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