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Self-Organizations in Frustrated Spinels

Self-Organizations in Frustrated Spinels. Seung-Hun Lee National Institute of Standards and Technology. Strongly Correlated Electron System. Lattice. Spin. Charge. Orbital. O. A. B. Geometrically frustrated. Spinel AB 2 O 4.

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Self-Organizations in Frustrated Spinels

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  1. Self-Organizations in Frustrated Spinels Seung-Hun Lee National Institute of Standards and Technology

  2. Strongly Correlated Electron System Lattice Spin Charge Orbital

  3. O A B Geometrically frustrated Spinel AB2O4 Crystal structure Lattice of B sites : Corner-sharing tetrahedra Edge-sharing octahedra • Frustration • Macroscopic ground state degeneracy  New physics ?

  4. SPIN TYPE SPIN LOW T METHOD REFERENCE Value PHASE Isotropic S=1/2 SpinLiquid Exact Diag. Canals and Lacroix PRL ’98 Isotropic S= Spin Liquid MC sim. Reimers PRB ’92 Moessner, Chalker PRL ’98 Theory of spins with AFM interactions on corner-sharing tetrahedra The most frustrated case is a system with isotropic uniform nearest neighbor interactions only: H = -JS Si. Sj

  5. Self-Organizations in Frustrated Spinels • ZnCr2O4: The most frustrating magnet 1. Composite antiferromagnetic hexagons 2. Spin-Peierls-like phase transition • ZnV2O4 and LiV2O4 with orbital degeneracy 1. Orbital and spin chains in ZnV2O4 2. LiV2O4: d-electron heavy fermon? • GeNi2O4 1. A simple frustration and spin-flops • Summary

  6. Collaborators on ZnCr2O4, ZnV2O4, LiV2O4, GeNi2O4 C.Broholm (Johns Hopkins Univ.) M. Matsuda (JAERI) S-W. Cheong (Rutgers Univ.) J.-H. Chung(NIST) G. Gasparovic (Johns Hopkins Univ.) R. Erwin (NIST) Q. Huang (NIST) K. Kamazawa (Waseda U) J. Iniques (NIST) Y. Tsunoda (Waseda U) M. Isobe (ISSP, U of Tokyo, Japan) K. Matsuno (U of Tokyo) T.H. Kim (Rutgers Univ.) H. Aruga-Katori (RIKEN) Y.J. Kim (Brookhaven National Lab.) H. Takagi (U of Tokyo) D. Louca(Univ. of Virginia) O. Tchernyshyov (JHU) R. Osborn (Argonne National Lab.) R. Moessner (CNRS-ENS) S. Park (NIST, now at KAERI, Korea) S. Sondhi (Princeton U) Y.Qiu (NIST) D. Khomskii (Cologne U) W. Ratcliff (Rutgers Univ., now at NIST) C. Henley (Cornell U) S. Rosenkranz (Argonne National Lab.) J. Rush (NIST) T. Sato (ISSP, U of Tokyo, Japan) H. Ueda (ISSP, U of Tokyo, Japan) Y. Ueda(ISSP, U of Tokyo, Japan) P. Zschack (Univ. of Illinois)

  7. Spinels AB2O4 (B = Cr, V, Ni) Cr3+ (3d3) eg 3d t2g dxy, dyz, dzx Free Ion Cubic Field Ni2+ (3d8) V3+ (3d2) with orbital degeneracy eg dx2-y2, dz2 eg 3d 3d t2g dxy, dyz, dzx t2g dxy, dyz, dzx Free Ion Cubic Field Free Ion Cubic Field

  8. ZnCr2O4 (3d3) W. Ratcliff, S-W. Cheong (2000) ZnV2O4 (3d2) with orbital degeneracy Y. Ueda et al., (1997) QCW = -390 K TN = 12.5 K GeNi2O4 (3d8) M. Crawford et al. (2004) II I QCW = -1000 K TN = 40 K

  9. 3d t2g 3d t2g T (K) LixZn1-xV2O4 Zn2+V2O4: V3+ (3d2) Li1+V2O4: V3.5+ (3d1.5)

  10. UBe13 CeAl3 CeCu6 Bulk measurement data from LiV2O4 at low T exhibit Fermi liquid behaviors CeCu2Si2 LiV2O4 UPt3 • Cv ~ gT • ~ r0+AT2 c ~ const CeB6 USn3 UAl2 UPt2 UPt CePd3 UIn3 UGa3 0 50 100 150 200 T (K) LiV2O4 with d-electrons is as heavy as UPt3 ! LiV2O4: d-Electron Heavy Fermion S. Kondo et al. (1997)

  11. Kondo screening RKKY interaction Heavy Fermion Heavy fermion behavior with a heavy mass m ~ 100-1000 me are usually found in Ce- or U-based compounds that have two different types of electrons: (1) localized f-electrons and (2) conduction (s,p)-electrons. Why does LiV2O4 exhibit heavy fermionic behavior even though only d-electrons are crossing the Fermi energy?

  12. Outstanding issues Geometrical frustration: 1. What is nature of the spin liquid phase? 2. What are the zero-energy mode excitations? ZnCr2O4: 1. Why does it undergo a transition? 2. What is the nature of the phase transition? ZnV2O4: 1. What role does orbital degeneracy play in its physics? 2. Why are there two transitions? 3. What is the nature of the phase transitions? LiV2O4: 1. Why does it exhibit heavy fermionic behavior? GeNi2O4: 1. Why two transitions?

  13. Lee/Broholm et al. (2000) Spin-Peierls-like (spin-lattice) transition Phase Transition due to Spin-Lattice coupling ZnCr2O4 (3d3) W. Ratcliff, S-W. Cheong (2000) QCW = -390 K TN = 12.5 K

  14. Nature of the Spin Liquid State in GF magnets Emergence of Composite Spin Excitations

  15. 200mg Spin liquid phase T > TN The fundamental spin degree of freedom is an Antiferromagnetic hexagonal spin loop ! Composite Spin Excitations in ZnCr2O4 Lee/Broholm et al. (2002)

  16. Summary Geometrical frustration: 1. Emergence of composite spin degrees of freedom 2. Existence of zero energy mode ZnCr2O4: 1. Antiferromagnetic hexagonal spin loops 2. Spin-Peierls-like phase transition

  17. ZnV2O4 (3d2) with orbital degeneracy Lee/Louca et al. (2004) Spin-Peierls-like (spin-lattice) transition Phase Transitions ZnCr2O4 (3d3) W. Ratcliff, S-W. Cheong (2000) QCW = -390 K TN = 12.5 K Why TWO separate transitions?

  18. Theoretical works on ZnV2O4 • Spin-Peierls-like models (or spin-lattice coupling) • Y. Yamashita and K. Ueda (2000) Spin-driven Jahn-Teller distortion in a Pyrochlore system • O. Tchernyshyov, R. Moessner, and S. L. Sondhi (2002) Order by distortion and string modes in Pyrochlore AFMs CANNOT explain why there are TWO separate transitions. Orbital models • Antiferro-orbital model H. Tsunetsugu and Y. Motome (2003) Magnetic transition and orbital degrees of freedom in vanadium spinels • Ferro-orbital model O. Tchernyshyov (2004) Structural, orbital, and magnetic order in vanadium spinels

  19. dxy, dyz, dzx ZnCr2O4 Cubic phase (a = b = c) Tetragonal (c < a = b) Tsunetsugu/Motome (2003) Inelastic neutron scattering from ZnV2O4 Lee/Louca et al. (2004) 100K 60K 45K 10K

  20. Cubic phase Summary on ZnV2O4 (3d2) with orbital degeneracy Tetragonal phase • In cubic phase, ZnV2O4 is a system of three-dimensionally tangled spin chains. In tetragonal phase, it is a very good model system forone-dimensional spin chains. • The antiferro-orbital model seems to be consistent with our neutron results.

  21. UBe13 CeAl3 CeCu6 Bulk measurement data from LiV2O4 at low T exhibits Fermi liquid behavior CeCu2Si2 LiV2O4 UPt3 • Cv ~ gT • ~ r0+AT2 c ~ const CeB6 USn3 UAl2 UPt2 UPt CePd3 UIn3 UGa3 0 50 100 150 200 T (K) LiV2O4 with d-electrons is as heavy as UPt3 ! LiV2O4: d-Electron Heavy Fermion

  22. Spin correlations become antiferromagnetic as LiV2O4 enters the heavy fermion phase LiV2O4 (3d1.5) : Dynamic Spin Correlations Lee/Broholm et al. (2001) AFM

  23. LiV2O4 (3d1.5) • It remains cubic down to 20 mK. • The formation of three dimensionally tangled orbital chains may occur in LiV2O4. • The metallic character of LiV2O4 may produce a spin-density wave along the orbital chains that is responsible for the enhancement of the low energy density of states at low temperatures

  24. I II I Phase II Phase I II GeNi2O4 (3d8) Matsuda/Chung et al. (2004)

  25. Summary Geometrical frustration: 1. Emergence of composite spin degrees of freedom 2. Existence of zero energy mode ZnCr2O4: 1. Antiferromagnetic hexagonal spin loops 2. Spin-Peierls-like phase transition ZnV2O4 and LiV2O4: 1. Orbital degree of freedom plays the central role 2. Orbital and spin chains GeNi2O4: 1. Simple frustration and spin flops Self-organizations of spin, “orbital”, and lattice degrees of freedom to minimize their competing interactions

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