outline

1
outline

• Part 1 the manganite system La1-xSrxMnO3
• Phase diagram of La1-xSrxMnO3
• ESR results
• spin relaxation in La0.95Sr0.05MnO3 orbital
  ordering
• Part 2 ESR in 1D Heisenberg spin chains
• Magnetic properties of spin S 1/2 chains
• temperature dependence of the ESR linewidth in
  the model systems NaV2O5, LiCuVO4, CuGeO3
• the case of TiOCl

2
phase diagram of La1-xSrxMnO3
3
Jahn-Teller distortion in LaMnO3

• cooperative JT-distortions of MnO6 octahedra in
  the orthorhombic O'-phase up to TJT 750 K
• A-type AFM (TN 140 K)
• FM coupling in ac-planes
• AFM coupling between ac-planes

Huang et al., PRB 55, 14987 (1997)
4

orbital physics in LaMnO3
OO
?

• estimate for DJT? (0.1eV instead of 1eV)
• orbital excitations (orbitons) in LaMnO3 or
  multiphonon processes?
• OO due to electron-phonon and/or
  electron-electron interaction?
• What is the value of q ? Suggestions
  90, 102, 106, 120

5
the ESR Signal
parameters intensity local spin
susceptibility resonance field ?g g -
2.0023 local symmetry linewidth
?H spin-relaxation, anisotropic interactions
q !!!
6
ESR in La1-xSrxMnO3 (0 x 0.2)
phase diagram
linewidth
Paraskevopoulos et al., J. Phys.Cond.Mat. 12,
3993 (2000).

• La0.95Sr0.05MnO3
• still an AFM insulator (TN 140 K)
• reduced JT transition temperature TJT 600 K
• Þ effective treatment like LaMnO3

Ivanshin et al., PRB 61, 6213 (2000)
7
T-dependence of the linewidth
8
Line broadening mechanisms

• Observed linewidth 1-2 kOe
• Zero-Field Splitting (crystal field) 1 kOe
• Anisotropic exchange interactions
• Symmetric anisotropic exchange 1 Oe
• Antisymmetric anisotropic exchange 1 kOe
• (Dzyaloshinsky-Moriya interaction)
• Hyperfine interaction 10 Oe
• Dipole-dipole interaction 1 Oe
• Anisotropic Zeeman interaction 1 Oe

9
Crystal field zero-field splitting

• two independent elements for orthorhombic
  symmetry
• perturbation theory (spin-orbit coupling perturbs
  the crystal-field levels)

10
Dzyaloshinsky-Moriya interaction

• Effective spin Hamiltonian of the antisymmetric
  exchange in form of a cross-product
• direction of D (Dzyaloshinsky-Moriya vector)

11
fitting the T-dependence of the linewidth
JD et al., PRB 68, 214427 (2003).
3(1) fit parameters GZFS 0.57 kOe GDM 1.0
kOe b 0.16 (critical JT-exponent) ZFS-ratio
E/D0.37
Kochelaev et al., Mod. Phys. Lett. B 17, 459
(2003).
12
consistent ESR fitparameters
ZFS ratio E/D0.37 was obtained from fitting
the g-factor anisotropy
Deisenhofer et al., PRB 68, 214427 (2003). .
13
zero-field splitting and orbital order
ESR
perturbation theory
excellent agreement!
qESR 106
qND 106
14
summary - part I

• KT-approach allows to describe the temperature
  dependence and the anisotropy of the linewidth
• Dominant contribution are the ZFS and the DM
  interaction in agreement with neutron diffraction
  data
• type of orbital ordering in La0.95Sr0.05MnO3 has
  been derived from the analysis of the ESR
  g-factor and linewidth (ZFS)

15
outline

• Part 1 the manganite system La1-xSrxMnO3
• Phase diagram of La1-xSrxMnO3
• ESR results
• spin relaxation in La0.95Sr0.05MnO3 orbital
  ordering
• Part 2 ESR in 1D Heisenberg spin chains
• Magnetic properties of spin S 1/2 chains
• temperature dependence of the ESR linewidth in
  the model systems NaV2O5, LiCuVO4, CuGeO3
• the case of TiOCl

16
Susceptibility of free spins
17
Interacting spins (3D)
18
Interacting spins (1D)
19
Real spin chains

• Only in ideal 1D antiferromagnets no phase
  transition
• In real systems
• weak inter-chain coupling not negligible
• ? 3D antiferromagnetic order at T ltlt J
• electron-phonon interaction
• ? Spin-Peierls transition into dimerized
  ground state

20
Spin-Peierls transition
21
Model systems

• NaV2O5
• S 1/2 per 2 V4.5
• ¼-filled ladder
• J 570 K
• TCO 34 K
• dimerization
• via
• charge order

• LiCuVO4
• Cu2
• S 1/2 chain
• J 40 K
• TN 2.1 K
• antiferromagnetic
• order

CuGeO3 Cu2 S 1/2 chain J 120 K TSP 14
K dimerized, spin-Peierls S 0 ground state
22
Temperature dependence of the ESR linewidth

• LiCuVO4 CuGeO3 NaV2O5

23
Universal temperature law
24
Limits of the KT-approach

• High-temperature approximation fails for T lt J
  (!)
• Field theoretical approach
• (M. Oshikawa and I. Affleck, Phys. Rev. B 65,
  134410, 2002)
• For temperatures T ltlt J
• ?H (T ) T for
  symmetric anisotropic exchange
• ?H (T ) 1/T 2 for
  antisymmetric DM interaction
• ? in LiCuVO4, CuGeO3 and NaV2O5 symmetric
  anisotropic
• exchange is the dominant relaxation
  process

25
Universal behavior of the linewidth
low temperatures T ltlt J ?H
(T) T for symmetric anisotropic
exchange ?H (T) 1/T 2 for
antisymmetric DM interaction
What about the antisymmetric interaction?
Observation of a low-temperature 1/T2 divergence
due to this interaction?
26
The system TiOCl
There is no center of inversion between the ions
in the Ti-O-layers ? antisymmetric anisotropic
exchange
Isotropic exchange constant J 660 K
A. Seidel et al., Phys. Rev. B 67, 020405(R)
(2003)
27
Analysis of the anisotropic exchange mechanisms
Dzyaloshinsky-Moriya interaction
Pseudo-dipol interaction
D is almost parallel to the b-direction Dominant
component of the tensor of the pseudo-dipol
interaction is G(aa)
28
Temperature dependence of DH
The temperature and angular dependence of DH can
be described as a competition of the symmetric
and the antisymmetric exchange interactions!
Oe KAE (8) KDM (8) H a
1429 1.397 H b 765
2.319 H c 930 1.344
Zakharov et al., PRB 73, 094452 (2006)
29
Summary

• Anisotropic exchange dominates the ESR line
  broadening in low dimensional S1/2
  transition-metal oxides
• ? in contrast to estimations based on the
  KT-approach
• Universal temperature dependence of the ESR
  linewidth in spin chains with dominant symmetric
  anisotropic exchange
• Interplay of antisymmetric Dzyaloshinsky-Moriya
  and symmetric anisotropic exchange in TiOCl