# Presentation: 195479

## Self-Organizations in Frustrated Spinels  

**                             ****Seung-Hun Lee**
-      National Institute of Standards and Technology

## Lattice

- Spin

- Charge

- Orbital

**Strongly Correlated Electron System**

##                   Spinel AB2O4 

** ****: Corner-sharing tetrahedra**

**Crystal structure**

-                   Spinel AB2O4

- Edge-sharing
- octahedra

**                        ****Frustration **
** ****Macroscopic ground state degeneracy **
**                  ******** ****New physics ?**

## Theory of spins with AFM interactions on  corner-sharing tetrahedra

- H = -J **S****i**** ****. ****S****j**

- The most frustrated case is a system with
- isotropic uniform nearest neighbor interactions only:

## Self-Organizations in Frustrated Spinels  

-      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 ZnV2O4
-      2. LiV2O4: d-electron heavy fermon?
-  **GeNi****2****O****4**
-      1. A simple frustration and spin-flops
** ****Summary**

**Self-Organizations in Frustrated Spinels  **

## Collaborators on ZnCr2O4, ZnV2O4, LiV2O4, GeNi2O4 

**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**** **

##  Spinels AB2O4 (B = Cr, V, Ni) 

- 3d

- eg

- t2g

- Free Ion       Cubic Field

**Cr****3+**** (3d****3****)**

-  dxy, dyz, dzx

- 3d

- eg

- t2g

- Free Ion       Cubic Field

**V****3+**** (3d****2****) with orbital degeneracy**

-  dxy, dyz, dzx

** ****Spinels AB****2****O****4 ****(B = Cr, V, Ni) **

- 3d

- eg

- t2g

- Free Ion       Cubic Field

**Ni****2+**** (3d****8****)**

-  dxy, dyz, dzx

-  dx2-y2, dz2

## ZnCr2O4 (3d3)

- CW = -390 K
- TN = 12.5 K

**ZnCr****2****O****4**** (3d****3****)**

**ZnV****2****O****4**** (3d****2****) with orbital degeneracy**

- CW = -1000 K
- TN = 40 K

***W. Ratcliff, S-W. Cheong***** (2000)**

***Y. Ueda***** et al., (1997)**

**GeNi****2****O****4**** (3d****8****)**

- I

- II

***M. Crawford et al.***** (2004)**

## LixZn1-xV2O4

**Li****x****Zn****1-x****V****2****O****4**

**Zn****2+****V****2****O****4****:**** V****3+**** (3d****2****)**

**Li****1+****V****2****O****4****:**** V****3.5+**** (3d****1.5****)**

## LiV2O4: d-Electron Heavy Fermion

**LiV****2****O****4****: d-Electron Heavy Fermion**

*S. Kondo* et al. (1997)

## 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.

**Heavy Fermion**

- Why does LiV2O4 exhibit heavy fermionic behavior
- even though only d-electrons are crossing the Fermi energy?

## Outstanding issues

**                ****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**

## Phase Transition due to Spin-Lattice coupling

**Phase Transition due to Spin-Lattice coupling**

- CW = -390 K
- TN = 12.5 K

**ZnCr****2****O****4**** (3d****3****)**

***W. Ratcliff, S-W. Cheong***** (2000)**

## Nature of the Spin Liquid State in GF magnets

**    ****Emergence of Composite Spin Excitations**

## Composite Spin Excitations in ZnCr2O4

**Composite Spin Excitations in ZnCr****2****O****4**

***Lee/Broholm et al. *****(2002)**

## Slide 16

## Phase Transitions

**Phase Transitions**

- CW = -390 K
- TN = 12.5 K

**ZnCr****2****O****4**** (3d****3****)**

**Why *****TWO***** separate transitions?**

***W. Ratcliff, S-W. Cheong***** (2000)**

## 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*

## Inelastic neutron scattering from ZnV2O4

**Inelastic neutron scattering from ZnV****2****O****4**

**100K**

**60K**

**45K**

**10K**

***Lee/Louca***** et al. (2004)**

## Summary on ZnV2O4 (3d2) with orbital degeneracy

**Summary on ZnV****2****O****4**** (3d****2****) 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

## LiV2O4: d-Electron Heavy Fermion

**LiV****2****O****4****: d-Electron Heavy Fermion**

## LiV2O4  (3d1.5) : Dynamic Spin Correlations           

***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

## GeNi2O4 (3d8)

**GeNi****2****O****4 ****(****3d****8****)**

***Matsuda/Chung***** et al. (2004)**

## Summary

**  ****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**