{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T22:02:27Z","timestamp":1790719347861,"version":"4.1.0"},"reference-count":30,"publisher":"American Physical Society (APS)","issue":"6","license":[{"start":{"date-parts":[[2025,8,11]],"date-time":"2025-08-11T00:00:00Z","timestamp":1754870400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100009318","name":"Helmholtz Association","doi-asserted-by":"publisher","award":["VH-NG-1432"],"award-info":[{"award-number":["VH-NG-1432"]}],"id":[{"id":"10.13039\/501100009318","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000781","name":"European Research Council","doi-asserted-by":"publisher","award":["951459"],"award-info":[{"award-number":["951459"]}],"id":[{"id":"10.13039\/501100000781","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["454252928"],"award-info":[{"award-number":["454252928"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["SFB 1527"],"award-info":[{"award-number":["SFB 1527"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["journals.aps.org"],"crossmark-restriction":true},"short-container-title":["Phys. Rev. B"],"accepted":{"date-parts":[[2025,6,27]]},"abstract":"<jats:p>\n                    High field magnetic resonance of nuclear spins is normally carried out at or near the Larmor frequency\n                    <a:math xmlns:a=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                      <a:msub>\n                        <a:mi mathvariant=\"normal\">\u03a9<\/a:mi>\n                        <a:mn>0<\/a:mn>\n                      <\/a:msub>\n                    <\/a:math>\n                    . Here, we report an observation of nonsecular nuclear spin resonances far off\n                    <c:math xmlns:c=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                      <c:msub>\n                        <c:mi mathvariant=\"normal\">\u03a9<\/c:mi>\n                        <c:mn>0<\/c:mn>\n                      <\/c:msub>\n                    <\/c:math>\n                    . These originate from nonsecular terms of the nuclear spin-spin interaction and provide means for the control of coupled two level systems. In systems of equivalent nuclear spins, nonsecular resonances were predicted to lead to anomalous, fast relaxation of the nuclear spin polarization. We report experimental results that are in excellent agreement with the predicted behavior.\n                  <\/jats:p>","DOI":"10.1103\/h2sn-wvzm","type":"journal-article","created":{"date-parts":[[2025,6,27]],"date-time":"2025-06-27T12:38:12Z","timestamp":1751027892000},"update-policy":"https:\/\/doi.org\/10.1103\/crossmark-policy","source":"Crossref","is-referenced-by-count":4,"title":["Nuclear magnetic resonance far off the Larmor frequency: Nonsecular resonances in\n                    <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                      <mml:msub>\n                        <mml:mi>CaF<\/mml:mi>\n                        <mml:mn>2<\/mml:mn>\n                      <\/mml:msub>\n                    <\/mml:math>"],"prefix":"10.1103","volume":"112","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1058-3532","authenticated-orcid":true,"given":"Michael","family":"Jurkutat","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/04t3en479","id-type":"ROR","asserted-by":"publisher"}],"name":"Karlsruhe Institute of Technology"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7296-9326","authenticated-orcid":true,"given":"Kajum","family":"Safiullin","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/04t3en479","id-type":"ROR","asserted-by":"publisher"}],"name":"Karlsruhe Institute of Technology"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pooja","family":"Singh","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/04t3en479","id-type":"ROR","asserted-by":"publisher"}],"name":"Karlsruhe Institute of Technology"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0958-5300","authenticated-orcid":true,"given":"Stephan L.","family":"Grage","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/04t3en479","id-type":"ROR","asserted-by":"publisher"}],"name":"Karlsruhe Institute of Technology"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0140-6964","authenticated-orcid":true,"given":"J\u00fcrgen","family":"Haase","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/03s7gtk40","id-type":"ROR","asserted-by":"publisher"}],"name":"University of Leipzig"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-1156-4158","authenticated-orcid":true,"given":"Boris V.","family":"Fine","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/03s7gtk40","id-type":"ROR","asserted-by":"publisher"}],"name":"University of Leipzig"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2258-1507","authenticated-orcid":true,"given":"Benno","family":"Meier","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/04t3en479","id-type":"ROR","asserted-by":"publisher"}],"name":"Karlsruhe Institute of Technology"},{"id":[{"id":"https:\/\/ror.org\/04t3en479","id-type":"ROR","asserted-by":"publisher"}],"name":"Karlsruhe Institute of Technology"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"16","published-online":{"date-parts":[[2025,8,11]]},"reference":[{"key":"h2sn-wvzmCc1R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRev.128.2042","type":"journal-article"},{"key":"h2sn-wvzmCc2R1","doi-asserted-by":"publisher","DOI":"10.1016\/0022-2364(88)90190-4","type":"journal-article"},{"key":"h2sn-wvzmCc3R1","doi-asserted-by":"publisher","DOI":"10.1139\/p86-271","type":"journal-article"},{"key":"h2sn-wvzmCc4R1","doi-asserted-by":"publisher","DOI":"10.1039\/C4CP03994G","type":"journal-article"},{"key":"h2sn-wvzmCc5R1","doi-asserted-by":"publisher","DOI":"10.1063\/1.445483","type":"journal-article"},{"key":"h2sn-wvzmCc6R1","doi-asserted-by":"publisher","DOI":"10.1021\/ja00360a005","type":"journal-article"},{"key":"h2sn-wvzmCc7R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.86.094401","type":"journal-article"},{"key":"h2sn-wvzmCc8R1","doi-asserted-by":"publisher","DOI":"10.1002\/prop.201600023","type":"journal-article"},{"key":"h2sn-wvzmCc9R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRev.74.1168","type":"journal-article"},{"key":"h2sn-wvzmCc10R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRev.98.1787","type":"journal-article"},{"key":"h2sn-wvzmCc11R1","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-09441-9","type":"book","volume-title":"Principles of Magnetic Resonance","author":"C.\u00a0P. Slichter","year":"1990"},{"key":"h2sn-wvzmCc12R1","volume-title":"Spin Dynamics: Basics of Nuclear Magnetic Resonance","author":"M.\u00a0H. Levitt","year":"2008","type":"book"},{"key":"h2sn-wvzmCc13R1","volume-title":"Principles of Nuclear Magnetic Resonance in One and Two Dimensions","author":"R.\u00a0R. Ernst","year":"1987","type":"book"},{"key":"h2sn-wvzmCc14R1","volume-title":"Nuclear Magnetism: Order and Disorder","author":"A. Abragam","year":"1982","type":"book"},{"key":"h2sn-wvzmCc15R1","first-page":"527","type":"journal-article","volume":"98","author":"A.\u00a0N. Kolmogorov","year":"1954","journal-title":"Dokl. Acad. Nauk USSR"},{"key":"h2sn-wvzmCc16R1","first-page":"1","type":"journal-article","volume":"1","author":"J. Moser","year":"1962","journal-title":"Nach. Akad. Wiss. G\u00f6ttingen, Math. Phys. Kl. II"},{"key":"h2sn-wvzmCc17R1","doi-asserted-by":"publisher","DOI":"10.1070\/RM1963v018n06ABEH001143","type":"journal-article"},{"key":"h2sn-wvzmCc18R1","doi-asserted-by":"publisher","DOI":"10.1016\/0370-1573(79)90023-1","type":"journal-article"},{"key":"h2sn-wvzmCc19R1","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-1693-1","type":"book","volume-title":"Mathematical Methods of Classical Mechanics","author":"V.\u00a0I. Arnold","year":"1978"},{"key":"h2sn-wvzmCc20R1","unstructured":"In keeping with Ref.   [7], we use the definition \u03a90=+\u03b3B0, opposite in sign to the more common definition. Owing to this, e.g., irradiation on resonance for Rabi rotation is at \u03c9=\u2212\u03a90 as shown in Fig.\u00a0  1.","type":"other"},{"key":"h2sn-wvzmCc21R1","unstructured":"The signs of the nonsecular resonances are immaterial for our experiments, since the applied rf field is linearly polarized. The field is written as a superposition of two counter-rotating circularly polarized fields, and only the circularly polarized part with the correct sign\/polarization affects the spins.","type":"other"},{"key":"h2sn-wvzmCc22R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.101.067601","type":"journal-article"},{"key":"h2sn-wvzmCc23R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.108.177602","type":"journal-article"},{"key":"h2sn-wvzmCc24R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.72.054427","type":"journal-article"},{"key":"h2sn-wvzmCc25R1","unstructured":"To emphasize averaged Hamiltonians, we use \u2329\u2329...\u232aB0\u232aB1 to denote the consecutive averages over the action of B0 and B1 in the Van Vleck\u2013Redfield two-step truncation. The averaging over the full rotation after Kropf and Fine   [7] is denoted by \u2329...\u232aB0,B1.","type":"other"},{"key":"h2sn-wvzmCc26R1","unstructured":"In this work we explicitly mark doubly rotating frame Hamiltonians using the \u2032 symbol. In the earlier works   [7, 8], the frame is defined implicitly via the spin operators that appear within the Hamiltonian.","type":"other"},{"key":"h2sn-wvzmCc27R1","unstructured":"See Supplemental Material at http:\/\/link.aps.org\/supplemental\/10.1103\/h2sn-wvzm for details regarding the predictions for all five homonuclear NSRs as well as additional experimental details and supplementary data.","type":"other"},{"key":"h2sn-wvzmCc28R1","doi-asserted-by":"publisher","DOI":"10.1039\/B206263A","type":"journal-article"},{"key":"h2sn-wvzmCc29R1","doi-asserted-by":"publisher","DOI":"10.1039\/C6CP02853E","type":"journal-article"},{"key":"h2sn-wvzmCc30R1","unstructured":"We increased the frequency by 5\u00a0kHz every 1 ms (990 \u00b5s irradiation with 10 \u00b5s breaks).","type":"other"}],"container-title":["Physical Review B"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.aps.org\/article\/10.1103\/h2sn-wvzm","content-type":"unspecified","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/harvest.aps.org\/v2\/journals\/articles\/10.1103\/h2sn-wvzm\/fulltext","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T21:17:17Z","timestamp":1790716637000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.aps.org\/doi\/10.1103\/h2sn-wvzm"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,8,11]]},"references-count":30,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2025,8]]}},"URL":"https:\/\/doi.org\/10.1103\/h2sn-wvzm","relation":{},"ISSN":["2469-9950","2469-9969"],"issn-type":[{"value":"2469-9950","type":"print"},{"value":"2469-9969","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,8,11]]},"assertion":[{"value":"2025-03-12","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"Published by the 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":"2025","name":"copyright_year","label":"Copyright year","group":{"name":"copyright","label":"copyright"}},{"value":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/","name":"creative_commons_license","label":"Creative Commons license","group":{"name":"licenses","label":"Licenses"}},{"value":"\u00a92025 The authors","name":"copyright_holder","label":"Copyright holder","group":{"name":"copyright","label":"copyright"}}],"article-number":"L060302"}}