High-field NMR study on the topologically nontrivial 1/3 magnetization plateau state in dopedNa2⁢Cu3⁢Ge4−𝑥⁢Si𝑥⁢O12

IF 3.7 2区 物理与天体物理 Q1 Physics and Astronomy
Yuyan Han, Bocheng Yu, Zan Du, Langsheng Ling, Lei Zhang, Wei Tong, Chuanying Xi, Jinglei Zhang, Tian Shang, Li Pi, Long Ma
{"title":"High-field NMR study on the topologically nontrivial 1/3 magnetization plateau state in dopedNa2⁢Cu3⁢Ge4−𝑥⁢Si𝑥⁢O12","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}
引用次数: 0

Abstract

The spin-1/2 trimer system Na2Cu3Ge4O12 is proposed to host topologically nontrivial 1/3 magnetization (𝑀) plateau state. In this paper, we report a high-field nuclear magnetic resonance (NMR) study on the low-energy spin excitations of the 1/3𝑀 plateau state in Na2Cu3Ge4O12 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 1/3𝑀 plateau state. Second, by substituting Ge4+ with Si4+, the critical field for the 1/3-𝑀 plateau significantly decreases, e.g., 𝜇0𝐻𝑐=17 T in the 𝑥=1.0 sample, which results from the suppressed intertrimer coupling 𝐽2. The gapped spin excitation is observed above 17 T whose size shows the temperature-dependent behavior for 𝜇0𝐻25.72 T. These observations support the topological nontrivial characteristic of the 1/3𝑀 plateau state.
对掺杂 Na2Cu3Ge4-𝑥Si𝑥O12 中拓扑非难 1/3 磁化高原态的高场核磁共振研究
有人提出自旋-1/2 三聚体系统 Na2Cu3Ge4O12 中存在拓扑学上非难的 1/3 磁化(𝑀)高原态。本文报告了对 Na2Cu3Ge4O12 和掺硅样品中 1/3-𝑀 高原态的低能自旋激发的高场核磁共振(NMR)研究。首先,1/3-𝑀高原态自旋晶格弛豫率的热激活行为表明了支持高场霍尔丹相的自旋激发间隙。其次,用 Si4+ 替代 Ge4+,1/3-𝑀高原的临界场显著降低,例如,在 𝑥=1.0 样品中,临界场为 𝐻𝑐=17 T,这是三元间耦合𝐽2 被抑制的结果。这些观察结果支持了 1/3-𝑀 高原态的拓扑非难特性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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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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