{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,12]],"date-time":"2026-10-12T11:25:42Z","timestamp":1791804342434,"version":"4.3.4"},"reference-count":74,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2024,8,30]],"date-time":"2024-08-30T00:00:00Z","timestamp":1724976000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2024,8,30]],"date-time":"2024-08-30T00:00:00Z","timestamp":1724976000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["npj 2D Mater Appl"],"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Although chromium trihalides are widely regarded as a promising class of two-dimensional magnets for next-generation devices, an accurate description of their electronic structure and magnetic interactions has proven challenging to achieve. Here, we quantify electronic excitations and spin interactions in Cr<jats:italic>X<\/jats:italic><jats:sub>3<\/jats:sub> (<jats:italic>X<\/jats:italic> = Cl, Br, I) using embedded many-body wavefunction calculations and fully generalized spin Hamiltonians. We find that the three trihalides feature comparable <jats:italic>d<\/jats:italic>-shell excitations, consisting of a high-spin <jats:sup>4<\/jats:sup><jats:italic>A<\/jats:italic><jats:sub>2<\/jats:sub><jats:inline-formula><jats:alternatives><jats:tex-math>$$({t}_{2g}^{3}{e}_{g}^{0})$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mo>(<\/mml:mo>\n                    <mml:mrow>\n                      <mml:msubsup>\n                        <mml:mrow>\n                          <mml:mi>t<\/mml:mi>\n                        <\/mml:mrow>\n                        <mml:mrow>\n                          <mml:mn>2<\/mml:mn>\n                          <mml:mi>g<\/mml:mi>\n                        <\/mml:mrow>\n                        <mml:mrow>\n                          <mml:mn>3<\/mml:mn>\n                        <\/mml:mrow>\n                      <\/mml:msubsup>\n                      <mml:msubsup>\n                        <mml:mrow>\n                          <mml:mi>e<\/mml:mi>\n                        <\/mml:mrow>\n                        <mml:mrow>\n                          <mml:mi>g<\/mml:mi>\n                        <\/mml:mrow>\n                        <mml:mrow>\n                          <mml:mn>0<\/mml:mn>\n                        <\/mml:mrow>\n                      <\/mml:msubsup>\n                    <\/mml:mrow>\n                    <mml:mo>)<\/mml:mo>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> ground state lying 1.5\u20131.7\u2009eV below the first excited state <jats:sup>4<\/jats:sup><jats:italic>T<\/jats:italic><jats:sub>2<\/jats:sub> (<jats:inline-formula><jats:alternatives><jats:tex-math>$${t}_{2g}^{2}{e}_{g}^{1}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:msubsup>\n                      <mml:mrow>\n                        <mml:mi>t<\/mml:mi>\n                      <\/mml:mrow>\n                      <mml:mrow>\n                        <mml:mn>2<\/mml:mn>\n                        <mml:mi>g<\/mml:mi>\n                      <\/mml:mrow>\n                      <mml:mrow>\n                        <mml:mn>2<\/mml:mn>\n                      <\/mml:mrow>\n                    <\/mml:msubsup>\n                    <mml:msubsup>\n                      <mml:mrow>\n                        <mml:mi>e<\/mml:mi>\n                      <\/mml:mrow>\n                      <mml:mrow>\n                        <mml:mi>g<\/mml:mi>\n                      <\/mml:mrow>\n                      <mml:mrow>\n                        <mml:mn>1<\/mml:mn>\n                      <\/mml:mrow>\n                    <\/mml:msubsup>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>). CrCl<jats:sub>3<\/jats:sub> exhibits a single-ion anisotropy <jats:italic>A<\/jats:italic><jats:sub>sia<\/jats:sub>\u2009=\u2009\u2212\u20090.02\u2009meV, while the Cr spin-3\/2 moments are ferromagnetically coupled through bilinear and biquadratic exchange interactions of <jats:italic>J<\/jats:italic><jats:sub>1<\/jats:sub>\u2009=\u2009\u2212\u20090.97\u2009meV and <jats:italic>J<\/jats:italic><jats:sub>2<\/jats:sub>\u2009=\u2009\u2212\u20090.05\u2009meV, respectively. The corresponding values for CrBr<jats:sub>3<\/jats:sub> and CrI<jats:sub>3<\/jats:sub> increase to <jats:italic>A<\/jats:italic><jats:sub>sia<\/jats:sub>\u2009=\u2009\u22120.08\u2009meV and <jats:italic>A<\/jats:italic><jats:sub>sia<\/jats:sub>=\u2009\u2212\u20090.12\u2009meV for the single-ion anisotropy, <jats:italic>J<\/jats:italic><jats:sub>1<\/jats:sub>\u2009=\u2009\u22121.21\u2009meV, <jats:italic>J<\/jats:italic><jats:sub>2<\/jats:sub>\u2009=\u2009\u22120.05\u2009meV and <jats:italic>J<\/jats:italic><jats:sub>1<\/jats:sub>\u2009=\u2009\u22121.38 meV, <jats:italic>J<\/jats:italic><jats:sub>2<\/jats:sub>\u2009=\u2009\u22120.06 meV for the exchange couplings, respectively. We find that the overall magnetic anisotropy is defined by the interplay between <jats:italic>A<\/jats:italic><jats:sub>sia<\/jats:sub> and <jats:italic>A<\/jats:italic><jats:sub>dip<\/jats:sub> due to magnetic dipole\u2013dipole interaction that favors in-plane orientation of magnetic moments in ferromagnetic monolayers and bulk layered magnets. The competition between the two contributions sets CrCl<jats:sub>3<\/jats:sub> and CrI<jats:sub>3<\/jats:sub> as the easy-plane (<jats:italic>A<\/jats:italic><jats:sub>sia<\/jats:sub> + <jats:italic>A<\/jats:italic><jats:sub>dip<\/jats:sub> &gt;0) and easy-axis (<jats:italic>A<\/jats:italic><jats:sub>sia<\/jats:sub> + <jats:italic>A<\/jats:italic><jats:sub>dip<\/jats:sub> &lt;0) ferromagnets, respectively. The differences between the magnets trace back to the atomic radii of the halogen ligands and the magnitude of spin\u2013orbit coupling. Our findings are in excellent agreement with recent experiments, thus providing reference values for the fundamental interactions in chromium trihalides.<\/jats:p>","DOI":"10.1038\/s41699-024-00494-5","type":"journal-article","created":{"date-parts":[[2024,8,30]],"date-time":"2024-08-30T17:02:34Z","timestamp":1725037354000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Electronic excitations and spin interactions in chromium trihalides from embedded many-body wavefunctions"],"prefix":"10.1038","volume":"8","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9394-6863","authenticated-orcid":false,"given":"Ravi","family":"Yadav","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3933-5521","authenticated-orcid":false,"given":"Lei","family":"Xu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Michele","family":"Pizzochero","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6594-9610","authenticated-orcid":false,"given":"Jeroen","family":"van den Brink","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5165-7553","authenticated-orcid":false,"given":"Mikhail I.","family":"Katsnelson","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7281-3199","authenticated-orcid":false,"given":"Oleg V.","family":"Yazyev","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2024,8,30]]},"reference":[{"key":"494_CR1","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1038\/s41586-018-0631-z","volume":"563","author":"KS Burch","year":"2018","unstructured":"Burch, K. 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