1. Spin-lattice Interaction Effects in Frustrated Antiferromagnets
韓 政勳, 賈 成龍
(成均館大)

2. Lattice-Coupled Antiferromagnetic Spin Modelj ui uj
Rij
Spin and lattice are coupled
through magneto-striction
effect (Pytte, PRB 1974)
Lattice displacement related to
local spin-spin correlation by

3. Application to Frustrated Lattice – Triangular, Kagome
NO LATTICE DEFORMATION!

4. 3D Frustrated Lattice - Pyrochlore
Tetrahedron as a building block
Ground state condition
for each tetrahedron
Macroscopic ground state degeneracy in
pristine Heisenberg model

5. Experiments on Pyrochlore – ZnCr2O4
Spins on Cr3+(S=3/2) order antiferromagnetically
acccompanied by cubic-to-tetragonal distortion
(SHLee, PRL, 2000)
Below Tc
Neutron scattering structure factor consistent with
hexagon spin cluster, i.e. neutrons scatter off a hexagon cluster of spins
(SHLee, Nature, 2002)
Above Tc

6. Lifting of degeneracy through spin-lattice coupling
Tetrahedron
Unit (Tschernyshyov et al. PRL 2002)
Hexagon
Unit
(Jia et al. PRB 2005)

7. Energy Comparison In comparing energies for both distortion modes,
Tetrahedron-based distortion has a lower energy, but hexagon shrinkage is a viable,
metastable state
SHLee et al. Nature 2002

8. Hexagon Organization of Spins in Pyrochlore 3 types of spin directions
(b)
Arrangement of
4 types of hexagons
Arrangement of
3 types of spin directions

9. Experiments on Triangular S=2 AFM – YMnO3
S Lee et al. PRB 2005
Expansion of Mn triangles (red) at the onset of magnetic order

10. IDEA: Spin-Lattice Coupling-induced VBS ?
Magnetic order doesn’t work, but valence-bond order might.
PARTIAL VBS ORDER
At most 4 VB’s can form
for coordination = 6
Some links must lack a VB and expand.

11. Calculations
Schwinger boson mean-field theory calculation (cond-mat/ ) supports a ground state with lattice distortion and modulated bond amplitudes, consistent with our picture of partial VBS

12. We calculate excitation spectra for the VBS within SMA
A New Excitation
We calculate excitation spectra for the VBS within SMA
Spin wave
Comparison
VBS