{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,20]],"date-time":"2026-02-20T03:13:20Z","timestamp":1771557200239,"version":"3.50.1"},"reference-count":65,"publisher":"IOP Publishing","issue":"1","license":[{"start":{"date-parts":[[2023,12,15]],"date-time":"2023-12-15T00:00:00Z","timestamp":1702598400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2023,12,15]],"date-time":"2023-12-15T00:00:00Z","timestamp":1702598400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/iopscience.iop.org\/info\/page\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100003407","name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca","doi-asserted-by":"crossref","award":["2017Z8TS5B"],"award-info":[{"award-number":["2017Z8TS5B"]}],"id":[{"id":"10.13039\/501100003407","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100021856","name":"Ministero dell\u2019Universit\u00e0 e della Ricerca","doi-asserted-by":"crossref","award":["2022ZY8HJY"],"award-info":[{"award-number":["2022ZY8HJY"]}],"id":[{"id":"10.13039\/501100021856","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["iopscience.iop.org"],"crossmark-restriction":false},"short-container-title":["2D Mater."],"published-print":{"date-parts":[[2024,1,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Bilayer CrI<jats:sub>3<\/jats:sub> attracted much attention due to stacking-induced switching between the layered ferromagnetic and antiferromagnetic order. This discovery brought under the spotlight the interlayer Cr\u2013Cr exchange interaction, which despite being much weaker than the intralayer exchange, plays an important role in shaping the magnetic properties of bilayer CrI<jats:sub>3<\/jats:sub>. In this work we delve into the anisotropic part of the interlayer exchange with the aim to separate the contributions from the Dzyaloshinskii\u2013Moriya (DMI) and the Kitaev interactions (KI). We leverage the density functional theory calculations with spin Hamiltonian modeling and develop an energy mapping procedure to assess these anisotropic interactions with <jats:inline-formula>\n                     <jats:tex-math\/>\n                     <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mi>\u03bc<\/mml:mi>\n                        <mml:mrow>\n                           <mml:mi mathvariant=\"normal\">e<\/mml:mi>\n                           <mml:mi mathvariant=\"normal\">V<\/mml:mi>\n                        <\/mml:mrow>\n                     <\/mml:math>\n                     <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"tdmad1313ieqn1.gif\" xlink:type=\"simple\"\/>\n                  <\/jats:inline-formula> accuracy. After inspecting the rhombohedral and monoclinic stacking sequences of bilayer CrI<jats:sub>3<\/jats:sub>, we reveal a considerable DMI and a weak interlayer KI between the sublattices of a monoclinic bilayer. We explain the dependence of DMI and KI on the interlayer distance, stacking sequence, and the spin\u2013orbit coupling strength, and we suggest the dominant superexchange processes at play. In addition, we demonstrate that the single-ion anisotropy in bilayer CrI<jats:sub>3<\/jats:sub> is highly stacking-dependent, increasing by 50% from monoclinic to rhombohedral bilayer. Remarkably, our findings prove that iodines are highly efficient in mediating the DMI across the van der Waals gap, much owing to spatially extended 5<jats:italic>p<\/jats:italic> orbitals which feature strong spin\u2013orbit coupling. Our study gives promise that the interlayer chiral control of spin textures, demonstrated in thin metallic films where the DMI is with a much longer range, can be achieved with similar efficiency in semiconducting two-dimensional van der Waals magnets.<\/jats:p>","DOI":"10.1088\/2053-1583\/ad1313","type":"journal-article","created":{"date-parts":[[2023,12,6]],"date-time":"2023-12-06T22:55:33Z","timestamp":1701903333000},"page":"015020","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":8,"title":["Delving into the anisotropic interlayer exchange in bilayer CrI<sub>3<\/sub>"],"prefix":"10.1088","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2097-0955","authenticated-orcid":true,"given":"Srdjan","family":"Stavri\u0107","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7222-8627","authenticated-orcid":true,"given":"Paolo","family":"Barone","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Silvia","family":"Picozzi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"266","published-online":{"date-parts":[[2023,12,15]]},"reference":[{"key":"tdmad1313bib1","doi-asserted-by":"publisher","first-page":"270","DOI":"10.1038\/nature22391","article-title":"Layer-dependent ferromagnetism in a van der Waals crystal down to the monolayer limit","volume":"546","author":"Huang","year":"2017","journal-title":"Nature"},{"key":"tdmad1313bib2","doi-asserted-by":"publisher","first-page":"265","DOI":"10.1038\/nature22060","article-title":"Discovery of intrinsic ferromagnetism in two-dimensional van der Waals crystals","volume":"546","author":"Gong","year":"2017","journal-title":"Nature"},{"key":"tdmad1313bib3","doi-asserted-by":"publisher","first-page":"1218","DOI":"10.1126\/science.aar3617","article-title":"Probing magnetism in 2D van der Waals crystalline insulators via electron tunneling","volume":"360","author":"Klein","year":"2018","journal-title":"Science"},{"key":"tdmad1313bib4","doi-asserted-by":"publisher","first-page":"1214","DOI":"10.1126\/science.aar4851","article-title":"Giant tunneling magnetoresistance in spin-filter van der Waals heterostructures","volume":"360","author":"Song","year":"2018","journal-title":"Science"},{"key":"tdmad1313bib5","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1038\/s41467-018-04953-8","article-title":"Very large tunneling magnetoresistance in layered magnetic semiconductor CrI3","volume":"9","author":"Wang","year":"2018","journal-title":"Nat. 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