求助PDF
{"title":"Spin orbital lattice entanglement in the ideal𝑗=12compoundK2IrCl6","authors":"P. Warzanowski, M. Magnaterra, Ch. J. Sahle, M. Moretti Sala, P. Becker, L. Bohatý, I. Císařová, G. Monaco, T. Lorenz, P. H. M. van Loosdrecht, J. van den Brink, M. Grüninger","doi":"10.1103/physrevb.110.195120","DOIUrl":null,"url":null,"abstract":"Mott insulators with spin-orbit entangled <mjx-container ctxtmenu_counter=\"59\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(6 0 1 (5 2 3 4))\"><mjx-mrow data-semantic-children=\"0,5\" data-semantic-content=\"1\" data-semantic- data-semantic-owns=\"0 1 5\" data-semantic-role=\"equality\" data-semantic-speech=\"j equals 1 divided by 2\" data-semantic-type=\"relseq\"><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>𝑗</mjx-c></mjx-mi><mjx-mo data-semantic- data-semantic-operator=\"relseq,=\" data-semantic-parent=\"6\" 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=\"2,4\" data-semantic-content=\"3\" data-semantic- data-semantic-owns=\"2 3 4\" data-semantic-parent=\"6\" data-semantic-role=\"division\" data-semantic-type=\"infixop\" space=\"4\"><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>2</mjx-c></mjx-mn></mjx-mrow></mjx-mrow></mjx-math></mjx-container> moments host intriguing magnetic properties. The <mjx-container ctxtmenu_counter=\"60\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(6 0 1 (5 2 3 4))\"><mjx-mrow data-semantic-children=\"0,5\" data-semantic-content=\"1\" data-semantic- data-semantic-owns=\"0 1 5\" data-semantic-role=\"equality\" data-semantic-speech=\"j equals 1 divided by 2\" data-semantic-type=\"relseq\"><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>𝑗</mjx-c></mjx-mi><mjx-mo data-semantic- data-semantic-operator=\"relseq,=\" data-semantic-parent=\"6\" 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=\"2,4\" data-semantic-content=\"3\" data-semantic- data-semantic-owns=\"2 3 4\" data-semantic-parent=\"6\" data-semantic-role=\"division\" data-semantic-type=\"infixop\" space=\"4\"><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>2</mjx-c></mjx-mn></mjx-mrow></mjx-mrow></mjx-math></mjx-container> wave function requires cubic symmetry, while a noncubic crystal field mixes <mjx-container ctxtmenu_counter=\"61\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(6 0 1 (5 2 3 4))\"><mjx-mrow data-semantic-children=\"0,5\" data-semantic-content=\"1\" data-semantic- data-semantic-owns=\"0 1 5\" data-semantic-role=\"equality\" data-semantic-speech=\"j equals 1 divided by 2\" data-semantic-type=\"relseq\"><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>𝑗</mjx-c></mjx-mi><mjx-mo data-semantic- data-semantic-operator=\"relseq,=\" data-semantic-parent=\"6\" 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=\"2,4\" data-semantic-content=\"3\" data-semantic- data-semantic-owns=\"2 3 4\" data-semantic-parent=\"6\" data-semantic-role=\"division\" data-semantic-type=\"infixop\" space=\"4\"><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>2</mjx-c></mjx-mn></mjx-mrow></mjx-mrow></mjx-math></mjx-container> and 3/2 character. Spectroscopic studies of <mjx-container ctxtmenu_counter=\"62\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(5 0 4 (3 1 2))\"><mjx-mrow data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"0,3\" data-semantic-content=\"4\" data-semantic- data-semantic-owns=\"0 4 3\" data-semantic-role=\"implicit\" data-semantic-speech=\"5 d Superscript 5\" 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>5</mjx-c></mjx-mn><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,\" data-semantic-parent=\"5\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\"><mjx-c></mjx-c></mjx-mo><mjx-msup data-semantic-children=\"1,2\" data-semantic- data-semantic-owns=\"1 2\" data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"superscript\"><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>𝑑</mjx-c></mjx-mi><mjx-script style=\"vertical-align: 0.363em;\"><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\" size=\"s\"><mjx-c>5</mjx-c></mjx-mn></mjx-script></mjx-msup></mjx-mrow></mjx-math></mjx-container> iridates typically claim noncubic symmetry, e.g., based on a splitting of the excited <mjx-container ctxtmenu_counter=\"63\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(6 0 1 (5 2 3 4))\"><mjx-mrow data-semantic-children=\"0,5\" data-semantic-content=\"1\" data-semantic- data-semantic-owns=\"0 1 5\" data-semantic-role=\"equality\" data-semantic-speech=\"j equals 3 divided by 2\" data-semantic-type=\"relseq\"><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>𝑗</mjx-c></mjx-mi><mjx-mo data-semantic- data-semantic-operator=\"relseq,=\" data-semantic-parent=\"6\" 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=\"2,4\" data-semantic-content=\"3\" data-semantic- data-semantic-owns=\"2 3 4\" data-semantic-parent=\"6\" data-semantic-role=\"division\" data-semantic-type=\"infixop\" space=\"4\"><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-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>2</mjx-c></mjx-mn></mjx-mrow></mjx-mrow></mjx-math></mjx-container> quartet. A sizable splitting is particularly puzzling in antifluorite-type <mjx-container ctxtmenu_counter=\"64\" 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=\"normal upper K 2 upper I r upper C l 6\" 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=\"latinletter\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>K</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=\"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;\">I</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.706em;\">r</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.706em;\">C</mjx-c><mjx-c style=\"padding-top: 0.706em;\">l</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>6</mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-mrow></mjx-math></mjx-container>, a frustrated fcc quantum magnet with global cubic symmetry. It raises the fundamental question about the stability of <mjx-container ctxtmenu_counter=\"65\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(6 0 1 (5 2 3 4))\"><mjx-mrow data-semantic-children=\"0,5\" data-semantic-content=\"1\" data-semantic- data-semantic-owns=\"0 1 5\" data-semantic-role=\"equality\" data-semantic-speech=\"j equals 1 divided by 2\" data-semantic-type=\"relseq\"><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>𝑗</mjx-c></mjx-mi><mjx-mo data-semantic- data-semantic-operator=\"relseq,=\" data-semantic-parent=\"6\" 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=\"2,4\" data-semantic-content=\"3\" data-semantic- data-semantic-owns=\"2 3 4\" data-semantic-parent=\"6\" data-semantic-role=\"division\" data-semantic-type=\"infixop\" space=\"4\"><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>2</mjx-c></mjx-mn></mjx-mrow></mjx-mrow></mjx-math></mjx-container> moments against magnetoelastic coupling. Combining resonant inelastic x-ray scattering with optical spectroscopy, we demonstrate that the multi-peak line shape in <mjx-container ctxtmenu_counter=\"66\" 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=\"normal upper K 2 upper I r upper C l 6\" 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=\"latinletter\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>K</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=\"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;\">I</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.706em;\">r</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.706em;\">C</mjx-c><mjx-c style=\"padding-top: 0.706em;\">l</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>6</mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-mrow></mjx-math></mjx-container> reflects a vibronic character of the <mjx-container ctxtmenu_counter=\"67\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(6 0 1 (5 2 3 4))\"><mjx-mrow data-semantic-children=\"0,5\" data-semantic-content=\"1\" data-semantic- data-semantic-owns=\"0 1 5\" data-semantic-role=\"equality\" data-semantic-speech=\"j equals 3 divided by 2\" data-semantic-type=\"relseq\"><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>𝑗</mjx-c></mjx-mi><mjx-mo data-semantic- data-semantic-operator=\"relseq,=\" data-semantic-parent=\"6\" 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=\"2,4\" data-semantic-content=\"3\" data-semantic- data-semantic-owns=\"2 3 4\" data-semantic-parent=\"6\" data-semantic-role=\"division\" data-semantic-type=\"infixop\" space=\"4\"><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-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>2</mjx-c></mjx-mn></mjx-mrow></mjx-mrow></mjx-math></mjx-container> states rather than a noncubic crystal field. The quasimolecular crystal structure with well separated <mjx-container ctxtmenu_counter=\"68\" 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=\"unknown\" data-semantic-speech=\"upper I r upper C l 6\" 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: 0.706em;\">I</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.706em;\">r</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.706em;\">C</mjx-c><mjx-c style=\"padding-top: 0.706em;\">l</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>6</mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-math></mjx-container> octahedra explains the existence of well-defined sidebands that are usually smeared out in solids. Our results highlight the spin orbital lattice entangled character of cubic <mjx-container ctxtmenu_counter=\"69\" 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=\"normal upper K 2 upper I r upper C l 6\" 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=\"latinletter\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>K</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=\"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;\">I</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.706em;\">r</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.706em;\">C</mjx-c><mjx-c style=\"padding-top: 0.706em;\">l</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>6</mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-mrow></mjx-math></mjx-container> with ideal <mjx-container ctxtmenu_counter=\"70\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(6 0 1 (5 2 3 4))\"><mjx-mrow data-semantic-children=\"0,5\" data-semantic-content=\"1\" data-semantic- data-semantic-owns=\"0 1 5\" data-semantic-role=\"equality\" data-semantic-speech=\"j equals 1 divided by 2\" data-semantic-type=\"relseq\"><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>𝑗</mjx-c></mjx-mi><mjx-mo data-semantic- data-semantic-operator=\"relseq,=\" data-semantic-parent=\"6\" 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=\"2,4\" data-semantic-content=\"3\" data-semantic- data-semantic-owns=\"2 3 4\" data-semantic-parent=\"6\" data-semantic-role=\"division\" data-semantic-type=\"infixop\" space=\"4\"><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>2</mjx-c></mjx-mn></mjx-mrow></mjx-mrow></mjx-math></mjx-container> moments.","PeriodicalId":20082,"journal":{"name":"Physical Review B","volume":"245 1","pages":""},"PeriodicalIF":3.7000,"publicationDate":"2024-11-07","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.110.195120","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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Abstract
Mott insulators with spin-orbit entangled
𝑗 = 1 / 2 moments host intriguing magnetic properties. The
𝑗 = 1 / 2 wave function requires cubic symmetry, while a noncubic crystal field mixes
𝑗 = 1 / 2 and 3/2 character. Spectroscopic studies of
5 𝑑 5 iridates typically claim noncubic symmetry, e.g., based on a splitting of the excited
𝑗 = 3 / 2 quartet. A sizable splitting is particularly puzzling in antifluorite-type
K 2 I r C l 6 , a frustrated fcc quantum magnet with global cubic symmetry. It raises the fundamental question about the stability of
𝑗 = 1 / 2 moments against magnetoelastic coupling. Combining resonant inelastic x-ray scattering with optical spectroscopy, we demonstrate that the multi-peak line shape in
K 2 I r C l 6 reflects a vibronic character of the
𝑗 = 3 / 2 states rather than a noncubic crystal field. The quasimolecular crystal structure with well separated
I r C l 6 octahedra explains the existence of well-defined sidebands that are usually smeared out in solids. Our results highlight the spin orbital lattice entangled character of cubic
K 2 I r C l 6 with ideal
𝑗 = 1 / 2 moments.