{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,11,7]],"date-time":"2026-11-07T03:30:59Z","timestamp":1794022259026,"version":"4.8.0"},"reference-count":200,"publisher":"Springer Science and Business Media LLC","issue":"8098","license":[{"start":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T00:00:00Z","timestamp":1768953600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T00:00:00Z","timestamp":1768953600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Nature"],"published-print":{"date-parts":[[2026,1,22]]},"DOI":"10.1038\/s41586-025-09883-2","type":"journal-article","created":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T16:02:40Z","timestamp":1769011360000},"page":"837-847","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":67,"title":["Symmetry, microscopy and spectroscopy signatures of altermagnetism"],"prefix":"10.1038","volume":"649","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9910-1674","authenticated-orcid":false,"given":"Tomas","family":"Jungwirth","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9490-2333","authenticated-orcid":false,"given":"Jairo","family":"Sinova","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3584-5180","authenticated-orcid":false,"given":"Rafael M.","family":"Fernandes","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9843-2482","authenticated-orcid":false,"given":"Qihang","family":"Liu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hikaru","family":"Watanabe","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shuichi","family":"Murakami","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Satoru","family":"Nakatsuji","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1193-1372","authenticated-orcid":false,"given":"Libor","family":"\u0160mejkal","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,1,21]]},"reference":[{"key":"9883_CR1","first-page":"031042","volume":"12","author":"L \u0160mejkal","year":"2022","unstructured":"\u0160mejkal, 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.","journal-title":"Phys. Rev. X"},{"key":"9883_CR2","first-page":"040501","volume":"12","author":"L \u0160mejkal","year":"2022","unstructured":"\u0160mejkal, L., Sinova, J. & Jungwirth, T. Emerging research landscape of altermagnetism. Phys. Rev. X 12, 040501 (2022). This perspective outlined envisaged research directions of altermagnetism.","journal-title":"Phys. Rev. X"},{"key":"9883_CR3","doi-asserted-by":"publisher","first-page":"eaaz8809","DOI":"10.1126\/sciadv.aaz8809","volume":"6","author":"L \u0160mejkal","year":"2020","unstructured":"\u0160mejkal, L., Gonz\u00e1lez-Hern\u00e1ndez, 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\u2013orbit coupling is included, to the anomalous Hall effect.","journal-title":"Sci. Adv."},{"key":"9883_CR4","doi-asserted-by":"publisher","first-page":"100162","DOI":"10.1016\/j.newton.2025.100162","volume":"1","author":"T Jungwirth","year":"2025","unstructured":"Jungwirth, T. et al. Altermagnetism: an unconventional spin-ordered phase of matter. Newton 1, 100162 (2025).","journal-title":"Newton"},{"key":"9883_CR5","doi-asserted-by":"publisher","first-page":"18","DOI":"10.1007\/s43673-025-00158-6","volume":"35","author":"II Mazin","year":"2025","unstructured":"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.","journal-title":"AAPPS Bull."},{"key":"9883_CR6","doi-asserted-by":"publisher","first-page":"075425","DOI":"10.1103\/PhysRevB.108.075425","volume":"108","author":"CWJ Beenakker","year":"2023","unstructured":"Beenakker, C. W. J. & Vakhtel, T. Phase-shifted Andreev levels in an altermagnet Josephson junction. Phys. Rev. B 108, 075425 (2023).","journal-title":"Phys. Rev. B"},{"key":"9883_CR7","unstructured":"Mazin, I., Gonz\u00e1lez-Hern\u00e1ndez, R. & \u0160mejkal, L. Induced monolayer altermagnetism in MnP(S,Se)3 and FeSe. Preprint at http:\/\/arxiv.org\/abs\/2309.02355 (2023)."},{"key":"9883_CR8","doi-asserted-by":"publisher","first-page":"224421","DOI":"10.1103\/PhysRevB.108.224421","volume":"108","author":"B Brekke","year":"2023","unstructured":"Brekke, B., Brataas, A. & Sudb\u00f8, A. Two-dimensional altermagnets: superconductivity in a minimal microscopic model. Phys. Rev. B 108, 224421 (2023).","journal-title":"Phys. Rev. B"},{"key":"9883_CR9","doi-asserted-by":"publisher","first-page":"205410","DOI":"10.1103\/PhysRevB.108.205410","volume":"108","author":"Y-X Li","year":"2023","unstructured":"Li, Y.-X. & Liu, C.-C. Majorana corner modes and tunable patterns in an altermagnet heterostructure. Phys. Rev. B 108, 205410 (2023).","journal-title":"Phys. Rev. B"},{"key":"9883_CR10","doi-asserted-by":"publisher","first-page":"184505","DOI":"10.1103\/PhysRevB.108.184505","volume":"108","author":"D Zhu","year":"2023","unstructured":"Zhu, D., Zhuang, Z.-Y., Wu, Z. & Yan, Z. Topological superconductivity in two-dimensional altermagnetic metals. Phys. Rev. B 108, 184505 (2023).","journal-title":"Phys. Rev. B"},{"key":"9883_CR11","doi-asserted-by":"publisher","first-page":"043171","DOI":"10.1103\/PhysRevResearch.5.043171","volume":"5","author":"S Sumita","year":"2023","unstructured":"Sumita, S., Naka, M. & Seo, H. Fulde\u2013Ferrell\u2013Larkin\u2013Ovchinnikov state induced by antiferromagnetic order in k-type organic conductors. Phys. Rev. Res. 5, 043171 (2023).","journal-title":"Phys. Rev. Res."},{"key":"9883_CR12","doi-asserted-by":"publisher","first-page":"106601","DOI":"10.1103\/PhysRevLett.133.106601","volume":"133","author":"SAA Ghorashi","year":"2024","unstructured":"Ghorashi, S. A. A., Hughes, T. L. & Cano, J. Altermagnetic routes to Majorana modes in zero net magnetization. Phys. Rev. Lett. 133, 106601 (2024).","journal-title":"Phys. Rev. Lett."},{"key":"9883_CR13","doi-asserted-by":"publisher","first-page":"L060508","DOI":"10.1103\/PhysRevB.108.L060508","volume":"108","author":"M Papaj","year":"2023","unstructured":"Papaj, M. Andreev reflection at the altermagnet-superconductor interface. Phys. Rev. B 108, L060508 (2023).","journal-title":"Phys. Rev. B"},{"key":"9883_CR14","doi-asserted-by":"publisher","first-page":"L201404","DOI":"10.1103\/PhysRevB.109.L201404","volume":"109","author":"M Wei","year":"2023","unstructured":"Wei, M. et al. Gapless superconducting state and mirage gap in altermagnets. Phys. Rev. B 109, L201404 (2023).","journal-title":"Phys. Rev. B"},{"key":"9883_CR15","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-024-45951-3","volume":"15","author":"S-B Zhang","year":"2024","unstructured":"Zhang, S.-B., Hu, L.-H. & Neupert, T. Finite-momentum Cooper pairing in proximitized altermagnets. Nat. Commun. 15, 1801 (2024).","journal-title":"Nat. Commun."},{"key":"9883_CR16","doi-asserted-by":"publisher","first-page":"024517","DOI":"10.1103\/PhysRevB.109.024517","volume":"109","author":"Q Cheng","year":"2024","unstructured":"Cheng, Q. & Sun, Q.-F. Orientation-dependent Josephson effect in spin-singlet superconductor\/altermagnet\/spin-triplet superconductor junctions. Phys. Rev. B 109, 024517 (2024).","journal-title":"Phys. Rev. B"},{"key":"9883_CR17","doi-asserted-by":"publisher","first-page":"205111","DOI":"10.1103\/PhysRevB.110.205111","volume":"110","author":"Y Zhao","year":"2024","unstructured":"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).","journal-title":"Phys. Rev. B"},{"key":"9883_CR18","doi-asserted-by":"publisher","first-page":"134515","DOI":"10.1103\/PhysRevB.109.134515","volume":"109","author":"K M\u00e6land","year":"2024","unstructured":"M\u00e6land, K., Brekke, B. & Sudb\u00f8, A. Many-body effects on superconductivity mediated by double-magnon processes in altermagnets. Phys. Rev. B 109, 134515 (2024).","journal-title":"Phys. Rev. B"},{"key":"9883_CR19","doi-asserted-by":"publisher","first-page":"L060508","DOI":"10.1103\/PhysRevB.110.L060508","volume":"110","author":"D Chakraborty","year":"2024","unstructured":"Chakraborty, D. & Black-Schaffer, A. M. Zero-field finite-momentum and field-induced superconductivity in altermagnets. Phys. Rev. B 110, L060508 (2024).","journal-title":"Phys. Rev. B"},{"key":"9883_CR20","doi-asserted-by":"publisher","first-page":"024503","DOI":"10.1103\/PhysRevB.110.024503","volume":"110","author":"S Banerjee","year":"2024","unstructured":"Banerjee, S. & Scheurer, M. S. Altermagnetic superconducting diode effect. Phys. Rev. B 110, 024503 (2024).","journal-title":"Phys. Rev. B"},{"key":"9883_CR21","doi-asserted-by":"publisher","first-page":"L220412","DOI":"10.1103\/PhysRevB.109.L220412","volume":"109","author":"HO Jeschke","year":"2024","unstructured":"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).","journal-title":"Phys. Rev. B"},{"key":"9883_CR22","doi-asserted-by":"publisher","first-page":"L042018","DOI":"10.1103\/PhysRevResearch.5.L042018","volume":"5","author":"XH Verbeek","year":"2023","unstructured":"Verbeek, X. H., Urru, A. & Spaldin, N. A. Hidden orders and (anti-)magnetoelectric effects in Cr2O3 and Fe2O3. Phys. Rev. Res. 5, L042018 (2023).","journal-title":"Phys. Rev. Res."},{"key":"9883_CR23","doi-asserted-by":"crossref","unstructured":"Bernardini, F., Fiebig, M. & Cano, A. Ruddlesden\u2013Popper and perovskite phases as a material platform for altermagnetism. J. Appl. Phys. 137, 103903 (2025).","DOI":"10.1063\/5.0252836"},{"key":"9883_CR24","doi-asserted-by":"publisher","first-page":"L220505","DOI":"10.1103\/PhysRevB.109.L220505","volume":"109","author":"AA Zyuzin","year":"2024","unstructured":"Zyuzin, A. A. Magnetoelectric effect in superconductors with d-wave magnetization. Phys. Rev. B 109, L220505 (2024).","journal-title":"Phys. Rev. B"},{"key":"9883_CR25","doi-asserted-by":"publisher","first-page":"L020502","DOI":"10.1103\/b7rh-v7nq","volume":"112","author":"G Sim","year":"2025","unstructured":"Sim, G. & Knolle, J. Pair density waves and supercurrent diode effect in altermagnets. Phys. Rev. B 112, L020502 (2025).","journal-title":"Phys. Rev. B"},{"key":"9883_CR26","doi-asserted-by":"publisher","first-page":"026001","DOI":"10.1103\/PhysRevLett.134.026001","volume":"134","author":"J-X Hu","year":"2025","unstructured":"Hu, J.-X., Matsyshyn, O. & Song, J. C. W. Nonlinear superconducting magnetoelectric effect. Phys. Rev. Lett. 134, 026001 (2025).","journal-title":"Phys. Rev. Lett."},{"key":"9883_CR27","unstructured":"\u0160mejkal, 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."},{"key":"9883_CR28","doi-asserted-by":"publisher","first-page":"106801","DOI":"10.1103\/PhysRevLett.134.106801","volume":"134","author":"X Duan","year":"2025","unstructured":"Duan, X. et al. Antiferroelectric altermagnets: antiferroelectricity alters magnets. Phys. Rev. Lett. 134, 106801 (2025).","journal-title":"Phys. Rev. Lett."},{"key":"9883_CR29","doi-asserted-by":"publisher","first-page":"106802","DOI":"10.1103\/PhysRevLett.134.106802","volume":"134","author":"M Gu","year":"2024","unstructured":"Gu, M. et al. Ferroelectric switchable altermagnetism. Phys. Rev. Lett. 134, 106802 (2024).","journal-title":"Phys. Rev. Lett."},{"key":"9883_CR30","doi-asserted-by":"crossref","unstructured":"Parthenios, N. et al. Spin and pair density waves in two-dimensional altermagnetic metals. Phys. Rev. B 112, 214410 (2025).","DOI":"10.1103\/llrq-1k9k"},{"key":"9883_CR31","doi-asserted-by":"publisher","first-page":"482","DOI":"10.1038\/s41578-022-00430-3","volume":"7","author":"L \u0160mejkal","year":"2022","unstructured":"\u0160mejkal, L., MacDonald, A. H., Sinova, J., Nakatsuji, S. & Jungwirth, T. Anomalous Hall antiferromagnets. Nat. Rev. Mater. 7, 482\u2013496 (2022). This paper reviewed the anomalous Hall effect in altermagnets and non-collinear compensated magnets.","journal-title":"Nat. Rev. Mater."},{"key":"9883_CR32","doi-asserted-by":"crossref","unstructured":"Bai, L. et al. Altermagnetism: exploring new frontiers in magnetism and spintronics. Adv. Funct. Mater. 34, 2409327 (2024).","DOI":"10.1002\/adfm.202409327"},{"key":"9883_CR33","doi-asserted-by":"publisher","first-page":"329","DOI":"10.1038\/s41567-024-02750-3","volume":"21","author":"Q Liu","year":"2025","unstructured":"Liu, Q., Dai, X. & Bl\u00fcgel, S. Different facets of unconventional magnetism. Nat. Phys. 21, 329\u2013331 (2025).","journal-title":"Nat. Phys."},{"key":"9883_CR34","doi-asserted-by":"crossref","unstructured":"Song, C. et al. Altermagnets as a new class of functional materials. Nat. Rev. Mater. 10, 473\u2013485 (2025).","DOI":"10.1038\/s41578-025-00779-1"},{"key":"9883_CR35","unstructured":"Jungwirth, T. et al. Altermagnetic spintronics. Preprint at http:\/\/arxiv.org\/abs\/2508.09748 (2025)."},{"key":"9883_CR36","first-page":"21016","volume":"12","author":"P Liu","year":"2022","unstructured":"Liu, P., Li, J., Han, J., Wan, X. & Liu, Q. Spin-group symmetry in magnetic materials with negligible spin\u2013orbit 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.","journal-title":"Phys. Rev. X"},{"key":"9883_CR37","doi-asserted-by":"publisher","first-page":"538","DOI":"10.1016\/0031-8914(74)90157-8","volume":"76","author":"DB Litvin","year":"1974","unstructured":"Litvin, D. B. & Opechowski, W. Spin groups. Physica 76, 538\u2013554 (1974). This paper describes the mathematical spin-group formalism.","journal-title":"Physica"},{"key":"9883_CR38","first-page":"267","volume":"60","author":"A Andreev","year":"1984","unstructured":"Andreev, A. & Grishchuk, I. Spin nematics. Sov. Phys. JETP 60, 267 (1984).","journal-title":"Sov. Phys. JETP"},{"key":"9883_CR39","doi-asserted-by":"publisher","first-page":"2586","DOI":"10.1103\/PhysRevLett.69.2586","volume":"69","author":"LP Gor\u2019kov","year":"1992","unstructured":"Gor\u2019kov, L. P. & Sokol, A. Nontrivial magnetic order: localized versus itinerant systems. Phys. Rev. Lett. 69, 2586\u20132589 (1992).","journal-title":"Phys. Rev. Lett."},{"key":"9883_CR40","doi-asserted-by":"publisher","first-page":"999","DOI":"10.1103\/RevModPhys.76.999","volume":"76","author":"AJ Leggett","year":"2004","unstructured":"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.","journal-title":"Rev. Mod. Phys."},{"key":"9883_CR41","doi-asserted-by":"crossref","unstructured":"Moessner, R. & Moore, J. E. Topological Phases of Matter (Cambridge Univ. Press, 2021).","DOI":"10.1017\/9781316226308"},{"key":"9883_CR42","doi-asserted-by":"crossref","unstructured":"Strange, P. Relativistic Quantum Mechanics 1 edn (Cambridge Univ. Press, Cambridge, 1998).","DOI":"10.1017\/CBO9780511622755"},{"key":"9883_CR43","doi-asserted-by":"crossref","unstructured":"Winkler, R. Spin\u2013Orbit Coupling Effects in Two-Dimensional Electron and Hole Systems Springer Tracts in Modern Physics Vol. 191 (Springer, 2003).","DOI":"10.1007\/b13586"},{"key":"9883_CR44","unstructured":"Landau, L. & Lifshitz, E. Electrodynamics of Continuous Media 2 edn, Course of Theoretical Physics Vol. 8 (Pergamon Press, 1965)."},{"key":"9883_CR45","doi-asserted-by":"publisher","first-page":"1213","DOI":"10.1103\/RevModPhys.87.1213","volume":"87","author":"J Sinova","year":"2015","unstructured":"Sinova, J., Valenzuela, S. O., Wunderlich, J., Back, C. H. & Jungwirth, T. Spin Hall effects. Rev. Mod. Phys. 87, 1213\u20131260 (2015).","journal-title":"Rev. Mod. Phys."},{"key":"9883_CR46","doi-asserted-by":"publisher","first-page":"1539","DOI":"10.1103\/RevModPhys.82.1539","volume":"82","author":"N Nagaosa","year":"2010","unstructured":"Nagaosa, N., Sinova, J., Onoda, S., MacDonald, A. H. & Ong, N. P. Anomalous Hall effect. Rev. Mod. Phys. 82, 1539\u20131592 (2010).","journal-title":"Rev. Mod. Phys."},{"key":"9883_CR47","unstructured":"Franz, M. & Molenkamp, L. (eds) Contemporary Concepts of Condensed Matter Science Topological Insulators Vol. 6 (Elsevier, 2013)."},{"key":"9883_CR48","doi-asserted-by":"crossref","unstructured":"Murakami, S. & Yokoyama, T. Quantum Spin Hall Effect and Topological Insulators Vol. 1 (Oxford Univ. Press, 2017).","DOI":"10.1093\/oso\/9780198787075.003.0017"},{"key":"9883_CR49","doi-asserted-by":"publisher","first-page":"298","DOI":"10.1038\/nature23268","volume":"547","author":"B Bradlyn","year":"2017","unstructured":"Bradlyn, B. et al. Topological quantum chemistry. Nature 547, 298\u2013305 (2017).","journal-title":"Nature"},{"key":"9883_CR50","doi-asserted-by":"publisher","first-page":"015001","DOI":"10.1103\/RevModPhys.90.015001","volume":"90","author":"NP Armitage","year":"2018","unstructured":"Armitage, N. P., Mele, E. J. & Vishwanath, A. Weyl and Dirac semimetals in three-dimensional solids. Rev. Mod. Phys. 90, 015001 (2018).","journal-title":"Rev. Mod. Phys."},{"key":"9883_CR51","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-021-26241-8","volume":"12","author":"L Elcoro","year":"2021","unstructured":"Elcoro, L. et al. Magnetic topological quantum chemistry. Nat. Commun. 12, 5965 (2021).","journal-title":"Nat. Commun."},{"key":"9883_CR52","doi-asserted-by":"publisher","first-page":"e2108924118","DOI":"10.1073\/pnas.2108924118","volume":"118","author":"II Mazin","year":"2021","unstructured":"Mazin, I. I., Koepernik, K., Johannes, M. D., Gonz\u00e1lez-Hern\u00e1ndez, R. & \u0160mejkal, L. Prediction of unconventional magnetism in doped FeSb2. Proc. Natl Acad. Sci. USA 118, e2108924118 (2021).","journal-title":"Proc. Natl Acad. Sci. USA"},{"key":"9883_CR53","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-024-48493-w","volume":"15","author":"H Reichlova","year":"2024","unstructured":"Reichlova, H. et al. Observation of a spontaneous anomalous Hall response in the Mn5Si d-wave altermagnet candidate. Nat. Commun. 15, 4961 (2024).","journal-title":"Nat. Commun."},{"key":"9883_CR54","first-page":"011028","volume":"12","author":"L \u0160mejkal","year":"2022","unstructured":"\u0160mejkal, L., Hellenes, A. B., Gonz\u00e1lez-Hern\u00e1ndez, R., Sinova, J. & Jungwirth, T. Giant and tunneling magnetoresistance in unconventional collinear antiferromagnets with nonrelativistic spin\u2013momentum coupling. Phys. Rev. X 12, 011028 (2022).","journal-title":"Phys. Rev. X"},{"key":"9883_CR55","doi-asserted-by":"publisher","first-page":"036702","DOI":"10.1103\/PhysRevLett.130.036702","volume":"130","author":"RD Gonzalez Betancourt","year":"2023","unstructured":"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).","journal-title":"Phys. Rev. Lett."},{"key":"9883_CR56","doi-asserted-by":"publisher","first-page":"256703","DOI":"10.1103\/PhysRevLett.131.256703","volume":"131","author":"L \u0160mejkal","year":"2023","unstructured":"\u0160mejkal, L. et al. Chiral magnons in altermagnetic RuO2. Phys. Rev. Lett. 131, 256703 (2023).","journal-title":"Phys. Rev. Lett."},{"key":"9883_CR57","doi-asserted-by":"publisher","first-page":"349","DOI":"10.1038\/s41586-025-08715-7","volume":"640","author":"X Chen","year":"2025","unstructured":"Chen, X. et al. Unconventional magnons in collinear magnets dictated by spin space groups. Nature 640, 349\u2013354 (2025).","journal-title":"Nature"},{"key":"9883_CR58","doi-asserted-by":"publisher","first-page":"176701","DOI":"10.1103\/PhysRevLett.132.176701","volume":"132","author":"A Hariki","year":"2024","unstructured":"Hariki, A. et al. X-ray magnetic circular dichroism in altermagnetic \u03b1-MnTe. Phys. Rev. Lett. 132, 176701 (2024).","journal-title":"Phys. Rev. Lett."},{"key":"9883_CR59","unstructured":"Hellenes, A. B. et al. P-wave magnets. Preprint at http:\/\/arxiv.org\/abs\/2309.01607 (2023)."},{"key":"9883_CR60","unstructured":"Hellenes, A. B., Jungwirth, T., Sinova, J. & \u0160mejkal, L. Exchange spin\u2013orbit coupling and unconventional p-wave magnetism. Preprint at http:\/\/arxiv.org\/abs\/2309.01607v1 (2023)."},{"key":"9883_CR61","doi-asserted-by":"publisher","first-page":"176702","DOI":"10.1103\/PhysRevLett.132.176702","volume":"132","author":"PA McClarty","year":"2023","unstructured":"McClarty, P. A. & Rau, J. G. Landau theory of altermagnetism. Phys. Rev. Lett. 132, 176702 (2023).","journal-title":"Phys. Rev. Lett."},{"key":"9883_CR62","first-page":"1","volume":"30","author":"A Smolyanyuk","year":"2024","unstructured":"Smolyanyuk, A., \u0160mejkal, L. & Mazin, I. I. A tool to check whether a symmetry-compensated collinear magnetic material is antiferro- or altermagnetic. SciPost Phys. Codebases 30, 1\u201316 (2024).","journal-title":"SciPost Phys. Codebases"},{"key":"9883_CR63","doi-asserted-by":"publisher","first-page":"94","DOI":"10.1107\/S2053273323009257","volume":"80","author":"K Shinohara","year":"2024","unstructured":"Shinohara, K. et al. Algorithm for spin symmetry operation search. Acta Crystallogr. A 80, 94\u2013103 (2024).","journal-title":"Acta Crystallogr. A"},{"key":"9883_CR64","doi-asserted-by":"publisher","first-page":"094438","DOI":"10.1103\/PhysRevB.109.094438","volume":"109","author":"H Watanabe","year":"2024","unstructured":"Watanabe, H., Shinohara, K., Nomoto, T., Togo, A. & Arita, R. Symmetry analysis with spin crystallographic groups: disentangling effects free of spin\u2013orbit coupling in emergent electromagnetism. Phys. Rev. B 109, 094438 (2024).","journal-title":"Phys. Rev. B"},{"key":"9883_CR65","first-page":"031039","volume":"14","author":"Y Jiang","year":"2024","unstructured":"Jiang, Y. et al. Enumeration of spin-space groups: toward a complete description of symmetries of magnetic orders. Phys. Rev. X 14, 031039 (2024).","journal-title":"Phys. Rev. X"},{"key":"9883_CR66","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-025-60128-2","volume":"16","author":"H Zhu","year":"2025","unstructured":"Zhu, H., Li, J., Chen, X., Yu, Y. & Liu, Q. Magnetic geometry induced quantum geometry and nonlinear transports. Nat. Commun. 16, 4882 (2025).","journal-title":"Nat. Commun."},{"key":"9883_CR67","first-page":"031038","volume":"14","author":"X Chen","year":"2024","unstructured":"Chen, X. et al. Enumeration and representation theory of spin space groups. Phys. Rev. X 14, 031038 (2024).","journal-title":"Phys. Rev. X"},{"key":"9883_CR68","doi-asserted-by":"crossref","unstructured":"Schiff, H., Corticelli, A., Guerreiro, A., Romh\u00e1nyi, J. & McClarty, P. The crystallographic spin point groups and their representations. SciPost Phys. 18, 109 (2025).","DOI":"10.21468\/SciPostPhys.18.3.109"},{"key":"9883_CR69","first-page":"031037","volume":"14","author":"Z Xiao","year":"2024","unstructured":"Xiao, Z., Zhao, J., Li, Y., Shindou, R. & Song, Z.-D. Spin space groups: full classification and applications. Phys. Rev. X 14, 031037 (2024).","journal-title":"Phys. Rev. X"},{"key":"9883_CR70","unstructured":"Litvin, D. B. Magnetic Group Tables (IUCr, 2013). http:\/\/www.iucr.org\/publ\/978-0-9553602-2-0."},{"key":"9883_CR71","doi-asserted-by":"publisher","first-page":"077201","DOI":"10.1103\/PhysRevLett.118.077201","volume":"118","author":"T Berlijn","year":"2017","unstructured":"Berlijn, T. et al. Itinerant antiferromagnetism in RuO2. Phys. Rev. Lett. 118, 077201 (2017).","journal-title":"Phys. Rev. Lett."},{"key":"9883_CR72","doi-asserted-by":"publisher","first-page":"017202","DOI":"10.1103\/PhysRevLett.122.017202","volume":"122","author":"ZH Zhu","year":"2019","unstructured":"Zhu, Z. H. et al. Anomalous antiferromagnetism in metallic RuO2 determined by resonant X-ray scattering. Phys. Rev. Lett. 122, 017202 (2019).","journal-title":"Phys. Rev. Lett."},{"key":"9883_CR73","doi-asserted-by":"publisher","first-page":"014403","DOI":"10.1103\/PhysRevB.105.014403","volume":"105","author":"SW Lovesey","year":"2022","unstructured":"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).","journal-title":"Phys. Rev. B"},{"key":"9883_CR74","doi-asserted-by":"publisher","first-page":"033214","DOI":"10.1103\/PhysRevResearch.3.033214","volume":"3","author":"CA Occhialini","year":"2021","unstructured":"Occhialini, C. A. et al. Local electronic structure of rutile RuO2. Phys. Rev. Res. 3, 033214 (2021).","journal-title":"Phys. Rev. Res."},{"key":"9883_CR75","doi-asserted-by":"publisher","first-page":"735","DOI":"10.1038\/s41928-022-00866-z","volume":"5","author":"Z Feng","year":"2022","unstructured":"Feng, Z. et al. An anomalous Hall effect in altermagnetic ruthenium dioxide. Nat. Electron. 5, 735\u2013743 (2022).","journal-title":"Nat. Electron."},{"key":"9883_CR76","doi-asserted-by":"publisher","first-page":"267","DOI":"10.1038\/s41928-022-00744-8","volume":"5","author":"A Bose","year":"2022","unstructured":"Bose, A. et al. Tilted spin current generated by the collinear antiferromagnet ruthenium dioxide. Nat. Electron. 5, 267\u2013274 (2022).","journal-title":"Nat. Electron."},{"key":"9883_CR77","doi-asserted-by":"publisher","first-page":"197202","DOI":"10.1103\/PhysRevLett.128.197202","volume":"128","author":"H Bai","year":"2022","unstructured":"Bai, H. et al. Observation of spin splitting torque in a collinear antiferromagnet RuO2. Phys. Rev. Lett. 128, 197202 (2022).","journal-title":"Phys. Rev. Lett."},{"key":"9883_CR78","doi-asserted-by":"publisher","first-page":"137201","DOI":"10.1103\/PhysRevLett.129.137201","volume":"129","author":"S Karube","year":"2022","unstructured":"Karube, S. et al. Observation of spin-splitter torque in collinear antiferromagnetic RuO2. Phys. Rev. Lett. 129, 137201 (2022).","journal-title":"Phys. Rev. Lett."},{"key":"9883_CR79","doi-asserted-by":"publisher","first-page":"L121103","DOI":"10.1103\/PhysRevB.108.L121103","volume":"108","author":"SW Lovesey","year":"2023","unstructured":"Lovesey, S. W., Khalyavin, D. D. & van der Laan, G. Magnetic structure of RuO2 in view of altermagnetism. Phys. Rev. B 108, L121103 (2023).","journal-title":"Phys. Rev. B"},{"key":"9883_CR80","doi-asserted-by":"publisher","first-page":"2300177","DOI":"10.1002\/adom.202300177","volume":"11","author":"Y Liu","year":"2023","unstructured":"Liu, Y. et al. Inverse altermagnetic spin splitting effect-induced terahertz emission in RuO2. Adv. Opt. Mater. 11, 2300177 (2023).","journal-title":"Adv. Opt. Mater."},{"key":"9883_CR81","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1126\/sciadv.adj4883","volume":"10","author":"O Fedchenko","year":"2024","unstructured":"Fedchenko, O. et al. Observation of time-reversal symmetry breaking in the band structure of altermagnetic RuO2. Sci. Adv. 10, 31 (2024).","journal-title":"Sci. Adv."},{"key":"9883_CR82","doi-asserted-by":"publisher","first-page":"134424","DOI":"10.1103\/PhysRevB.109.134424","volume":"109","author":"A Smolyanyuk","year":"2024","unstructured":"Smolyanyuk, A., Mazin, I. I., Garcia-Gassull, L. & Valent\u00ed, R. Fragility of the magnetic order in the prototypical altermagnet RuO2. Phys. Rev. B 109, 134424 (2024).","journal-title":"Phys. Rev. B"},{"key":"9883_CR83","unstructured":"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)."},{"key":"9883_CR84","doi-asserted-by":"crossref","unstructured":"Ke\u00dfler, P. et al. Absence of magnetic order in RuO2: insights from \u03bcSR spectroscopy and neutron diffraction. npj Spintronics 2, 50 (2024).","DOI":"10.1038\/s44306-024-00055-y"},{"key":"9883_CR85","doi-asserted-by":"crossref","unstructured":"Li, Z. et al. Fully field-free spin-orbit torque switching induced by spin splitting effect in altermagnetic RuO2. Adv. Mater. 37, 2416712 (2025).","DOI":"10.1002\/adma.202416712"},{"key":"9883_CR86","doi-asserted-by":"publisher","first-page":"L041115","DOI":"10.1103\/PhysRevB.111.L041115","volume":"111","author":"M Wenzel","year":"2025","unstructured":"Wenzel, M. et al. Fermi-liquid behavior of nonaltermagnetic RuO2. Phys. Rev. B 111, L041115 (2025).","journal-title":"Phys. Rev. B"},{"key":"9883_CR87","unstructured":"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)."},{"key":"9883_CR88","doi-asserted-by":"publisher","first-page":"166702","DOI":"10.1103\/PhysRevLett.132.166702","volume":"132","author":"M Hiraishi","year":"2024","unstructured":"Hiraishi, M. et al. Nonmagnetic ground state in RuO2 revealed by muon spin rotation. Phys. Rev. Lett. 132, 166702 (2024).","journal-title":"Phys. Rev. Lett."},{"key":"9883_CR89","doi-asserted-by":"publisher","first-page":"33250","DOI":"10.1039\/C6CP05467F","volume":"18","author":"S L\u00f3pez-Moreno","year":"2016","unstructured":"L\u00f3pez-Moreno, S., Romero, A. H., Mej\u00eda-L\u00f3pez, J. & Mu\u00f1oz, A. First-principles study of pressure-induced structural phase transitions in MnF2. Phys. Chem. Chem. Phys. 18, 33250\u201333263 (2016). This paper reported density-functional-theory calculations of non-relativistic band structure of MnF2.","journal-title":"Phys. Chem. Chem. Phys."},{"key":"9883_CR90","doi-asserted-by":"publisher","first-page":"13294","DOI":"10.1039\/C5CP07806G","volume":"18","author":"Y Noda","year":"2016","unstructured":"Noda, Y., Ohno, K. & Nakamura, S. Momentum-dependent band spin splitting in semiconducting MnO2: a density functional calculation. Phys. Chem. Chem. Phys. 18, 13294\u201313303 (2016).","journal-title":"Phys. Chem. Chem. Phys."},{"key":"9883_CR91","doi-asserted-by":"publisher","first-page":"123702","DOI":"10.7566\/JPSJ.88.123702","volume":"88","author":"S Hayami","year":"2019","unstructured":"Hayami, S., Yanagi, Y. & Kusunose, H. Momentum-dependent spin splitting by collinear antiferromagnetic ordering. J. Phys. Soc. Jpn 88, 123702 (2019).","journal-title":"J. Phys. Soc. Jpn"},{"key":"9883_CR92","doi-asserted-by":"publisher","first-page":"014422","DOI":"10.1103\/PhysRevB.102.014422","volume":"102","author":"L-D Yuan","year":"2020","unstructured":"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).","journal-title":"Phys. Rev. B"},{"key":"9883_CR93","first-page":"011019","volume":"14","author":"S Bhowal","year":"2024","unstructured":"Bhowal, S. & Spaldin, N. A. Ferroically ordered magnetic octupoles in d-wave altermagnets. Phys. Rev. X 14, 011019 (2024).","journal-title":"Phys. Rev. X"},{"key":"9883_CR94","unstructured":"Jaeschke-Ubiergo, R. et al. Atomic altermagnetism. Preprint at https:\/\/arxiv.org\/pdf\/2503.10797 (2025)."},{"key":"9883_CR95","doi-asserted-by":"publisher","first-page":"174437","DOI":"10.1103\/PhysRevB.108.174437","volume":"108","author":"SW Lovesey","year":"2023","unstructured":"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).","journal-title":"Phys. Rev. B"},{"key":"9883_CR96","doi-asserted-by":"publisher","first-page":"L100418","DOI":"10.1103\/PhysRevB.107.L100418","volume":"107","author":"II Mazin","year":"2023","unstructured":"Mazin, I. I. Altermagnetism in MnTe: origin, predicted manifestations, and routes to detwinning. Phys. Rev. B 107, L100418 (2023).","journal-title":"Phys. Rev. B"},{"key":"9883_CR97","doi-asserted-by":"publisher","first-page":"517","DOI":"10.1038\/s41586-023-06907-7","volume":"626","author":"J Krempask\u00fd","year":"2024","unstructured":"Krempask\u00fd, J. et al. Altermagnetic lifting of Kramers spin degeneracy. Nature 626, 517\u2013522 (2024). This paper and refs. 99\u2013101 reported experimental spectroscopic observations of a g-wave altermagnetic band structure of MnTe.","journal-title":"Nature"},{"key":"9883_CR98","doi-asserted-by":"publisher","first-page":"036702","DOI":"10.1103\/PhysRevLett.132.036702","volume":"132","author":"SS Lee","year":"2024","unstructured":"Lee, S. S. et al. Broken Kramers degeneracy in altermagnetic MnTe. Phys. Rev. Lett. 132, 036702 (2024).","journal-title":"Phys. Rev. Lett."},{"key":"9883_CR99","doi-asserted-by":"publisher","first-page":"115102","DOI":"10.1103\/PhysRevB.109.115102","volume":"109","author":"T Osumi","year":"2024","unstructured":"Osumi, T. et al. Observation of a giant band splitting in altermagnetic MnTe. Phys. Rev. B 109, 115102 (2024).","journal-title":"Phys. Rev. B"},{"key":"9883_CR100","doi-asserted-by":"publisher","first-page":"2314076","DOI":"10.1002\/adma.202314076","volume":"36","author":"M Hajlaoui","year":"2024","unstructured":"Hajlaoui, M. et al. Temperature dependence of relativistic valence band splitting induced by an altermagnetic phase transition. Adv. Mater. 36, 2314076 (2024).","journal-title":"Adv. Mater."},{"key":"9883_CR101","doi-asserted-by":"publisher","first-page":"L041402","DOI":"10.1103\/PhysRevMaterials.8.L041402","volume":"8","author":"T Aoyama","year":"2024","unstructured":"Aoyama, T. & Ohgushi, K. Piezomagnetic properties in altermagnetic MnTe. Phys. Rev. Mater. 8, L041402 (2024).","journal-title":"Phys. Rev. Mater."},{"key":"9883_CR102","doi-asserted-by":"publisher","first-page":"155201","DOI":"10.1103\/PhysRevB.110.155201","volume":"110","author":"KP Kluczyk","year":"2024","unstructured":"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).","journal-title":"Phys. Rev. B"},{"key":"9883_CR103","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-024-46476-5","volume":"15","author":"S Reimers","year":"2024","unstructured":"Reimers, S. et al. Direct observation of altermagnetic band splitting in CrSb thin films. Nat. Commun. 15, 2116 (2024).","journal-title":"Nat. Commun."},{"key":"9883_CR104","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-025-56647-7","volume":"16","author":"G Yang","year":"2025","unstructured":"Yang, G. et al. Three-dimensional mapping of the altermagnetic spin splitting in CrSb. Nat. Commun. 16, 1442 (2025).","journal-title":"Nat. Commun."},{"key":"9883_CR105","doi-asserted-by":"publisher","first-page":"206401","DOI":"10.1103\/PhysRevLett.133.206401","volume":"133","author":"J Ding","year":"2024","unstructured":"Ding, J. et al. Large band splitting in g-wave altermagnet CrSb. Phys. Rev. Lett. 133, 206401 (2024).","journal-title":"Phys. Rev. Lett."},{"key":"9883_CR106","doi-asserted-by":"crossref","unstructured":"Li, C. et al. Topological Weyl altermagnetism in CrSb. Commun. Phys. 8, 311 (2025).","DOI":"10.1038\/s42005-025-02232-9"},{"key":"9883_CR107","doi-asserted-by":"publisher","first-page":"7343","DOI":"10.1021\/acs.nanolett.5c00482","volume":"25","author":"W Lu","year":"2025","unstructured":"Lu, W. et al. Signature of topological surface bands in altermagnetic Weyl semimetal CrSb. Nano Lett. 25, 7343\u20137350 (2025).","journal-title":"Nano Lett."},{"key":"9883_CR108","doi-asserted-by":"publisher","first-page":"2406529","DOI":"10.1002\/advs.202406529","volume":"11","author":"M Zeng","year":"2024","unstructured":"Zeng, M. et al. Observation of spin splitting in room-temperature metallic antiferromagnet CrSb. Adv. Sci. 11, 2406529 (2024).","journal-title":"Adv. Sci."},{"key":"9883_CR109","unstructured":"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)."},{"key":"9883_CR110","doi-asserted-by":"publisher","first-page":"156702","DOI":"10.1103\/PhysRevLett.133.156702","volume":"133","author":"Z Liu","year":"2024","unstructured":"Liu, Z., Ozeki, M., Asai, S., Itoh, S. & Masuda, T. Chiral-split magnon in altermagnetic MnTe. Phys. Rev. Lett. 133, 156702 (2024).","journal-title":"Phys. Rev. Lett."},{"key":"9883_CR111","doi-asserted-by":"publisher","first-page":"754","DOI":"10.1038\/s41567-025-02822-y","volume":"21","author":"B Jiang","year":"2025","unstructured":"Jiang, B. et al. A metallic room-temperature d-wave altermagnet. Nat. Phys. 21, 754\u2013759 (2025). This paper and ref. 113 reported experimental spectroscopic observations of a d-wave altermagnetic band structure.","journal-title":"Nat. Phys."},{"key":"9883_CR112","doi-asserted-by":"publisher","first-page":"760","DOI":"10.1038\/s41567-025-02864-2","volume":"21","author":"F Zhang","year":"2025","unstructured":"Zhang, F. et al. Crystal-symmetry-paired spin\u2013valley locking in a layered room-temperature metallic altermagnet candidate. Nat. Phys. 21, 760\u2013767 (2025).","journal-title":"Nat. Phys."},{"key":"9883_CR113","doi-asserted-by":"publisher","first-page":"096703","DOI":"10.1103\/PhysRevLett.134.096703","volume":"134","author":"DS Antonenko","year":"2025","unstructured":"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.","journal-title":"Phys. Rev. Lett."},{"key":"9883_CR114","doi-asserted-by":"crossref","unstructured":"Kaushal, N. & Franz, M. Altermagnetism in modified Lieb lattice Hubbard model. Phys. Rev. Lett. 135, 156502 (2025).","DOI":"10.1103\/s31h-hk2v"},{"key":"9883_CR115","doi-asserted-by":"publisher","first-page":"24402","DOI":"10.1103\/PhysRevMaterials.9.024402","volume":"9","author":"CC Wei","year":"2025","unstructured":"Wei, C. C. et al. La2O3Mn2Se2: a correlated insulating layered d-wave altermagnet. Phys. Rev. Mater. 9, 24402 (2025).","journal-title":"Phys. Rev. Mater."},{"key":"9883_CR116","doi-asserted-by":"publisher","first-page":"87206","DOI":"10.1103\/PhysRevLett.124.087206","volume":"124","author":"DD Maharaj","year":"2020","unstructured":"Maharaj, D. D. et al. Octupolar versus N\u00e9el order in cubic 5d2 double perovskites. Phys. Rev. Lett. 124, 87206 (2020).","journal-title":"Phys. Rev. Lett."},{"key":"9883_CR117","doi-asserted-by":"publisher","first-page":"985","DOI":"10.1126\/science.174.4013.985","volume":"174","author":"L N\u00e9el","year":"1971","unstructured":"N\u00e9el, L. Magnetism and local molecular field. Science 174, 985\u2013992 (1971).","journal-title":"Science"},{"key":"9883_CR118","doi-asserted-by":"publisher","first-page":"144421","DOI":"10.1103\/PhysRevB.109.144421","volume":"109","author":"A Chakraborty","year":"2024","unstructured":"Chakraborty, A., Gonz\u00e1lez Hern\u00e1ndez, R., \u0160mejkal, L. & Sinova, J. Strain-induced phase transition from antiferromagnet to altermagnet. Phys. Rev. B 109, 144421 (2024).","journal-title":"Phys. Rev. B"},{"key":"9883_CR119","doi-asserted-by":"publisher","first-page":"206702","DOI":"10.1103\/PhysRevLett.133.206702","volume":"133","author":"Y Liu","year":"2024","unstructured":"Liu, Y., Yu, J. & Liu, C.-C. Twisted magnetic van der Waals bilayers: an ideal platform for altermagnetism. Phys. Rev. Lett. 133, 206702 (2024).","journal-title":"Phys. Rev. Lett."},{"key":"9883_CR120","doi-asserted-by":"publisher","first-page":"236701","DOI":"10.1103\/PhysRevLett.132.236701","volume":"132","author":"V Leeb","year":"2024","unstructured":"Leeb, V., Mook, A., \u0160mejkal, L. & Knolle, J. Spontaneous formation of altermagnetism from orbital ordering. Phys. Rev. Lett. 132, 236701 (2024).","journal-title":"Phys. Rev. Lett."},{"key":"9883_CR121","doi-asserted-by":"publisher","first-page":"024404","DOI":"10.1103\/PhysRevB.109.024404","volume":"109","author":"RM Fernandes","year":"2024","unstructured":"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).","journal-title":"Phys. Rev. B"},{"key":"9883_CR122","doi-asserted-by":"publisher","first-page":"435302","DOI":"10.1088\/1361-648X\/acea12","volume":"35","author":"S Das","year":"2023","unstructured":"Das, S., Suri, D. & Soori, A. Transport across junctions of altermagnets with normal metals and ferromagnets. J. Phys. Condensed Matter 35, 435302 (2023).","journal-title":"J. Phys. Condensed Matter"},{"key":"9883_CR123","doi-asserted-by":"publisher","first-page":"L100402","DOI":"10.1103\/PhysRevB.108.L100402","volume":"108","author":"TA Maier","year":"2023","unstructured":"Maier, T. A. & Okamoto, S. Weak-coupling theory of neutron scattering as a probe of altermagnetism. Phys. Rev. B 108, L100402 (2023).","journal-title":"Phys. Rev. B"},{"key":"9883_CR124","doi-asserted-by":"publisher","first-page":"086503","DOI":"10.1103\/PhysRevLett.133.086503","volume":"133","author":"T Sato","year":"2024","unstructured":"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).","journal-title":"Phys. Rev. Lett."},{"key":"9883_CR125","doi-asserted-by":"publisher","first-page":"144412","DOI":"10.1103\/PhysRevB.110.144412","volume":"110","author":"M Roig","year":"2024","unstructured":"Roig, M., Kreisel, A., Yu, Y., Andersen, B. M. & Agterberg, D. F. Minimal models for altermagnetism. Phys. Rev. B 110, 144412 (2024).","journal-title":"Phys. Rev. B"},{"key":"9883_CR126","doi-asserted-by":"publisher","first-page":"205120","DOI":"10.1103\/PhysRevB.110.205120","volume":"110","author":"A Bose","year":"2024","unstructured":"Bose, A., Vadnais, S. & Paramekanti, A. Altermagnetism and superconductivity in a multiorbital t\u2013J model. Phys. Rev. B 110, 205120 (2024).","journal-title":"Phys. Rev. B"},{"key":"9883_CR127","doi-asserted-by":"publisher","first-page":"205140","DOI":"10.1103\/PhysRevB.110.205140","volume":"110","author":"F Ferrari","year":"2024","unstructured":"Ferrari, F. & Valent\u00ed, R. Altermagnetism on the Shastry\u2013Sutherland lattice. Phys. Rev. B 110, 205140 (2024).","journal-title":"Phys. Rev. B"},{"key":"9883_CR128","doi-asserted-by":"publisher","first-page":"014434","DOI":"10.1103\/PhysRevB.111.014434","volume":"111","author":"S Rooj","year":"2025","unstructured":"Rooj, S., Saxena, S. & Ganguli, N. Altermagnetism in the orthorhombic Pnm structure through group theory and DFT calculations. Phys. Rev. B 111, 014434 (2025).","journal-title":"Phys. Rev. B"},{"key":"9883_CR129","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1006\/jssc.1997.7287","volume":"130","author":"J T\u00f6pfer","year":"1997","unstructured":"T\u00f6pfer, J. & Goodenough, J. LaMnO3+\u03b4 revisited. J. Solid State Chem. 130, 117\u2013128 (1997).","journal-title":"J. Solid State Chem."},{"key":"9883_CR130","doi-asserted-by":"publisher","first-page":"017205","DOI":"10.1103\/PhysRevLett.112.017205","volume":"112","author":"H Chen","year":"2014","unstructured":"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.","journal-title":"Phys. Rev. Lett."},{"key":"9883_CR131","doi-asserted-by":"publisher","first-page":"256601","DOI":"10.1103\/PhysRevLett.116.256601","volume":"116","author":"J Zhou","year":"2016","unstructured":"Zhou, J. et al. Predicted quantum topological Hall effect and noncoplanar antiferromagnetism in K0.5RhO2. Phys. Rev. Lett. 116, 256601 (2016).","journal-title":"Phys. Rev. Lett."},{"key":"9883_CR132","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-019-13968-8","volume":"11","author":"W Feng","year":"2020","unstructured":"Feng, W. et al. Topological magneto-optical effects and their quantization in noncoplanar antiferromagnets. Nat. Commun. 11, 118 (2020).","journal-title":"Nat. Commun."},{"key":"9883_CR133","doi-asserted-by":"publisher","first-page":"184432","DOI":"10.1103\/PhysRevB.99.184432","volume":"99","author":"K-H Ahn","year":"2019","unstructured":"Ahn, K.-H., Hariki, A., Lee, K.-W. & Kune\u0161, J. Antiferromagnetism in RuO2 as d-wave Pomeranchuk instability. Phys. Rev. B 99, 184432 (2019).","journal-title":"Phys. Rev. B"},{"key":"9883_CR134","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-019-12229-y","volume":"10","author":"M Naka","year":"2019","unstructured":"Naka, M. et al. Spin current generation in organic antiferromagnets. Nat. Commun. 10, 4305 (2019).","journal-title":"Nat. Commun."},{"key":"9883_CR135","doi-asserted-by":"publisher","first-page":"100991","DOI":"10.1016\/j.mtphys.2023.100991","volume":"32","author":"Y Guo","year":"2023","unstructured":"Guo, Y. et al. Spin-split collinear antiferromagnets: a large-scale ab-initio study. Mater. Today Phys. 32, 100991 (2023).","journal-title":"Mater. Today Phys."},{"key":"9883_CR136","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-021-23127-7","volume":"12","author":"H-Y Ma","year":"2021","unstructured":"Ma, H.-Y. et al. Multifunctional antiferromagnetic materials with giant piezomagnetism and noncollinear spin current. Nat. Commun. 12, 2846 (2021).","journal-title":"Nat. Commun."},{"key":"9883_CR137","doi-asserted-by":"publisher","first-page":"2363","DOI":"10.1021\/acs.jpclett.1c00282","volume":"12","author":"SA Egorov","year":"2021","unstructured":"Egorov, S. A. & Evarestov, R. A. Colossal spin splitting in the monolayer of the collinear antiferromagnet MnF2. J. Phys. Chem. Lett. 12, 2363\u20132369 (2021).","journal-title":"J. Phys. Chem. Lett."},{"key":"9883_CR138","doi-asserted-by":"publisher","first-page":"024410","DOI":"10.1103\/PhysRevB.108.024410","volume":"108","author":"Q Cui","year":"2023","unstructured":"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).","journal-title":"Phys. Rev. B"},{"key":"9883_CR139","doi-asserted-by":"crossref","unstructured":"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).","DOI":"10.1063\/5.0147450"},{"key":"9883_CR140","doi-asserted-by":"publisher","first-page":"182409","DOI":"10.1063\/5.0198285","volume":"124","author":"J S\u00f8dequist","year":"2024","unstructured":"S\u00f8dequist, J. & Olsen, T. Two-dimensional altermagnets from high throughput computational screening: symmetry requirements, chiral magnons, and spin\u2013orbit effects. Appl. Phys. Lett. 124, 182409 (2024).","journal-title":"Appl. Phys. Lett."},{"key":"9883_CR141","doi-asserted-by":"publisher","first-page":"523","DOI":"10.1038\/s41586-024-07023-w","volume":"626","author":"Y-P Zhu","year":"2024","unstructured":"Zhu, Y.-P. et al. Observation of plaid-like spin splitting in a noncoplanar antiferromagnet. Nature 626, 523\u2013528 (2024).","journal-title":"Nature"},{"key":"9883_CR142","doi-asserted-by":"publisher","first-page":"472","DOI":"10.1021\/acs.nanolett.3c04330","volume":"24","author":"Y Zhu","year":"2024","unstructured":"Zhu, Y. et al. Multipiezo effect in altermagnetic V2SeTeO monolayer. Nano Lett. 24, 472\u2013478 (2024).","journal-title":"Nano Lett."},{"key":"9883_CR143","first-page":"546","volume":"1932","author":"E Wigner","year":"1932","unstructured":"Wigner, E. Ueber die Operation der Zeitumkehr in der Quantenmechanik. Nachr. Ges. Wiss. Gott. Math. Phys. Kl. 1932, 546\u2013559 (1932).","journal-title":"Nachr. Ges. Wiss. Gott. Math. Phys. Kl."},{"key":"9883_CR144","doi-asserted-by":"publisher","first-page":"1100","DOI":"10.1038\/nphys3839","volume":"12","author":"P Tang","year":"2016","unstructured":"Tang, P., Zhou, Q., Xu, G. & Zhang, S.-C. Dirac fermions in an antiferromagnetic semimetal. Nat. Phys. 12, 1100\u20131104 (2016).","journal-title":"Nat. Phys."},{"key":"9883_CR145","doi-asserted-by":"publisher","first-page":"106402","DOI":"10.1103\/PhysRevLett.118.106402","volume":"118","author":"L \u0160mejkal","year":"2017","unstructured":"\u0160mejkal, L., \u017delezn\u00fd, J., Sinova, J. & Jungwirth, T. Electric control of Dirac quasiparticles by spin\u2013orbit torque in an antiferromagnet. Phys. Rev. Lett. 118, 106402 (2017).","journal-title":"Phys. Rev. Lett."},{"key":"9883_CR146","doi-asserted-by":"publisher","first-page":"242","DOI":"10.1038\/s41567-018-0064-5","volume":"14","author":"L \u0160mejkal","year":"2018","unstructured":"\u0160mejkal, L., Mokrousov, Y., Yan, B. & MacDonald, A. H. Topological antiferromagnetic spintronics. Nat. Phys. 14, 242\u2013251 (2018).","journal-title":"Nat. Phys."},{"key":"9883_CR147","doi-asserted-by":"publisher","first-page":"67001","DOI":"10.1209\/0295-5075\/108\/67001","volume":"108","author":"J K\u00fcbler","year":"2014","unstructured":"K\u00fcbler, J. & Felser, C. Non-collinear antiferromagnets and the anomalous Hall effect. Europhys. Lett. 108, 67001 (2014).","journal-title":"Europhys. Lett."},{"key":"9883_CR148","doi-asserted-by":"publisher","first-page":"212","DOI":"10.1038\/nature15723","volume":"527","author":"S Nakatsuji","year":"2015","unstructured":"Nakatsuji, S., Kiyohara, N. & Higo, T. Large anomalous Hall effect in a non-collinear antiferromagnet at room temperature. Nature 527, 212\u2013215 (2015). This paper reported the experimental observation of the anomalous Hall effect in a non-collinear compensated magnet.","journal-title":"Nature"},{"key":"9883_CR149","doi-asserted-by":"publisher","first-page":"064009","DOI":"10.1103\/PhysRevApplied.5.064009","volume":"5","author":"N Kiyohara","year":"2016","unstructured":"Kiyohara, N., Tomita, T. & Nakatsuji, S. Giant anomalous Hall effect in the chiral antiferromagnet Mn3Ge. Phys. Rev. Appl. 5, 064009 (2016).","journal-title":"Phys. Rev. Appl."},{"key":"9883_CR150","doi-asserted-by":"publisher","first-page":"e1501870","DOI":"10.1126\/sciadv.1501870","volume":"2","author":"AK Nayak","year":"2016","unstructured":"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).","journal-title":"Sci. Adv."},{"key":"9883_CR151","doi-asserted-by":"publisher","first-page":"961","DOI":"10.1038\/s41567-023-02017-3","volume":"19","author":"H Takagi","year":"2023","unstructured":"Takagi, H. et al. Spontaneous topological Hall effect induced by non-coplanar antiferromagnetic order in intercalated van der Waals materials. Nat. Phys. 19, 961\u2013968 (2023).","journal-title":"Nat. Phys."},{"key":"9883_CR152","doi-asserted-by":"publisher","first-page":"1085","DOI":"10.1038\/nphys4181","volume":"13","author":"M Ikhlas","year":"2017","unstructured":"Ikhlas, M. et al. Large anomalous Nernst effect at room temperature in a chiral antiferromagnet. Nat. Phys. 13, 1085\u20131090 (2017).","journal-title":"Nat. Phys."},{"key":"9883_CR153","doi-asserted-by":"publisher","first-page":"056601","DOI":"10.1103\/PhysRevLett.119.056601","volume":"119","author":"X Li","year":"2017","unstructured":"Li, X. et al. Anomalous Nernst and Righi-Leduc effects in Mn3Sn: Berry curvature and entropy flow. Phys. Rev. Lett. 119, 056601 (2017).","journal-title":"Phys. Rev. Lett."},{"key":"9883_CR154","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1038\/s41566-017-0086-z","volume":"12","author":"T Higo","year":"2018","unstructured":"Higo, T. et al. Large magneto-optical Kerr effect and imaging of magnetic octupole domains in an antiferromagnetic metal. Nat. Photon. 12, 73\u201378 (2018).","journal-title":"Nat. Photon."},{"key":"9883_CR155","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-020-14690-6","volume":"11","author":"T Matsuda","year":"2020","unstructured":"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).","journal-title":"Nat. Commun."},{"key":"9883_CR156","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-021-25834-7","volume":"12","author":"M Kimata","year":"2021","unstructured":"Kimata, M. et al. X-ray study of ferroic octupole order producing anomalous Hall effect. Nat. Commun. 12, 5582 (2021).","journal-title":"Nat. Commun."},{"key":"9883_CR157","doi-asserted-by":"publisher","first-page":"134431","DOI":"10.1103\/PhysRevB.104.134431","volume":"104","author":"S Sakamoto","year":"2021","unstructured":"Sakamoto, S. et al. Observation of spontaneous X-ray magnetic circular dichroism in a chiral antiferromagnet. Phys. Rev. B 104, 134431 (2021).","journal-title":"Phys. Rev. B"},{"key":"9883_CR158","doi-asserted-by":"publisher","first-page":"187204","DOI":"10.1103\/PhysRevLett.119.187204","volume":"119","author":"J \u017delezn\u00fd","year":"2017","unstructured":"\u017delezn\u00fd, J., Zhang, Y., Felser, C. & Yan, B. Spin-polarized current in noncollinear antiferromagnets. Phys. Rev. Lett. 119, 187204 (2017).","journal-title":"Phys. Rev. Lett."},{"key":"9883_CR159","doi-asserted-by":"publisher","first-page":"073028","DOI":"10.1088\/1367-2630\/aad1eb","volume":"20","author":"Y Zhang","year":"2018","unstructured":"Zhang, Y., \u017delezn\u00fd, J., Sun, Y., van den Brink, J. & Yan, B. Spin Hall effect emerging from a noncollinear magnetic lattice without spin\u2013orbit coupling. New J. Phys. 20, 073028 (2018).","journal-title":"New J. Phys."},{"key":"9883_CR160","doi-asserted-by":"publisher","first-page":"627","DOI":"10.1038\/s41586-018-0853-0","volume":"565","author":"M Kimata","year":"2019","unstructured":"Kimata, M. et al. Magnetic and magnetic inverse spin Hall effects in a non-collinear antiferromagnet. Nature 565, 627\u2013630 (2019).","journal-title":"Nature"},{"key":"9883_CR161","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-022-32179-2","volume":"13","author":"S Hu","year":"2022","unstructured":"Hu, S. et al. Efficient perpendicular magnetization switching by a magnetic spin Hall effect in a noncollinear antiferromagnet. Nat. Commun. 13, 4447 (2022).","journal-title":"Nat. Commun."},{"key":"9883_CR162","doi-asserted-by":"publisher","first-page":"608","DOI":"10.1038\/s41586-020-2211-2","volume":"580","author":"H Tsai","year":"2020","unstructured":"Tsai, H. et al. Electrical manipulation of a topological antiferromagnetic state. Nature 580, 608\u2013613 (2020).","journal-title":"Nature"},{"key":"9883_CR163","doi-asserted-by":"publisher","first-page":"1364","DOI":"10.1038\/s41563-021-01005-3","volume":"20","author":"Y Takeuchi","year":"2021","unstructured":"Takeuchi, Y. et al. Chiral-spin rotation of non-collinear antiferromagnet by spin\u2013orbit torque. Nat. Mater. 20, 1364\u20131370 (2021).","journal-title":"Nat. Mater."},{"key":"9883_CR164","doi-asserted-by":"publisher","first-page":"474","DOI":"10.1038\/s41586-022-04864-1","volume":"607","author":"T Higo","year":"2022","unstructured":"Higo, T. et al. Perpendicular full switching of chiral antiferromagnetic order by current. Nature 607, 474\u2013479 (2022).","journal-title":"Nature"},{"key":"9883_CR165","doi-asserted-by":"publisher","first-page":"eabo5930","DOI":"10.1126\/sciadv.abo5930","volume":"8","author":"B Pal","year":"2022","unstructured":"Pal, B. et al. Setting of the magnetic structure of chiral kagome antiferromagnets by a seeded spin\u2013orbit torque. Sci. Adv. 8, eabo5930 (2022).","journal-title":"Sci. Adv."},{"key":"9883_CR166","doi-asserted-by":"publisher","first-page":"490","DOI":"10.1038\/s41586-022-05463-w","volume":"613","author":"X Chen","year":"2023","unstructured":"Chen, X. et al. Octupole-driven magnetoresistance in an antiferromagnetic tunnel junction. Nature 613, 490\u2013495 (2023).","journal-title":"Nature"},{"key":"9883_CR167","doi-asserted-by":"publisher","first-page":"485","DOI":"10.1038\/s41586-022-05461-y","volume":"613","author":"P Qin","year":"2023","unstructured":"Qin, P. et al. Room-temperature magnetoresistance in an all-antiferromagnetic tunnel junction. Nature 613, 485\u2013489 (2023).","journal-title":"Nature"},{"key":"9883_CR168","doi-asserted-by":"crossref","unstructured":"Nakatsuji, S. & Arita, R. Topological magnets: functions based on Berry phase and multipoles. Annu. Rev. Condensed Matter Phys. 13, 119\u2013142 (2022).","DOI":"10.1146\/annurev-conmatphys-031620-103859"},{"key":"9883_CR169","doi-asserted-by":"crossref","unstructured":"Rimmler, B. H., Pal, B. & Parkin, S. S. P. Non-collinear antiferromagnetic spintronics. Nat. Rev. Mater. 10, 109\u2013127 (2024).","DOI":"10.1038\/s41578-024-00706-w"},{"key":"9883_CR170","doi-asserted-by":"publisher","first-page":"100012","DOI":"10.1016\/j.newton.2025.100012","volume":"1","author":"J Han","year":"2025","unstructured":"Han, J., Yoon, J.-Y., Ohno, H. & Fukami, S. Unconventional responses in non-collinear antiferromagnets. Newton 1, 100012 (2025).","journal-title":"Newton"},{"key":"9883_CR171","doi-asserted-by":"publisher","first-page":"236703","DOI":"10.1103\/PhysRevLett.133.236703","volume":"133","author":"B Brekke","year":"2024","unstructured":"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).","journal-title":"Phys. Rev. Lett."},{"key":"9883_CR172","doi-asserted-by":"publisher","first-page":"165429","DOI":"10.1103\/PhysRevB.110.165429","volume":"110","author":"M Ezawa","year":"2024","unstructured":"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).","journal-title":"Phys. Rev. B"},{"key":"9883_CR173","doi-asserted-by":"publisher","first-page":"196907","DOI":"10.1103\/PhysRevLett.134.196907","volume":"134","author":"J Sivianes","year":"2025","unstructured":"Sivianes, J., dos Santos, F. J. & Iba\u00f1ez-Azpiroz, J. Optical signatures of spin symmetries in unconventional magnets. Phys. Rev. Lett. 134, 196907 (2025).","journal-title":"Phys. Rev. Lett."},{"key":"9883_CR174","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-025-62516-0","volume":"16","author":"A Chakraborty","year":"2023","unstructured":"Chakraborty, A. et al. Highly efficient non-relativistic Edelstein effect in p-wave magnets. Nat. Commun. 16, 7270 (2023).","journal-title":"Nat. Commun."},{"key":"9883_CR175","doi-asserted-by":"crossref","unstructured":"Yu, Y. et al. Odd-parity magnetism driven by antiferromagnetic exchange. Phys. Rev. Lett. 135, 046701 (2025).","DOI":"10.1103\/zk69-k6b2"},{"key":"9883_CR176","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-023-43962-0","volume":"14","author":"M Wang","year":"2023","unstructured":"Wang, M. et al. Emergent zero-field anomalous Hall effect in a reconstructed rutile antiferromagnetic metal. Nat. Commun. 14, 8240 (2023).","journal-title":"Nat. Commun."},{"key":"9883_CR177","doi-asserted-by":"publisher","first-page":"eadn0479","DOI":"10.1126\/sciadv.adn0479","volume":"10","author":"L Han","year":"2024","unstructured":"Han, L. et al. Electrical 180\u00b0 switching of N\u00e9el vector in spin-splitting antiferromagnet. Sci. Adv. 10, eadn0479 (2024).","journal-title":"Sci. Adv."},{"key":"9883_CR178","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1038\/s41563-024-02058-w","volume":"24","author":"R Takagi","year":"2025","unstructured":"Takagi, R. et al. Spontaneous Hall effect induced by collinear antiferromagnetic order at room temperature. Nat. Mater. 24, 63\u201368 (2025).","journal-title":"Nat. Mater."},{"key":"9883_CR179","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-025-58476-0","volume":"16","author":"MK Ray","year":"2025","unstructured":"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).","journal-title":"Nat. Commun."},{"key":"9883_CR180","doi-asserted-by":"publisher","first-page":"115138","DOI":"10.1103\/PhysRevB.108.115138","volume":"108","author":"A Fakhredine","year":"2023","unstructured":"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).","journal-title":"Phys. Rev. B"},{"key":"9883_CR181","doi-asserted-by":"publisher","first-page":"106701","DOI":"10.1103\/PhysRevLett.133.106701","volume":"133","author":"Y Fang","year":"2024","unstructured":"Fang, Y., Cano, J. & Ghorashi, S. A. A. Quantum geometry induced nonlinear transport in altermagnets. Phys. Rev. Lett. 133, 106701 (2024).","journal-title":"Phys. Rev. Lett."},{"key":"9883_CR182","doi-asserted-by":"publisher","first-page":"L201109","DOI":"10.1103\/PhysRevB.109.L201109","volume":"109","author":"Y-X Li","year":"2024","unstructured":"Li, Y.-X., Liu, Y. & Liu, C.-C. Creation and manipulation of higher-order topological states by altermagnets. Phys. Rev. B 109, L201109 (2024).","journal-title":"Phys. Rev. B"},{"key":"9883_CR183","doi-asserted-by":"publisher","first-page":"056701","DOI":"10.1103\/PhysRevLett.132.056701","volume":"132","author":"X Zhou","year":"2024","unstructured":"Zhou, X. et al. Crystal thermal transport in altermagnetic RuO2. Phys. Rev. Lett.s 132, 056701 (2024).","journal-title":"Phys. Rev. Lett.s"},{"key":"9883_CR184","doi-asserted-by":"publisher","first-page":"224402","DOI":"10.1103\/PhysRevB.107.224402","volume":"107","author":"J Zhan","year":"2023","unstructured":"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).","journal-title":"Phys. Rev. B"},{"key":"9883_CR185","doi-asserted-by":"publisher","first-page":"224436","DOI":"10.1103\/PhysRevB.110.224436","volume":"110","author":"J Nag","year":"2024","unstructured":"Nag, J. et al. GdAlSi: an antiferromagnetic topological Weyl semimetal with nonrelativistic spin splitting. Phys. Rev. B 110, 224436 (2024).","journal-title":"Phys. Rev. B"},{"key":"9883_CR186","doi-asserted-by":"crossref","unstructured":"Parshukov, K., Wiedmann, R. & Schnyder, A. P. Topological responses from gapped Weyl points in 2D altermagnets. Phys. Rev. B 111, 224406 (2025).","DOI":"10.1103\/PhysRevB.111.224406"},{"key":"9883_CR187","doi-asserted-by":"publisher","first-page":"024425","DOI":"10.1103\/PhysRevB.110.024425","volume":"110","author":"P Rao","year":"2024","unstructured":"Rao, P., Mook, A. & Knolle, J. Tunable band topology and optical conductivity in altermagnets. Phys. Rev. B 110, 024425 (2024).","journal-title":"Phys. Rev. B"},{"key":"9883_CR188","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-018-05137-0","volume":"9","author":"LL Tao","year":"2018","unstructured":"Tao, L. L. & Tsymbal, E. Y. Persistent spin texture enforced by symmetry. Nat. Commun. 9, 2763 (2018).","journal-title":"Nat. Commun."},{"key":"9883_CR189","doi-asserted-by":"publisher","first-page":"L041404","DOI":"10.1103\/PhysRevB.105.L041404","volume":"105","author":"J Ji","year":"2022","unstructured":"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).","journal-title":"Phys. Rev. B"},{"key":"9883_CR190","doi-asserted-by":"publisher","first-page":"236601","DOI":"10.1103\/PhysRevLett.97.236601","volume":"97","author":"BA Bernevig","year":"2006","unstructured":"Bernevig, B. A., Orenstein, J. & Zhang, S. C. Exact SU(2) symmetry and persistent spin helix in a spin\u2013orbit coupled system. Phys. Rev. Lett. 97, 236601 (2006).","journal-title":"Phys. Rev. Lett."},{"key":"9883_CR191","doi-asserted-by":"publisher","first-page":"610","DOI":"10.1038\/nature07871","volume":"458","author":"JD Koralek","year":"2009","unstructured":"Koralek, J. D. et al. Emergence of the persistent spin helix in semiconductor quantum wells. Nature 458, 610\u2013613 (2009).","journal-title":"Nature"},{"key":"9883_CR192","doi-asserted-by":"publisher","first-page":"1090","DOI":"10.1038\/nmat4987","volume":"16","author":"K Kuroda","year":"2017","unstructured":"Kuroda, K. et al. Evidence for magnetic Weyl fermions in a correlated metal. Nat. Mater. 16, 1090\u20131095 (2017).","journal-title":"Nat. Mater."},{"key":"9883_CR193","doi-asserted-by":"publisher","first-page":"172","DOI":"10.1038\/s41928-018-0040-1","volume":"1","author":"ZQ Liu","year":"2018","unstructured":"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\u2013177 (2018).","journal-title":"Nat. Electron."},{"key":"9883_CR194","doi-asserted-by":"publisher","first-page":"eaaz3522","DOI":"10.1126\/sciadv.aaz3522","volume":"6","author":"L Xu","year":"2020","unstructured":"Xu, L. et al. Finite-temperature violation of the anomalous transverse Wiedemann\u2013Franz law. Sci. Adv. 6, eaaz3522 (2020).","journal-title":"Sci. Adv."},{"key":"9883_CR195","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-020-20838-1","volume":"12","author":"T Chen","year":"2021","unstructured":"Chen, T. et al. Anomalous transport due to Weyl fermions in the chiral antiferromagnets Mn3X, X = Sn, Ge. Nat. Commun. 12, 572 (2021).","journal-title":"Nat. Commun."},{"key":"9883_CR196","unstructured":"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)."},{"key":"9883_CR197","doi-asserted-by":"publisher","first-page":"046811","DOI":"10.1103\/PhysRevLett.103.046811","volume":"103","author":"K Sun","year":"2009","unstructured":"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).","journal-title":"Phys. Rev. Lett."},{"key":"9883_CR198","doi-asserted-by":"publisher","first-page":"144418","DOI":"10.1103\/PhysRevB.108.144418","volume":"108","author":"CRW Steward","year":"2023","unstructured":"Steward, C. R. W., Fernandes, R. M. & Schmalian, J. Dynamic paramagnon-polarons in altermagnets. Phys. Rev. B 108, 144418 (2023).","journal-title":"Phys. Rev. B"},{"key":"9883_CR199","doi-asserted-by":"publisher","first-page":"156402","DOI":"10.1103\/PhysRevLett.101.156402","volume":"101","author":"I Martin","year":"2008","unstructured":"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).","journal-title":"Phys. Rev. Lett."},{"key":"9883_CR200","unstructured":"MAGNDATA: A Collection of Magnetic Structures with Portable cif-type Files. https:\/\/www.cryst.ehu.es\/magndata\/."}],"container-title":["Nature"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.nature.com\/articles\/s41586-025-09883-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s41586-025-09883-2","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s41586-025-09883-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,24]],"date-time":"2026-01-24T00:13:01Z","timestamp":1769213581000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.nature.com\/articles\/s41586-025-09883-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,1,21]]},"references-count":200,"journal-issue":{"issue":"8098","published-print":{"date-parts":[[2026,1,22]]}},"alternative-id":["9883"],"URL":"https:\/\/doi.org\/10.1038\/s41586-025-09883-2","relation":{},"ISSN":["0028-0836","1476-4687"],"issn-type":[{"value":"0028-0836","type":"print"},{"value":"1476-4687","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,1,21]]},"assertion":[{"value":"28 February 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 November 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 January 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare no competing interests.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}]}}