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Lattice instability in frustrated systems

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Lattice instability in frustrated systems. Maxim Mostovoy. MPI, Stuttgart ... H. Mamiya et al., J. Appl. Phys. 81, 5289 (1997) Interactions between t2g-orbitals ... – PowerPoint PPT presentation

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Title: Lattice instability in frustrated systems


1
Lattice instability in frustrated systems
  • Maxim Mostovoy
  • MPI, Stuttgart

D. Khomskii, Cologne
N.V. Prokofev, Amherst
J. Knoester, Groningen
R. Moessner, Paris
Groningen, April 22, 2004
2
Outline
  • Geometrical frustration
  • Magnetoelastic transitions in
  • frustrated spin systems
  • Orbital interactions
  • Frustration of orbital ordering
  • and its lifting

3
Geometrical frustration
4
AFM Ising on triangular lattice
Ground state entropy
(Wannier, Houtappel, 1950)
Spin correlations at T0
(Stephenson, 1970)
5
Ordered state
6
Hard sphere liquid
Alder Wainwright (1957)
Hoover Ree (1968)
Ssolid gt Sliquid
7
Kinks
Kink energy
Interactions between kinks in neighboring chains
8
Kink crystal
1 kink / 3 sites
M.M., N.Prokofev, D.Khomskii J.Knoester, PRL
90 (2003)
9
Frustrated spins coupled to lattice
Strains
10
Free energy
11
Frustration-induced transition
Ordered state
Disordered state
12
ZnCr2O4
?CW -390K
first order
TN 12.5K
O. Tchernyshyov et al., PRL 88, 067203 (2001)
S.-H. Lee et al., PRL 84, 3718 (2000)
13
AV2O4
H. Mamiya et al., J. Appl. Phys. 81, 5289 (1997)
first order cubic to tetragonal c lt a
14
Interactions between t2g-orbitals
15
Tetrahedron states
16
Frustration and its lifting
Jahn-Teller
S.-H. Lee et al., cond-mat/0312558
17
Orbital interactions
  • Jahn-Teller interaction
  • Coupled orbital spin exchange
  • (Kugel-Khomskii)
  • Orbital Casimir effect
  • Peierls-like interaction

18
eg-orbitals
19
Jahn-Teller interaction
20
Lattice-mediated interaction
21
Kugel-Khomskii model
(b)
(c)
(d)
(a)
(a)
(b)(c)
22
Orbital Casimir effect (Up,Ud ?)
M.M. D. Khomskii, Phys.Rev.Lett 89, 227203
(2002),
cond-mat 0304494
Holes
Electrons
23
1800-exchange in 2D
K2CuF4 1eg hole/Cu
q
q
canted antiferroorbital ferromagnetic
24
Frustrated orbital models
90o-exchange
180o-exchange
triangular
pyrochlore
cubic
LiNiO2
KCuF3
ZnMn2O4
25
Mean field
Cubic antiferro-orbital G-type
Triangular, pyrochlore ferro-obital
arbitrary superposition
Disordered ground states
26
Order from disorder
Quantum orbital fluctuations chose six unform
states
G.Khaliullin, PR B 64, 212405 (2001) M.M.
D.Khomskii,PRL 89, 227203 (2002)
27
Strains
28
Orbital-strain interaction
Jahn-Teller coupling
electron
Peierls coupling
Strain energy
hole
29
Ordered state
layered canted antiferroorbital
30
Ordered state
KCuF3
holes
electrons
LaMnO3
31
Conclusions
  • Frustration of spin and orbital ordering
  • makes the crystal lattice instable
  • JT distortion occurs together with lattice
    distortion lifting the frustration of orbital
    ordering
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