Role of orbital degrees of freedom in investigating the magnetic properties of geometrically frustrated vanadium spinels

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• 作者：Sohan Lal ; ^{goluthakur2007@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Sudhir K. Pandey ^{sudhir@iitmandi.ac.in" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Frustration indices ; Magnetic moments ; Band gap ; Exchange coupling constant ; Curie-Weiss temperature ; Magnetic transition temperature
• 刊名：Computational Materials Science
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：126
• 期：Complete
• 页码：373-381
• 全文大小：984 K

文摘

The inconsistency about the degree of geometrical frustration has been a long issue in AV₂O₄ (A class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S092702561630492X&_mathId=si1.gif&_user=111111111&_pii=S092702561630492X&_rdoc=1&_issn=09270256&md5=b14afd5073f617282814a605bc801b74" title="Click to view the MathML source">≡class="mathContainer hidden">class="mathCode">$\equiv$ Zn, Cd and Mg) compounds, which arises from the two experimental results: (i) frustration indices and (ii) magnetic moments. In the present study, we try to understand such inconsistency by using ab initio electronic structure calculations. The orbital degrees of freedom are found to play an important role in understanding the geometrically frustrated magnetic behavior of these compounds. The magnitude of the maximum calculated values of orbital magnetic moment per formula unit for ZnV₂O₄, MgV₂O₄ and CdV₂O₄ compounds are found to be class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S092702561630492X&_mathId=si35.gif&_user=111111111&_pii=S092702561630492X&_rdoc=1&_issn=09270256&md5=6b78141e172f5403bfbcd82a5ed3a987" title="Click to view the MathML source">∼class="mathContainer hidden">class="mathCode">$\sim$1.54 class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S092702561630492X&_mathId=si26.gif&_user=111111111&_pii=S092702561630492X&_rdoc=1&_issn=09270256&md5=56fcc20e1acc1a4c528ac8740738ed4b" title="Click to view the MathML source">μ_Bclass="mathContainer hidden">class="mathCode">${\mu }_B$, class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S092702561630492X&_mathId=si35.gif&_user=111111111&_pii=S092702561630492X&_rdoc=1&_issn=09270256&md5=6b78141e172f5403bfbcd82a5ed3a987" title="Click to view the MathML source">∼class="mathContainer hidden">class="mathCode">$\sim$0.92 class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S092702561630492X&_mathId=si26.gif&_user=111111111&_pii=S092702561630492X&_rdoc=1&_issn=09270256&md5=56fcc20e1acc1a4c528ac8740738ed4b" title="Click to view the MathML source">μ_Bclass="mathContainer hidden">class="mathCode">${\mu }_B$ and class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S092702561630492X&_mathId=si35.gif&_user=111111111&_pii=S092702561630492X&_rdoc=1&_issn=09270256&md5=6b78141e172f5403bfbcd82a5ed3a987" title="Click to view the MathML source">∼class="mathContainer hidden">class="mathCode">$\sim$1.74 class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S092702561630492X&_mathId=si26.gif&_user=111111111&_pii=S092702561630492X&_rdoc=1&_issn=09270256&md5=56fcc20e1acc1a4c528ac8740738ed4b" title="Click to view the MathML source">μ_Bclass="mathContainer hidden">class="mathCode">${\mu }_B$, respectively. The inclusion of the orbital and spin angular momenta for calculating the frustration indices improves the understanding about the degree of geometrical frustration in these compounds. The calculated values of the frustration indices (class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S092702561630492X&_mathId=si8.gif&_user=111111111&_pii=S092702561630492X&_rdoc=1&_issn=09270256&md5=9e3ea0e1b8aac14d37c38fb9b3c506dc" title="Click to view the MathML source">f_Jclass="mathContainer hidden">class="mathCode">$f_J$) are largest for MgV₂O₄ and smallest for CdV₂O₄ for 3.3 class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S092702561630492X&_mathId=si42.gif&_user=111111111&_pii=S092702561630492X&_rdoc=1&_issn=09270256&md5=f1f29ac5cd65de99869c68c9b0a2aee6" title="Click to view the MathML source">⩽class="mathContainer hidden">class="mathCode">$⩽$ class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S092702561630492X&_mathId=si43.gif&_user=111111111&_pii=S092702561630492X&_rdoc=1&_issn=09270256&md5=24acd89d3126f4565c4941afb361cc5b" title="Click to view the MathML source">U⩽class="mathContainer hidden">class="mathCode">$U⩽$ 5.3 eV. In this range of U  , the calculated values of class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S092702561630492X&_mathId=si44.gif&_user=111111111&_pii=S092702561630492X&_rdoc=1&_issn=09270256&md5=b60f683349195d004ad0d6a9ca920ba2" title="Click to view the MathML source">Δclass="mathContainer hidden">class="mathCode">$\mathrm{\Delta }$M₂ = class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S092702561630492X&_mathId=si45.gif&_user=111111111&_pii=S092702561630492X&_rdoc=1&_issn=09270256&md5=cc3e19b4ceb84965fc80a5c5d9b442dd" title="Click to view the MathML source">M_total-M_expclass="mathContainer hidden">class="mathCode">$M_{\text{total}}-M_{\text{exp}}$ (where, class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S092702561630492X&_mathId=si46.gif&_user=111111111&_pii=S092702561630492X&_rdoc=1&_issn=09270256&md5=6ca786850274dcd5099c40fbdf7bff81" title="Click to view the MathML source">M_total=M_spin-|M_orbital|class="mathContainer hidden">class="mathCode">$M_{\text{total}}=M_{\text{spin}}-|M_{\text{orbital}}|$) are also found to be largest for MgV₂O₄ and smallest for CdV₂O₄. Hence, the consistency about the degree of geometrical frustration, which arises from the class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S092702561630492X&_mathId=si8.gif&_user=111111111&_pii=S092702561630492X&_rdoc=1&_issn=09270256&md5=9e3ea0e1b8aac14d37c38fb9b3c506dc" title="Click to view the MathML source">f_Jclass="mathContainer hidden">class="mathCode">$f_J$ as well as from the class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S092702561630492X&_mathId=si44.gif&_user=111111111&_pii=S092702561630492X&_rdoc=1&_issn=09270256&md5=b60f683349195d004ad0d6a9ca920ba2" title="Click to view the MathML source">Δclass="mathContainer hidden">class="mathCode">$\mathrm{\Delta }$M₂ is achieved and improves the understanding about the degree of geometrical frustration in these compounds. Calculated values of band gap in this range of U   are found to be closer to that of experimentally observed values for all three compounds. The absolute values of the nearest neighbor exchange coupling constant (class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S092702561630492X&_mathId=si10.gif&_user=111111111&_pii=S092702561630492X&_rdoc=1&_issn=09270256&md5=825990a7bc64b95e3109dc47ae6302d7" title="Click to view the MathML source">J_nnclass="mathContainer hidden">class="mathCode">$J_{\mathit{nn}}$) between V spins are found to be largest for MgV₂O₄ and smallest for CdV₂O₄, which indicate that the calculated absolute values of the Curie-Weiss temperature class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S092702561630492X&_mathId=si17.gif&_user=111111111&_pii=S092702561630492X&_rdoc=1&_issn=09270256&md5=459aa8bf629b24c254a15bc74617372e" title="Click to view the MathML source">(Θ_CW)_Jclass="mathContainer hidden">class="mathCode">${({\Theta }_{\mathit{CW}})}_J$ are highest for MgV₂O₄ and smallest for CdV₂O₄ for 3.3 class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S092702561630492X&_mathId=si42.gif&_user=111111111&_pii=S092702561630492X&_rdoc=1&_issn=09270256&md5=f1f29ac5cd65de99869c68c9b0a2aee6" title="Click to view the MathML source">⩽class="mathContainer hidden">class="mathCode">$⩽$ class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S092702561630492X&_mathId=si43.gif&_user=111111111&_pii=S092702561630492X&_rdoc=1&_issn=09270256&md5=24acd89d3126f4565c4941afb361cc5b" title="Click to view the MathML source">U⩽class="mathContainer hidden">class="mathCode">$U⩽$ 5.3 eV. In this range of U  , the magnetic transition temperatureclass="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S092702561630492X&_mathId=si20.gif&_user=111111111&_pii=S092702561630492X&_rdoc=1&_issn=09270256&md5=516da6e6870df4617eadb0390b904ebf" title="Click to view the MathML source">(T_N)_Jclass="mathContainer hidden">class="mathCode">${(T_N)}_J$ is found to be class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S092702561630492X&_mathId=si35.gif&_user=111111111&_pii=S092702561630492X&_rdoc=1&_issn=09270256&md5=6b78141e172f5403bfbcd82a5ed3a987" title="Click to view the MathML source">∼class="mathContainer hidden">class="mathCode">$\sim$150 K, class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S092702561630492X&_mathId=si35.gif&_user=111111111&_pii=S092702561630492X&_rdoc=1&_issn=09270256&md5=6b78141e172f5403bfbcd82a5ed3a987" title="Click to view the MathML source">∼class="mathContainer hidden">class="mathCode">$\sim$60 K and class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S092702561630492X&_mathId=si35.gif&_user=111111111&_pii=S092702561630492X&_rdoc=1&_issn=09270256&md5=6b78141e172f5403bfbcd82a5ed3a987" title="Click to view the MathML source">∼class="mathContainer hidden">class="mathCode">$\sim$22 K for MgV₂O₄, ZnV₂O₄ and CdV₂O₄, respectively, which shows that the order of class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S092702561630492X&_mathId=si20.gif&_user=111111111&_pii=S092702561630492X&_rdoc=1&_issn=09270256&md5=516da6e6870df4617eadb0390b904ebf" title="Click to view the MathML source">(T_N)_Jclass="mathContainer hidden">class="mathCode">${(T_N)}_J$ is similar to that of class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S092702561630492X&_mathId=si23.gif&_user=111111111&_pii=S092702561630492X&_rdoc=1&_issn=09270256&md5=793000a919022479fe8e8aad78f0c988" title="Click to view the MathML source">(T_N)_expclass="mathContainer hidden">class="mathCode">${(T_N)}_{\text{exp}}$ for these compounds. Hence, all the magnetic properties studied in the present work are well explained in these spinels for 3.3 class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S092702561630492X&_mathId=si42.gif&_user=111111111&_pii=S092702561630492X&_rdoc=1&_issn=09270256&md5=f1f29ac5cd65de99869c68c9b0a2aee6" title="Click to view the MathML source">⩽class="mathContainer hidden">class="mathCode">$⩽$ class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S092702561630492X&_mathId=si43.gif&_user=111111111&_pii=S092702561630492X&_rdoc=1&_issn=09270256&md5=24acd89d3126f4565c4941afb361cc5b" title="Click to view the MathML source">U⩽class="mathContainer hidden">class="mathCode">$U⩽$ 5.3 eV. This work is expected to provide a valuable input in understanding the geometrically frustrated magnetic behavior for those systems for which the orbital part of the angular momenta are not quenched.