Šmejkal, L., Sinova, J. & Jungwirth, T. Beyond conventional ferromagnetism and antiferromagnetism: a phase with nonrelativistic spin and crystal rotation symmetry. Phys. Rev. X 12, 031042 (2022). This paper delineated altermagnetism as an exclusively distinct spin-group symmetry class of d-, g- or i-wave spin-ordered phases.


Google Scholar
 

Šmejkal, L., Sinova, J. & Jungwirth, T. Emerging research landscape of altermagnetism. Phys. Rev. X 12, 040501 (2022). This perspective outlined envisaged research directions of altermagnetism.


Google Scholar
 

Šmejkal, L., González-Hernández, R., Jungwirth, T. & Sinova, J. Crystal time-reversal symmetry breaking and spontaneous Hall effect in collinear antiferromagnets. Sci. Adv. 6, eaaz8809 (2020). This paper predicted that an interplay of crystal and collinear spin orders in a class of materials can lead to a time-reversal-symmetry-breaking spin-split electronic structure and, when spin–orbit coupling is included, to the anomalous Hall effect.

Article 
PubMed 
PubMed Central 

Google Scholar
 

Jungwirth, T. et al. Altermagnetism: an unconventional spin-ordered phase of matter. Newton 1, 100162 (2025).

Article 

Google Scholar
 

Mazin, I. I. Notes on altermagnetism and superconductivity. AAPPS Bull. 35, 18 (2025). These informal notes, originally posted as a preprint on the arXiv server, aimed to stimulate the exploration of the interplay of altermagnetism with superconductivity.

Article 

Google Scholar
 

Beenakker, C. W. J. & Vakhtel, T. Phase-shifted Andreev levels in an altermagnet Josephson junction. Phys. Rev. B 108, 075425 (2023).

Article 
CAS 

Google Scholar
 

Mazin, I., González-Hernández, R. & Šmejkal, L. Induced monolayer altermagnetism in MnP(S,Se)3 and FeSe. Preprint at http://arxiv.org/abs/2309.02355 (2023).

Brekke, B., Brataas, A. & Sudbø, A. Two-dimensional altermagnets: superconductivity in a minimal microscopic model. Phys. Rev. B 108, 224421 (2023).

Article 
CAS 

Google Scholar
 

Li, Y.-X. & Liu, C.-C. Majorana corner modes and tunable patterns in an altermagnet heterostructure. Phys. Rev. B 108, 205410 (2023).

Article 
CAS 

Google Scholar
 

Zhu, D., Zhuang, Z.-Y., Wu, Z. & Yan, Z. Topological superconductivity in two-dimensional altermagnetic metals. Phys. Rev. B 108, 184505 (2023).

Article 
CAS 

Google Scholar
 

Sumita, S., Naka, M. & Seo, H. Fulde–Ferrell–Larkin–Ovchinnikov state induced by antiferromagnetic order in k-type organic conductors. Phys. Rev. Res. 5, 043171 (2023).

Article 
CAS 

Google Scholar
 

Ghorashi, S. A. A., Hughes, T. L. & Cano, J. Altermagnetic routes to Majorana modes in zero net magnetization. Phys. Rev. Lett. 133, 106601 (2024).

Article 
CAS 
PubMed 

Google Scholar
 

Papaj, M. Andreev reflection at the altermagnet-superconductor interface. Phys. Rev. B 108, L060508 (2023).

Article 
CAS 

Google Scholar
 

Wei, M. et al. Gapless superconducting state and mirage gap in altermagnets. Phys. Rev. B 109, L201404 (2023).

Article 

Google Scholar
 

Zhang, S.-B., Hu, L.-H. & Neupert, T. Finite-momentum Cooper pairing in proximitized altermagnets. Nat. Commun. 15, 1801 (2024).

Article 
CAS 
PubMed 
PubMed Central 

Google Scholar
 

Cheng, Q. & Sun, Q.-F. Orientation-dependent Josephson effect in spin-singlet superconductor/altermagnet/spin-triplet superconductor junctions. Phys. Rev. B 109, 024517 (2024).

Article 
CAS 

Google Scholar
 

Zhao, Y. et al. Hybrid-order topology in unconventional magnets of Eu-based Zintl compounds with surface-dependent quantum geometry. Phys. Rev. B 110, 205111 (2024).

Article 
CAS 

Google Scholar
 

Mæland, K., Brekke, B. & Sudbø, A. Many-body effects on superconductivity mediated by double-magnon processes in altermagnets. Phys. Rev. B 109, 134515 (2024).

Article 

Google Scholar
 

Chakraborty, D. & Black-Schaffer, A. M. Zero-field finite-momentum and field-induced superconductivity in altermagnets. Phys. Rev. B 110, L060508 (2024).

Article 
CAS 

Google Scholar
 

Banerjee, S. & Scheurer, M. S. Altermagnetic superconducting diode effect. Phys. Rev. B 110, 024503 (2024).

Article 
CAS 

Google Scholar
 

Jeschke, H. O., Shimizu, M. & Mazin, I. I. CuAg(SO4)2: a doubly strongly correlated altermagnetic three-dimensional analog of the parent compounds of high-Tc cuprates. Phys. Rev. B 109, L220412 (2024).

Article 
CAS 

Google Scholar
 

Verbeek, X. H., Urru, A. & Spaldin, N. A. Hidden orders and (anti-)magnetoelectric effects in Cr2O3 and Fe2O3. Phys. Rev. Res. 5, L042018 (2023).

Article 
CAS 

Google Scholar
 

Bernardini, F., Fiebig, M. & Cano, A. Ruddlesden–Popper and perovskite phases as a material platform for altermagnetism. J. Appl. Phys. 137, 103903 (2025).

Zyuzin, A. A. Magnetoelectric effect in superconductors with d-wave magnetization. Phys. Rev. B 109, L220505 (2024).

Article 
CAS 

Google Scholar
 

Sim, G. & Knolle, J. Pair density waves and supercurrent diode effect in altermagnets. Phys. Rev. B 112, L020502 (2025).

Article 
CAS 

Google Scholar
 

Hu, J.-X., Matsyshyn, O. & Song, J. C. W. Nonlinear superconducting magnetoelectric effect. Phys. Rev. Lett. 134, 026001 (2025).

Article 
MathSciNet 
CAS 
PubMed 

Google Scholar
 

Šmejkal, L. Altermagnetic multiferroics and altermagnetoelectric effect. Preprint at http://arxiv.org/abs/2411.19928 (2024). This paper and refs. 28 and 29 theoretically predicted an interplay of altermagnetism with ferroelectricity.

Duan, X. et al. Antiferroelectric altermagnets: antiferroelectricity alters magnets. Phys. Rev. Lett. 134, 106801 (2025).

Article 
CAS 
PubMed 

Google Scholar
 

Gu, M. et al. Ferroelectric switchable altermagnetism. Phys. Rev. Lett. 134, 106802 (2024).

Article 

Google Scholar
 

Parthenios, N. et al. Spin and pair density waves in two-dimensional altermagnetic metals. Phys. Rev. B 112, 214410 (2025).

Šmejkal, L., MacDonald, A. H., Sinova, J., Nakatsuji, S. & Jungwirth, T. Anomalous Hall antiferromagnets. Nat. Rev. Mater. 7, 482–496 (2022). This paper reviewed the anomalous Hall effect in altermagnets and non-collinear compensated magnets.

Article 

Google Scholar
 

Bai, L. et al. Altermagnetism: exploring new frontiers in magnetism and spintronics. Adv. Funct. Mater. 34, 2409327 (2024).

Liu, Q., Dai, X. & Blügel, S. Different facets of unconventional magnetism. Nat. Phys. 21, 329–331 (2025).

Article 
CAS 

Google Scholar
 

Song, C. et al. Altermagnets as a new class of functional materials. Nat. Rev. Mater. 10, 473–485 (2025).

Jungwirth, T. et al. Altermagnetic spintronics. Preprint at http://arxiv.org/abs/2508.09748 (2025).

Liu, P., Li, J., Han, J., Wan, X. & Liu, Q. Spin-group symmetry in magnetic materials with negligible spin–orbit coupling. Phys. Rev. X 12, 21016 (2022). This paper discusses spin space-group symmetries of magnetic materials and corresponding band degeneracies and emergent topological phases.

CAS 

Google Scholar
 

Litvin, D. B. & Opechowski, W. Spin groups. Physica 76, 538–554 (1974). This paper describes the mathematical spin-group formalism.

Article 
MathSciNet 
CAS 

Google Scholar
 

Andreev, A. & Grishchuk, I. Spin nematics. Sov. Phys. JETP 60, 267 (1984).


Google Scholar
 

Gor’kov, L. P. & Sokol, A. Nontrivial magnetic order: localized versus itinerant systems. Phys. Rev. Lett. 69, 2586–2589 (1992).

Article 
PubMed 

Google Scholar
 

Leggett, A. J. Nobel Lecture: Superfluid 3-He: the early days as seen by a theorist. Rev. Mod. Phys. 76, 999 (2004). This paper reviews the superfluid phase of 3He, including the spontaneous breaking of real-space and spin-space rotation symmetries.

Article 
CAS 

Google Scholar
 

Moessner, R. & Moore, J. E. Topological Phases of Matter (Cambridge Univ. Press, 2021).

Strange, P. Relativistic Quantum Mechanics 1 edn (Cambridge Univ. Press, Cambridge, 1998).

Winkler, R. Spin–Orbit Coupling Effects in Two-Dimensional Electron and Hole Systems Springer Tracts in Modern Physics Vol. 191 (Springer, 2003).

Landau, L. & Lifshitz, E. Electrodynamics of Continuous Media 2 edn, Course of Theoretical Physics Vol. 8 (Pergamon Press, 1965).

Sinova, J., Valenzuela, S. O., Wunderlich, J., Back, C. H. & Jungwirth, T. Spin Hall effects. Rev. Mod. Phys. 87, 1213–1260 (2015).

Article 

Google Scholar
 

Nagaosa, N., Sinova, J., Onoda, S., MacDonald, A. H. & Ong, N. P. Anomalous Hall effect. Rev. Mod. Phys. 82, 1539–1592 (2010).

Article 

Google Scholar
 

Franz, M. & Molenkamp, L. (eds) Contemporary Concepts of Condensed Matter Science Topological Insulators Vol. 6 (Elsevier, 2013).

Murakami, S. & Yokoyama, T. Quantum Spin Hall Effect and Topological Insulators Vol. 1 (Oxford Univ. Press, 2017).

Bradlyn, B. et al. Topological quantum chemistry. Nature 547, 298–305 (2017).

Article 
CAS 
PubMed 

Google Scholar
 

Armitage, N. P., Mele, E. J. & Vishwanath, A. Weyl and Dirac semimetals in three-dimensional solids. Rev. Mod. Phys. 90, 015001 (2018).

Article 
MathSciNet 
CAS 

Google Scholar
 

Elcoro, L. et al. Magnetic topological quantum chemistry. Nat. Commun. 12, 5965 (2021).

Article 
CAS 
PubMed 
PubMed Central 

Google Scholar
 

Mazin, I. I., Koepernik, K., Johannes, M. D., González-Hernández, R. & Šmejkal, L. Prediction of unconventional magnetism in doped FeSb2. Proc. Natl Acad. Sci. USA 118, e2108924118 (2021).

Article 
CAS 
PubMed 
PubMed Central 

Google Scholar
 

Reichlova, H. et al. Observation of a spontaneous anomalous Hall response in the Mn5Si d-wave altermagnet candidate. Nat. Commun. 15, 4961 (2024).

Article 
CAS 
PubMed 
PubMed Central 

Google Scholar
 

Šmejkal, L., Hellenes, A. B., González-Hernández, R., Sinova, J. & Jungwirth, T. Giant and tunneling magnetoresistance in unconventional collinear antiferromagnets with nonrelativistic spin–momentum coupling. Phys. Rev. X 12, 011028 (2022).


Google Scholar
 

Gonzalez Betancourt, R. D. et al. Spontaneous anomalous Hall effect arising from an unconventional compensated magnetic phase in a semiconductor. Phys. Rev. Lett. 130, 036702 (2023).

Article 
CAS 
PubMed 

Google Scholar
 

Šmejkal, L. et al. Chiral magnons in altermagnetic RuO2. Phys. Rev. Lett. 131, 256703 (2023).

Article 
PubMed 

Google Scholar
 

Chen, X. et al. Unconventional magnons in collinear magnets dictated by spin space groups. Nature 640, 349–354 (2025).

Article 
CAS 
PubMed 
PubMed Central 

Google Scholar
 

Hariki, A. et al. X-ray magnetic circular dichroism in altermagnetic α-MnTe. Phys. Rev. Lett. 132, 176701 (2024).

Article 
CAS 
PubMed 

Google Scholar
 

Hellenes, A. B. et al. P-wave magnets. Preprint at http://arxiv.org/abs/2309.01607 (2023).

Hellenes, A. B., Jungwirth, T., Sinova, J. & Šmejkal, L. Exchange spin–orbit coupling and unconventional p-wave magnetism. Preprint at http://arxiv.org/abs/2309.01607v1 (2023).

McClarty, P. A. & Rau, J. G. Landau theory of altermagnetism. Phys. Rev. Lett. 132, 176702 (2023).

Article 
MathSciNet 

Google Scholar
 

Smolyanyuk, A., Šmejkal, L. & Mazin, I. I. A tool to check whether a symmetry-compensated collinear magnetic material is antiferro- or altermagnetic. SciPost Phys. Codebases 30, 1–16 (2024).


Google Scholar
 

Shinohara, K. et al. Algorithm for spin symmetry operation search. Acta Crystallogr. A 80, 94–103 (2024).

Article 
CAS 

Google Scholar
 

Watanabe, H., Shinohara, K., Nomoto, T., Togo, A. & Arita, R. Symmetry analysis with spin crystallographic groups: disentangling effects free of spin–orbit coupling in emergent electromagnetism. Phys. Rev. B 109, 094438 (2024).

Article 
CAS 

Google Scholar
 

Jiang, Y. et al. Enumeration of spin-space groups: toward a complete description of symmetries of magnetic orders. Phys. Rev. X 14, 031039 (2024).

CAS 

Google Scholar
 

Zhu, H., Li, J., Chen, X., Yu, Y. & Liu, Q. Magnetic geometry induced quantum geometry and nonlinear transports. Nat. Commun. 16, 4882 (2025).

Article 
CAS 
PubMed 
PubMed Central 

Google Scholar
 

Chen, X. et al. Enumeration and representation theory of spin space groups. Phys. Rev. X 14, 031038 (2024).

CAS 

Google Scholar
 

Schiff, H., Corticelli, A., Guerreiro, A., Romhányi, J. & McClarty, P. The crystallographic spin point groups and their representations. SciPost Phys. 18, 109 (2025).

Xiao, Z., Zhao, J., Li, Y., Shindou, R. & Song, Z.-D. Spin space groups: full classification and applications. Phys. Rev. X 14, 031037 (2024).

CAS 

Google Scholar
 

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

Berlijn, T. et al. Itinerant antiferromagnetism in RuO2. Phys. Rev. Lett. 118, 077201 (2017).

Article 
CAS 
PubMed 

Google Scholar
 

Zhu, Z. H. et al. Anomalous antiferromagnetism in metallic RuO2 determined by resonant X-ray scattering. Phys. Rev. Lett. 122, 017202 (2019).

Article 
CAS 
PubMed 

Google Scholar
 

Lovesey, S. W., Khalyavin, D. D. & van der Laan, G. Magnetic properties of RuO2 and charge-magnetic interference in Bragg diffraction of circularly polarized X-rays. Phys. Rev. B 105, 014403 (2022).

Article 
CAS 

Google Scholar
 

Occhialini, C. A. et al. Local electronic structure of rutile RuO2. Phys. Rev. Res. 3, 033214 (2021).

Article 
CAS 

Google Scholar
 

Feng, Z. et al. An anomalous Hall effect in altermagnetic ruthenium dioxide. Nat. Electron. 5, 735–743 (2022).

Article 
CAS 

Google Scholar
 

Bose, A. et al. Tilted spin current generated by the collinear antiferromagnet ruthenium dioxide. Nat. Electron. 5, 267–274 (2022).

Article 
CAS 

Google Scholar
 

Bai, H. et al. Observation of spin splitting torque in a collinear antiferromagnet RuO2. Phys. Rev. Lett. 128, 197202 (2022).

Article 
CAS 
PubMed 

Google Scholar
 

Karube, S. et al. Observation of spin-splitter torque in collinear antiferromagnetic RuO2. Phys. Rev. Lett. 129, 137201 (2022).

Article 
CAS 
PubMed 

Google Scholar
 

Lovesey, S. W., Khalyavin, D. D. & van der Laan, G. Magnetic structure of RuO2 in view of altermagnetism. Phys. Rev. B 108, L121103 (2023).

Article 
CAS 

Google Scholar
 

Liu, Y. et al. Inverse altermagnetic spin splitting effect-induced terahertz emission in RuO2. Adv. Opt. Mater. 11, 2300177 (2023).

Article 
CAS 

Google Scholar
 

Fedchenko, O. et al. Observation of time-reversal symmetry breaking in the band structure of altermagnetic RuO2. Sci. Adv. 10, 31 (2024).

Article 

Google Scholar
 

Smolyanyuk, A., Mazin, I. I., Garcia-Gassull, L. & Valentí, R. Fragility of the magnetic order in the prototypical altermagnet RuO2. Phys. Rev. B 109, 134424 (2024).

Article 
CAS 

Google Scholar
 

Lin, Z. et al. Observation of giant spin splitting and d-wave spin texture in room temperature altermagnet RuO2. Preprint at http://arxiv.org/abs/2402.04995 (2024).

Keßler, P. et al. Absence of magnetic order in RuO2: insights from μSR spectroscopy and neutron diffraction. npj Spintronics 2, 50 (2024).

Li, Z. et al. Fully field-free spin-orbit torque switching induced by spin splitting effect in altermagnetic RuO2. Adv. Mater. 37, 2416712 (2025).

Wenzel, M. et al. Fermi-liquid behavior of nonaltermagnetic RuO2. Phys. Rev. B 111, L041115 (2025).

Article 
CAS 

Google Scholar
 

Jeong, S. G. et al. Altermagnetic polar metallic phase in ultra-thin epitaxially-strained RuO2 films. Preprint at http://arxiv.org/abs/2405.05838 (2024).

Hiraishi, M. et al. Nonmagnetic ground state in RuO2 revealed by muon spin rotation. Phys. Rev. Lett. 132, 166702 (2024).

Article 
CAS 
PubMed 

Google Scholar
 

López-Moreno, S., Romero, A. H., Mejía-López, J. & Muñoz, A. First-principles study of pressure-induced structural phase transitions in MnF2. Phys. Chem. Chem. Phys. 18, 33250–33263 (2016). This paper reported density-functional-theory calculations of non-relativistic band structure of MnF2.

Article 
PubMed 

Google Scholar
 

Noda, Y., Ohno, K. & Nakamura, S. Momentum-dependent band spin splitting in semiconducting MnO2: a density functional calculation. Phys. Chem. Chem. Phys. 18, 13294–13303 (2016).

Article 
CAS 
PubMed 

Google Scholar
 

Hayami, S., Yanagi, Y. & Kusunose, H. Momentum-dependent spin splitting by collinear antiferromagnetic ordering. J. Phys. Soc. Jpn 88, 123702 (2019).

Article 

Google Scholar
 

Yuan, L.-D., Wang, Z., Luo, J.-W., Rashba, E. I. & Zunger, A. Giant momentum-dependent spin splitting in centrosymmetric low-Z antiferromagnets. Phys. Rev. B 102, 014422 (2020).

Article 
CAS 

Google Scholar
 

Bhowal, S. & Spaldin, N. A. Ferroically ordered magnetic octupoles in d-wave altermagnets. Phys. Rev. X 14, 011019 (2024).

CAS 

Google Scholar
 

Jaeschke-Ubiergo, R. et al. Atomic altermagnetism. Preprint at https://arxiv.org/pdf/2503.10797 (2025).

Lovesey, S. W., Khalyavin, D. D. & van der Laan, G. Templates for magnetic symmetry and altermagnetism in hexagonal MnTe. Phys. Rev. B 108, 174437 (2023).

Article 
CAS 

Google Scholar
 

Mazin, I. I. Altermagnetism in MnTe: origin, predicted manifestations, and routes to detwinning. Phys. Rev. B 107, L100418 (2023).

Article 
CAS 

Google Scholar
 

Krempaský, J. et al. Altermagnetic lifting of Kramers spin degeneracy. Nature 626, 517–522 (2024). This paper and refs. 99–101 reported experimental spectroscopic observations of a g-wave altermagnetic band structure of MnTe.

Article 
PubMed 
PubMed Central 

Google Scholar
 

Lee, S. S. et al. Broken Kramers degeneracy in altermagnetic MnTe. Phys. Rev. Lett. 132, 036702 (2024).

Article 
CAS 
PubMed 

Google Scholar
 

Osumi, T. et al. Observation of a giant band splitting in altermagnetic MnTe. Phys. Rev. B 109, 115102 (2024).

Article 
CAS 

Google Scholar
 

Hajlaoui, M. et al. Temperature dependence of relativistic valence band splitting induced by an altermagnetic phase transition. Adv. Mater. 36, 2314076 (2024).

Article 
CAS 

Google Scholar
 

Aoyama, T. & Ohgushi, K. Piezomagnetic properties in altermagnetic MnTe. Phys. Rev. Mater. 8, L041402 (2024).

Article 
CAS 

Google Scholar
 

Kluczyk, K. P. et al. Coexistence of anomalous Hall effect and weak magnetization in a nominally collinear antiferromagnet MnTe. Phys. Rev. B 110, 155201 (2024).

Article 
CAS 

Google Scholar
 

Reimers, S. et al. Direct observation of altermagnetic band splitting in CrSb thin films. Nat. Commun. 15, 2116 (2024).

Article 
CAS 
PubMed 
PubMed Central 

Google Scholar
 

Yang, G. et al. Three-dimensional mapping of the altermagnetic spin splitting in CrSb. Nat. Commun. 16, 1442 (2025).

Article 
PubMed 
PubMed Central 

Google Scholar
 

Ding, J. et al. Large band splitting in g-wave altermagnet CrSb. Phys. Rev. Lett. 133, 206401 (2024).

Article 
CAS 
PubMed 

Google Scholar
 

Li, C. et al. Topological Weyl altermagnetism in CrSb. Commun. Phys. 8, 311 (2025).

Lu, W. et al. Signature of topological surface bands in altermagnetic Weyl semimetal CrSb. Nano Lett. 25, 7343–7350 (2025).

Article 
CAS 
PubMed 
PubMed Central 

Google Scholar
 

Zeng, M. et al. Observation of spin splitting in room-temperature metallic antiferromagnet CrSb. Adv. Sci. 11, 2406529 (2024).

Article 
CAS 

Google Scholar
 

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

Liu, Z., Ozeki, M., Asai, S., Itoh, S. & Masuda, T. Chiral-split magnon in altermagnetic MnTe. Phys. Rev. Lett. 133, 156702 (2024).

Article 
CAS 
PubMed 

Google Scholar
 

Jiang, B. et al. A metallic room-temperature d-wave altermagnet. Nat. Phys. 21, 754–759 (2025). This paper and ref. 113 reported experimental spectroscopic observations of a d-wave altermagnetic band structure.

Article 
CAS 

Google Scholar
 

Zhang, F. et al. Crystal-symmetry-paired spin–valley locking in a layered room-temperature metallic altermagnet candidate. Nat. Phys. 21, 760–767 (2025).

Article 
CAS 

Google Scholar
 

Antonenko, D. S., Fernandes, R. M. & Venderbos, J. W. F. Mirror Chern bands and Weyl nodal loops in altermagnets. Phys. Rev. Lett. 134, 096703 (2025). This paper reported a theoretical study of topological phenomena in 2D (Lieb lattice) and 3D minimal models of altermagnetism.

Article 
CAS 
PubMed 

Google Scholar
 

Kaushal, N. & Franz, M. Altermagnetism in modified Lieb lattice Hubbard model. Phys. Rev. Lett. 135, 156502 (2025).

Wei, C. C. et al. La2O3Mn2Se2: a correlated insulating layered d-wave altermagnet. Phys. Rev. Mater. 9, 24402 (2025).

Article 
CAS 

Google Scholar
 

Maharaj, D. D. et al. Octupolar versus Néel order in cubic 5d2 double perovskites. Phys. Rev. Lett. 124, 87206 (2020).

Article 
CAS 

Google Scholar
 

Néel, L. Magnetism and local molecular field. Science 174, 985–992 (1971).

Article 
PubMed 

Google Scholar
 

Chakraborty, A., González Hernández, R., Šmejkal, L. & Sinova, J. Strain-induced phase transition from antiferromagnet to altermagnet. Phys. Rev. B 109, 144421 (2024).

Article 
CAS 

Google Scholar
 

Liu, Y., Yu, J. & Liu, C.-C. Twisted magnetic van der Waals bilayers: an ideal platform for altermagnetism. Phys. Rev. Lett. 133, 206702 (2024).

Article 
CAS 
PubMed 

Google Scholar
 

Leeb, V., Mook, A., Šmejkal, L. & Knolle, J. Spontaneous formation of altermagnetism from orbital ordering. Phys. Rev. Lett. 132, 236701 (2024).

Article 
CAS 
PubMed 

Google Scholar
 

Fernandes, R. M., de Carvalho, V. S., Birol, T. & Pereira, R. G. Topological transition from nodal to nodeless Zeeman splitting in altermagnets. Phys. Rev. B 109, 024404 (2024).

Article 
CAS 

Google Scholar
 

Das, S., Suri, D. & Soori, A. Transport across junctions of altermagnets with normal metals and ferromagnets. J. Phys. Condensed Matter 35, 435302 (2023).

Article 
CAS 

Google Scholar
 

Maier, T. A. & Okamoto, S. Weak-coupling theory of neutron scattering as a probe of altermagnetism. Phys. Rev. B 108, L100402 (2023).

Article 
CAS 

Google Scholar
 

Sato, T., Haddad, S., Fulga, I. C., Assaad, F. F. & van den Brink, J. Altermagnetic anomalous Hall effect emerging from electronic correlations. Phys. Rev. Lett. 133, 086503 (2024).

Article 
MathSciNet 
CAS 
PubMed 

Google Scholar
 

Roig, M., Kreisel, A., Yu, Y., Andersen, B. M. & Agterberg, D. F. Minimal models for altermagnetism. Phys. Rev. B 110, 144412 (2024).

Article 
CAS 

Google Scholar
 

Bose, A., Vadnais, S. & Paramekanti, A. Altermagnetism and superconductivity in a multiorbital t–J model. Phys. Rev. B 110, 205120 (2024).

Article 
CAS 

Google Scholar
 

Ferrari, F. & Valentí, R. Altermagnetism on the Shastry–Sutherland lattice. Phys. Rev. B 110, 205140 (2024).

Article 
CAS 

Google Scholar
 

Rooj, S., Saxena, S. & Ganguli, N. Altermagnetism in the orthorhombic Pnm structure through group theory and DFT calculations. Phys. Rev. B 111, 014434 (2025).

Article 
CAS 

Google Scholar
 

Töpfer, J. & Goodenough, J. LaMnO3+δ revisited. J. Solid State Chem. 130, 117–128 (1997).

Article 

Google Scholar
 

Chen, H., Niu, Q. & Macdonald, A. H. Anomalous Hall effect arising from noncollinear antiferromagnetism. Phys. Rev. Lett. 112, 017205 (2014). This paper predicted the anomalous Hall effect in a non-collinear compensated magnet.

Article 
PubMed 

Google Scholar
 

Zhou, J. et al. Predicted quantum topological Hall effect and noncoplanar antiferromagnetism in K0.5RhO2. Phys. Rev. Lett. 116, 256601 (2016).

Article 
PubMed 

Google Scholar
 

Feng, W. et al. Topological magneto-optical effects and their quantization in noncoplanar antiferromagnets. Nat. Commun. 11, 118 (2020).

Article 
CAS 
PubMed 
PubMed Central 

Google Scholar
 

Ahn, K.-H., Hariki, A., Lee, K.-W. & Kuneš, J. Antiferromagnetism in RuO2 as d-wave Pomeranchuk instability. Phys. Rev. B 99, 184432 (2019).

Article 
CAS 

Google Scholar
 

Naka, M. et al. Spin current generation in organic antiferromagnets. Nat. Commun. 10, 4305 (2019).

Article 
PubMed 
PubMed Central 

Google Scholar
 

Guo, Y. et al. Spin-split collinear antiferromagnets: a large-scale ab-initio study. Mater. Today Phys. 32, 100991 (2023).

Article 
CAS 

Google Scholar
 

Ma, H.-Y. et al. Multifunctional antiferromagnetic materials with giant piezomagnetism and noncollinear spin current. Nat. Commun. 12, 2846 (2021).

Article 
CAS 
PubMed 
PubMed Central 

Google Scholar
 

Egorov, S. A. & Evarestov, R. A. Colossal spin splitting in the monolayer of the collinear antiferromagnet MnF2. J. Phys. Chem. Lett. 12, 2363–2369 (2021).

Article 
CAS 
PubMed 

Google Scholar
 

Cui, Q., Zhu, Y., Yao, X., Cui, P. & Yang, H. Giant spin-Hall and tunneling magnetoresistance effects based on a two-dimensional nonrelativistic antiferromagnetic metal. Phys. Rev. B 108, 024410 (2023).

Article 
CAS 

Google Scholar
 

Chen, X., Wang, D., Li, L. & Sanyal, B. Giant spin-splitting and tunable spin-momentum locked transport in room temperature collinear antiferromagnetic semimetallic CrO monolayer. Appl. Phys. Lett. 123, 022402 (2023).

Sødequist, J. & Olsen, T. Two-dimensional altermagnets from high throughput computational screening: symmetry requirements, chiral magnons, and spin–orbit effects. Appl. Phys. Lett. 124, 182409 (2024).

Article 

Google Scholar
 

Zhu, Y.-P. et al. Observation of plaid-like spin splitting in a noncoplanar antiferromagnet. Nature 626, 523–528 (2024).

Article 
CAS 
PubMed 

Google Scholar
 

Zhu, Y. et al. Multipiezo effect in altermagnetic V2SeTeO monolayer. Nano Lett. 24, 472–478 (2024).

Article 
CAS 
PubMed 

Google Scholar
 

Wigner, E. Ueber die Operation der Zeitumkehr in der Quantenmechanik. Nachr. Ges. Wiss. Gott. Math. Phys. Kl. 1932, 546–559 (1932).


Google Scholar
 

Tang, P., Zhou, Q., Xu, G. & Zhang, S.-C. Dirac fermions in an antiferromagnetic semimetal. Nat. Phys. 12, 1100–1104 (2016).

Article 
CAS 

Google Scholar
 

Šmejkal, L., Železný, J., Sinova, J. & Jungwirth, T. Electric control of Dirac quasiparticles by spin–orbit torque in an antiferromagnet. Phys. Rev. Lett. 118, 106402 (2017).

Article 
PubMed 

Google Scholar
 

Šmejkal, L., Mokrousov, Y., Yan, B. & MacDonald, A. H. Topological antiferromagnetic spintronics. Nat. Phys. 14, 242–251 (2018).

Article 

Google Scholar
 

Kübler, J. & Felser, C. Non-collinear antiferromagnets and the anomalous Hall effect. Europhys. Lett. 108, 67001 (2014).

Article 

Google Scholar
 

Nakatsuji, S., Kiyohara, N. & Higo, T. Large anomalous Hall effect in a non-collinear antiferromagnet at room temperature. Nature 527, 212–215 (2015). This paper reported the experimental observation of the anomalous Hall effect in a non-collinear compensated magnet.

Article 
CAS 
PubMed 

Google Scholar
 

Kiyohara, N., Tomita, T. & Nakatsuji, S. Giant anomalous Hall effect in the chiral antiferromagnet Mn3Ge. Phys. Rev. Appl. 5, 064009 (2016).

Article 

Google Scholar
 

Nayak, A. K. et al. Large anomalous Hall effect driven by a nonvanishing Berry curvature in the noncolinear antiferromagnet Mn3Ge. Sci. Adv. 2, e1501870 (2016).

Article 
PubMed 
PubMed Central 

Google Scholar
 

Takagi, H. et al. Spontaneous topological Hall effect induced by non-coplanar antiferromagnetic order in intercalated van der Waals materials. Nat. Phys. 19, 961–968 (2023).

Article 
CAS 

Google Scholar
 

Ikhlas, M. et al. Large anomalous Nernst effect at room temperature in a chiral antiferromagnet. Nat. Phys. 13, 1085–1090 (2017).

Article 
CAS 

Google Scholar
 

Li, X. et al. Anomalous Nernst and Righi-Leduc effects in Mn3Sn: Berry curvature and entropy flow. Phys. Rev. Lett. 119, 056601 (2017).

Article 
PubMed 

Google Scholar
 

Higo, T. et al. Large magneto-optical Kerr effect and imaging of magnetic octupole domains in an antiferromagnetic metal. Nat. Photon. 12, 73–78 (2018).

Article 
CAS 

Google Scholar
 

Matsuda, T., Kanda, N., Higo, T. & Matsunaga, R. Room-temperature terahertz anomalous Hall effect in Weyl antiferromagnet Mn3Sn thin films. Nat. Commun. 11, 909 (2020).

Article 
CAS 
PubMed 
PubMed Central 

Google Scholar
 

Kimata, M. et al. X-ray study of ferroic octupole order producing anomalous Hall effect. Nat. Commun. 12, 5582 (2021).

Article 
CAS 
PubMed 
PubMed Central 

Google Scholar
 

Sakamoto, S. et al. Observation of spontaneous X-ray magnetic circular dichroism in a chiral antiferromagnet. Phys. Rev. B 104, 134431 (2021).

Article 
CAS 

Google Scholar
 

Železný, J., Zhang, Y., Felser, C. & Yan, B. Spin-polarized current in noncollinear antiferromagnets. Phys. Rev. Lett. 119, 187204 (2017).

Article 
PubMed 

Google Scholar
 

Zhang, Y., Železný, J., Sun, Y., van den Brink, J. & Yan, B. Spin Hall effect emerging from a noncollinear magnetic lattice without spin–orbit coupling. New J. Phys. 20, 073028 (2018).

Article 

Google Scholar
 

Kimata, M. et al. Magnetic and magnetic inverse spin Hall effects in a non-collinear antiferromagnet. Nature 565, 627–630 (2019).

Article 
CAS 
PubMed 

Google Scholar
 

Hu, S. et al. Efficient perpendicular magnetization switching by a magnetic spin Hall effect in a noncollinear antiferromagnet. Nat. Commun. 13, 4447 (2022).

Article 
CAS 
PubMed 
PubMed Central 

Google Scholar
 

Tsai, H. et al. Electrical manipulation of a topological antiferromagnetic state. Nature 580, 608–613 (2020).

Article 
CAS 
PubMed 

Google Scholar
 

Takeuchi, Y. et al. Chiral-spin rotation of non-collinear antiferromagnet by spin–orbit torque. Nat. Mater. 20, 1364–1370 (2021).

Article 
CAS 
PubMed 

Google Scholar
 

Higo, T. et al. Perpendicular full switching of chiral antiferromagnetic order by current. Nature 607, 474–479 (2022).

Article 
CAS 
PubMed 

Google Scholar
 

Pal, B. et al. Setting of the magnetic structure of chiral kagome antiferromagnets by a seeded spin–orbit torque. Sci. Adv. 8, eabo5930 (2022).

Article 
CAS 
PubMed 
PubMed Central 

Google Scholar
 

Chen, X. et al. Octupole-driven magnetoresistance in an antiferromagnetic tunnel junction. Nature 613, 490–495 (2023).

Article 
CAS 
PubMed 
PubMed Central 

Google Scholar
 

Qin, P. et al. Room-temperature magnetoresistance in an all-antiferromagnetic tunnel junction. Nature 613, 485–489 (2023).

Article 
CAS 
PubMed 

Google Scholar
 

Nakatsuji, S. & Arita, R. Topological magnets: functions based on Berry phase and multipoles. Annu. Rev. Condensed Matter Phys. 13, 119–142 (2022).

Rimmler, B. H., Pal, B. & Parkin, S. S. P. Non-collinear antiferromagnetic spintronics. Nat. Rev. Mater. 10, 109–127 (2024).

Han, J., Yoon, J.-Y., Ohno, H. & Fukami, S. Unconventional responses in non-collinear antiferromagnets. Newton 1, 100012 (2025).

Article 

Google Scholar
 

Brekke, B., Sukhachov, P., Giil, H. G., Brataas, A. & Linder, J. Minimal models and transport properties of unconventional p-wave magnets. Phys. Rev. Lett. 133, 236703 (2024).

Article 
MathSciNet 
CAS 
PubMed 

Google Scholar
 

Ezawa, M. Topological insulators and superconductors based on p-wave magnets: electrical control and detection of a domain wall. Phys. Rev. B 110, 165429 (2024).

Article 
CAS 

Google Scholar
 

Sivianes, J., dos Santos, F. J. & Ibañez-Azpiroz, J. Optical signatures of spin symmetries in unconventional magnets. Phys. Rev. Lett. 134, 196907 (2025).

Article 
CAS 
PubMed 

Google Scholar
 

Chakraborty, A. et al. Highly efficient non-relativistic Edelstein effect in p-wave magnets. Nat. Commun. 16, 7270 (2023).

Article 

Google Scholar
 

Yu, Y. et al. Odd-parity magnetism driven by antiferromagnetic exchange. Phys. Rev. Lett. 135, 046701 (2025).

Wang, M. et al. Emergent zero-field anomalous Hall effect in a reconstructed rutile antiferromagnetic metal. Nat. Commun. 14, 8240 (2023).

Article 
CAS 
PubMed 
PubMed Central 

Google Scholar
 

Han, L. et al. Electrical 180° switching of Néel vector in spin-splitting antiferromagnet. Sci. Adv. 10, eadn0479 (2024).

Article 
CAS 
PubMed 
PubMed Central 

Google Scholar
 

Takagi, R. et al. Spontaneous Hall effect induced by collinear antiferromagnetic order at room temperature. Nat. Mater. 24, 63–68 (2025).

Article 
CAS 
PubMed 

Google Scholar
 

Ray, M. K. et al. Zero-field Hall effect emerging from a non-Fermi liquid in a collinear antiferromagnet V1/3NbS2. Nat. Commun. 16, 3532 (2025).

Article 
CAS 
PubMed 
PubMed Central 

Google Scholar
 

Fakhredine, A., Sattigeri, R. M., Cuono, G. & Autieri, C. Interplay between altermagnetism and nonsymmorphic symmetries generating large anomalous Hall conductivity by semi-Dirac points induced anticrossings. Phys. Rev. B 108, 115138 (2023).

Article 
CAS 

Google Scholar
 

Fang, Y., Cano, J. & Ghorashi, S. A. A. Quantum geometry induced nonlinear transport in altermagnets. Phys. Rev. Lett. 133, 106701 (2024).

Article 
MathSciNet 
CAS 
PubMed 

Google Scholar
 

Li, Y.-X., Liu, Y. & Liu, C.-C. Creation and manipulation of higher-order topological states by altermagnets. Phys. Rev. B 109, L201109 (2024).

Article 
CAS 

Google Scholar
 

Zhou, X. et al. Crystal thermal transport in altermagnetic RuO2. Phys. Rev. Lett.s 132, 056701 (2024).

Article 
CAS 

Google Scholar
 

Zhan, J., Li, J., Shi, W., Chen, X. Q. & Sun, Y. Coexistence of Weyl semimetal and Weyl nodal loop semimetal phases in a collinear antiferromagnet. Phys. Rev. B 107, 224402 (2023).

Article 
CAS 

Google Scholar
 

Nag, J. et al. GdAlSi: an antiferromagnetic topological Weyl semimetal with nonrelativistic spin splitting. Phys. Rev. B 110, 224436 (2024).

Article 
CAS 

Google Scholar
 

Parshukov, K., Wiedmann, R. & Schnyder, A. P. Topological responses from gapped Weyl points in 2D altermagnets. Phys. Rev. B 111, 224406 (2025).

Rao, P., Mook, A. & Knolle, J. Tunable band topology and optical conductivity in altermagnets. Phys. Rev. B 110, 024425 (2024).

Article 
CAS 

Google Scholar
 

Tao, L. L. & Tsymbal, E. Y. Persistent spin texture enforced by symmetry. Nat. Commun. 9, 2763 (2018).

Article 
CAS 
PubMed 
PubMed Central 

Google Scholar
 

Ji, J., Lou, F., Yu, R., Feng, J. S. & Xiang, H. J. Symmetry-protected full-space persistent spin texture in two-dimensional materials. Phys. Rev. B 105, L041404 (2022).

Article 
CAS 

Google Scholar
 

Bernevig, B. A., Orenstein, J. & Zhang, S. C. Exact SU(2) symmetry and persistent spin helix in a spin–orbit coupled system. Phys. Rev. Lett. 97, 236601 (2006).

Article 
PubMed 

Google Scholar
 

Koralek, J. D. et al. Emergence of the persistent spin helix in semiconductor quantum wells. Nature 458, 610–613 (2009).

Article 
CAS 
PubMed 

Google Scholar
 

Kuroda, K. et al. Evidence for magnetic Weyl fermions in a correlated metal. Nat. Mater. 16, 1090–1095 (2017).

Article 
CAS 
PubMed 

Google Scholar
 

Liu, Z. Q. et al. Electrical switching of the topological anomalous Hall effect in a non-collinear antiferromagnet above room temperature. Nat. Electron. 1, 172–177 (2018).

Article 
CAS 

Google Scholar
 

Xu, L. et al. Finite-temperature violation of the anomalous transverse Wiedemann–Franz law. Sci. Adv. 6, eaaz3522 (2020).

Article 
CAS 
PubMed 
PubMed Central 

Google Scholar
 

Chen, T. et al. Anomalous transport due to Weyl fermions in the chiral antiferromagnets Mn3X, X = Sn, Ge. Nat. Commun. 12, 572 (2021).

Article 
PubMed 
PubMed Central 

Google Scholar
 

Ghosh, S. et al. Raman spectroscopic evidence for linearly dispersed nodes and magnetic ordering in the topological semimetal V1/3NbS2. Preprint at http://arxiv.org/abs/2504.04590 (2025).

Sun, K., Yao, H., Fradkin, E. & Kivelson, S. A. Topological insulators and nematic phases from spontaneous symmetry breaking in 2D Fermi systems with a quadratic band crossing. Phys. Rev. Lett. 103, 046811 (2009).

Article 
PubMed 

Google Scholar
 

Steward, C. R. W., Fernandes, R. M. & Schmalian, J. Dynamic paramagnon-polarons in altermagnets. Phys. Rev. B 108, 144418 (2023).

Article 
CAS 

Google Scholar
 

Martin, I. & Batista, C. D. Itinerant electron-driven chiral magnetic ordering and spontaneous quantum Hall effect in triangular lattice models. Phys. Rev. Lett. 101, 156402 (2008).

Article 
PubMed 

Google Scholar
 

MAGNDATA: A Collection of Magnetic Structures with Portable cif-type Files. https://www.cryst.ehu.es/magndata/.