{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,11,2]],"date-time":"2026-11-02T23:04:50Z","timestamp":1793660690417,"version":"4.5.1"},"reference-count":65,"publisher":"American Physical Society (APS)","issue":"10","license":[{"start":{"date-parts":[[2026,8,31]],"date-time":"2026-08-31T00:00:00Z","timestamp":1788134400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/link.aps.org\/licenses\/aps-default-license"}],"funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["KN1254\/1-2"],"award-info":[{"award-number":["KN1254\/1-2"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["KN1254\/2-1 TRR 360\u2013492547816"],"award-info":[{"award-number":["KN1254\/2-1 TRR 360\u2013492547816"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["SFB 1143"],"award-info":[{"award-number":["SFB 1143"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["EXC-2111-390814868"],"award-info":[{"award-number":["EXC-2111-390814868"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Bavarian State Government","id":[{"id":"https:\/\/ror.org\/035dsh769","id-type":"ROR","asserted-by":"crossref"}]},{"name":"Hightech Agenda Bayern Plus"},{"name":"Imperial-TUM Flagship Partnership"}],"content-domain":{"domain":["journals.aps.org"],"crossmark-restriction":true},"short-container-title":["Phys. Rev. Lett."],"accepted":{"date-parts":[[2026,7,13]]},"DOI":"10.1103\/ydjj-6r9l","type":"journal-article","created":{"date-parts":[[2026,7,13]],"date-time":"2026-07-13T17:36:48Z","timestamp":1783964208000},"update-policy":"https:\/\/doi.org\/10.1103\/crossmark-policy","source":"Crossref","is-referenced-by-count":2,"title":["Collinear\n                    <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n                      <mml:mi>p<\/mml:mi>\n                    <\/mml:math>\n                    -Wave Magnetism and Hidden Orbital Ferrimagnetism"],"prefix":"10.1103","volume":"137","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7099-0682","authenticated-orcid":true,"given":"Valentin","family":"Leeb","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/02crff812","id-type":"ROR","asserted-by":"publisher"}],"name":"University of Z\u00fcrich"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Johannes","family":"Knolle","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/02kkvpp62","id-type":"ROR","asserted-by":"publisher"}],"name":"Technical University of Munich"},{"id":[{"id":"https:\/\/ror.org\/04xrcta15","id-type":"ROR","asserted-by":"publisher"}],"name":"Munich Center for Quantum Science and Technology (MCQST)"},{"id":[{"id":"https:\/\/ror.org\/041kmwe10","id-type":"ROR","asserted-by":"publisher"}],"name":"Imperial College London"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"16","published-online":{"date-parts":[[2026,8,31]]},"reference":[{"key":"ydjj-6r9lCc1R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevX.12.031042","type":"journal-article"},{"key":"ydjj-6r9lCc2R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevX.12.040501","type":"journal-article"},{"key":"ydjj-6r9lCc3R1","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.1966.0211","type":"journal-article"},{"key":"ydjj-6r9lCc4R1","doi-asserted-by":"publisher","DOI":"10.1016\/0031-8914(74)90157-8","type":"journal-article"},{"key":"ydjj-6r9lCc5R1","doi-asserted-by":"publisher","DOI":"10.1107\/S0567739477000709","type":"journal-article"},{"key":"ydjj-6r9lCc6R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.105.064430","type":"journal-article"},{"key":"ydjj-6r9lCc7R1","first-page":"361","type":"journal-article","volume":"8","author":"I.\u2009I. Pomeranchuk","year":"1958","journal-title":"Sov. Phys. JETP","ISSN":"https:\/\/id.crossref.org\/issn\/0038-5646","issn-type":"print"},{"key":"ydjj-6r9lCc8R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.75.115103","type":"journal-article"},{"key":"ydjj-6r9lCc9R1","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-025-62516-0","type":"journal-article"},{"key":"ydjj-6r9lCc11R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.133.236703","type":"journal-article"},{"key":"ydjj-6r9lCc12R1","doi-asserted-by":"publisher","DOI":"10.1038\/s41586-025-09633-4","type":"journal-article"},{"key":"ydjj-6r9lCc13R1","doi-asserted-by":"publisher","DOI":"10.1038\/s41586-025-09034-7","type":"journal-article"},{"key":"ydjj-6r9lCc15R1","doi-asserted-by":"publisher","DOI":"10.1103\/zk69-k6b2","type":"journal-article"},{"key":"ydjj-6r9lCc16R1","doi-asserted-by":"publisher","DOI":"10.1103\/9346-9jpf","type":"journal-article"},{"key":"ydjj-6r9lCc17R1","doi-asserted-by":"publisher","DOI":"10.1103\/xzm1-l6yf","type":"journal-article"},{"key":"ydjj-6r9lCc19R1","doi-asserted-by":"publisher","DOI":"10.1103\/wnqs-3djt","type":"journal-article"},{"key":"ydjj-6r9lCc20R1","doi-asserted-by":"publisher","DOI":"10.1103\/7kmk-yl2t","type":"journal-article"},{"key":"ydjj-6r9lCc24R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.37.3774","type":"journal-article"},{"key":"ydjj-6r9lCc25R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.39.11538","type":"journal-article"},{"key":"ydjj-6r9lCc26R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.39.11413","type":"journal-article"},{"key":"ydjj-6r9lCc27R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.43.2866","type":"journal-article"},{"key":"ydjj-6r9lCc28R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.55.14554","type":"journal-article"},{"key":"ydjj-6r9lCc29R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.83.3538","type":"journal-article"},{"key":"ydjj-6r9lCc30R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.63.094503","type":"journal-article"},{"key":"ydjj-6r9lCc31R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.73.155113","type":"journal-article"},{"key":"ydjj-6r9lCc32R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRev.75.502","type":"journal-article"},{"key":"ydjj-6r9lCc33R1","doi-asserted-by":"publisher","DOI":"10.1007\/s10955-019-02386-1","type":"journal-article"},{"key":"ydjj-6r9lCc34R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.96.197001","type":"journal-article"},{"key":"ydjj-6r9lCc35R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.96.214504","type":"journal-article"},{"key":"ydjj-6r9lCc36R1","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.87.457","type":"journal-article"},{"key":"ydjj-6r9lCc37R1","doi-asserted-by":"publisher","DOI":"10.5802\/crphys.84","type":"journal-article"},{"key":"ydjj-6r9lCc38R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.104.165136","type":"journal-article"},{"key":"ydjj-6r9lCc39R1","doi-asserted-by":"publisher","DOI":"10.1038\/s41586-021-04327-z","type":"journal-article"},{"key":"ydjj-6r9lCc40R1","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-024-52688-6","type":"journal-article"},{"key":"ydjj-6r9lCc41R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.92.195140","type":"journal-article"},{"key":"ydjj-6r9lCc42R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.112.117001","type":"journal-article"},{"key":"ydjj-6r9lCc43R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.102.017005","type":"journal-article"},{"key":"ydjj-6r9lCc44R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.90.224507","type":"journal-article"},{"key":"ydjj-6r9lCc45R1","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-023-42952-6","type":"journal-article"},{"key":"ydjj-6r9lCc46R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.132.146501","type":"journal-article"},{"key":"ydjj-6r9lCc47R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.74.1171","type":"journal-article"},{"key":"ydjj-6r9lCc48R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.134.116703","type":"journal-article"},{"key":"ydjj-6r9lCc49R1","doi-asserted-by":"publisher","DOI":"10.1103\/qnwp-8sx5","type":"journal-article"},{"key":"ydjj-6r9lCc50R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.132.236701","type":"journal-article"},{"key":"ydjj-6r9lCc51R1","doi-asserted-by":"publisher","DOI":"10.1103\/261t-cs82","type":"journal-article"},{"key":"ydjj-6r9lCc52R1","doi-asserted-by":"publisher","DOI":"10.1103\/mm8t-82q4","type":"journal-article"},{"key":"ydjj-6r9lCc53R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.133.086503","type":"journal-article"},{"key":"ydjj-6r9lCc54R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevMaterials.8.L041402","type":"journal-article"},{"key":"ydjj-6r9lCc55R1","unstructured":"See Supplemental Material at http:\/\/link.aps.org\/supplemental\/10.1103\/ydjj-6r9l, which includes details on the Bloch Hamiltonians and the derivation of the nonlinear Drude conductivity.","type":"other"},{"key":"ydjj-6r9lCc56R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.126.127701","type":"journal-article"},{"key":"ydjj-6r9lCc57R1","doi-asserted-by":"publisher","DOI":"10.1016\/0038-1098(90)90963-C","type":"journal-article"},{"key":"ydjj-6r9lCc58R1","first-page":"881","type":"journal-article","volume":"37","author":"I. Dzyaloshinski\u012d","year":"1959","journal-title":"Sov. Phys. JETP"},{"key":"ydjj-6r9lCc59R1","first-page":"2219","type":"journal-article","volume":"93","author":"L. Gorkov","year":"1987","journal-title":"Zh. Eksp. Teor. Fiz.","ISSN":"https:\/\/id.crossref.org\/issn\/0044-4510","issn-type":"print"},{"key":"ydjj-6r9lCc60R1","doi-asserted-by":"publisher","DOI":"10.1063\/5.0250823","type":"journal-article"},{"key":"ydjj-6r9lCc61R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.134.146001","type":"journal-article"},{"key":"ydjj-6r9lCc62R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.111.115134","type":"journal-article"},{"key":"ydjj-6r9lCc63R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.physc.2009.12.053","type":"journal-article"},{"key":"ydjj-6r9lCc64R1","doi-asserted-by":"publisher","DOI":"10.1126\/sciadv.adn3662","type":"journal-article"},{"key":"ydjj-6r9lCc65R1","doi-asserted-by":"publisher","DOI":"10.1038\/s41565-018-0121-3","type":"journal-article"},{"key":"ydjj-6r9lCc66R1","doi-asserted-by":"publisher","DOI":"10.1039\/d2tc01889f","type":"journal-article"},{"key":"ydjj-6r9lCc67R1","doi-asserted-by":"publisher","DOI":"10.1103\/fv52-pd3h","type":"journal-article"},{"key":"ydjj-6r9lCc68R1","doi-asserted-by":"publisher","DOI":"10.5281\/zenodo.18456373","type":"dataset"},{"key":"ydjj-6r9lCc69R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.79.104416","type":"journal-article"},{"key":"ydjj-6r9lCc70R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.58.2794","type":"journal-article"},{"key":"ydjj-6r9lCc71R1","doi-asserted-by":"publisher","DOI":"10.1103\/vx12-r2k1","type":"journal-article"}],"container-title":["Physical Review Letters"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.aps.org\/article\/10.1103\/ydjj-6r9l","content-type":"unspecified","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/harvest.aps.org\/v2\/journals\/articles\/10.1103\/ydjj-6r9l\/fulltext","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T18:22:09Z","timestamp":1790878929000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.aps.org\/doi\/10.1103\/ydjj-6r9l"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,8,31]]},"references-count":65,"journal-issue":{"issue":"10","published-print":{"date-parts":[[2026,8]]}},"URL":"https:\/\/doi.org\/10.1103\/ydjj-6r9l","relation":{},"ISSN":["0031-9007","1079-7114"],"issn-type":[{"value":"0031-9007","type":"print"},{"value":"1079-7114","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,8,31]]},"assertion":[{"value":"2026-01-19","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"\u00a9 2026 American Physical Society. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright_statement","label":"Copyright statement","group":{"name":"copyright","label":"copyright"}},{"value":"2026","name":"copyright_year","label":"Copyright year","group":{"name":"copyright","label":"copyright"}},{"value":"American Physical Society","name":"copyright_holder","label":"Copyright holder","group":{"name":"copyright","label":"copyright"}}],"article-number":"106701"}}