# Presentation: 546447

## Magnetic Frustration at Triple-Axis

-  Magnetism, Neutron Scattering, Geometrical Frustration
-  ZnCr2O4: The Most Frustrated Magnet
-     How are the fluctuating spins in the Spin Liquid phase correlated with each other?
-      How does nature respond to the ground state degeneracy?
-  Summary

**S.-H. Lee, S. Park, P.M. Gehring **
-                        NCNR

##                       ZnCr2O4

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

**Space group Fd3m**

-                       ZnCr2O4

-  dxy, dyz, dzx

- Edge-sharing
- octahedra

## Magnetic Neutron Scattering

- Neutron:
-  Wavelength comparable with interatomic spacings
-  Penetrating  bulk properties are measured
-  has spin *s* = 1⁄2 so interacts with atomic moments
- Scattering by atomic
-   magnetic moments: *I = (0.54)**2 **S (S+1)*

- Magnetic scattering intensities can be comparable to nuclear scattering !!

**Notes:**
Test

## Neutron Scattering

- ?

- Incident neutrons

- Sample

- Scattered neutrons

-  measures scattering cross section as a function of Q and 

* ****k******i**** , E**i** , s*

* ****k******f**** , E**f** , s*

##      Magnetic Neutron 

- Scattering Cross Section

- 	Spin-Spin
- Correlation Function

- Fourier Transform

## Phase Diagram for an Ordinary Magnet

- T (K)

- CW= JzS(S+1)/3kB

- AFM or FM

- Paramagnet

- Ground State : Long range (anti)ferromagnetically ordered state.
- Low Energy Excitations : linear spin waves around the ordered state.

- F = Hmag – TS = -  J Si Sj  - TS

- TS > | Hmag |

- | Hmag | > TS

## Neel phase: 

- (2) Any Inelastic signal?

- (1) Any Elastic signal?

- If any, what kind of shape in the - and Q-space?

- Neel phase:
- What kind of magnetic scattering signal in Q and  space would you expect?

## Slide 8

##                   Why ZnCr2O4  ?

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

**Space group Fd3m**

-                   Why ZnCr2O4  ?

-  dxy, dyz, dzx

- Edge-sharing
- octahedra

-  Interaction between nearest neighbor Cr3+ ions
-  through direct overlap of t2g orbitals is dominant.

-  Best candidate for a system with

## ?

- T (K)

- CW= JzS(S+1)/3kB

- Paramagnet

- Phase Diagram for Geometrical Frustration

- Geometrically
- frustrated

- F = Hmag – TS = -  J Si Sj  - TS

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

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

## Issues

** ****Nature of the Spin Liquid State**
**    **How are the fluctuating spins in the SL phase correlated
-     with each other?
-  **Novel Phase Transition?**
-      How does nature respond to the ground state degeneracy?

** ****You will be able to answer the questions **
**after the demonstration session at SPINS!**

## A Phase Transition in ZnCr2O4

- A Phase Transition in ZnCr2O4

- CW = -390 K
- TN = 12.5 K

- Phase transition

- What is the nature of the phase transition?

*A.P. Ramirez, unpublished*

## Neutron Scattering from ZnCr2O4

- Paramagnetic
- fluctuations in
- frustrated AFM

- Local spin resonance
- in magneto-elastic
- LRO phase

- Neutron Scattering from ZnCr2O4

*SHL et al., PRL 84, 3718 (2000)*

## Keep in mind !!!

- Fourier Transform

- Ordered moment

- Fluctuating moment

- 

- 0

- Q

- Time

-  ~ 1/

-  : relaxation time
-  : intrinsic linewidth

-  : lifetime
-  : correlation length

- Long range order

- Short range order

- 0

**Keep in mind !!!**

- Neutron scattering is the most powerful technique to study magnetism!!

## SPINS : Cold Neutron Triple-Axis Spectrometer