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In this study we consider electronic and magnetic properties of MXene Fe\n                    <jats:sub>2<\/jats:sub>\n                    C within the DFT+DMFT approach. We establish the existence of local magnetic moments\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:msub>\n                          <mml:mi>\u03bc<\/mml:mi>\n                          <mml:mrow>\n                            <mml:mrow>\n                              <mml:mi mathvariant=\"normal\">l<\/mml:mi>\n                              <mml:mi mathvariant=\"normal\">o<\/mml:mi>\n                              <mml:mi mathvariant=\"normal\">c<\/mml:mi>\n                            <\/mml:mrow>\n                          <\/mml:mrow>\n                        <\/mml:msub>\n                        <mml:mo>=<\/mml:mo>\n                        <mml:mn>3.3<\/mml:mn>\n                        <mml:msub>\n                          <mml:mi>\u03bc<\/mml:mi>\n                          <mml:mi>B<\/mml:mi>\n                        <\/mml:msub>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    in this compound, characterized by sufficiently long lifetime of\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:mi>\u03c4<\/mml:mi>\n                        <mml:mo>\u223c<\/mml:mo>\n                        <mml:mn>350<\/mml:mn>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    \u2009fs. We also calculate exchange interaction parameters accounting for electronic correlations using the recently developed approach for paramagnetic phase. At low temperatures, we obtain the strongest exchange interaction 11\u2009meV between next nearest neighboring Fe atoms, located above (or below) the carbon plane, and the subleading interaction 6\u2009meV between the next to next nearest neighboring atoms, located across the carbon plane. The resulting dependence of the Berzinskii\u2013Kosterlitz\u2013Thouless (BKT) and Curie temperatures on magnetic anisotropy is obtained. The BKT temperature for the pristine Fe\n                    <jats:sub>2<\/jats:sub>\n                    C is\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:msub>\n                          <mml:mi>T<\/mml:mi>\n                          <mml:mrow>\n                            <mml:mrow>\n                              <mml:mi mathvariant=\"normal\">B<\/mml:mi>\n                              <mml:mi mathvariant=\"normal\">K<\/mml:mi>\n                              <mml:mi mathvariant=\"normal\">T<\/mml:mi>\n                            <\/mml:mrow>\n                          <\/mml:mrow>\n                        <\/mml:msub>\n                        <mml:mo>\u2243<\/mml:mo>\n                        <mml:mn>300<\/mml:mn>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    \u2009K, which makes this compound a good candidate for the two-dimensional ferromagnet with XY anisotropy.\n                  <\/jats:p>","DOI":"10.1088\/2053-1583\/ad10bc","type":"journal-article","created":{"date-parts":[[2023,11,29]],"date-time":"2023-11-29T17:23:45Z","timestamp":1701278625000},"page":"025001","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":9,"title":["MXene Fe\n                    <sub>2<\/sub>\n                    C as a promising candidate for the 2D XY ferromagnet"],"prefix":"10.1088","volume":"11","author":[{"given":"E M","family":"Agapov","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"I A","family":"Kruglov","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1574-657X","authenticated-orcid":true,"given":"A A","family":"Katanin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"266","published-online":{"date-parts":[[2024,1,4]]},"reference":[{"key":"tdmad10bcbib1","doi-asserted-by":"publisher","first-page":"197","DOI":"10.1038\/nature04233","volume":"438","author":"Novoselov","year":"2005","journal-title":"Nature"},{"key":"tdmad10bcbib2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.88.201402","volume":"88","author":"Sachs","year":"2013","journal-title":"Phys. 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