Yuyan Han, Bocheng Yu, Zan Du, Langsheng Ling, Lei Zhang, Wei Tong, Chuanying Xi, Jinglei Zhang, Tian Shang, Li Pi, Long Ma
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{"title":"High-field NMR study on the topologically nontrivial 1/3 magnetization plateau state in dopedNa2Cu3Ge4−𝑥Si𝑥O12","authors":"Yuyan Han, Bocheng Yu, Zan Du, Langsheng Ling, Lei Zhang, Wei Tong, Chuanying Xi, Jinglei Zhang, Tian Shang, Li Pi, Long Ma","doi":"10.1103/physrevb.110.l201102","DOIUrl":null,"url":null,"abstract":"The spin-1/2 trimer system <mjx-container ctxtmenu_counter=\"35\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(15 (2 0 1) 12 (5 3 4) 13 (8 6 7) 14 (11 9 10))\"><mjx-mrow data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"2,5,8,11\" data-semantic-content=\"12,13,14\" data-semantic- data-semantic-owns=\"2 12 5 13 8 14 11\" data-semantic-role=\"implicit\" data-semantic-speech=\"upper N a 2 upper C u 3 upper G e 4 normal upper O 12\" data-semantic-type=\"infixop\"><mjx-msub data-semantic-children=\"0,1\" data-semantic- data-semantic-owns=\"0 1\" data-semantic-parent=\"15\" 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: 0.657em;\">N</mjx-c><mjx-c style=\"padding-top: 0.657em;\">a</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>2</mjx-c></mjx-mn></mjx-script></mjx-msub><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,\" data-semantic-parent=\"15\" 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=\"15\" 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: 0.669em;\">C</mjx-c><mjx-c style=\"padding-top: 0.669em;\">u</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>3</mjx-c></mjx-mn></mjx-script></mjx-msub><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,\" data-semantic-parent=\"15\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\"><mjx-c></mjx-c></mjx-mo><mjx-msub data-semantic-children=\"6,7\" data-semantic- data-semantic-owns=\"6 7\" data-semantic-parent=\"15\" data-semantic-role=\"unknown\" data-semantic-type=\"subscript\" space=\"2\"><mjx-mi data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"8\" data-semantic-role=\"unknown\" data-semantic-type=\"identifier\"><mjx-c noic=\"true\" style=\"padding-top: 0.669em;\">G</mjx-c><mjx-c style=\"padding-top: 0.669em;\">e</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=\"8\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c>4</mjx-c></mjx-mn></mjx-script></mjx-msub><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,\" data-semantic-parent=\"15\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\"><mjx-c></mjx-c></mjx-mo><mjx-msub data-semantic-children=\"9,10\" data-semantic- data-semantic-owns=\"9 10\" data-semantic-parent=\"15\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\" space=\"2\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"11\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>O</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=\"11\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c noic=\"true\" style=\"padding-top: 0.644em;\">1</mjx-c><mjx-c style=\"padding-top: 0.644em;\">2</mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-mrow></mjx-math></mjx-container> is proposed to host topologically nontrivial 1/3 magnetization <mjx-container ctxtmenu_counter=\"36\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-children=\"1\" data-semantic-content=\"0,2\" data-semantic- data-semantic-owns=\"0 1 2\" data-semantic-role=\"leftright\" data-semantic-speech=\"left parenthesis upper M right parenthesis\" data-semantic-structure=\"(3 0 1 2)\" data-semantic-type=\"fenced\"><mjx-mo data-semantic- data-semantic-operator=\"fenced\" data-semantic-parent=\"3\" data-semantic-role=\"open\" data-semantic-type=\"fence\" style=\"vertical-align: -0.02em;\"><mjx-c>(</mjx-c></mjx-mo><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝑀</mjx-c></mjx-mi><mjx-mo data-semantic- data-semantic-operator=\"fenced\" data-semantic-parent=\"3\" data-semantic-role=\"close\" data-semantic-type=\"fence\" style=\"vertical-align: -0.02em;\"><mjx-c>)</mjx-c></mjx-mo></mjx-math></mjx-container> plateau state. In this paper, we report a high-field nuclear magnetic resonance (NMR) study on the low-energy spin excitations of the <mjx-container ctxtmenu_counter=\"37\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-children=\"5,4\" data-semantic-content=\"3\" data-semantic- data-semantic-owns=\"5 3 4\" data-semantic-role=\"subtraction\" data-semantic-speech=\"1 divided by 3 minus upper M\" data-semantic-structure=\"(6 (5 0 1 2) 3 4)\" data-semantic-type=\"infixop\"><mjx-mrow data-semantic-added=\"true\" data-semantic-children=\"0,2\" data-semantic-content=\"1\" data-semantic- data-semantic-owns=\"0 1 2\" data-semantic-parent=\"6\" data-semantic-role=\"division\" data-semantic-type=\"infixop\"><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\"><mjx-c>1</mjx-c></mjx-mn><mjx-mo data-semantic- data-semantic-operator=\"infixop,/\" data-semantic-parent=\"5\" data-semantic-role=\"division\" data-semantic-type=\"operator\"><mjx-c>/</mjx-c></mjx-mo><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\"><mjx-c>3</mjx-c></mjx-mn></mjx-mrow><mjx-mtext data-semantic-annotation=\"general:text\" data-semantic- data-semantic-operator=\"infixop,−\" data-semantic-parent=\"6\" data-semantic-role=\"subtraction\" data-semantic-type=\"operator\" style='font-family: MJX-STX-ZERO, \"Helvetica Neue\", Helvetica, Roboto, Arial, sans-serif;'><mjx-utext style=\"font-size: 90.6%; padding: 0.828em 0px 0.221em; width: 7px;\" variant=\"-explicitFont\">−</mjx-utext></mjx-mtext><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"6\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝑀</mjx-c></mjx-mi></mjx-math></mjx-container> plateau state in <mjx-container ctxtmenu_counter=\"38\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(15 (2 0 1) 12 (5 3 4) 13 (8 6 7) 14 (11 9 10))\"><mjx-mrow data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"2,5,8,11\" data-semantic-content=\"12,13,14\" data-semantic- data-semantic-owns=\"2 12 5 13 8 14 11\" data-semantic-role=\"implicit\" data-semantic-speech=\"upper N a 2 upper C u 3 upper G e 4 normal upper O 12\" data-semantic-type=\"infixop\"><mjx-msub data-semantic-children=\"0,1\" data-semantic- data-semantic-owns=\"0 1\" data-semantic-parent=\"15\" 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: 0.657em;\">N</mjx-c><mjx-c style=\"padding-top: 0.657em;\">a</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>2</mjx-c></mjx-mn></mjx-script></mjx-msub><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,\" data-semantic-parent=\"15\" 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=\"15\" 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: 0.669em;\">C</mjx-c><mjx-c style=\"padding-top: 0.669em;\">u</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>3</mjx-c></mjx-mn></mjx-script></mjx-msub><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,\" data-semantic-parent=\"15\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\"><mjx-c></mjx-c></mjx-mo><mjx-msub data-semantic-children=\"6,7\" data-semantic- data-semantic-owns=\"6 7\" data-semantic-parent=\"15\" data-semantic-role=\"unknown\" data-semantic-type=\"subscript\" space=\"2\"><mjx-mi data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"8\" data-semantic-role=\"unknown\" data-semantic-type=\"identifier\"><mjx-c noic=\"true\" style=\"padding-top: 0.669em;\">G</mjx-c><mjx-c style=\"padding-top: 0.669em;\">e</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=\"8\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c>4</mjx-c></mjx-mn></mjx-script></mjx-msub><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,\" data-semantic-parent=\"15\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\"><mjx-c></mjx-c></mjx-mo><mjx-msub data-semantic-children=\"9,10\" data-semantic- data-semantic-owns=\"9 10\" data-semantic-parent=\"15\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\" space=\"2\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"11\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>O</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=\"11\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c noic=\"true\" style=\"padding-top: 0.644em;\">1</mjx-c><mjx-c style=\"padding-top: 0.644em;\">2</mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-mrow></mjx-math></mjx-container> and Si-doped samples. First, the spin excitation gap supporting the high-field Haldane phase is indicated by the thermally activated behavior of spin-lattice relaxation rates in the <mjx-container ctxtmenu_counter=\"39\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-children=\"5,4\" data-semantic-content=\"3\" data-semantic- data-semantic-owns=\"5 3 4\" data-semantic-role=\"subtraction\" data-semantic-speech=\"1 divided by 3 minus upper M\" data-semantic-structure=\"(6 (5 0 1 2) 3 4)\" data-semantic-type=\"infixop\"><mjx-mrow data-semantic-added=\"true\" data-semantic-children=\"0,2\" data-semantic-content=\"1\" data-semantic- data-semantic-owns=\"0 1 2\" data-semantic-parent=\"6\" data-semantic-role=\"division\" data-semantic-type=\"infixop\"><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\"><mjx-c>1</mjx-c></mjx-mn><mjx-mo data-semantic- data-semantic-operator=\"infixop,/\" data-semantic-parent=\"5\" data-semantic-role=\"division\" data-semantic-type=\"operator\"><mjx-c>/</mjx-c></mjx-mo><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\"><mjx-c>3</mjx-c></mjx-mn></mjx-mrow><mjx-mtext data-semantic-annotation=\"general:text\" data-semantic- data-semantic-operator=\"infixop,−\" data-semantic-parent=\"6\" data-semantic-role=\"subtraction\" data-semantic-type=\"operator\" style='font-family: MJX-STX-ZERO, \"Helvetica Neue\", Helvetica, Roboto, Arial, sans-serif;'><mjx-utext style=\"font-size: 90.6%; padding: 0.828em 0px 0.221em; width: 7px;\" variant=\"-explicitFont\">−</mjx-utext></mjx-mtext><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"6\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝑀</mjx-c></mjx-mi></mjx-math></mjx-container> plateau state. Second, by substituting <mjx-container ctxtmenu_counter=\"40\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(4 0 (3 1 2))\"><mjx-msup data-semantic-children=\"0,3\" data-semantic- data-semantic-owns=\"0 3\" data-semantic-role=\"unknown\" data-semantic-speech=\"upper G e Superscript 4 plus\" data-semantic-type=\"superscript\"><mjx-mrow><mjx-mi data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"4\" data-semantic-role=\"unknown\" data-semantic-type=\"identifier\"><mjx-c noic=\"true\" style=\"padding-top: 0.669em;\">G</mjx-c><mjx-c style=\"padding-top: 0.669em;\">e</mjx-c></mjx-mi></mjx-mrow><mjx-script style=\"vertical-align: 0.396em;\"><mjx-mrow data-semantic-children=\"1\" data-semantic-content=\"2\" data-semantic- data-semantic-owns=\"1 2\" data-semantic-parent=\"4\" data-semantic-role=\"addition\" data-semantic-type=\"postfixop\" size=\"s\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"integer\" data-semantic-type=\"number\"><mjx-c>4</mjx-c></mjx-mn><mjx-mo data-semantic- data-semantic-operator=\"postfixop,+\" data-semantic-parent=\"3\" data-semantic-role=\"addition\" data-semantic-type=\"operator\"><mjx-c>+</mjx-c></mjx-mo></mjx-mrow></mjx-script></mjx-msup></mjx-math></mjx-container> with <mjx-container ctxtmenu_counter=\"41\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(4 0 (3 1 2))\"><mjx-msup data-semantic-children=\"0,3\" data-semantic- data-semantic-owns=\"0 3\" data-semantic-role=\"unknown\" data-semantic-speech=\"upper S i Superscript 4 plus\" data-semantic-type=\"superscript\"><mjx-mrow><mjx-mi data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"4\" data-semantic-role=\"unknown\" data-semantic-type=\"identifier\"><mjx-c noic=\"true\" style=\"padding-top: 0.673em;\">S</mjx-c><mjx-c style=\"padding-top: 0.673em;\">i</mjx-c></mjx-mi></mjx-mrow><mjx-script style=\"vertical-align: 0.4em;\"><mjx-mrow data-semantic-children=\"1\" data-semantic-content=\"2\" data-semantic- data-semantic-owns=\"1 2\" data-semantic-parent=\"4\" data-semantic-role=\"addition\" data-semantic-type=\"postfixop\" size=\"s\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"integer\" data-semantic-type=\"number\"><mjx-c>4</mjx-c></mjx-mn><mjx-mo data-semantic- data-semantic-operator=\"postfixop,+\" data-semantic-parent=\"3\" data-semantic-role=\"addition\" data-semantic-type=\"operator\"><mjx-c>+</mjx-c></mjx-mo></mjx-mrow></mjx-script></mjx-msup></mjx-math></mjx-container>, the critical field for the 1/3-<mjx-container ctxtmenu_counter=\"42\" 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=\"italic\" data-semantic- data-semantic-role=\"latinletter\" data-semantic-speech=\"upper M\" data-semantic-type=\"identifier\"><mjx-c>𝑀</mjx-c></mjx-mi></mjx-math></mjx-container> plateau significantly decreases, e.g., <mjx-container ctxtmenu_counter=\"43\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(10 (9 (2 0 1) 8 (5 3 4)) 6 7)\"><mjx-mrow data-semantic-children=\"9,7\" data-semantic-content=\"6\" data-semantic- data-semantic-owns=\"9 6 7\" data-semantic-role=\"equality\" data-semantic-speech=\"mu 0 upper H Subscript c Baseline equals 17\" data-semantic-type=\"relseq\"><mjx-mrow data-semantic-added=\"true\" data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"2,5\" data-semantic-content=\"8\" data-semantic- data-semantic-owns=\"2 8 5\" data-semantic-parent=\"10\" data-semantic-role=\"implicit\" data-semantic-type=\"infixop\"><mjx-msub data-semantic-children=\"0,1\" data-semantic- data-semantic-owns=\"0 1\" data-semantic-parent=\"9\" data-semantic-role=\"greekletter\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"greekletter\" data-semantic-type=\"identifier\"><mjx-c>𝜇</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>0</mjx-c></mjx-mn></mjx-script></mjx-msub><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,\" data-semantic-parent=\"9\" 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=\"9\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝐻</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em; margin-left: -0.048em;\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\" size=\"s\"><mjx-c>𝑐</mjx-c></mjx-mi></mjx-script></mjx-msub></mjx-mrow><mjx-mo data-semantic- data-semantic-operator=\"relseq,=\" data-semantic-parent=\"10\" data-semantic-role=\"equality\" data-semantic-type=\"relation\" space=\"4\"><mjx-c>=</mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"10\" data-semantic-role=\"integer\" data-semantic-type=\"number\" space=\"4\"><mjx-c noic=\"true\" style=\"padding-top: 0.639em;\">1</mjx-c><mjx-c style=\"padding-top: 0.639em;\">7</mjx-c></mjx-mn></mjx-mrow></mjx-math></mjx-container> T in the <mjx-container ctxtmenu_counter=\"44\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(3 0 1 2)\"><mjx-mrow data-semantic-children=\"0,2\" data-semantic-content=\"1\" data-semantic- data-semantic-owns=\"0 1 2\" data-semantic-role=\"equality\" data-semantic-speech=\"x equals 1.0\" data-semantic-type=\"relseq\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝑥</mjx-c></mjx-mi><mjx-mo data-semantic- data-semantic-operator=\"relseq,=\" data-semantic-parent=\"3\" data-semantic-role=\"equality\" data-semantic-type=\"relation\" space=\"4\"><mjx-c>=</mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"float\" data-semantic-type=\"number\" space=\"4\"><mjx-c noic=\"true\" style=\"padding-top: 0.642em;\">1</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.642em;\">.</mjx-c><mjx-c style=\"padding-top: 0.642em;\">0</mjx-c></mjx-mn></mjx-mrow></mjx-math></mjx-container> sample, which results from the suppressed intertrimer coupling <mjx-container ctxtmenu_counter=\"45\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(2 0 1)\"><mjx-msub data-semantic-children=\"0,1\" data-semantic- data-semantic-owns=\"0 1\" data-semantic-role=\"latinletter\" data-semantic-speech=\"upper J 2\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝐽</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em; margin-left: -0.063em;\"><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>2</mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-math></mjx-container>. The gapped spin excitation is observed above 17 T whose size shows the temperature-dependent behavior for <mjx-container ctxtmenu_counter=\"46\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(8 (7 (2 0 1) 6 3) 4 5)\"><mjx-mrow data-semantic-children=\"7,5\" data-semantic-content=\"4\" data-semantic- data-semantic-owns=\"7 4 5\" data-semantic-role=\"inequality\" data-semantic-speech=\"mu 0 upper H greater than or equals 25.72\" data-semantic-type=\"relseq\"><mjx-mrow data-semantic-added=\"true\" data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"2,3\" data-semantic-content=\"6\" data-semantic- data-semantic-owns=\"2 6 3\" data-semantic-parent=\"8\" data-semantic-role=\"implicit\" 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=\"greekletter\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"greekletter\" data-semantic-type=\"identifier\"><mjx-c>𝜇</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>0</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-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"7\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝐻</mjx-c></mjx-mi></mjx-mrow><mjx-mo data-semantic- data-semantic-operator=\"relseq,≥\" data-semantic-parent=\"8\" data-semantic-role=\"inequality\" data-semantic-type=\"relation\" space=\"4\"><mjx-c>≥</mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"8\" data-semantic-role=\"float\" data-semantic-type=\"number\" space=\"4\"><mjx-c noic=\"true\" style=\"padding-top: 0.644em;\">2</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.644em;\">5</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.644em;\">.</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.644em;\">7</mjx-c><mjx-c style=\"padding-top: 0.644em;\">2</mjx-c></mjx-mn></mjx-mrow></mjx-math></mjx-container> T. These observations support the topological nontrivial characteristic of the <mjx-container ctxtmenu_counter=\"47\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-children=\"5,4\" data-semantic-content=\"3\" data-semantic- data-semantic-owns=\"5 3 4\" data-semantic-role=\"subtraction\" data-semantic-speech=\"1 divided by 3 minus upper M\" data-semantic-structure=\"(6 (5 0 1 2) 3 4)\" data-semantic-type=\"infixop\"><mjx-mrow data-semantic-added=\"true\" data-semantic-children=\"0,2\" data-semantic-content=\"1\" data-semantic- data-semantic-owns=\"0 1 2\" data-semantic-parent=\"6\" data-semantic-role=\"division\" data-semantic-type=\"infixop\"><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\"><mjx-c>1</mjx-c></mjx-mn><mjx-mo data-semantic- data-semantic-operator=\"infixop,/\" data-semantic-parent=\"5\" data-semantic-role=\"division\" data-semantic-type=\"operator\"><mjx-c>/</mjx-c></mjx-mo><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\"><mjx-c>3</mjx-c></mjx-mn></mjx-mrow><mjx-mtext data-semantic-annotation=\"general:text\" data-semantic- data-semantic-operator=\"infixop,−\" data-semantic-parent=\"6\" data-semantic-role=\"subtraction\" data-semantic-type=\"operator\" style='font-family: MJX-STX-ZERO, \"Helvetica Neue\", Helvetica, Roboto, Arial, sans-serif;'><mjx-utext style=\"font-size: 90.6%; padding: 0.828em 0px 0.221em; width: 7px;\" variant=\"-explicitFont\">−</mjx-utext></mjx-mtext><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"6\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝑀</mjx-c></mjx-mi></mjx-math></mjx-container> plateau state.","PeriodicalId":20082,"journal":{"name":"Physical Review B","volume":null,"pages":null},"PeriodicalIF":3.7000,"publicationDate":"2024-11-05","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.l201102","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}
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