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

2. Lattice SpinCharge Orbital Strongly Correlated Electron System

3. Lattice of B sites : Corner-sharing tetrahedra Geometrically frustrated Crystal structure O A B Spinel AB 2 O 4 Edge-sharing octahedra Frustration  Macroscopic ground state degeneracy  New physics ?

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

5.  ZnCr 2 O 4 : The most frustrating magnet 1. Composite antiferromagnetic hexagons 2. Spin-Peierls-like phase transition  ZnV 2 O 4 and LiV 2 O 4 with orbital degeneracy 1. Orbital and spin chains in ZnV 2 O 4 2. LiV 2 O 4 : d-electron heavy fermon?  GeNi 2 O 4 1. A simple frustration and spin-flops  Summary Self-Organizations in Frustrated Spinels

6. 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) Collaborators on ZnCr 2 O 4, ZnV 2 O 4, LiV 2 O 4, GeNi 2 O 4

7. 3d egeg t 2g Free Ion Cubic Field Cr 3+ (3d 3 ) d xy, d yz, d zx 3d egeg t 2g Free Ion Cubic Field V 3+ (3d 2 ) with orbital degeneracy d xy, d yz, d zx Spinels AB 2 O 4 (B = Cr, V, Ni) 3d egeg t 2g Free Ion Cubic Field Ni 2+ (3d 8 ) d xy, d yz, d zx d x 2 -y 2, d z 2

8.  CW = -390 K T N = 12.5 K ZnCr 2 O 4 (3d 3 ) ZnV 2 O 4 (3d 2 ) with orbital degeneracy  CW = -1000 K T N = 40 K W. Ratcliff, S-W. Cheong (2000) Y. Ueda et al., (1997) GeNi 2 O 4 (3d 8 ) III M. Crawford et al. (2004)

9. Li x Zn 1-x V 2 O 4 Zn 2+ V 2 O 4 : V 3+ (3d 2 ) 3d t 2g Li 1+ V 2 O 4 : V 3.5+ (3d 1.5 ) 3d t 2g T (K)

10. C v ~  T    AT 2  const Bulk measurement data from LiV 2 O 4 at low T exhibit Fermi liquid behaviors LiV 2 O 4 : d-Electron Heavy Fermion CePd 3 CeB 6 CeCu 2 Si 2 CeCu 6 CeAl 3 UGa 3 UIn 3 UPt UPt 2 UAl 2 USn 3 UPt 3 UBe 13 LiV 2 O 4 LiV 2 O 4 with d-electrons is as heavy as UPt 3 ! 0 50 100 150 200 T (K) S. Kondo et al. (1997)

11. Kondo screening RKKY interaction Heavy fermion behavior with a heavy mass m ~ 100-1000 m e 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. Heavy Fermion Why does LiV 2 O 4 exhibit heavy fermionic behavior even though only d-electrons are crossing the Fermi energy?

12. Geometrical frustration: 1. What is nature of the spin liquid phase? 2. What are the zero-energy mode excitations? ZnCr 2 O 4 : 1. Why does it undergo a transition? 2. What is the nature of the phase transition? ZnV 2 O 4 : 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? LiV 2 O 4 : 1. Why does it exhibit heavy fermionic behavior? GeNi 2 O 4 : 1. Why two transitions? Outstanding issues

13. Phase Transition due to Spin-Lattice coupling  CW = -390 K T N = 12.5 K ZnCr 2 O 4 (3d 3 ) W. Ratcliff, S-W. Cheong (2000) Spin-Peierls-like (spin-lattice) transition Lee/Broholm et al. (2000)

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

15. Spin liquid phase T > T N 200mg Composite Spin Excitations in ZnCr 2 O 4 Lee/Broholm et al. (2002) The fundamental spin degree of freedom is an Antiferromagnetic hexagonal spin loop !

16. Geometrical frustration: 1. Emergence of composite spin degrees of freedom 2. Existence of zero energy mode ZnCr 2 O 4 : 1. Antiferromagnetic hexagonal spin loops 2. Spin-Peierls-like phase transition Summary

17. Phase Transitions  CW = -390 K T N = 12.5 K ZnCr 2 O 4 (3d 3 ) Why TWO separate transitions? W. Ratcliff, S-W. Cheong (2000) Spin-Peierls-like (spin-lattice) transition ZnV 2 O 4 (3d 2 ) with orbital degeneracy Lee/Louca et al. (2004)

18. Theoretical works on ZnV 2 O 4 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. Inelastic neutron scattering from ZnV 2 O 4 100K 60K 45K 10K Cubic phase (a = b = c) d xy, d yz, d zx ZnCr 2 O 4 Tetragonal (c < a = b) Tsunetsugu/Motome (2003) Lee/Louca et al. (2004)

20. Summary on ZnV 2 O 4 (3d 2 ) with orbital degeneracy In cubic phase, ZnV 2 O 4 is a system of three-dimensionally tangled spin chains. In tetragonal phase, it is a very good model system for one-dimensional spin chains. The antiferro-orbital model seems to be consistent with our neutron results. Tetragonal phase Cubic phase

21. C v ~  T    AT 2  const Bulk measurement data from LiV 2 O 4 at low T exhibits Fermi liquid behavior LiV 2 O 4 : d-Electron Heavy Fermion CePd 3 CeB 6 CeCu 2 Si 2 CeCu 6 CeAl 3 UGa 3 UIn 3 UPt UPt 2 UAl 2 USn 3 UPt 3 UBe 13 LiV 2 O 4 LiV 2 O 4 with d-electrons is as heavy as UPt 3 ! 0 50 100 150 200 T (K)

22. LiV 2 O 4 (3d 1.5 ) : Dynamic Spin Correlations Spin correlations become antiferromagnetic as LiV 2 O 4 enters the heavy fermion phase Lee/Broholm et al. (2001) AFM

23. LiV 2 O 4 (3d 1.5 ) It remains cubic down to 20 mK. The formation of three dimensionally tangled orbital chains may occur in LiV 2 O 4. The metallic character of LiV 2 O 4 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. III GeNi 2 O 4 (3d 8 ) Phase I Phase II I II Matsuda/Chung et al. (2004)

25. Geometrical frustration: 1. Emergence of composite spin degrees of freedom 2. Existence of zero energy mode ZnCr 2 O 4 : 1. Antiferromagnetic hexagonal spin loops 2. Spin-Peierls-like phase transition ZnV 2 O 4 and LiV 2 O 4 : 1. Orbital degree of freedom plays the central role 2. Orbital and spin chains GeNi 2 O 4 : 1. Simple frustration and spin flops Self-organizations of spin, “orbital”, and lattice degrees of freedom to minimize their competing interactions Summary