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Using density functional theory, we compute contributions from the spin and orbital angular momentum as well as lattice-mediated (LM) and clamped-ion (CI) analogs to fully characterize the linear ME tensor in the static limit. We observe a general trend that AFM ordering gives rise to a larger ME response compared to FM ordered MLs. Using a typical van der Waals interlayer distance, we find that AFM\n                    <jats:inline-formula>\n                      <jats:tex-math>\n                        \n                      <\/jats:tex-math>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mrow>\n                          <mml:msub>\n                            <mml:mrow>\n                              <mml:mi>Mn<\/mml:mi>\n                            <\/mml:mrow>\n                            <mml:mn>2<\/mml:mn>\n                          <\/mml:msub>\n                          <mml:msub>\n                            <mml:mrow>\n                              <mml:mi>SI<\/mml:mi>\n                            <\/mml:mrow>\n                            <mml:mn>2<\/mml:mn>\n                          <\/mml:msub>\n                        <\/mml:mrow>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    exhibits the strongest component of linear ME response, providing approximately 580\u2009ps\u2009m\n                    <jats:sup>\u22121<\/jats:sup>\n                    . This is two orders of magnitude greater than in prototypical\n                    <jats:inline-formula>\n                      <jats:tex-math>\n                        \n                      <\/jats:tex-math>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mrow>\n                          <mml:msub>\n                            <mml:mrow>\n                              <mml:mi>Cr<\/mml:mi>\n                            <\/mml:mrow>\n                            <mml:mn>2<\/mml:mn>\n                          <\/mml:msub>\n                          <mml:msub>\n                            <mml:mrow>\n                              <mml:mi mathvariant=\"normal\">O<\/mml:mi>\n                            <\/mml:mrow>\n                            <mml:mn>3<\/mml:mn>\n                          <\/mml:msub>\n                        <\/mml:mrow>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    but comparable to the largest ME response measured in bulk\n                    <jats:inline-formula>\n                      <jats:tex-math>\n                        \n                      <\/jats:tex-math>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mrow>\n                          <mml:msub>\n                            <mml:mrow>\n                              <mml:mi>TbPO<\/mml:mi>\n                            <\/mml:mrow>\n                            <mml:mn>4<\/mml:mn>\n                          <\/mml:msub>\n                        <\/mml:mrow>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    (280\u2013740\u2009ps\u2009m\n                    <jats:sup>\u22121<\/jats:sup>\n                    ). We also search for antimagnetoelectricity and find a number of FM and AFM compounds with antiferroic tensor entries. By demonstration of select examples and analysis of our full data set, we argue that inclusion of all contributions (spin, orbital, LM and CI) is of crucial importance for reliable predictions of the total ME response.\n                  <\/jats:p>","DOI":"10.1088\/2053-1583\/ae1d91","type":"journal-article","created":{"date-parts":[[2025,11,10]],"date-time":"2025-11-10T22:48:43Z","timestamp":1762814923000},"page":"015011","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":1,"title":["Fully characterized linear magnetoelectric response of 2D monolayers from high-throughput first-principles calculations"],"prefix":"10.1088","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8531-613X","authenticated-orcid":true,"given":"John","family":"Mangeri","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6256-9284","authenticated-orcid":true,"given":"Thomas","family":"Olsen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"266","published-online":{"date-parts":[[2025,11,26]]},"reference":[{"key":"tdmae1d91bib1","doi-asserted-by":"publisher","DOI":"10.1063\/1.4812323","type":"journal-article","volume":"1","author":"Jain","year":"2013","journal-title":"APL Mater."},{"key":"tdmae1d91bib2","doi-asserted-by":"publisher","first-page":"11","DOI":"10.1007\/s11837-013-0755-4","type":"journal-article","volume":"65","author":"Saal","year":"2013","journal-title":"JOM"},{"key":"tdmae1d91bib3","doi-asserted-by":"publisher","DOI":"10.1088\/2053-1583\/ac1059","type":"journal-article","volume":"8","author":"Gjerding","year":"2021","journal-title":"2D Mater."},{"key":"tdmae1d91bib4","doi-asserted-by":"publisher","first-page":"299","DOI":"10.1140\/epjb\/e2009-00336-7","type":"journal-article","volume":"71","author":"Rivera","year":"2009","journal-title":"Eur. 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