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Self-Organizations in Frustrated Spinels
Seung-Hun Lee National Institute of Standards and Technology
Lattice
Spin Charge
Orbital
Strongly Correlated Electron System
Lattice of B sites : Corner-sharing tetrahedra
Geometricallyfrustrated
Crystal structure
O
AB
Spinel AB2O4
Edge-sharingoctahedra
Frustration Macroscopic ground state degeneracy New physics ?
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 ’98Isotropic S= Spin Liquid MC sim. Reimers PRB ’92
Moessner, Chalker PRL ’98
H = -J Si . Sj
The most frustrated case is a system with isotropic uniform nearest neighbor interactions only:
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
Self-Organizations in Frustrated Spinels
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 ZnCr2O4, ZnV2O4, LiV2O4, GeNi2O4
3d
eg
t2g
Free Ion Cubic Field
Cr3+ (3d3)
dxy, dyz, dzx
3d
eg
t2g
Free Ion Cubic Field
V3+ (3d2) with orbital degeneracy
dxy, dyz, dzx
Spinels AB2O4 (B = Cr, V, Ni)
3d
eg
t2g
Free Ion Cubic Field
Ni2+ (3d8)
dxy, dyz, dzx
dx2-y2, dz2
CW = -390 KTN = 12.5 K
ZnCr2O4 (3d3)ZnV2O4 (3d2) with orbital degeneracy
CW = -1000 KTN = 40 K
W. Ratcliff, S-W. Cheong (2000)
Y. Ueda et al., (1997)
GeNi2O4 (3d8)
III
M. Crawford et al. (2004)
LixZn1-xV2O4 Zn2+V2O4: V3+ (3d2)
3dt2g
Li1+V2O4: V3.5+ (3d1.5)
3dt2g
T (
K)
Cv ~ TAT2
const
Bulk measurement data from LiV2O4 at low T exhibit Fermi liquid behaviors
LiV2O4: d-Electron Heavy Fermion
CePd3
CeB6
CeCu2Si2CeCu6
CeAl3
UGa3
UIn3
UPtUPt2
UAl2
USn3
UPt3
UBe13
LiV2O4
LiV2O4 with d-electrons is as heavy as UPt3 !
0 50 100 150 200 T (K)
S. Kondo et al. (1997)
Kondo screening RKKY interaction
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.
Heavy Fermion
Why does LiV2O4 exhibit heavy fermionic behavioreven though only d-electrons are crossing the Fermi energy?
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?
Outstanding issues
Phase Transition due to Spin-Lattice coupling
CW = -390 KTN = 12.5 K
ZnCr2O4 (3d3)
W. Ratcliff, S-W. Cheong (2000)
Spin-Peierls-like (spin-lattice) transition
Lee/Broholm et al. (2000)
Nature of the Spin Liquid State in GF magnets
Emergence of Composite Spin Excitations
Spin liquid phase T > TN
200mg
Composite Spin Excitations in ZnCr2O4
Lee/Broholm et al. (2002)
The fundamental spin degree of freedom is an Antiferromagnetic hexagonal spin loop !
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
Summary
Phase Transitions
CW = -390 KTN = 12.5 K
ZnCr2O4 (3d3)
Why TWO separate transitions?
W. Ratcliff, S-W. Cheong (2000)
Spin-Peierls-like (spin-lattice) transition
ZnV2O4 (3d2) with orbital degeneracy
Lee/Louca et al. (2004)
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 modelO. Tchernyshyov (2004)Structural, orbital, and magnetic order in vanadium spinels
Inelastic neutron scattering from ZnV2O4
100K
60K
45K
10K
Cubic phase(a = b = c)
dxy, dyz, dzx
ZnCr2O4
Tetragonal(c < a = b)
Tsunetsugu/Motome (2003)
Lee/Louca et al. (2004)
Summary on ZnV2O4 (3d2) with orbital degeneracy
In cubic phase, ZnV2O4 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
Cv ~ TAT2
const
Bulk measurement data from LiV2O4 at low T exhibits Fermi liquid behavior
LiV2O4: d-Electron Heavy Fermion
CePd3
CeB6
CeCu2Si2CeCu6
CeAl3
UGa3
UIn3
UPtUPt2
UAl2
USn3
UPt3
UBe13
LiV2O4
LiV2O4 with d-electrons is as heavy as UPt3 !
0 50 100 150 200 T (K)
LiV2O4 (3d1.5) : Dynamic Spin Correlations
Spin correlations become antiferromagnetic as LiV2O4 enters the heavy fermion phase
Lee/Broholm et al. (2001)
AFM
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
III
GeNi2O4 (3d8)
Phase IPhase II
I
II
Matsuda/Chung et al. (2004)
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
Summary