{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,11,5]],"date-time":"2026-11-05T03:56:29Z","timestamp":1793850989032,"version":"4.6.1"},"reference-count":39,"publisher":"American Physical Society (APS)","issue":"1","license":[{"start":{"date-parts":[[2025,7,17]],"date-time":"2025-07-17T00:00:00Z","timestamp":1752710400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000769","name":"University of Oxford","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100000769","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["journals.aps.org"],"crossmark-restriction":true},"short-container-title":["Phys. Rev. B"],"accepted":{"date-parts":[[2025,6,12]]},"abstract":"<jats:p>\n                    We present a formalism based on color symmetry to analyze the momentum-space spin textures of noncollinear antiferromagnets. We show that, out of the spin textures allowed by the magnetic point group, one can extract a component that is invariant by general rotations in spin space, and can exist in the absence of spin-orbit coupling, in complete analogy to spin textures in altermagnets. We demonstrate this approach in the case of three complex, noncollinear magnets,\n                    <a:math xmlns:a=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                      <a:mrow>\n                        <a:msub>\n                          <a:mi>Mn<\/a:mi>\n                          <a:mn>3<\/a:mn>\n                        <\/a:msub>\n                        <a:mi>Ir<\/a:mi>\n                        <a:mo>(<\/a:mo>\n                        <a:mi>Ge<\/a:mi>\n                        <a:mo>,<\/a:mo>\n                        <a:mi>Si<\/a:mi>\n                        <a:mo>)<\/a:mo>\n                      <\/a:mrow>\n                    <\/a:math>\n                    ,\n                    <b:math xmlns:b=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                      <b:mrow>\n                        <b:msub>\n                          <b:mi>Pb<\/b:mi>\n                          <b:mn>2<\/b:mn>\n                        <\/b:msub>\n                        <b:msub>\n                          <b:mi>MnO<\/b:mi>\n                          <b:mn>4<\/b:mn>\n                        <\/b:msub>\n                      <\/b:mrow>\n                    <\/b:math>\n                    , and\n                    <c:math xmlns:c=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                      <c:mrow>\n                        <c:msub>\n                          <c:mi>Mn<\/c:mi>\n                          <c:mn>3<\/c:mn>\n                        <\/c:msub>\n                        <c:mi>GaN<\/c:mi>\n                      <\/c:mrow>\n                    <\/c:math>\n                    . For\n                    <d:math xmlns:d=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                      <d:mrow>\n                        <d:msub>\n                          <d:mi>Mn<\/d:mi>\n                          <d:mn>3<\/d:mn>\n                        <\/d:msub>\n                        <d:mi>GaN<\/d:mi>\n                      <\/d:mrow>\n                    <\/d:math>\n                    , we also show that the predictions of color-symmetry analysis are consistent with density functional theory calculations performed on the same system both with and without spin-orbit coupling.\n                  <\/jats:p>","DOI":"10.1103\/r34k-xjpx","type":"journal-article","created":{"date-parts":[[2025,6,12]],"date-time":"2025-06-12T17:36:01Z","timestamp":1749749761000},"update-policy":"https:\/\/doi.org\/10.1103\/crossmark-policy","source":"Crossref","is-referenced-by-count":9,"title":["Color symmetry and altermagneticlike spin textures in noncollinear antiferromagnets"],"prefix":"10.1103","volume":"112","author":[{"given":"Paolo G.","family":"Radaelli","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/052gg0110","id-type":"ROR","asserted-by":"publisher"}],"name":"University of Oxford"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gautam","family":"Gurung","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/052gg0110","id-type":"ROR","asserted-by":"publisher"}],"name":"University of Oxford"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"16","published-online":{"date-parts":[[2025,7,17]]},"reference":[{"key":"r34k-xjpxCc1R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevX.12.031042","type":"journal-article"},{"key":"r34k-xjpxCc2R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevX.12.040501","type":"journal-article"},{"key":"r34k-xjpxCc3R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.110.214428","type":"journal-article"},{"key":"r34k-xjpxCc4R1","doi-asserted-by":"publisher","DOI":"10.1038\/s41535-024-00626-6","type":"journal-article"},{"key":"r34k-xjpxCc6R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.101.220403","type":"journal-article"},{"key":"r34k-xjpxCc7R1","unstructured":"Here \u201ck\/\u2212ksymmetric\/antisymmetric\u201d means that the spin texture, defined as snk=\u2329\u03a8nk|\u03c3|\u03a8nk\u232a (see below), is the same\/changes sign by exchanging k and \u2212k. \u201cTime-reversal odd\/even\u201d means that the spin texture in the time-reversed magnetic domain (i.e., the domain obtained by flipping all the magnetic moments) is opposite\/the same for a given k.","type":"other"},{"key":"r34k-xjpxCc8R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRev.100.580","type":"journal-article"},{"key":"r34k-xjpxCc9R1","first-page":"62","type":"journal-article","volume":"2","author":"E.\u00a0I. Rashba","year":"1959","journal-title":"Fiz. Tverd. Tela: Collected Papers"},{"key":"r34k-xjpxCc9R2","doi-asserted-by":"publisher","DOI":"10.1088\/1367-2630\/17\/5\/050202","type":"journal-article"},{"key":"r34k-xjpxCc10R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.119.187204","type":"journal-article"},{"key":"r34k-xjpxCc11R1","doi-asserted-by":"publisher","DOI":"10.1088\/0953-8984\/1\/43\/016","type":"journal-article"},{"key":"r34k-xjpxCc12R1","unstructured":"As explained in the remainder, the CG approach can be employed to describe the magnetic structures of k\/\u2212k-antisymmetric magnets, but colored tensors as defined here would require some modifications. For this reason, we will exclude k\/\u2212k-antisymmetric magnets from our treatment.","type":"other"},{"key":"r34k-xjpxCc13R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.133.236703","type":"journal-article"},{"key":"r34k-xjpxCc14R1","doi-asserted-by":"publisher","DOI":"10.1107\/S0567739481000697","type":"journal-article"},{"key":"r34k-xjpxCc15R1","doi-asserted-by":"publisher","DOI":"10.1107\/S0108767384001197","type":"journal-article"},{"key":"r34k-xjpxCc16R1","doi-asserted-by":"publisher","DOI":"10.1107\/S0108767385001039","type":"journal-article"},{"key":"r34k-xjpxCc17R1","doi-asserted-by":"publisher","DOI":"10.1107\/S0108767388005549","type":"journal-article"},{"key":"r34k-xjpxCc18R1","doi-asserted-by":"publisher","DOI":"10.1107\/S0108767388008335","type":"journal-article"},{"key":"r34k-xjpxCc19R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.26.6947","type":"journal-article"},{"key":"r34k-xjpxCc20R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.46.8725","type":"journal-article"},{"key":"r34k-xjpxCc21R1","doi-asserted-by":"publisher","DOI":"10.1107\/S0567739468000306","type":"journal-article"},{"key":"r34k-xjpxCc22R1","doi-asserted-by":"publisher","DOI":"10.1016\/0304-8853(80)91147-6","type":"journal-article"},{"key":"r34k-xjpxCc23R1","doi-asserted-by":"publisher","DOI":"10.1107\/S0567739477000709","type":"journal-article"},{"key":"r34k-xjpxCc24R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jssc.2004.07.001","type":"journal-article"},{"key":"r34k-xjpxCc25R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.69.054422","type":"journal-article"},{"key":"r34k-xjpxCc27R1","doi-asserted-by":"publisher","DOI":"10.1039\/b704361a","type":"journal-article"},{"key":"r34k-xjpxCc28R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.99.195129","type":"journal-article"},{"key":"r34k-xjpxCc30R1","doi-asserted-by":"publisher","DOI":"10.1016\/0038-1098(68)90098-7","type":"journal-article"},{"key":"r34k-xjpxCc31R1","doi-asserted-by":"publisher","DOI":"10.1002\/adma.201600310","type":"journal-article"},{"key":"r34k-xjpxCc32R1","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-020-17999-4","type":"journal-article"},{"key":"r34k-xjpxCc33R1","doi-asserted-by":"publisher","DOI":"10.1038\/s41524-021-00566-w","type":"journal-article"},{"key":"r34k-xjpxCc34R1","unstructured":"Note that the \u03934g magnetic structure is the same as for the compound Mn3Ir reported in Ref.   [10]. The schematic spin texture reported in their Fig.   3 is very similar to the one we calculate here.","type":"other"},{"key":"r34k-xjpxCc35R1","doi-asserted-by":"publisher","DOI":"10.1088\/1361-648X\/aa8f79","type":"journal-article"},{"key":"r34k-xjpxCc36R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.77.3865","type":"journal-article"},{"key":"r34k-xjpxCc37R1","unstructured":"See Supplemental Material at http:\/\/link.aps.org\/supplemental\/10.1103\/r34k-xjpx for I. Further discussion of the relation between color groups and spin groups; II. Spin-resolved band dispersions of Mn3GaN; III. Fermi surfaces of Mn3GaN; IV. Decompositions of the Fermi surfaces (Bands 0, 2, 3) spin textures of Mn3GaN onto tensorial expansions.","type":"other"},{"key":"r34k-xjpxCc38R1","unstructured":"Note that the net magnetization in the absence of SOC is identically zero for collinear altermagnets and also for noncollinear magnets where each color has a corresponding anticolor, since the magnetization of anticolored sublattices cancels.","type":"other"},{"key":"r34k-xjpxCc39R1","unstructured":"Very briefly, magnets with k\/\u2212kantisymmetric splitting are characterized by bond-type multipolar ordering   [6], and the staggered magnetization (in the collinear case) or the one-color axial unit vectors (noncollinear case) need to be replaced in the tensorial treatment by the cross product S1\u00d7S2, where sites 1 and 2 are those connected by the specific bond. This approach will be fully described in a future paper.","type":"other"},{"key":"r34k-xjpxCc40R1","doi-asserted-by":"publisher","DOI":"10.5281\/zenodo.22558","type":"dataset"},{"key":"r34k-xjpxCc41R1","doi-asserted-by":"publisher","DOI":"10.5287\/ora-ng7pyddap","type":"dataset"}],"container-title":["Physical Review B"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.aps.org\/article\/10.1103\/r34k-xjpx","content-type":"unspecified","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/harvest.aps.org\/v2\/journals\/articles\/10.1103\/r34k-xjpx\/fulltext","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T20:59:14Z","timestamp":1790715554000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.aps.org\/doi\/10.1103\/r34k-xjpx"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,7,17]]},"references-count":39,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2025,7]]}},"URL":"https:\/\/doi.org\/10.1103\/r34k-xjpx","relation":{"has-preprint":[{"id-type":"doi","id":"10.48550\/arXiv.2501.02947","asserted-by":"subject"}]},"ISSN":["2469-9950","2469-9969"],"issn-type":[{"value":"2469-9950","type":"print"},{"value":"2469-9969","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,7,17]]},"assertion":[{"value":"2025-01-14","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"Published by the American Physical Society. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright_statement","label":"Copyright statement","group":{"name":"copyright","label":"copyright"}},{"value":"2025","name":"copyright_year","label":"Copyright year","group":{"name":"copyright","label":"copyright"}},{"value":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/","name":"creative_commons_license","label":"Creative Commons license","group":{"name":"licenses","label":"Licenses"}},{"value":"\u00a92025 The authors","name":"copyright_holder","label":"Copyright holder","group":{"name":"copyright","label":"copyright"}}],"article-number":"014431"}}