利用中子衍射寻找神户超导体 CsV3Sb5 中的轨道磁性

IF 3.7 2区 物理与天体物理 Q1 Physics and Astronomy
William Liège, Yaofeng Xie, Dalila Bounoua, Yvan Sidis, Frédéric Bourdarot, Yongkai Li, Zhiwei Wang, Jia-Xin Yin, Pengcheng Dai, Philippe Bourges
{"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 superconductorCsV3⁢Sb5using 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\\\" 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\\\" 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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\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Physical Review B\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1103/physrevb.110.195109\",\"RegionNum\":2,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"Physics and Astronomy\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physical Review 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引用次数: 0

摘要

与许多卡戈米金属一样,拓扑超导体 AV3Sb5(A = K、Rb、Cs)也含有电荷密度波。人们从理论上进一步预测了这些材料中打破时间反转对称性的相关手性通量相。磁通相与产生有序轨道磁矩的环流有关,而有序轨道磁矩会出现在动量点𝐌上,这正是电荷密度波状态的特征。我们对 CsV3Sb5 的单晶体组件进行了偏振中子衍射实验,以寻找这种轨道磁矩。在布里渊区第一𝐌1=(1/2,0,0)点的任何温度下,在极小的实验不确定性范围内(即每个钒原子的 m=±0.01𝜇𝐵),都没有发现存在三维有序磁矩的证据。然而,这些数据可能表明,在第二布里渊区的𝐌𝟐=(1/2,1/2,0)处有一个假定的磁轨道矩,处于实验的探测极限。一些仅在钒三角上流动的环流模式能够解释这一发现,表明每个钒三角的有序轨道磁矩最多为 ∼0.02±0.01𝜇𝐵。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Search for orbital magnetism in the kagome superconductorCsV3⁢Sb5using neutron diffraction
As many kagome metals, the topological superconductor AV3Sb5 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, 𝐌, characterizing the charge-density wave state. Polarized neutron-diffraction experiments have been performed on an assembly of single crystals of CsV3Sb5 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 𝐌1=(1/2,0,0) point in the Brillouin zone within an excellent experimental uncertainty, i.e., m=0±0.01𝜇𝐵 per vanadium atom. However, the data might be suggestive of a putative magnetic orbital moment in the second Brillouin zone at 𝐌𝟐=(1/2,1/2,0) at the detection limit of the experiment. Some loop currents patterns flowing only on vanadium triangles are able to account for this finding suggesting an ordered orbital magnetic moment of, at most, 0.02±0.01𝜇𝐵 per vanadium triangle.
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来源期刊
Physical Review B
Physical Review B 物理-物理:凝聚态物理
CiteScore
6.70
自引率
32.40%
发文量
0
审稿时长
3.0 months
期刊介绍: Physical Review B (PRB) is the world’s largest dedicated physics journal, publishing approximately 100 new, high-quality papers each week. The most highly cited journal in condensed matter physics, PRB provides outstanding depth and breadth of coverage, combined with unrivaled context and background for ongoing research by scientists worldwide. PRB covers the full range of condensed matter, materials physics, and related subfields, including: -Structure and phase transitions -Ferroelectrics and multiferroics -Disordered systems and alloys -Magnetism -Superconductivity -Electronic structure, photonics, and metamaterials -Semiconductors and mesoscopic systems -Surfaces, nanoscience, and two-dimensional materials -Topological states of matter
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