Transcript Elektronenspinresonanz an niedrigdimensionalen Spinsystemen

Anisotropic Superexchange
in low-dimensional systems:
Electron Spin Resonance
Dmitry Zakharov
Experimental Physics V
Electronic Correlations and Magnetism
University of Augsburg
Germany
Motivation
 Anisotropic Exchange
• Dominant source of anisotropy for S=1/2 systems
• Produces canted spin structures
• Ising or XY model are limit cases
• Can be estimated by Electron Spin Resonance (ESR)
 Electron spin resonance
• Microscopic probe for local electronic properties
• Ideally suited for systems with intrinsic magnetic moments
 Spin systems of low dimensions
• Variety of ground states different from 3D order
e.g. spin-Peierls, Kosterlitz-Thouless
• Short-range order phenomena and fluctuations at temperatures far
above magnetic phase transitions
Outline
• Basic theory of anisotropic exchange
• Introduction to electron spin resonance (ESR)
• Full microscopical picture of the symmetric anisotropic
exchange: NaV2O5
• Temperature dependence of the ESR linewidth in lowdimensional systems: NaV2O5, LiCuVO4, CuGeO3, TiOCl
Outline
Isotropic superexchange
Two magnetic ions can interact indirect
intermediate diamagnetic ion (O2-, F-,..)
via
an
 potential exchange: like direct exchange describes the
self-energy of the charge distribution → ferromagnetic;
 kinetic exchange: the
delocalized electrons
can hop, what leads
to the stabilization of
the singlet state over
the triplet:
→ antiferromagnetic
spin ordering
can be described
through the
perturbation
treatment:
Vˆ     Vˆ
H    H     
, with Vˆ   t a b  h.c.

H    H    J ab 1 2  2  Sa  Sb   , J ab  2
Basic theory of anisotropic exchange
2
t

.
Mechanism of anisotropic exchange interaction
The free spin couples to the lattice via the spin-lattice interaction HLS=l(l·s)
 the excited orbital states are involved in the exchange process
 can be described as virtual hoppings of electrons via the excited orbital states
(the additional perturbation term – (LS)-coupling – acts on one site between the orbital
levels)
 This effect adds to the isotropic exchange interaction an anisotropic part
(dominant source of anisotropy for S=½ systems!)
Basic theory of anisotropic exchange
Theoretical treatment
Clear theoretical description can be carried out in the framework of the perturbation
theory:
•
Fourth order: describes 4 virtual electrons
hoppings
 Isotropic superexchange
•
Fifth order: 4 hoppings + on-site (LS)-coupling
 Antisymmetric part of anisotropic exchange
= Dzyaloshinsky-Moriya interaction
•
Sixth order: 4 hoppings + 2 times on-site (LS)coupling
 Symmetric part of anisotropic exchange
= Pseudo-dipol interaction
Basic theory of anisotropic exchange
Antisymmetric part of anisotropic exchange
There is a simple geometric rule allowed to
determine the anisotropy produced by
Dzyaloshinsky-Moriya interaction:
Spin variables are going into the
Hamiltonian of the antisymmetric
exchange in form of a cross-product:
Dj  
i
2 S a Sb
l

H DM
H LS  H IsoSE
H DM  D ab   Sa  Sb 
 lj   J
Dab  d ra  rb 

j = {x, y, z},
,  – orbital levels,
 – energy splitting,
lj – operator of the LS-coupling,
J – exchange integral.
 la  sa  sa  sb 
The direction of
D (DzyaloshinskyMoriya vector) can
be determined from:
ra
sa
It should be no center of inversion between the ions!
Basic theory of anisotropic exchange
rb
sb
Symmetric part of anisotropic exchange
I I>
I >
a
Exchange constant of the pseudo-dipol
interaction is a tensor of second rank G and
does not allow a simple graphical presentation.
2
1 3
I>
I>
b
,  = {x, y, z};
, , ’ – orbital levels.
H LS  H IsoSE  H LS
H AE
 la  sa  sa  sb  la  sa 
H AE  Sa  Г(ab )  Sb 


2
a
8 Sa Sb

 la 

J  
  l a 
 


Sa S b  S a Sb

Nonzero elements of G can be determined by the nonnegligible product of the
matrix elements of the (LS)-coupling and the hopping integrals.
Basic theory of anisotropic exchange
Outline
• Basic theory of anisotropic exchange
• Introduction to electron spin resonance (ESR)
• Full microscopical picture of the symmetric anisotropic
exchange: NaV2O5
• Temperature dependence of the ESR linewidth in lowdimensional systems: LiCuVO4, CuGeO3, TiOCl
How to study all this?
Zeeman effect
Zeeman energy in magnetic field H:
E
SZ = +1/2
H  μ  H  g B HSz
SZ = -1/2
eigen energies of the spin SZ = 1/2
1
E   g B H
2
H
E
SZ = +1/2
  L
magnetic microwave field ^ H with E = h
induces dipolar transitions
SZ = -1/2
Hres
Introduction to electron spin resonance
H
Experimental Set-Up
microwave
source 9 GHz
~
diode
sample
magnet
0...18 kOe
resonator
microwave field <1Oe
Introduction to electron spin resonance
ESR signal
ESR quantities:
NaV2O5
intensity:
local spin susceptibility
9.4 GHz
36 K
Lorentz
resonance field:
intensity
absorption P
ESR signal dP/dH
ESR signal
g = g - 2.0023
local symmetry
linewidth
2 H
3.3
3.4
3.5
Hres
ħ=gBHres
3.6
H (kOe)
linewidth H:
spin relaxation,
anisotropic interactions
Introduction to electron spin resonance
Theory of line broadening
Hamiltonian for strongly correlated spin systems:
H  g BH   Si
 J  Si  Si 1  H int
i
Zeeman
energy
Strong isotropic coupling
 averages local fields like in the case
of fast motion of the spins
 Narrowing of the ESR signals
i
isotropic
exchange
additional
couplings
Local fluctuating fields
 local, statistic resonance shift
 inhomogeneous broadening of
the ESR signal
Introduction to electron spin resonance
Possible mechanisms of the ESR-line broadening
Only the following mechanisms are dominant
in concentrated low-dimensional spin systems:
• Crystal field
is absent for S = ½ (topic of this work)
• Anisotropic Zeeman interaction
negligible in case of nearly equivalent
g-tensors on all sites;
characteristic value of H ~ 1 Oe
• Hyperfine structure & Dipol interaction
characteristic broadening about H~10 Oe
as result of the large isotropic exchange
• Relaxation to the lattice produces a divergent behavior of H(T)
• Anisotropic exchange interactions
are the main broadening sources
of the ESR line
[R. M. Eremina.., PRB 68, 014417 (2003)]
[Krug von Nidda.., PRB 65, 134445(2002)]
Introduction to electron spin resonance
Theoretical approach
Linewidth of the exchange
narrowed ESR line in the hightemperature approximation (T ≥J ):
Schematic representation
of the „exchange narrowing“
H ESR
1 M2

gB J
[R.Kubo et al., JPSJ 9, 888 (1954)]
Second
moment
of a line:
H int
M 2     0 
2
Sp([H int , S  ] [H int , S  ])

Sp[ S  , S  ]
 M  D , T , ,   
 H  D , T ,  ,   
H DM   Dab  Sa  Sb 
2
ab
ESR
ab

 





 & 
&
&
&
  
 

 H   S  G ( ) S 




( )
( )
M
G
,
T
,

,


H
G
,
T
,

,

 AE   a ab b 




ESR
ab
 2 ab



Introduction to electron spin resonance
Outline
• Basic theory of anisotropic exchange
• Introduction to electron spin resonance (ESR)
• Full microscopical picture of the symmetric anisotropic
exchange: NaV2O5
• Temperature dependence of the ESR linewidth in lowdimensional systems: LiCuVO4, CuGeO3, TiOCl
Let‘s start at last!
NaV2O5 structure
a
c
b
VO5
V4.5+
O2one electron
S = 1/2
Na
ladder 1
ladder 2
Full microscopical picture of AE: NaV2O5
NaV2O5 susceptibility / ESR linewidth
NaV2O5
2.5
Bonner-Fisher
J = 578 K
3
mean field
(0) = 98 K
TCO = 34 K
500
2
H // c
H // b
H // a
400
TCO
1
0
0.0
0
• ESR linewidth at T > 200 K is about 102 Oe
H(Oe)
-4
cESR (10 emu/mol)
5.0
• One-dimensional system at T > 200 K;
• Charge-ordering fluctuations 34K<T<200K;
• “Zigzag” charge ordering at TCO= 34 K;
20
200
30
400
T (K)
40
600
300
200
NaV2O5
100
0
0
100
200
300
400
T (K)
Full microscopical picture of AE: NaV2O5
500
600
700
Antisymmetric vs. symmetric exchange
Dzyaloshinsky-Moriya interaction
ra
sa
Pseudo-dipol interaction
Dab  d ra  rb 
rb
sb
Dzyaloshinsky-Moriya interaction
is negligible because of two
almost equal exchange paths
which calcel each other
Standard
mechanism
by
Bleaney & Bowers is not
effective due to the orthogonality
of the orbital wave functions
What is the broadening source of the ESR line?!
Full microscopical picture of AE: NaV2O5
Conventional anisotropic exchange processes
Г(ab )
A
I I>
I >
a
1 4
I>
A
I >
4
I>
2
d

2
a
8 Sa Sb
 la  t t    la 


AI
A
I >
I >
3
1
I>
I>
AI
I >
A
I >
b
 ab
  
AI
I >
A
II>
4
e
2 3
I >
1
2
I>
4
I>
3
I>
I>
AI
I >
A
I >
AI
I >
f
2
2
1
4 2
I >
I>
3
3 1
c
AI
I>
1
I>
3
4
I>
[B. Bleaney and K. D. Bowers, Proc. R. Soc. A 214, 451 (1952)]
Full microscopical picture of AE
AE with the spin-orbit coupling on both sites
are not so effective
because of the larger
energy in denominator 
A
I I>
I >
a
1 4
I>
A
I >
4
I>
2
d
Г
a b
( )
ab
AI
A
I >
I >
3
1
I>
I>
AI
I >
A
I >
8 Sa Sb
b

AI
I >
II>
4
e
2 3
 la 

A
I >
1
I>
I>
AI
I >
A
I >
2
I>
4
I>
2
1
 ab
c
4 2
 
t
AI
I >
3
I>
f
AI
I >
2
3
3 1
b
t  l  
I>
1
I>
3
4
I>
[Eremin, Zakharov, Eremina…, PRL 96, 027209 (2006)]
Full microscopical picture of AE
AE with hoppings between the excited levels
is of great importance in chain
systems due to the big hopping
integrals t and tbetween
the nonorthogonal orbital levels
A
I I>
I >
a
1 4
I>
A
I >
4
I>
2
d
Г
a b
( )
ab
AI
A
I >
I >
3
1
I>
I>
AI
I >
A
I >
8 Sa Sb
b
AI
I >
II>
4
e
2 3
 lb  t  la 
 t

A
I >
1
2
I>
4
I>
I >
3
I>
I>
AI
I >
A
I >
AI
I >
f
2
2
1
4 2

AI
I>
3
3 1
c
 ab
I>
1
I>
3
4
I>
[Eremin, Zakharov, Eremina…, PRL 96, 027209 (2006)]
Full microscopical picture of AE
Schematic pathways of intra-ladder AE
A
I >
e
AI
I >
A
I >
2
3
4
2
I>
1
f
AI
I >
I>
1
I>
3
4
x 2  y 2 l z xy  2i
I>
 ,   xy
 ,   x2  y2
Only one type of the
anisotropic exchange –
pseudo-dipol interaction
with electron hoppings
between the excited
orbital levels – is
possible in the ladders
of NaV2O5
G(zz) – dominant!
ground
states
x2  y2
Full microscopical picture of AE: NaV2O5
excited
states
xy
Schematic pathways of inter-ladder AE
A
I I>
I >
a
1 4
I>
A
I >
4
I>
2
d
AI
A
I >
I >
3
1
I>
I>
b
AI
I >
II>
4
2 3
I>
A
I >
1
I>
c
4 2
AI
I >
3
I>
Instead, the “conventional”
exchange mechanisms are
dominant for the exchange of
the spins from the different
ladders
AI
I >
3 1
2
I>
Full microscopical picture of AE: NaV2O5
Estimation of the exchange parameters
40 K
60 K
0.8
100 K
0.6
300 K
300 K
10
40 K
30
60
a
30
60
c
30
60
b
angle (deg.)
Temperature dependence of H clearly
shows the development of the chargeordering fluctuations at T < 200 K
[Eremin.., PRL 96, 027209 (2006)]
NaV2O5
Ginter / G
2
1.0
(zz)
Ha/Hc
0.8
Hb/Hc
1
0.6
0
TCO ~ 34 K
0
100
Full microscopical picture of AE: NaV2O5
200
T (K)
300
400
Ha,b/Hc
b
3
intra-ladder
inter-ladder
(zz)
H (Oe)
100
Ginter / G
H / Hc
1.0
Theoretical description of the angular
dependence of the ESR linewidth by
the moments method allows to
determine the parameter of the
dominant exchange path at high
temperatures
G(zz) ≈ 5 K
in good agreement with the estimations
based on the values of hopping
integrals and crystal-field splittings
NaV2O5
Temperature dependence of H in NaV2O5
Are there other systems to corroborate these findings?
TCO = 34 K
500
H // c
H // b
H // a
H(Oe)
400
300
200
NaV2O5
100
0
0
100
200
300
400
500
600
700
T (K)
Which temperature dependence of the ESR linewidth is characteristic
for the symmetric and antisymmetric part of anisotropic exchange
in low-dimensional systems?
Open questions
Outline
• Basic theory of anisotropic exchange
• Introduction to electron spin resonance (ESR)
• Full microscopical picture of the symmetric anisotropic
exchange: NaV2O5
• Temperature dependence of the ESR linewidth in lowdimensional systems: NaV2O5, LiCuVO4, CuGeO3, TiOCl
→ Empirical answer!
Temperature dependence of the ESR linewidth
1.5
2.0
H || a
H || b
H || c
 H (kOe)
1.5
H || a
H || b
H || c
H || a
H || b
H || c
0.4
1.0
1.0
0.2
0.5
0.5
LiCuVO4
0.0
0
TN
100
200
T (K)
LiCuVO4
300
NaV2O5
CuGeO3
0.0
0
T SP
100
200
300
T(K)
CuGeO3
H(T) in low-dimensional systems
0.0
0
T CO
200
400
T(K)
NaV2O5
600
 H (kOe)
Universal temperature law
1.5
2.0
H || a
H || b
H || c
1.5
NaV2O5
CuGeO3
LiCuVO4
H || a
H || b
H || c
1.0
H || a
H || b
H || c
0.4
1.0
0.2
0.5
0.5
C 1 = 60 (5) K
C 2 = 15 (5) K
0.0
0
TN
100
200
T (K)
300
C 1 = 235 (5) K
C 2 = 40 (2) K
0.0
0
T SP
100
200
T(K)
300
C 1 = 420 (20) K
C 2 = 80 (10) K
0.0
0
T CO

C1 
H (T )  H ()  exp  

 T  C2 
H(T) in low-dimensional systems
200
400
T(K)
600
Theoretical predictions
High-temperature approximation fails for T < J (!)
Field theory (M. Oshikawa and I. Affleck, Phys. Rev. B 65, 134410, 2002):
(1) if only one interaction determines the linewidth:
H (T, , ) = f (T ) · H (T , , )
 linewidth ratio independent of temperature
(2) low temperatures T << J :
H (T ) ~ T
H (T ) ~ 1/T
2
for symmetric anisotropic exchange
for antisymmetric DM interaction
 in LiCuVO4, CuGeO3 and NaV2O5 symmetric anisotropic
exchange dominant
H(T) in low-dimensional systems
Linewidth ratio: deviations from universality
→ (1):
linewidth ratio
1.0
if only one interaction determines the linewidth:
H (T, , ) = f (T ) · H (T , , )
 linewidth ratio independent of temperature
LiCuVO4
CuGeO3
NaV2O5
spin fluctuations
(T > TN= 2.1 K)
lattice fluctuations
(T > TSP= 14.3 K)
charge fluctuations
(T > TCO= 34 K)
1.0
Ha/Hc
Hb/Hc
 Ha/ Hc
 Hb/ Hc
1.0
 Ha/ Hb
 Hc/ Hb
0.8
0.8
0.5
0.6
0.6
CuGeO3
LiCuVO4
0.4
0
100
200
T (K)
300
0
100
200
NaV2O5
300
T(K)
H(T) in low-dimensional systems
0.0
0
200
400
T(K)
600
Universal behavior of the linewidth
→(2):
low temperatures T << J :
H (T) ~ T
for symmetric anisotropic exchange
2
H (T) ~ 1/T for antisymmetric DM interaction
2.0
1.5
H || a
H || b
H || c
 H (kOe)
1.5
H || a
H || b
H || c
H || a
H || b
H || c
0.4
1.0
1.0
0.2
0.5
0.5
LiCuVO4
0.0
0
TN
100
200
T (K)
300
NaV2O5
CuGeO3
0.0
0
T SP
100
200
300
T(K)
0.0
0
T CO
200
400
600
T(K)
Is it possible to find a system with a large antisymmetric interaction and a high
isotropic exchange constant J to observe a low-temperature 1/T2 divergence due
to this interaction?
H(T) in low-dimensional systems
TiOCl
•
There is no center of
inversion between the ions
in the Ti-O layers
 Strong antisymmetric
anisotropic exchange
•
Isotropic exchange constant
J = 660 K
[A. Seidel et al., Phys. Rev. B 67, 020405(R) (2003)]
H(T) in low-dimensional systems: TiOCl
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)
H(T) in low-dimensional systems: TiOCl
Temperature dependence of H

C1 
J
H (T )  K DM ()     K AE ()  exp  

T 
 T  C2 
2
500
400
H (Oe)
The temperature and
angular dependence of
H can be described
as a competition of the
symmetric and the
antisymmetric
exchange interactions!
300
Tc1
a-axis
b-axis
c-axis
TiOCl
Tc2
200
100
[Oe]
H || a
H || b
H || c
KAE (∞)
1429
KDM (∞)
1.397
765
930
2.319
1.344
0
60
90
120
150
T (K)
[Zakharov et al., PRB 73, 094452 (2006)]
H(T) in low-dimensional systems
Summary
 Anisotropic exchange dominates the ESR line broadening in
low dimensional S=1/2 transition-metal oxides
 Unconventional symmetric anisotropic superexchange in
NaV2O5
 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
Summary
Acknowledgements
•
Crystal growth
NaV2O5: G. Obermeier, S. Horn (C1, Augsburg)
TiOCl: M. Hoinkis, M. Klemm, S. Horn, R. Claessen (B3, C1, Augsburg)
LiCuVO4: A. Prokofiev, W. Assmus (Frankfurt)
CuGeO3: L. I. Leonyuk (Moscow)
•
German-russian cooperation (DFG and RFBR)
M. V. Eremin (Kazan State University)
R. M. Eremina (Zavoisky Institute, Kazan)
V. N. Glazkov (Kapitza Institute, Moscow)
L. E. Svistov (Institute for Crystallography, Moscow)
•
ESR group, Experimental Physics V (Prof. A. Loidl)
H.-A. Krug von Nidda, J. Deisenhofer
Thanks for your attention!
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Direct exchange
Exchange interaction is a manifestation of the fact that, because of the Pauli
principle, the Coulomb interaction can give rise to the energies dependent on
the relative spin orientations of the different electrons in the system.
In case of the non negligible direct overlap of the wave functions i of two
neighbouring atoms, they should be modified because of the Pauli principle
 Modification of the Hamiltonian:
H    H    J 1 2  2  sa  sb   ,
e2
J ~  dr1dr2 (r1 ) (r2 )  b (r1 ) a (r2 ) ,
r12
*
a
*
b
J – „overlap integral“.
Direct exchange always stabilizes the triplet over the singlet according to the
Hund‘s rule, favoring a ferromagnetic pairing of the electrons.
Basic theory of anisotropic exchange
LiCuVO4 structure / susceptibility
LiCuVO4
Cu2+ S = 1/2 chains along b
orthorhombically distorted
inverse spinel
4
6
-3
IESR (arb. u.)
TN
9
cSQUID (10 emu/mol)
6
2
ESR intensity IESR
susceptibility cSQUID
3
Bonner-Fisher
(J = 45 K)
0
0
50
T (K)
H(T) in low-dimensional systems: LiCuVO4
100
0
Antisymmetric vs. symmetric exchange
Dzyaloshinsky-Moriya interaction
ra
Pseudo-dipol interaction
Dab  d ra  rb 
rb
px
sb
sa
x
b-axis
+Dab
Cu
+
O
dx2-y2
O
-Dab
Antisymmetric exchange is NOT
possible in LiCuVO4 (!)
y
O
Cu(i)
ground
state
-
+
dxy
Cu(j)
py
excited
state
Ring-exchange geometry strongly
intensifies the pseudo-dipol exchange!
H(T) in low-dimensional systems: LiCuVO4
Angular dependence of H
Jaa = 0.16 K, Jbb = -0.02 K, Jcc = -1.75 K
H (kOe)
1.5
H || c
1.2
ring-exchange geometry
high symmetric
anisotropic exchange
theoretically
expected Jcc  2K
H || a
0.9
0.6
H || b
LiCuVO4
0
T=200K
60
120
180
angle (°)
H(T) in low-dimensional systems: LiCuVO4
CuGeO3 structure / susceptibility
O1
x2
z2
z1
y2
y1
Cu2
Cu1
x1
O2
a
c
b

O2cSQUID
IESR
1.0
1.0
0.5
0.5
0.5
TSP
0.0
0.0
0
0
50
5
10
100
T (K)
J12
Cu2+
-3
IESR (arb. u.)
1.0
mean field
(0) = 22.4 K
J
1.5
cSQUID (10 emu/mol)
CuGeO3
15
150
0.0
2 Cu2+ S = 1/2 chains along c
J12  0.1 J
T > TSP: c(T ) not like Bonner-Fisher
T < TSP: c(T ) ~ exp{-(T )/T }
H(T) in low-dimensional systems: CuGeO3
Antisymmetric vs. symmetric exchange
Dzyaloshinsky-Moriya interaction
Pseudo-dipol interaction
• Intra-chain geometry is the same as with LiCuVO4
D≡0
G(zz) - dominant
• Inter-chain exchange:
?
G(yy) (Fig.a) and G(xx) (Fig.b) are not
negligible
H(T) in low-dimensional systems: CuGeO3
ESR anisotropy in CuGeO3
a
 H (Oe)
600
f = 0°
c
f =90°
b
 =90°
CuGeO3
a
120 K
intra chain
contribution
100 K
400
80 K
200
0
90
60 K
inter chain
contribution
 (°)
0 0
 (°)
90 90
f (°)
0
H(T) in low-dimensional systems: CuGeO3
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H(T) in low-dimensional systems
Model systems
LiCuVO4
CuGeO3
NaV2O5
Cu2+
Cu2+
S = 1/2 per 2 V4.5+
S = 1/2 chain
S = 1/2 chain
¼-filled ladder
J = 40 K
J = 120 K
J = 570 K
TN = 2.1 K
TSP = 14 K
TCO = 34 K
antiferromagnetic
dimerized,
dimerization
order
spin-Peierls S = 0
via
ground state
charge order
Introduction to electron spin resonance
Resonance field, g-values - local symmetry
LiCuVO4
CuGeO3
NaV2O5
ga= 2.07
ga= 2.16
ga= 1.979
gb= 2.10
gb= 2.26
gb= 1.977
gc= 2.07
gc= 1.938
sum of two tensors
V4.5+ 3d0.5: g-2 < 0
gc= 2.31
O1
x2
z2
z1
y2
y1
Cu2
Cu1
Cu2+ 3d9: g-2 > 0
x1
O2
a
c
b

c
c
highest g-value for H || c
local symmetry like in
strongest g-shift
longest Cu-O bond
LiCuVO4
for H || c
Introduction to electron spin resonance
Temperature dependence
2.0
1.5
H || a
H || b
H || c
 H (kOe)
1.5
H || a
H || b
H || c
H || a
H || b
H || c
0.4
1.0
1.0
0.2
0.5
0.5
LiCuVO4
0.0
0
TN
100
200
T (K)
300
NaV2O5
CuGeO3
0.0
0
T SP
100
200
300
0.0
0
T(K)
T CO
200
400
T(K)
Field theory (M. Oshikawa and I. Affleck, Phys. Rev. B 65, 134410, 2002):
T << J : H (T ) ~ T for symmetric anisotropic exchange
Introduction to electron spin resonance
600
Summary
 Electron spin resonance
• spin susceptibility, local symmetry, spin relaxation
 1D S = 1/2 systems LiCuVO4, CuGeO3 , NaV2O5
• H (T, , )  symmetric anisotropic exchange
 Charge order in Na1/3V2O5
• g-value: V1 sites occupied
• H (, ): CO not linear but blockwise
• H (T ): charge gap consistent with resistivity
IESR (arb. units)
Outlook – TiOCl, VOCl
2
TiOCl
1
(a)
0
g factor
1.96
1.92
T. Saha-Dasgupta et al., Europhys. Lett. Preprint (2004)
(b)
H (kOe)
1.0
Ti3+ (3d 1, S = 1/2) spin-Peierls
H || a
H || b
H || c
0.5
A. Seidel et al., Phys. Rev. B 67, 020405 (2003)
V. Kataev et al., Phys. Rev. B 68, 140405 (2003)
J. Deisenhofer unpublished (EPV)
0.0
(c)
0
100
T (K)
200
300
V3+ (3d 2, S = 1) Haldane
ESR spectrometer
temperature control
microwave
(9.4; 34 GHz)
control
unit
lock-in
electromagnet
(bis 18 kOe)
resonator, cryostat (He, N2: 1.6 – 670 K)
ESR in transition metal oxides
ESR measures locally at spin of interest
 materials with colossal magneto resistance
• orbital order in La1-xSrxMnO3
• magnetic structure in thio spinels FeCr2S4, MnCr2S4
 metal-insulator-transition
• heavy-fermion properties in Gd1-xSrxTi O3
• change of the spin state in GdBaCo2O5+
 Low-dimensional spin systems
• S = 1/2 chains: LiCuVO4, CuGeO3 - and ladders: NaV2O5
• chains of higher spin PbNi2V2O8 (S = 1), (NH4)2MnF5 (S = 2)
• 2D honeycomb lattice BaNi2V2O8
Anisotropic exchange

H AE  Si J ij S j  G ij  Si  S j
anisotropic
symmetric
conventional
estimate
~(g/g)2 ·J
2. order

anisotropic
antisymmetric
(Dzyaloshinsky-Moriya)
Gij ~ ri×rj
ri
rj
Si
~(g/g) ·J
1. order
antisymmetric exchange possible in CuGeO3 and NaV2O5
but not in LiCuVO4 (!)
+Gij
b-axis
Cu
O
-Gij
Sj
y2
y1
Cu1
Paths in CuGeO3 and NaV2O5
Cu2
x1
O2
a
c
b

CuGeO3
• chains like in LiCuVO4
• large contribution within chains
• additional contribution between
chains
 fully describable by symmetric
exchange
NaV2O5
• ladder more complicated than
chain
• high Jcc expected from ring
structure
• Up to now no theoretical
estimate
c
High-temperature linewidth
 Symmetric anisotropic exchange well describes the large
linewidth for T >> J in LiCuVO4, CuGeO3 und probably also in
NaV2O5
 Good agreement with recent theoretical results on the linewidth
in S = 1/2 chains:
(J. Choukroun et al., Phys. Rev. Lett. 87, 127207, 2001)
Contribution of symmetric anisotropic exchange
is always larger than that
of Dzyaloshinsky-Moriya interaction
Neutron scattering in CuGeO3
intensity
296 K
temperature dependence of
low-lying phonon modes in
CuGeO3
1.6 K
 (THz)
 (THz)
M. Braden et al., Phys. Rev. Lett. 80,
3634 (1998)
intensity
Electron diffraction in CuGeO3
CuGeO3
T (K)
temperature dependence of
diffusive scattering intensity
diffraction pattern of
CuGeO3 at 15 K
C. H. Chen and S.-W. Cheong, Phys.
Rev. B 51, 6777 (1995)
Comparison CuGeO3
linewidth ratio
1.0
Ha/Hb
Hc/Hb
0.8
0.6
CuGeO3
0
100
200
T(K)
300
Anisotropic-exchange parameter
O1
x2
z2
z1
y2
y1
Cu2
Cu1
x1
O2
a
c
b

J xx/J zz
0.0
J cc/J zz
1.0
-0.5
CuGeO3
0.5
0
100
200
T(K)
300
Outlook
 Open Questions
• anisotropic exchange in NaV2O5
• connections to charge fluctuations
• LiCuVO4: comparison to NMR
 ESR in the ground state
• AFMR in LiCuVO4
• triplet-excitations AFMR in CuGeO3
• impurity doping