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Phys.: Condens. Matter"],"published-print":{"date-parts":[[2021,4,7]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    We report the electronic structure and magnetic properties of Co\n                    <jats:sub>2<\/jats:sub>\n                    Ti\n                    <jats:sub>\n                      1\u2212\n                      <jats:italic>x<\/jats:italic>\n                    <\/jats:sub>\n                    Ge\n                    <jats:sub>\n                      <jats:italic>x<\/jats:italic>\n                    <\/jats:sub>\n                    O\n                    <jats:sub>4<\/jats:sub>\n                    (0 \u2a7d\n                    <jats:italic>x<\/jats:italic>\n                    \u2a7d 1) spinel by means of the first-principle methods of density functional theory involving generalized gradient approximation along with the on-site Coulomb interaction (\n                    <jats:italic>U<\/jats:italic>\n                    <jats:sub>eff<\/jats:sub>\n                    ) in the exchange-correlation energy functional. Special emphasis has been given to explore the site occupancy of Ge atoms in the spinel lattice by introducing the cationic disorder parameter (\n                    <jats:italic>y<\/jats:italic>\n                    ) which is done in such a way that one can tailor the pyrochlore geometry and determine the electronic\/magnetic structure quantitatively. For all the compositions (\n                    <jats:italic>x<\/jats:italic>\n                    ), the system exhibits weak tetragonal distortion (\n                    <jats:italic>c<\/jats:italic>\n                    \/\n                    <jats:italic>a<\/jats:italic>\n                    \u2260 1) due to the non-degenerate\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\" display=\"inline\" overflow=\"scroll\">\n                        <mml:msub>\n                          <mml:mrow>\n                            <mml:mi>d<\/mml:mi>\n                          <\/mml:mrow>\n                          <mml:mrow>\n                            <mml:msup>\n                              <mml:mrow>\n                                <mml:mi>z<\/mml:mi>\n                              <\/mml:mrow>\n                              <mml:mrow>\n                                <mml:mn>2<\/mml:mn>\n                              <\/mml:mrow>\n                            <\/mml:msup>\n                          <\/mml:mrow>\n                        <\/mml:msub>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    and\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\" display=\"inline\" overflow=\"scroll\">\n                        <mml:msub>\n                          <mml:mrow>\n                            <mml:mi>d<\/mml:mi>\n                          <\/mml:mrow>\n                          <mml:mrow>\n                            <mml:msup>\n                              <mml:mrow>\n                                <mml:mi>x<\/mml:mi>\n                              <\/mml:mrow>\n                              <mml:mrow>\n                                <mml:mn>2<\/mml:mn>\n                              <\/mml:mrow>\n                            <\/mml:msup>\n                            <mml:mo>\u2212<\/mml:mo>\n                            <mml:msup>\n                              <mml:mrow>\n                                <mml:mi>y<\/mml:mi>\n                              <\/mml:mrow>\n                              <mml:mrow>\n                                <mml:mn>2<\/mml:mn>\n                              <\/mml:mrow>\n                            <\/mml:msup>\n                          <\/mml:mrow>\n                        <\/mml:msub>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    states (\n                    <jats:italic>e<\/jats:italic>\n                    <jats:sub>\n                      <jats:italic>g<\/jats:italic>\n                    <\/jats:sub>\n                    orbitals) of the B-site Co. We observe large exchange splitting (\u0394\n                    <jats:sub>EX<\/jats:sub>\n                    \u223c 9\u00a0eV) between the up and down spin bands of\n                    <jats:italic>t<\/jats:italic>\n                    <jats:sub>\n                      2\n                      <jats:italic>g<\/jats:italic>\n                    <\/jats:sub>\n                    and\n                    <jats:italic>e<\/jats:italic>\n                    <jats:sub>\n                      <jats:italic>g<\/jats:italic>\n                    <\/jats:sub>\n                    states, respectively, of tetrahedral and octahedral Co\n                    <jats:sup>2+<\/jats:sup>\n                    (\n                    <jats:sup>4<\/jats:sup>\n                    A\n                    <jats:sub>\n                      2(\n                      <jats:italic>g<\/jats:italic>\n                      )\n                    <\/jats:sub>\n                    (F)) and moderate crystal-field splitting (\u0394\n                    <jats:sub>CF<\/jats:sub>\n                    \u223c 4\u00a0eV) and the Jahn\u2013Teller distortion (\u0394\n                    <jats:sub>JT<\/jats:sub>\n                    \u223c 0.9\u00a0eV). These features indicate the strong intra-atomic interaction which is also responsible for the alteration of energy band-gap (1.7\u00a0eV \u2a7d\n                    <jats:italic>E<\/jats:italic>\n                    <jats:sub>\n                      <jats:italic>g<\/jats:italic>\n                    <\/jats:sub>\n                    \u2a7d 3.3\u00a0eV). The exchange interaction (\n                    <jats:italic>J<\/jats:italic>\n                    <jats:sub>BB<\/jats:sub>\n                    \u223c \u22124.8 meV, for (\n                    <jats:italic>x<\/jats:italic>\n                    ,\n                    <jats:italic>y<\/jats:italic>\n                    ) = (0.25, 0)) between the Co\n                    <jats:sup>2+<\/jats:sup>\n                    dominates the overall antiferromagnetic behaviour of the system for all \u2018\n                    <jats:italic>x<\/jats:italic>\n                    \u2019 as compared to\n                    <jats:italic>J<\/jats:italic>\n                    <jats:sub>AA<\/jats:sub>\n                    (\u223c\u22122.2 meV, for (\n                    <jats:italic>x<\/jats:italic>\n                    ,\n                    <jats:italic>y<\/jats:italic>\n                    ) = (0.25, 0)) and\n                    <jats:italic>J<\/jats:italic>\n                    <jats:sub>AB<\/jats:sub>\n                    (\u223c\u22121.8 meV, for (\n                    <jats:italic>x<\/jats:italic>\n                    ,\n                    <jats:italic>y<\/jats:italic>\n                    ) = (0.25, 0)). For all the compositions without any disorderness in the system, the net ferrimagnetic moment (\u0394\n                    <jats:italic>\u03bc<\/jats:italic>\n                    ) remains constant, however, increases progressively with increasing\n                    <jats:italic>x<\/jats:italic>\n                    due to the imbalance of Co spins between the A- and B-sites.\n                  <\/jats:p>","DOI":"10.1088\/1361-648x\/abddfe","type":"journal-article","created":{"date-parts":[[2021,1,20]],"date-time":"2021-01-20T17:31:21Z","timestamp":1611163881000},"page":"145504","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":4,"title":["Tailoring the electronic structure and magnetic properties of pyrochlore Co\n                    <sub>2<\/sub>\n                    Ti\n                    <sub>\n                      1\u2212\n                      <i>x<\/i>\n                    <\/sub>\n                    Ge\n                    <sub>\n                      <i>x<\/i>\n                    <\/sub>\n                    O\n                    <sub>4<\/sub>\n                    : a GGA +\n                    <i>U<\/i>\n                    <i>ab initio<\/i>\n                    study"],"prefix":"10.1088","volume":"33","author":[{"given":"Sayandeep","family":"Ghosh","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sobhit","family":"Singh","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Debashish","family":"Das","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Subhradip","family":"Ghosh","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pankaj Kumar","family":"Mishra","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0740-2195","authenticated-orcid":false,"given":"Subhash","family":"Thota","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"266","published-online":{"date-parts":[[2021,2,16]]},"reference":[{"key":"cmabddfebib1","doi-asserted-by":"publisher","first-page":"99","DOI":"10.1143\/jpsj.17.99","type":"journal-article","article-title":"Magnetic properties of cobalt titanate","volume":"17","author":"Sakamoto","year":"1962","journal-title":"J. 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