{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,9]],"date-time":"2026-01-09T23:40:15Z","timestamp":1768002015292,"version":"3.49.0"},"reference-count":22,"publisher":"AIP Publishing","issue":"23","license":[{"start":{"date-parts":[[2024,6,17]],"date-time":"2024-06-17T00:00:00Z","timestamp":1718582400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2024,6,17]],"date-time":"2024-06-17T00:00:00Z","timestamp":1718582400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Max Planck Society"}],"content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2024,6,21]]},"abstract":"<jats:p>The interaction between the magnetic moment of an electron and the magnetic field generated by a moving charge is one component of the spin\u2013orbit interaction. The nuclei in a molecule or solid are charged, are generally in vibrational motion, and so contribute to this interaction, but the direct coupling between nuclear momentum and electron spin is normally ignored in discussions of spin-forbidden phenomena such as transitions between states of different spin, even when the nuclei are recognized as playing a fundamental role (spin\u2013vibronic coupling). Here, we investigate the spin\u2013orbit interaction in a Heisenberg model interacting with vibrating point charges representing nearby bridging ligands. To reach the model, we apply second order perturbation theory to the Hubbard model with the spin\u2013orbit interaction. In contrast to the other components of the spin\u2013orbit interaction, the part that directly couples the momentum of the charge and electron spin appears at first order as an effective magnetic field at each site. We find that the inclusion of this nuclear-motion induced spin\u2013orbit coupling can increase the rate of otherwise spin-forbidden transitions between different spin states of the Heisenberg model by many orders of magnitude. This overlooked interaction may, therefore, play a significant role in spin-forbidden phenomena such as spin relaxation in coupled spin-qubits.<\/jats:p>","DOI":"10.1063\/5.0209702","type":"journal-article","created":{"date-parts":[[2024,6,17]],"date-time":"2024-06-17T11:42:25Z","timestamp":1718624545000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":2,"title":["The direct role of nuclear motion in spin\u2013orbit coupling in strongly correlated spin systems"],"prefix":"10.1063","volume":"160","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2916-1233","authenticated-orcid":false,"given":"M. J.","family":"Willatt","sequence":"first","affiliation":[{"name":"Max Planck Institute for Solid State Research 1 , Heisenbergstra\u00dfe 1, 70569 Stuttgart, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0654-9489","authenticated-orcid":false,"given":"A.","family":"Alavi","sequence":"additional","affiliation":[{"name":"Max Planck Institute for Solid State Research 1 , Heisenbergstra\u00dfe 1, 70569 Stuttgart, Germany"},{"name":"Yusuf Hamied Department of Chemistry, University of Cambridge 2 , Lensfield Road, Cambridge CB2 1EW, United Kingdom"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"317","published-online":{"date-parts":[[2024,6,17]]},"reference":[{"key":"2024061711421467100_c1","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1126\/sciadv.aax7163","article-title":"How do phonons relax molecular spins?","volume":"5","year":"2019","journal-title":"Sci. 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