理想𝑗=12化合物K2IrCl6中的自旋轨道晶格纠缠

IF 3.7 2区 物理与天体物理 Q1 Physics and Astronomy Physical Review B Pub Date : 2024-11-07 DOI:10.1103/physrevb.110.195120
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
{"title":"理想𝑗=12化合物K2IrCl6中的自旋轨道晶格纠缠","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":"{\"title\":\"Spin orbital lattice entanglement in the ideal𝑗=12compoundK2⁢IrCl6\",\"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\\\" 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引用次数: 0

摘要

具有自旋轨道纠缠𝑗=1/2 矩的莫特绝缘体蕴藏着奇妙的磁性。𝑗=1/2波函数需要立方对称性,而非立方晶场则混合了𝑗=1/2和3/2特性。对 5𝑑5铱酸盐的光谱研究通常声称其具有非立方对称性,例如基于激发的𝑗=3/2四元组的分裂。反萤石型 K2IrCl6 是一种具有全局立方对称性的受挫 fcc 量子磁体,其显著的分裂尤其令人费解。它提出了𝑗=1/2 矩对磁弹性耦合的稳定性这一根本问题。结合共振非弹性 X 射线散射和光学光谱学,我们证明了 K2IrCl6 中的多峰线形反映了𝑗=3/2 态的振动特性,而不是非立方晶体场。具有分离良好的 IrCl6 八面体的准分子晶体结构解释了通常在固体中模糊不清的清晰边带的存在。我们的研究结果突显了具有理想𝑗=1/2 矩的立方 K2IrCl6 的自旋轨道晶格纠缠特性。
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Spin orbital lattice entanglement in the ideal𝑗=12compoundK2⁢IrCl6
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 5𝑑5 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 K2IrCl6, 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 K2IrCl6 reflects a vibronic character of the 𝑗=3/2 states rather than a noncubic crystal field. The quasimolecular crystal structure with well separated IrCl6 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 K2IrCl6 with ideal 𝑗=1/2 moments.
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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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