conductivity by semi-Dirac points induced anticrossings . journal Physical Review B volum...

2023 arXiv
[229]

, author Cano, J

author Fang, Y. , author Cano, J. & author Ghorashi, S. A. A. title Quantum Geometry Induced Nonlinear Transport in Altermagnets . journal Physical Review Letters volume 133 , pages 106701 ( year 2024 ). ://link.aps.org/doi/10.1103/PhysRevLett.133.106701

2024 doi
[230]

, author Liu, Y

author Li, Y.-X. , author Liu, Y. & author Liu, C.-C. title Creation and manipulation of higher-order topological states by altermagnets . journal Physical Review B volume 109 , pages L201109 ( year 2024 ). ://link.aps.org/doi/10.1103/PhysRevB.109.L201109

2024 doi
[231]

, author Li, J

author Zhan, J. , author Li, J. , author Shi, W. , author Chen, X. Q. & author Sun, Y. title Coexistence of Weyl semimetal and Weyl nodal loop semimetal phases in a collinear antiferromagnet . journal Physical Review B volume 107 , pages 224402 ( year 2023 ). ://doi.org/10.110...

2023 arXiv
[232]

author Nag, J. et al. title GdAlSi: An antiferromagnetic topological Weyl semimetal with nonrelativistic spin splitting . journal Physical Review B volume 110 , pages 224436 ( year 2024 ). ://link.aps.org/doi/10.1103/PhysRevB.110.224436

2024 doi
[233]

, author Wiedmann, R

author Parshukov, K. , author Wiedmann, R. & author Schnyder, A. P. title Topological responses from gapped Weyl points in 2D altermagnets . journal Arxiv Preprint pages 1--7 ( year 2024 ). ://arxiv.org/abs/2403.09520. 2403.09520

2024 arXiv
[234]

, author Mook, A

author Rao, P. , author Mook, A. & author Knolle, J. title Tunable band topology and optical conductivity in altermagnets . journal Physical Review B volume 110 , pages 024425 ( year 2024 ). ://arxiv.org/abs/2403.10509 http://dx.doi.org/10.1103/PhysRevB.110.024425 https://link...

2024 arXiv
[235]

author Bernevig, B. A. , author Orenstein, J. & author Zhang, S. C. title Exact SU(2) symmetry and persistent spin helix in a spin-orbit coupled system . journal Physical Review Letters volume 97 , pages 236601 ( year 2006 ). 0606196

2006
[236]

author Koralek, J. D. et al. title Emergence of the persistent spin helix in semiconductor quantum wells . journal Nature volume 458 , pages 610--613 ( year 2009 ). 0903.4709

2009 arXiv
[237]

author Ghosh, S. et al. title Raman spectroscopic evidence for linearly dispersed nodes and magnetic ordering in the topological semimetal V _ 1/3 NbS _2 ( year 2025 ). ://arxiv.org/abs/2504.04590. 2504.04590

2025 arXiv
[238]

, author Yao, H

author Sun, K. , author Yao, H. , author Fradkin, E. & author Kivelson, S. A. title Topological Insulators and Nematic Phases from Spontaneous Symmetry Breaking in 2D Fermi Systems with a Quadratic Band Crossing . journal Physical Review Letters volume 103 , pages 046811 ( yea...

2009 doi
[239]

, author Hu, L.-H

author Zhang, S.-B. , author Hu, L.-H. & author Neupert, T. title Finite-momentum Cooper pairing in proximitized altermagnets . journal Nature Communications volume 15 , pages 1801 ( year 2024 ). ://arxiv.org/abs/2302.13185 https://www.nature.com/articles/s41467-024-45951-3. 2...

2024 arXiv
[240]

author Steward, C. R. W. , author Fernandes, R. M. & author Schmalian, J. title Dynamic paramagnon-polarons in altermagnets . journal Physical Review B volume 108 , pages 144418 ( year 2023 ). ://arxiv.org/abs/2307.01855 https://link.aps.org/doi/10.1103/PhysRevB.108.144418. 2307.01855

2023 arXiv

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

[1] [1]

, author Sinova, J

author S mejkal, L. , author Sinova, J. & author Jungwirth, T. title Beyond Conventional Ferromagnetism and Antiferromagnetism: A Phase with Nonrelativistic Spin and Crystal Rotation Symmetry . journal Physical Review X volume 12 , pages 031042 ( year 2022 ). ://link.aps.org/doi/10.1103/PhysRevX.12.031042. 2105.05820

arXiv 2022

[2] [2]

, author Sinova, J

author S mejkal, L. , author Sinova, J. & author Jungwirth, T. title Emerging Research Landscape of Altermagnetism . journal Physical Review X volume 12 , pages 040501 ( year 2022 ). ://arxiv.org/abs/2204.10844 https://link.aps.org/doi/10.1103/PhysRevX.12.040501. 2204.10844

arXiv 2022

[3] [3]

, author Gonz \' a lez-Hern \' a ndez, R

author S mejkal, L. , author Gonz \' a lez-Hern \' a ndez, R. , author Jungwirth, T. & author Sinova, J. title Crystal time-reversal symmetry breaking and spontaneous Hall effect in collinear antiferromagnets . journal Science Advances volume 6 , pages eaaz8809 ( year 2020 ). ://www.science.org/doi/10.1126/sciadv.aaz8809. 1901.00445

arXiv 2020

[4] [4]

, author Gonz \' a lez-Hern \' a ndez, R

author Mazin, I. , author Gonz \' a lez-Hern \' a ndez, R. & author S mejkal, L. title Induced Monolayer Altermagnetism in MnP(S,Se) _3 and FeSe pages 1--11 ( year 2023 ). ://arxiv.org/abs/2309.02355. 2309.02355

arXiv 2023

[5] [5]

, author Brataas, A

author Brekke, B. , author Brataas, A. & author Sudb , A. title Two-dimensional altermagnets: Superconductivity in a minimal microscopic model . journal Physical Review B volume 108 , pages 224421 ( year 2023 ). ://arxiv.org/abs/2308.08606 https://link.aps.org/doi/10.1103/PhysRevB.108.224421. 2308.08606

arXiv 2023

[6] [6]

author Antonenko, D. S. , author Fernandes, R. M. & author Venderbos, J. W. F. title Mirror Chern Bands and Weyl Nodal Loops in Altermagnets . journal Physical Review Letters volume 134 , pages 096703 ( year 2025 ). ://link.aps.org/doi/10.1103/PhysRevLett.134.096703

doi:10.1103/physrevlett.134.096703 2025

[7] [7]

& author Franz, M

author Kaushal, N. & author Franz, M. title Altermagnetism in modified Lieb lattice Hubbard model . journal Arxiv Preprint ( year 2024 ). ://arxiv.org/abs/2412.16421. 2412.16421

arXiv 2024

[8] [8]

author Jungwirth, T. et al. title Altermagnetism: an unconventional spin-ordered phase of matter . journal ArXiv 2411.00717 ( year 2024 ). ://arxiv.org/abs/2411.00717. 2411.00717

arXiv 2024