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{"title":"利用中子衍射寻找神户超导体 CsV3Sb5 中的轨道磁性","authors":"William Liège, Yaofeng Xie, Dalila Bounoua, Yvan Sidis, Frédéric Bourdarot, Yongkai Li, Zhiwei Wang, Jia-Xin Yin, Pengcheng Dai, Philippe Bourges","doi":"10.1103/physrevb.110.195109","DOIUrl":null,"url":null,"abstract":"As many kagome metals, the topological superconductor <mjx-container ctxtmenu_counter=\"88\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(7 (2 0 1) 6 (5 3 4))\"><mjx-mrow data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"2,5\" data-semantic-content=\"6\" data-semantic- data-semantic-owns=\"2 6 5\" data-semantic-role=\"implicit\" data-semantic-speech=\"upper A upper V 3 upper S b 5\" data-semantic-type=\"infixop\"><mjx-msub data-semantic-children=\"0,1\" data-semantic- data-semantic-owns=\"0 1\" data-semantic-parent=\"7\" data-semantic-role=\"unknown\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"unknown\" data-semantic-type=\"identifier\"><mjx-c noic=\"true\" style=\"padding-top: 0.662em;\">A</mjx-c><mjx-c style=\"padding-top: 0.662em;\">V</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em; margin-left: 0.05em;\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c>3</mjx-c></mjx-mn></mjx-script></mjx-msub><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,\" data-semantic-parent=\"7\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\"><mjx-c></mjx-c></mjx-mo><mjx-msub data-semantic-children=\"3,4\" data-semantic- data-semantic-owns=\"3 4\" data-semantic-parent=\"7\" data-semantic-role=\"unknown\" data-semantic-type=\"subscript\" space=\"2\"><mjx-mi data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"unknown\" data-semantic-type=\"identifier\"><mjx-c noic=\"true\" style=\"padding-top: 0.706em;\">S</mjx-c><mjx-c style=\"padding-top: 0.706em;\">b</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c>5</mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-mrow></mjx-math></mjx-container> with (A = K,Rb,Cs) hosts a charge density wave. A related chiral flux phase that breaks the time-reversal symmetry has been further theoretically predicted in these materials. The flux phase is associated with loop currents that produce ordered orbital magnetic moments, which would occur at the momentum points, <mjx-container ctxtmenu_counter=\"89\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"0\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"bold\" data-semantic- data-semantic-role=\"latinletter\" data-semantic-speech=\"bold upper M\" data-semantic-type=\"identifier\"><mjx-c>𝐌</mjx-c></mjx-mi></mjx-math></mjx-container>, characterizing the charge-density wave state. Polarized neutron-diffraction experiments have been performed on an assembly of single crystals of <mjx-container ctxtmenu_counter=\"90\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(7 (2 0 1) 6 (5 3 4))\"><mjx-mrow data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"2,5\" data-semantic-content=\"6\" data-semantic- data-semantic-owns=\"2 6 5\" data-semantic-role=\"implicit\" data-semantic-speech=\"upper C s upper V 3 upper S b 5\" data-semantic-type=\"infixop\"><mjx-msub data-semantic-children=\"0,1\" data-semantic- data-semantic-owns=\"0 1\" data-semantic-parent=\"7\" data-semantic-role=\"unknown\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"unknown\" data-semantic-type=\"identifier\"><mjx-c noic=\"true\" style=\"padding-top: 0.669em;\">C</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.669em;\">s</mjx-c><mjx-c style=\"padding-top: 0.669em;\">V</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em; margin-left: 0.05em;\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c>3</mjx-c></mjx-mn></mjx-script></mjx-msub><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,\" data-semantic-parent=\"7\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\"><mjx-c></mjx-c></mjx-mo><mjx-msub data-semantic-children=\"3,4\" data-semantic- data-semantic-owns=\"3 4\" data-semantic-parent=\"7\" data-semantic-role=\"unknown\" data-semantic-type=\"subscript\" space=\"2\"><mjx-mi data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"unknown\" data-semantic-type=\"identifier\"><mjx-c noic=\"true\" style=\"padding-top: 0.706em;\">S</mjx-c><mjx-c style=\"padding-top: 0.706em;\">b</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c>5</mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-mrow></mjx-math></mjx-container> to search for such orbital magnetic moments. No evidence for the existence of a three-dimensionally ordered moment is found at any temperature at the first <mjx-container ctxtmenu_counter=\"91\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math breakable=\"true\" data-semantic-children=\"2,12\" data-semantic-content=\"3\" data-semantic- data-semantic-owns=\"2 3 12\" data-semantic-role=\"equality\" data-semantic-speech=\"bold upper M 1 equals left parenthesis Number 1 slash 2 comma 0 comma 0 right parenthesis\" data-semantic-structure=\"(13 (2 0 1) 3 (12 4 (11 5 6 7 8 9) 10))\" data-semantic-type=\"relseq\"><mjx-msub data-semantic-children=\"0,1\" data-semantic- data-semantic-owns=\"0 1\" data-semantic-parent=\"13\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"bold\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝐌</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c>1</mjx-c></mjx-mn></mjx-script></mjx-msub><mjx-break size=\"4\"></mjx-break><mjx-mo data-semantic- data-semantic-operator=\"relseq,=\" data-semantic-parent=\"13\" data-semantic-role=\"equality\" data-semantic-type=\"relation\"><mjx-c>=</mjx-c></mjx-mo><mjx-mrow data-semantic-children=\"11\" data-semantic-content=\"4,10\" data-semantic- data-semantic-owns=\"4 11 10\" data-semantic-parent=\"13\" data-semantic-role=\"leftright\" data-semantic-type=\"fenced\" space=\"4\"><mjx-mo data-semantic- data-semantic-operator=\"fenced\" data-semantic-parent=\"12\" data-semantic-role=\"open\" data-semantic-type=\"fence\" style=\"vertical-align: -0.02em;\"><mjx-c>(</mjx-c></mjx-mo><mjx-mrow data-semantic-added=\"true\" data-semantic-children=\"5,6,7,8,9\" data-semantic-content=\"6,8\" data-semantic- data-semantic-owns=\"5 6 7 8 9\" data-semantic-parent=\"12\" data-semantic-role=\"sequence\" data-semantic-type=\"punctuated\"><mjx-mn data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"11\" data-semantic-role=\"othernumber\" data-semantic-type=\"number\"><mjx-c noic=\"true\" style=\"padding-top: 0.709em;\">1</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.709em;\">/</mjx-c><mjx-c style=\"padding-top: 0.709em;\">2</mjx-c></mjx-mn><mjx-mo data-semantic- data-semantic-operator=\"punctuated\" data-semantic-parent=\"11\" data-semantic-role=\"comma\" data-semantic-type=\"punctuation\"><mjx-c>,</mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"11\" data-semantic-role=\"integer\" data-semantic-type=\"number\" space=\"2\"><mjx-c>0</mjx-c></mjx-mn><mjx-mo data-semantic- data-semantic-operator=\"punctuated\" data-semantic-parent=\"11\" data-semantic-role=\"comma\" data-semantic-type=\"punctuation\"><mjx-c>,</mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"11\" data-semantic-role=\"integer\" data-semantic-type=\"number\" space=\"2\"><mjx-c>0</mjx-c></mjx-mn></mjx-mrow><mjx-mo data-semantic- data-semantic-operator=\"fenced\" data-semantic-parent=\"12\" data-semantic-role=\"close\" data-semantic-type=\"fence\" style=\"vertical-align: -0.02em;\"><mjx-c>)</mjx-c></mjx-mo></mjx-mrow></mjx-math></mjx-container> point in the Brillouin zone within an excellent experimental uncertainty, i.e., <mjx-container ctxtmenu_counter=\"92\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(12 0 1 (11 2 3 (10 4 9 (8 6 7))))\"><mjx-mrow data-semantic-children=\"0,11\" data-semantic-content=\"1\" data-semantic- data-semantic-owns=\"0 1 11\" data-semantic-role=\"equality\" data-semantic-speech=\"normal m equals 0 plus or minus 0.01 mu Subscript upper B\" data-semantic-type=\"relseq\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"12\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>m</mjx-c></mjx-mi><mjx-mo data-semantic- data-semantic-operator=\"relseq,=\" data-semantic-parent=\"12\" data-semantic-role=\"equality\" data-semantic-type=\"relation\" space=\"4\"><mjx-c>=</mjx-c></mjx-mo><mjx-mrow data-semantic-added=\"true\" data-semantic-children=\"2,10\" data-semantic-content=\"3\" data-semantic- data-semantic-owns=\"2 3 10\" data-semantic-parent=\"12\" data-semantic-role=\"addition\" data-semantic-type=\"infixop\" space=\"4\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"11\" data-semantic-role=\"integer\" data-semantic-type=\"number\"><mjx-c>0</mjx-c></mjx-mn><mjx-mo data-semantic- data-semantic-operator=\"infixop,±\" data-semantic-parent=\"11\" data-semantic-role=\"addition\" data-semantic-type=\"operator\" space=\"3\"><mjx-c>±</mjx-c></mjx-mo><mjx-mrow data-semantic-added=\"true\" data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"4,8\" data-semantic-content=\"9\" data-semantic- data-semantic-owns=\"4 9 8\" data-semantic-parent=\"11\" data-semantic-role=\"implicit\" data-semantic-type=\"infixop\" space=\"3\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"10\" data-semantic-role=\"float\" data-semantic-type=\"number\"><mjx-c noic=\"true\" style=\"padding-top: 0.642em;\">0</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.642em;\">.</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.642em;\">0</mjx-c><mjx-c style=\"padding-top: 0.642em;\">1</mjx-c></mjx-mn><mjx-mspace data-semantic- data-semantic-operator=\"infixop,\" data-semantic-parent=\"10\" data-semantic-role=\"space\" data-semantic-type=\"operator\" style=\"width: 0.28em;\"></mjx-mspace><mjx-msub data-semantic-children=\"6,7\" data-semantic- data-semantic-owns=\"6 7\" data-semantic-parent=\"10\" data-semantic-role=\"greekletter\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"8\" data-semantic-role=\"greekletter\" data-semantic-type=\"identifier\"><mjx-c>𝜇</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"8\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\" size=\"s\"><mjx-c>𝐵</mjx-c></mjx-mi></mjx-script></mjx-msub></mjx-mrow></mjx-mrow></mjx-mrow></mjx-math></mjx-container> per vanadium atom. However, the data might be suggestive of a putative magnetic orbital moment in the second Brillouin zone at <mjx-container ctxtmenu_counter=\"93\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math breakable=\"true\" data-semantic-children=\"2,12\" data-semantic-content=\"3\" data-semantic- data-semantic-owns=\"2 3 12\" data-semantic-role=\"equality\" data-semantic-speech=\"bold upper M bold 2 equals left parenthesis Number 1 slash 2 comma Number 1 slash 2 comma 0 right parenthesis\" data-semantic-structure=\"(13 (2 0 1) 3 (12 4 (11 5 6 7 8 9) 10))\" data-semantic-type=\"relseq\"><mjx-msub data-semantic-children=\"0,1\" data-semantic- data-semantic-owns=\"0 1\" data-semantic-parent=\"13\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"bold\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝐌</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"bold\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c>𝟐</mjx-c></mjx-mn></mjx-script></mjx-msub><mjx-break size=\"4\"></mjx-break><mjx-mo data-semantic- data-semantic-operator=\"relseq,=\" data-semantic-parent=\"13\" data-semantic-role=\"equality\" data-semantic-type=\"relation\"><mjx-c>=</mjx-c></mjx-mo><mjx-mrow data-semantic-children=\"11\" data-semantic-content=\"4,10\" data-semantic- data-semantic-owns=\"4 11 10\" data-semantic-parent=\"13\" data-semantic-role=\"leftright\" data-semantic-type=\"fenced\" space=\"4\"><mjx-mo data-semantic- data-semantic-operator=\"fenced\" data-semantic-parent=\"12\" data-semantic-role=\"open\" data-semantic-type=\"fence\" style=\"vertical-align: -0.02em;\"><mjx-c>(</mjx-c></mjx-mo><mjx-mrow data-semantic-added=\"true\" data-semantic-children=\"5,6,7,8,9\" data-semantic-content=\"6,8\" data-semantic- data-semantic-owns=\"5 6 7 8 9\" data-semantic-parent=\"12\" data-semantic-role=\"sequence\" data-semantic-type=\"punctuated\"><mjx-mn data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"11\" data-semantic-role=\"othernumber\" data-semantic-type=\"number\"><mjx-c noic=\"true\" style=\"padding-top: 0.709em;\">1</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.709em;\">/</mjx-c><mjx-c style=\"padding-top: 0.709em;\">2</mjx-c></mjx-mn><mjx-mo data-semantic- data-semantic-operator=\"punctuated\" data-semantic-parent=\"11\" data-semantic-role=\"comma\" data-semantic-type=\"punctuation\"><mjx-c>,</mjx-c></mjx-mo><mjx-mn data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"11\" data-semantic-role=\"othernumber\" data-semantic-type=\"number\" space=\"2\"><mjx-c noic=\"true\" style=\"padding-top: 0.709em;\">1</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.709em;\">/</mjx-c><mjx-c style=\"padding-top: 0.709em;\">2</mjx-c></mjx-mn><mjx-mo data-semantic- data-semantic-operator=\"punctuated\" data-semantic-parent=\"11\" data-semantic-role=\"comma\" data-semantic-type=\"punctuation\"><mjx-c>,</mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"11\" data-semantic-role=\"integer\" data-semantic-type=\"number\" space=\"2\"><mjx-c>0</mjx-c></mjx-mn></mjx-mrow><mjx-mo data-semantic- data-semantic-operator=\"fenced\" data-semantic-parent=\"12\" data-semantic-role=\"close\" data-semantic-type=\"fence\" style=\"vertical-align: -0.02em;\"><mjx-c>)</mjx-c></mjx-mo></mjx-mrow></mjx-math></mjx-container> at the detection limit of the experiment. Some loop currents patterns flowing <i>only</i> on vanadium triangles are able to account for this finding suggesting an ordered orbital magnetic moment of, at most, <mjx-container ctxtmenu_counter=\"94\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(12 8 0 (11 1 2 (10 3 9 (7 5 6))))\"><mjx-mrow data-semantic-children=\"8,11\" data-semantic-content=\"0\" data-semantic- data-semantic-owns=\"8 0 11\" data-semantic-role=\"equality\" data-semantic-speech=\"tilde 0.02 plus or minus 0.01 mu Subscript upper B\" data-semantic-type=\"relseq\"><mjx-mrow data-semantic-added=\"true\" data-semantic- data-semantic-parent=\"12\" data-semantic-role=\"unknown\" data-semantic-type=\"empty\"></mjx-mrow><mjx-mo data-semantic- data-semantic-operator=\"relseq,∼\" data-semantic-parent=\"12\" data-semantic-role=\"equality\" data-semantic-type=\"relation\"><mjx-c>∼</mjx-c></mjx-mo><mjx-mrow data-semantic-added=\"true\" data-semantic-children=\"1,10\" data-semantic-content=\"2\" data-semantic- data-semantic-owns=\"1 2 10\" data-semantic-parent=\"12\" data-semantic-role=\"addition\" data-semantic-type=\"infixop\" space=\"4\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"11\" data-semantic-role=\"float\" data-semantic-type=\"number\"><mjx-c noic=\"true\" style=\"padding-top: 0.644em;\">0</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.644em;\">.</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.644em;\">0</mjx-c><mjx-c style=\"padding-top: 0.644em;\">2</mjx-c></mjx-mn><mjx-mo data-semantic- data-semantic-operator=\"infixop,±\" data-semantic-parent=\"11\" data-semantic-role=\"addition\" data-semantic-type=\"operator\" space=\"3\"><mjx-c>±</mjx-c></mjx-mo><mjx-mrow data-semantic-added=\"true\" data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"3,7\" data-semantic-content=\"9\" data-semantic- data-semantic-owns=\"3 9 7\" data-semantic-parent=\"11\" data-semantic-role=\"implicit\" data-semantic-type=\"infixop\" space=\"3\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"10\" data-semantic-role=\"float\" data-semantic-type=\"number\"><mjx-c noic=\"true\" style=\"padding-top: 0.642em;\">0</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.642em;\">.</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.642em;\">0</mjx-c><mjx-c style=\"padding-top: 0.642em;\">1</mjx-c></mjx-mn><mjx-mspace data-semantic- data-semantic-operator=\"infixop,\" data-semantic-parent=\"10\" data-semantic-role=\"space\" data-semantic-type=\"operator\" style=\"width: 0.28em;\"></mjx-mspace><mjx-msub data-semantic-children=\"5,6\" data-semantic- data-semantic-owns=\"5 6\" data-semantic-parent=\"10\" data-semantic-role=\"greekletter\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"7\" data-semantic-role=\"greekletter\" data-semantic-type=\"identifier\"><mjx-c>𝜇</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"7\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\" size=\"s\"><mjx-c>𝐵</mjx-c></mjx-mi></mjx-script></mjx-msub></mjx-mrow></mjx-mrow></mjx-mrow></mjx-math></mjx-container> per vanadium triangle.","PeriodicalId":20082,"journal":{"name":"Physical Review B","volume":null,"pages":null},"PeriodicalIF":3.7000,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Search for orbital magnetism in the kagome superconductorCsV3Sb5using neutron diffraction\",\"authors\":\"William Liège, Yaofeng Xie, Dalila Bounoua, Yvan Sidis, Frédéric Bourdarot, Yongkai Li, Zhiwei Wang, Jia-Xin Yin, Pengcheng Dai, Philippe Bourges\",\"doi\":\"10.1103/physrevb.110.195109\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"As many kagome metals, the topological superconductor <mjx-container ctxtmenu_counter=\\\"88\\\" ctxtmenu_oldtabindex=\\\"1\\\" jax=\\\"CHTML\\\" overflow=\\\"linebreak\\\" role=\\\"tree\\\" sre-explorer- style=\\\"font-size: 100.7%;\\\" tabindex=\\\"0\\\"><mjx-math data-semantic-structure=\\\"(7 (2 0 1) 6 (5 3 4))\\\"><mjx-mrow data-semantic-annotation=\\\"clearspeak:unit\\\" data-semantic-children=\\\"2,5\\\" data-semantic-content=\\\"6\\\" data-semantic- data-semantic-owns=\\\"2 6 5\\\" data-semantic-role=\\\"implicit\\\" data-semantic-speech=\\\"upper A upper V 3 upper S b 5\\\" data-semantic-type=\\\"infixop\\\"><mjx-msub data-semantic-children=\\\"0,1\\\" data-semantic- data-semantic-owns=\\\"0 1\\\" data-semantic-parent=\\\"7\\\" data-semantic-role=\\\"unknown\\\" data-semantic-type=\\\"subscript\\\"><mjx-mi data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"2\\\" data-semantic-role=\\\"unknown\\\" data-semantic-type=\\\"identifier\\\"><mjx-c noic=\\\"true\\\" style=\\\"padding-top: 0.662em;\\\">A</mjx-c><mjx-c style=\\\"padding-top: 0.662em;\\\">V</mjx-c></mjx-mi><mjx-script style=\\\"vertical-align: -0.15em; margin-left: 0.05em;\\\"><mjx-mn data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"2\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\" size=\\\"s\\\"><mjx-c>3</mjx-c></mjx-mn></mjx-script></mjx-msub><mjx-mo data-semantic-added=\\\"true\\\" data-semantic- data-semantic-operator=\\\"infixop,\\\" data-semantic-parent=\\\"7\\\" data-semantic-role=\\\"multiplication\\\" data-semantic-type=\\\"operator\\\"><mjx-c></mjx-c></mjx-mo><mjx-msub data-semantic-children=\\\"3,4\\\" data-semantic- data-semantic-owns=\\\"3 4\\\" data-semantic-parent=\\\"7\\\" data-semantic-role=\\\"unknown\\\" data-semantic-type=\\\"subscript\\\" space=\\\"2\\\"><mjx-mi data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"unknown\\\" data-semantic-type=\\\"identifier\\\"><mjx-c noic=\\\"true\\\" style=\\\"padding-top: 0.706em;\\\">S</mjx-c><mjx-c style=\\\"padding-top: 0.706em;\\\">b</mjx-c></mjx-mi><mjx-script style=\\\"vertical-align: -0.15em;\\\"><mjx-mn data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\" size=\\\"s\\\"><mjx-c>5</mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-mrow></mjx-math></mjx-container> with (A = K,Rb,Cs) hosts a charge density wave. A related chiral flux phase that breaks the time-reversal symmetry has been further theoretically predicted in these materials. The flux phase is associated with loop currents that produce ordered orbital magnetic moments, which would occur at the momentum points, <mjx-container ctxtmenu_counter=\\\"89\\\" ctxtmenu_oldtabindex=\\\"1\\\" jax=\\\"CHTML\\\" overflow=\\\"linebreak\\\" role=\\\"tree\\\" sre-explorer- style=\\\"font-size: 100.7%;\\\" tabindex=\\\"0\\\"><mjx-math data-semantic-structure=\\\"0\\\"><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"bold\\\" data-semantic- data-semantic-role=\\\"latinletter\\\" data-semantic-speech=\\\"bold upper M\\\" data-semantic-type=\\\"identifier\\\"><mjx-c>𝐌</mjx-c></mjx-mi></mjx-math></mjx-container>, characterizing the charge-density wave state. Polarized neutron-diffraction experiments have been performed on an assembly of single crystals of <mjx-container ctxtmenu_counter=\\\"90\\\" ctxtmenu_oldtabindex=\\\"1\\\" jax=\\\"CHTML\\\" overflow=\\\"linebreak\\\" role=\\\"tree\\\" sre-explorer- style=\\\"font-size: 100.7%;\\\" tabindex=\\\"0\\\"><mjx-math data-semantic-structure=\\\"(7 (2 0 1) 6 (5 3 4))\\\"><mjx-mrow data-semantic-annotation=\\\"clearspeak:unit\\\" data-semantic-children=\\\"2,5\\\" data-semantic-content=\\\"6\\\" data-semantic- data-semantic-owns=\\\"2 6 5\\\" data-semantic-role=\\\"implicit\\\" data-semantic-speech=\\\"upper C s upper V 3 upper S b 5\\\" data-semantic-type=\\\"infixop\\\"><mjx-msub data-semantic-children=\\\"0,1\\\" data-semantic- data-semantic-owns=\\\"0 1\\\" data-semantic-parent=\\\"7\\\" data-semantic-role=\\\"unknown\\\" data-semantic-type=\\\"subscript\\\"><mjx-mi data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"2\\\" data-semantic-role=\\\"unknown\\\" data-semantic-type=\\\"identifier\\\"><mjx-c noic=\\\"true\\\" style=\\\"padding-top: 0.669em;\\\">C</mjx-c><mjx-c noic=\\\"true\\\" style=\\\"padding-top: 0.669em;\\\">s</mjx-c><mjx-c style=\\\"padding-top: 0.669em;\\\">V</mjx-c></mjx-mi><mjx-script style=\\\"vertical-align: -0.15em; margin-left: 0.05em;\\\"><mjx-mn data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"2\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\" size=\\\"s\\\"><mjx-c>3</mjx-c></mjx-mn></mjx-script></mjx-msub><mjx-mo data-semantic-added=\\\"true\\\" data-semantic- data-semantic-operator=\\\"infixop,\\\" data-semantic-parent=\\\"7\\\" data-semantic-role=\\\"multiplication\\\" data-semantic-type=\\\"operator\\\"><mjx-c></mjx-c></mjx-mo><mjx-msub data-semantic-children=\\\"3,4\\\" data-semantic- data-semantic-owns=\\\"3 4\\\" data-semantic-parent=\\\"7\\\" data-semantic-role=\\\"unknown\\\" data-semantic-type=\\\"subscript\\\" space=\\\"2\\\"><mjx-mi data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"unknown\\\" data-semantic-type=\\\"identifier\\\"><mjx-c noic=\\\"true\\\" style=\\\"padding-top: 0.706em;\\\">S</mjx-c><mjx-c style=\\\"padding-top: 0.706em;\\\">b</mjx-c></mjx-mi><mjx-script style=\\\"vertical-align: -0.15em;\\\"><mjx-mn data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\" size=\\\"s\\\"><mjx-c>5</mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-mrow></mjx-math></mjx-container> to search for such orbital magnetic moments. No evidence for the existence of a three-dimensionally ordered moment is found at any temperature at the first <mjx-container ctxtmenu_counter=\\\"91\\\" ctxtmenu_oldtabindex=\\\"1\\\" jax=\\\"CHTML\\\" overflow=\\\"linebreak\\\" role=\\\"tree\\\" sre-explorer- style=\\\"font-size: 100.7%;\\\" tabindex=\\\"0\\\"><mjx-math breakable=\\\"true\\\" data-semantic-children=\\\"2,12\\\" data-semantic-content=\\\"3\\\" data-semantic- data-semantic-owns=\\\"2 3 12\\\" data-semantic-role=\\\"equality\\\" data-semantic-speech=\\\"bold upper M 1 equals left parenthesis Number 1 slash 2 comma 0 comma 0 right parenthesis\\\" data-semantic-structure=\\\"(13 (2 0 1) 3 (12 4 (11 5 6 7 8 9) 10))\\\" data-semantic-type=\\\"relseq\\\"><mjx-msub data-semantic-children=\\\"0,1\\\" data-semantic- data-semantic-owns=\\\"0 1\\\" data-semantic-parent=\\\"13\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"subscript\\\"><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"bold\\\" data-semantic- data-semantic-parent=\\\"2\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\"><mjx-c>𝐌</mjx-c></mjx-mi><mjx-script style=\\\"vertical-align: -0.15em;\\\"><mjx-mn data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"2\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\" size=\\\"s\\\"><mjx-c>1</mjx-c></mjx-mn></mjx-script></mjx-msub><mjx-break size=\\\"4\\\"></mjx-break><mjx-mo data-semantic- data-semantic-operator=\\\"relseq,=\\\" data-semantic-parent=\\\"13\\\" data-semantic-role=\\\"equality\\\" data-semantic-type=\\\"relation\\\"><mjx-c>=</mjx-c></mjx-mo><mjx-mrow data-semantic-children=\\\"11\\\" data-semantic-content=\\\"4,10\\\" data-semantic- data-semantic-owns=\\\"4 11 10\\\" data-semantic-parent=\\\"13\\\" data-semantic-role=\\\"leftright\\\" data-semantic-type=\\\"fenced\\\" space=\\\"4\\\"><mjx-mo data-semantic- data-semantic-operator=\\\"fenced\\\" data-semantic-parent=\\\"12\\\" data-semantic-role=\\\"open\\\" data-semantic-type=\\\"fence\\\" style=\\\"vertical-align: -0.02em;\\\"><mjx-c>(</mjx-c></mjx-mo><mjx-mrow data-semantic-added=\\\"true\\\" data-semantic-children=\\\"5,6,7,8,9\\\" data-semantic-content=\\\"6,8\\\" data-semantic- data-semantic-owns=\\\"5 6 7 8 9\\\" data-semantic-parent=\\\"12\\\" data-semantic-role=\\\"sequence\\\" data-semantic-type=\\\"punctuated\\\"><mjx-mn data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"11\\\" data-semantic-role=\\\"othernumber\\\" data-semantic-type=\\\"number\\\"><mjx-c noic=\\\"true\\\" style=\\\"padding-top: 0.709em;\\\">1</mjx-c><mjx-c noic=\\\"true\\\" style=\\\"padding-top: 0.709em;\\\">/</mjx-c><mjx-c style=\\\"padding-top: 0.709em;\\\">2</mjx-c></mjx-mn><mjx-mo data-semantic- data-semantic-operator=\\\"punctuated\\\" data-semantic-parent=\\\"11\\\" data-semantic-role=\\\"comma\\\" data-semantic-type=\\\"punctuation\\\"><mjx-c>,</mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"11\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\" space=\\\"2\\\"><mjx-c>0</mjx-c></mjx-mn><mjx-mo data-semantic- data-semantic-operator=\\\"punctuated\\\" data-semantic-parent=\\\"11\\\" data-semantic-role=\\\"comma\\\" data-semantic-type=\\\"punctuation\\\"><mjx-c>,</mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"11\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\" space=\\\"2\\\"><mjx-c>0</mjx-c></mjx-mn></mjx-mrow><mjx-mo data-semantic- data-semantic-operator=\\\"fenced\\\" data-semantic-parent=\\\"12\\\" data-semantic-role=\\\"close\\\" data-semantic-type=\\\"fence\\\" style=\\\"vertical-align: -0.02em;\\\"><mjx-c>)</mjx-c></mjx-mo></mjx-mrow></mjx-math></mjx-container> point in the Brillouin zone within an excellent experimental uncertainty, i.e., <mjx-container ctxtmenu_counter=\\\"92\\\" ctxtmenu_oldtabindex=\\\"1\\\" jax=\\\"CHTML\\\" overflow=\\\"linebreak\\\" role=\\\"tree\\\" sre-explorer- style=\\\"font-size: 100.7%;\\\" tabindex=\\\"0\\\"><mjx-math data-semantic-structure=\\\"(12 0 1 (11 2 3 (10 4 9 (8 6 7))))\\\"><mjx-mrow data-semantic-children=\\\"0,11\\\" data-semantic-content=\\\"1\\\" data-semantic- data-semantic-owns=\\\"0 1 11\\\" data-semantic-role=\\\"equality\\\" data-semantic-speech=\\\"normal m equals 0 plus or minus 0.01 mu Subscript upper B\\\" data-semantic-type=\\\"relseq\\\"><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"12\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\"><mjx-c>m</mjx-c></mjx-mi><mjx-mo data-semantic- data-semantic-operator=\\\"relseq,=\\\" data-semantic-parent=\\\"12\\\" data-semantic-role=\\\"equality\\\" data-semantic-type=\\\"relation\\\" space=\\\"4\\\"><mjx-c>=</mjx-c></mjx-mo><mjx-mrow data-semantic-added=\\\"true\\\" data-semantic-children=\\\"2,10\\\" data-semantic-content=\\\"3\\\" data-semantic- data-semantic-owns=\\\"2 3 10\\\" data-semantic-parent=\\\"12\\\" data-semantic-role=\\\"addition\\\" data-semantic-type=\\\"infixop\\\" space=\\\"4\\\"><mjx-mn data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"11\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\"><mjx-c>0</mjx-c></mjx-mn><mjx-mo data-semantic- data-semantic-operator=\\\"infixop,±\\\" data-semantic-parent=\\\"11\\\" data-semantic-role=\\\"addition\\\" data-semantic-type=\\\"operator\\\" space=\\\"3\\\"><mjx-c>±</mjx-c></mjx-mo><mjx-mrow data-semantic-added=\\\"true\\\" data-semantic-annotation=\\\"clearspeak:unit\\\" data-semantic-children=\\\"4,8\\\" data-semantic-content=\\\"9\\\" data-semantic- data-semantic-owns=\\\"4 9 8\\\" data-semantic-parent=\\\"11\\\" data-semantic-role=\\\"implicit\\\" data-semantic-type=\\\"infixop\\\" space=\\\"3\\\"><mjx-mn data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"10\\\" data-semantic-role=\\\"float\\\" data-semantic-type=\\\"number\\\"><mjx-c noic=\\\"true\\\" style=\\\"padding-top: 0.642em;\\\">0</mjx-c><mjx-c noic=\\\"true\\\" style=\\\"padding-top: 0.642em;\\\">.</mjx-c><mjx-c noic=\\\"true\\\" style=\\\"padding-top: 0.642em;\\\">0</mjx-c><mjx-c style=\\\"padding-top: 0.642em;\\\">1</mjx-c></mjx-mn><mjx-mspace data-semantic- data-semantic-operator=\\\"infixop,\\\" data-semantic-parent=\\\"10\\\" data-semantic-role=\\\"space\\\" data-semantic-type=\\\"operator\\\" style=\\\"width: 0.28em;\\\"></mjx-mspace><mjx-msub data-semantic-children=\\\"6,7\\\" data-semantic- data-semantic-owns=\\\"6 7\\\" data-semantic-parent=\\\"10\\\" data-semantic-role=\\\"greekletter\\\" data-semantic-type=\\\"subscript\\\"><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-parent=\\\"8\\\" data-semantic-role=\\\"greekletter\\\" data-semantic-type=\\\"identifier\\\"><mjx-c>𝜇</mjx-c></mjx-mi><mjx-script style=\\\"vertical-align: -0.15em;\\\"><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-parent=\\\"8\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\" size=\\\"s\\\"><mjx-c>𝐵</mjx-c></mjx-mi></mjx-script></mjx-msub></mjx-mrow></mjx-mrow></mjx-mrow></mjx-math></mjx-container> per vanadium atom. However, the data might be suggestive of a putative magnetic orbital moment in the second Brillouin zone at <mjx-container ctxtmenu_counter=\\\"93\\\" ctxtmenu_oldtabindex=\\\"1\\\" jax=\\\"CHTML\\\" overflow=\\\"linebreak\\\" role=\\\"tree\\\" sre-explorer- style=\\\"font-size: 100.7%;\\\" tabindex=\\\"0\\\"><mjx-math breakable=\\\"true\\\" data-semantic-children=\\\"2,12\\\" data-semantic-content=\\\"3\\\" data-semantic- data-semantic-owns=\\\"2 3 12\\\" data-semantic-role=\\\"equality\\\" data-semantic-speech=\\\"bold upper M bold 2 equals left parenthesis Number 1 slash 2 comma Number 1 slash 2 comma 0 right parenthesis\\\" data-semantic-structure=\\\"(13 (2 0 1) 3 (12 4 (11 5 6 7 8 9) 10))\\\" data-semantic-type=\\\"relseq\\\"><mjx-msub data-semantic-children=\\\"0,1\\\" data-semantic- data-semantic-owns=\\\"0 1\\\" data-semantic-parent=\\\"13\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"subscript\\\"><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"bold\\\" data-semantic- data-semantic-parent=\\\"2\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\"><mjx-c>𝐌</mjx-c></mjx-mi><mjx-script style=\\\"vertical-align: -0.15em;\\\"><mjx-mn data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"bold\\\" data-semantic- data-semantic-parent=\\\"2\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\" size=\\\"s\\\"><mjx-c>𝟐</mjx-c></mjx-mn></mjx-script></mjx-msub><mjx-break size=\\\"4\\\"></mjx-break><mjx-mo data-semantic- data-semantic-operator=\\\"relseq,=\\\" data-semantic-parent=\\\"13\\\" data-semantic-role=\\\"equality\\\" data-semantic-type=\\\"relation\\\"><mjx-c>=</mjx-c></mjx-mo><mjx-mrow data-semantic-children=\\\"11\\\" data-semantic-content=\\\"4,10\\\" data-semantic- data-semantic-owns=\\\"4 11 10\\\" data-semantic-parent=\\\"13\\\" data-semantic-role=\\\"leftright\\\" data-semantic-type=\\\"fenced\\\" space=\\\"4\\\"><mjx-mo data-semantic- data-semantic-operator=\\\"fenced\\\" data-semantic-parent=\\\"12\\\" data-semantic-role=\\\"open\\\" data-semantic-type=\\\"fence\\\" style=\\\"vertical-align: -0.02em;\\\"><mjx-c>(</mjx-c></mjx-mo><mjx-mrow data-semantic-added=\\\"true\\\" data-semantic-children=\\\"5,6,7,8,9\\\" data-semantic-content=\\\"6,8\\\" data-semantic- data-semantic-owns=\\\"5 6 7 8 9\\\" data-semantic-parent=\\\"12\\\" data-semantic-role=\\\"sequence\\\" data-semantic-type=\\\"punctuated\\\"><mjx-mn data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"11\\\" data-semantic-role=\\\"othernumber\\\" data-semantic-type=\\\"number\\\"><mjx-c noic=\\\"true\\\" style=\\\"padding-top: 0.709em;\\\">1</mjx-c><mjx-c noic=\\\"true\\\" style=\\\"padding-top: 0.709em;\\\">/</mjx-c><mjx-c style=\\\"padding-top: 0.709em;\\\">2</mjx-c></mjx-mn><mjx-mo data-semantic- data-semantic-operator=\\\"punctuated\\\" data-semantic-parent=\\\"11\\\" data-semantic-role=\\\"comma\\\" data-semantic-type=\\\"punctuation\\\"><mjx-c>,</mjx-c></mjx-mo><mjx-mn data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"11\\\" data-semantic-role=\\\"othernumber\\\" data-semantic-type=\\\"number\\\" space=\\\"2\\\"><mjx-c noic=\\\"true\\\" style=\\\"padding-top: 0.709em;\\\">1</mjx-c><mjx-c noic=\\\"true\\\" style=\\\"padding-top: 0.709em;\\\">/</mjx-c><mjx-c style=\\\"padding-top: 0.709em;\\\">2</mjx-c></mjx-mn><mjx-mo data-semantic- data-semantic-operator=\\\"punctuated\\\" data-semantic-parent=\\\"11\\\" data-semantic-role=\\\"comma\\\" data-semantic-type=\\\"punctuation\\\"><mjx-c>,</mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"11\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\" space=\\\"2\\\"><mjx-c>0</mjx-c></mjx-mn></mjx-mrow><mjx-mo data-semantic- data-semantic-operator=\\\"fenced\\\" data-semantic-parent=\\\"12\\\" data-semantic-role=\\\"close\\\" data-semantic-type=\\\"fence\\\" style=\\\"vertical-align: -0.02em;\\\"><mjx-c>)</mjx-c></mjx-mo></mjx-mrow></mjx-math></mjx-container> at the detection limit of the experiment. Some loop currents patterns flowing <i>only</i> on vanadium triangles are able to account for this finding suggesting an ordered orbital magnetic moment of, at most, <mjx-container ctxtmenu_counter=\\\"94\\\" ctxtmenu_oldtabindex=\\\"1\\\" jax=\\\"CHTML\\\" overflow=\\\"linebreak\\\" role=\\\"tree\\\" sre-explorer- style=\\\"font-size: 100.7%;\\\" tabindex=\\\"0\\\"><mjx-math data-semantic-structure=\\\"(12 8 0 (11 1 2 (10 3 9 (7 5 6))))\\\"><mjx-mrow data-semantic-children=\\\"8,11\\\" data-semantic-content=\\\"0\\\" data-semantic- data-semantic-owns=\\\"8 0 11\\\" data-semantic-role=\\\"equality\\\" data-semantic-speech=\\\"tilde 0.02 plus or minus 0.01 mu Subscript upper B\\\" data-semantic-type=\\\"relseq\\\"><mjx-mrow data-semantic-added=\\\"true\\\" data-semantic- data-semantic-parent=\\\"12\\\" data-semantic-role=\\\"unknown\\\" data-semantic-type=\\\"empty\\\"></mjx-mrow><mjx-mo data-semantic- data-semantic-operator=\\\"relseq,∼\\\" data-semantic-parent=\\\"12\\\" data-semantic-role=\\\"equality\\\" data-semantic-type=\\\"relation\\\"><mjx-c>∼</mjx-c></mjx-mo><mjx-mrow data-semantic-added=\\\"true\\\" data-semantic-children=\\\"1,10\\\" data-semantic-content=\\\"2\\\" data-semantic- data-semantic-owns=\\\"1 2 10\\\" data-semantic-parent=\\\"12\\\" data-semantic-role=\\\"addition\\\" data-semantic-type=\\\"infixop\\\" space=\\\"4\\\"><mjx-mn data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"11\\\" data-semantic-role=\\\"float\\\" data-semantic-type=\\\"number\\\"><mjx-c noic=\\\"true\\\" style=\\\"padding-top: 0.644em;\\\">0</mjx-c><mjx-c noic=\\\"true\\\" style=\\\"padding-top: 0.644em;\\\">.</mjx-c><mjx-c noic=\\\"true\\\" style=\\\"padding-top: 0.644em;\\\">0</mjx-c><mjx-c style=\\\"padding-top: 0.644em;\\\">2</mjx-c></mjx-mn><mjx-mo data-semantic- data-semantic-operator=\\\"infixop,±\\\" data-semantic-parent=\\\"11\\\" data-semantic-role=\\\"addition\\\" 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