{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,10]],"date-time":"2026-06-10T15:22:16Z","timestamp":1781104936543,"version":"3.54.1"},"reference-count":54,"publisher":"National Academy of Sciences","issue":"5","license":[{"start":{"date-parts":[[2026,1,29]],"date-time":"2026-01-29T00:00:00Z","timestamp":1769644800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"content-domain":{"domain":["www.pnas.org"],"crossmark-restriction":true},"short-container-title":["Proc. Natl. Acad. Sci. U.S.A."],"published-print":{"date-parts":[[2026,2,3]]},"abstract":"<jats:p>Magnetoelectric coupling enables the manipulation of magnetization by electric fields and polarization by magnetic fields. While typically found in heavy element materials with large spin\u2013orbit coupling, recent experiments on rhombohedral-stacked pentalayer graphene have demonstrated a longitudinal magnetoelectric coupling (LMC) without spin\u2013orbit coupling. Here, we develop a microscopic theory of LMC in layered quantum materials and identify how it is controlled by a \u201clayer-space\u201d quantum geometry. Focusing on rhombohedral multilayer graphene systems, we find that the interplay between LMC and valley-polarized order produces a butterfly shaped magnetic hysteresis controlled by out-of-plane electric field: a signature of LMC and a multiferroic valley order. Furthermore, we identify a nonlinear LMC in rhombohedral multilayer graphene under time-reversal symmetry, while the absence of centrosymmetry enables the generation of a second-order nonlinear electric dipole moment in response to an out-of-plane magnetic field. Our theoretical framework provides a quantitative understanding of LMC, as well as the emergent magnetoelectric properties of rhombohedral multilayer graphene.<\/jats:p>","DOI":"10.1073\/pnas.2506751123","type":"journal-article","created":{"date-parts":[[2026,1,29]],"date-time":"2026-01-29T17:08:08Z","timestamp":1769706488000},"update-policy":"https:\/\/doi.org\/10.1073\/pnas.cm10313","source":"Crossref","is-referenced-by-count":0,"title":["Orbital longitudinal magnetoelectric coupling in rhombohedral multilayer graphene"],"prefix":"10.1073","volume":"123","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5865-3704","authenticated-orcid":false,"given":"Jin-Xin","family":"Hu","sequence":"first","affiliation":[{"name":"Division of Physics and Applied Physics","place":["Singapore, Singapore"]},{"name":"School of Physical and Mathematical Sciences","place":["Singapore, Singapore"]},{"name":"Nanyang Technological University","place":["Singapore, Singapore"]},{"name":"Department of Physics","place":["Hong Kong, China"]},{"name":"Hong Kong University of Science and Technology, Clear Water Bay","place":["Hong Kong, China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5175-6970","authenticated-orcid":false,"given":"Justin C. 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