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Anisotropic Superexchangein low-dimensional systems:
Electron Spin Resonance
Dmitry Zakharov
Experimental Physics VElectronic 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
• 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 low-dimensional systems: NaV2O5, LiCuVO4, CuGeO3, TiOCl
Outline
Outline
Two magnetic ions can interact indirect via an intermediate diamagnetic ion (O2-, F-,..)
potential exchange: like direct exchange describes the self-energy of the charge distribution → ferromagnetic;
Isotropic superexchange
Basic theory of anisotropic exchange
2
ˆ ˆˆ, with h.c.
1 2 2 , 2 .ab a b ab
V VV t a b
tJ S S J
H H
H H
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:
Mechanism of anisotropic exchange interaction
Basic theory of anisotropic exchange
The free spin couples to the lattice via the spin-lattice interaction HLS=(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!)
Theoretical treatment
Basic theory of anisotropic exchange
• 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
Clear theoretical description can be carried out in the framework of the perturbation theory:
Antisymmetric part of anisotropic exchange
Basic theory of anisotropic exchange
There is a simple geometric rule allowed to determine the anisotropy produced by Dzyaloshinsky-Moriya interaction:
IsoSE 44444444444444
DM LS a a a b
abDM a b
l s s s
D S S
H H H
H
Spin variables are going into the Hamiltonian of the antisymmetric
exchange in form of a cross-product:
2j ja b
iD l J
S S
The direction of
D (Dzyaloshinsky-Moriya vector) can be determined from: sa sb
ra rb
d44444444444444ab a bD r r
j = {x, y, z}, – orbital levels,– energy splitting,lj – operator of the LS-coupling,J – exchange integral.
It should be no center of inversion between the ions!
Symmetric part of anisotropic exchange
Is
2
oSE
( )Г
8
AE LS LS a a a b a a
AE a ab
a b a b
aa
a
b
a b
l s s s l s
S S
lJ S S S S
S S
l
H H H H
H
Basic theory of anisotropic exchange
Exchange constant of the pseudo-dipol interaction is a tensor of second rank and does not allow a simple graphical presentation.
Nonzero elements of can be determined by the nonnegligible product of the matrix elements of the (LS)-coupling and the hopping integrals.
I >
I> I>
1 3 2
I I>
ba , = {x, y, z};’ – orbital levels.
• 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 low-dimensional systems: LiCuVO4, CuGeO3, TiOCl
Outline
How to study all this?
Zeeman energy in magnetic field H:
eigen energies of the spin SZ = 1/2
magnetic microwave field H with E = hinduces dipolar transitions
E
HHres
SZ = -1/2
L
SZ = +1/2
Zeeman effect
B zSHg μ HHSZ = +1/2
E
H
SZ = -1/2
B
1
2HE g
Introduction to electron spin resonance
Experimental Set-Up
~microwave
source 9 GHz diode
magnet0...18 kOe
sample
resonatormicrowave field <1Oe
ESR signal
Introduction to electron spin resonance
ESR signal
ESR quantities:
intensity:local spin susceptibility
resonance field:
ħ=gBHres
g = g - 2.0023local symmetry
linewidth H:
spin relaxation,anisotropic interactions
3.3 3.4 3.5 3.6
intensity
Hres
linewidth2 H
abso
rptio
n P
H (kOe)
9.4 GHz36 K Lorentz
NaV2O
5
ES
R s
igna
l dP
/dH
Introduction to electron spin resonance
Theory of line broadening
Hamiltonian for strongly correlated spin systems:
in1 tB ii
i ii
Jg S SH S HH
Zeemanenergy
isotropic exchange
additionalcouplings
Local fluctuating fields local, statistic resonance shift inhomogeneous broadening
of the ESR signal
Strong isotropic coupling averages local fields like in the
case of fast motion of the spins Narrowing of the ESR signals
Introduction to electron spin resonance
• 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)]
Possible mechanisms of the ESR-line broadening
Only the following mechanisms are dominant in concentrated low-dimensional spin systems:
Introduction to electron spin resonance
Theoretical approach
21
ESR
B
Hg
M
J[R.Kubo et al., JPSJ 9, 888 (1954)]
Second moment of a line:
Schematic representationof the „exchange narrowing“
Linewidth of the exchange narrowed ESR line in the high-temperature approximation (T
≥J ):
2
0int int
2
Sp([ , ] [ , ])
Sp[ , ]
S
SM
S
S
H H
( ) ( ) (
int
2
2)
, , , , , ,
& & & &
, , , , , ,
DM a b ESR
AE a b E
ab ab ab
ab ab abSR
SD DS M T H T
S S M T H
D
T
H
H
H
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 low-dimensional systems: LiCuVO4, CuGeO3, TiOCl
Let‘s start at last!
NaV2O5 structure
Full microscopical picture of AE: NaV2O5
one electron S = 1/2
V4.5+
O2-
ladder 1 ladder 2
ab
cVO5
Na
20 30 400
1
2
3
0 200 400 6000.0
2.5
5.0
Bonner-Fisher J = 578 K
NaV2O
5
ES
R (1
0-4 e
mu/
mol
)
T (K)
TCO
mean field(0) = 98 K
NaV2O5 susceptibility / ESR linewidth
0 100 200 300 400 500 600 7000
100
200
300
400
500
TCO
= 34 K
H // c H // b H // a
NaV2O
5
H(O
e)
T (K)
Full microscopical picture of AE: NaV2O5
• One-dimensional system at T > 200 K;• Charge-ordering fluctuations 34K<T<200K;• “Zigzag” charge ordering at TCO= 34 K;
• ESR linewidth at T > 200 K is about 102 Oe
Antisymmetric vs. symmetric exchange
Full microscopical picture of AE: NaV2O5
sa sb
ra rb
d44444444444444ab a bD r r
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 orthogonalityof the orbital wave functions
What is the broadening source of the ESR line?!
Dzyaloshinsky-Moriya interaction Pseudo-dipol interaction
Conventional anisotropic exchange processes
a
I >
I> I>
1 42
I >
3
I I>A AI
I >
I> I>
21
II>
4 3
bI >
A AI
I >
I> I>
1 34
I >
2
cA AI
2
I >
I> I>
4 3
I >
1
dA AI
2
I >
I> I>
4
I >
1
3
eA AI
I >
I> I>
1 3
I >
4
2
fA AI
Full microscopical picture of AE
[B. Bleaney and K. D. Bowers, Proc. R. Soc. A 214, 451 (1952)]
2( )Г
8
aa
b
aab
a ab
lt
S
l t
S
AE with the spin-orbit coupling on both sites
a
I >
I> I>
1 42
I >
3
I I>A AI
I >
I> I>
21
II>
4 3
bI >
A AI
I >
I> I>
1 34
I >
2
cA AI
2
I >
I> I>
4 3
I >
1
dA AI
2
I >
I> I>
4
I >
1
3
eA AI
I >
I> I>
1 3
I >
4
2
fA AI
Full microscopical picture of AE
[Eremin, Zakharov, Eremina…, PRL 96, 027209 (2006)]
are not so effective because of the larger
energy in denominator
( )
8Г
ba
ab
aa
b
a b b
tt
S S
ll
AE with hoppings between the excited levels
Full microscopical picture of AE
[Eremin, Zakharov, Eremina…, PRL 96, 027209 (2006)]
a
I >
I> I>
1 42
I >
3
I I>A AI
I >
I> I>
21
II>
4 3
bI >
A AI
I >
I> I>
1 34
I >
2
cA AI
2
I >
I> I>
4 3
I >
1
dA AI
2
I >
I> I>
4
I >
1
3
eA AI
I >
I> I>
1 3
I >
4
2
fA AI
is of great importance in chain systems due to the big hopping
integrals t and tbetween the nonorthogonal orbital levels
( )Г8
a b
ab
a b
abab S S
lt
lt
Schematic pathways of intra-ladder AE
Full microscopical picture of AE: NaV2O5
2
I >
I> I>
4
I >
1
3
eA AI
I >
I> I>
1 3
I >
4
2
fA AI
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
ground states
2 2x y excited states
xy
2 2, x y , xy
2 2 2zx y l xy i
(zz) – dominant!
Schematic pathways of inter-ladder AE
Full microscopical picture of AE: NaV2O5
a
I >
I> I>
1 42
I >
3
I I>A AI
I >
I> I>
21
II>
4 3
bI >
A AI
I >
I> I>
1 34
I >
2
cA AI
2
I >
I> I>
4 3
I >
1
dA AI
Instead, the “conventional” exchange mechanisms are dominant for the exchange of the spins from the different ladders
Estimation of the exchange parameters
0.6
0.8
1.0
bcab
H / H
c
40 K
300 K
100 K
60 K
NaV2O
5
300 K
30 60
10
100
H (
Oe)
30 60
angle (deg.)
inter-ladder
30 60
intra-ladder
40 K
Full microscopical picture of AE: NaV2O5
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 (zz) ≈ 5 Kin good agreement with the estimations based on the values of hopping integrals and crystal-field splittings
Temperature dependence of H clearly shows the development of the charge-ordering fluctuations at T < 200 K
[Eremin.., PRL 96, 027209 (2006)]
0.6
0.8
1.0
0 100 200 300 4000
1
2
3
in
ter / (z
z)
T (K)
inter
/ (zz)
NaV2O
5
Ha/H
c
Hb/H
c
H
a,b /H
c
TCO
~ 34 K
Temperature dependence of H in NaV2O5
Open questions
0 100 200 300 400 500 600 7000
100
200
300
400
500
TCO
= 34 K
H // c H // b H // a
NaV2O
5
H(O
e)
T (K)
Are there other systems to corroborate these findings?
Which temperature dependence of the ESR linewidth is characteristic for the symmetric and antisymmetric part of anisotropic exchange
in low-dimensional systems?
Outline
→ Empirical answer!
• 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 low-dimensional systems: NaV2O5, LiCuVO4, CuGeO3, TiOCl
Temperature dependence of the ESR linewidth
LiCuVO4 CuGeO3 NaV2O5
0 100 200 3000.0
0.5
1.0
1.5
2.0
TN
H || a H || b H || c
LiCuVO4
H (
kOe
)
T (K)0 100 200 300
0.0
0.5
1.0
1.5
TSP
CuGeO3
H || a H || b H || c
T(K)0 200 400 600
0.0
0.2
0.4
TCO
NaV2O
5
H || a H || b H || c
T(K)
H(T) in low-dimensional systems
Universal temperature law
0 100 200 3000.0
0.5
1.0
1.5
2.0
C1 = 60 (5) K
C2 = 15 (5) K
TN
H || a H || b H || c
LiCuVO4
H (
kO
e)
T (K)0 100 200 300
0.0
0.5
1.0
1.5
C1 = 235 (5) K
C2 = 40 (2) K
TSP
CuGeO3
H || a H || b H || c
T(K)0 200 400 600
0.0
0.2
0.4
C1 = 420 (20) K
C2 = 80 (10) K
TCO
NaV2O
5
H || a H || b H || c
T(K)
1
2
( ) ( ) expC
H T HT C
H(T) in low-dimensional systems
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 for symmetric anisotropic exchange H (T ) ~ 1/T 2 for antisymmetric DM interaction
in LiCuVO4, CuGeO3 and NaV2O5 symmetric anisotropic exchange dominant
H(T) in low-dimensional systems
Linewidth ratio: deviations from universality
CuGeO3
lattice fluctuations
(T > TSP= 14.3 K)
NaV2O5
charge fluctuations
(T > TCO= 34 K)
LiCuVO4
spin fluctuations
(T > TN= 2.1 K)
0 100 200 3000.4
0.6
0.8
1.0
Ha/H
c
Hb/H
c
LiCuVO4
linew
idth
ratio
T (K)0 100 200 300
0.6
0.8
1.0
CuGeO3
Ha/H
b
Hc/H
b
T(K)0 200 400 600
0.0
0.5
1.0
NaV2O
5
Ha/H
c
Hb/H
c
T(K)
H(T) in low-dimensional systems
→ (1): if only one interaction determines the linewidth: H (T, , ) = f (T ) · H (T , , )
linewidth ratio independent of temperature
Universal behavior of the linewidth
H(T) in low-dimensional systems
→(2): low temperatures T << J : H (T) ~ T for symmetric anisotropic exchange H (T) ~ 1/T 2 for antisymmetric DM interaction
0 100 200 3000.0
0.5
1.0
1.5
2.0
TN
H || a H || b H || c
LiCuVO4
H (
kO
e)
T (K)0 100 200 300
0.0
0.5
1.0
1.5
TSP
CuGeO3
H || a H || b H || c
T(K)0 200 400 600
0.0
0.2
0.4
TCO
NaV2O
5
H || a H || b H || c
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?
TiOCl
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
[A. Seidel et al., Phys. Rev. B 67, 020405(R) (2003)]
• Isotropic exchange constant J = 660 K
Analysis of the anisotropic exchange mechanisms
H(T) in low-dimensional systems: TiOCl
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 (aa)
Temperature dependence of H
60 90 120 1500
100
200
300
400
500TiOCl
a-axis b-axis c-axis
H (
Oe)
T (K)
Tc1
Tc2
H(T) in low-dimensional systems
2
1
2
( ) ( ) ( ) expDM AE
CJH T K K
T T C
[Oe] KAE (∞) KDM (∞)
H || a 1429 1.397H || b 765 2.319H || c 930 1.344
The temperature and angular dependence of H can be described as a competition of the symmetric and the antisymmetric exchange interactions!
[Zakharov et al., PRB 73, 094452 (2006)]
Summary
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
Acknowledgements
• Crystal growthNaV2O5: 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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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.
Direct exchange
Basic theory of anisotropic exchange
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:
J – „overlap integral“.
2
* *1 2 1 2 1 2
12
1 2 2 ,
~ r r (r ) (r ) (r ) (r ) ,
a b
a b b a
J s s
eJ d d
r
H H
Direct exchange always stabilizes the triplet over the singlet according to the Hund‘s rule, favoring a ferromagnetic pairing of the electrons.
LiCuVO4 structure / susceptibility
0 50 1000
2
4
6
TN
ESR intensity IESR
LiCuVO4
I ESR
(arb
. u.
)
T (K)
0
3
6
9
Bonner-Fisher (J = 45 K)
susceptibility SQUID SQ
UID (
10-3 e
mu/
mol
)
Cu2+ S = 1/2 chains along b
orthorhombically distorted inverse spinel
H(T) in low-dimensional systems: LiCuVO4
Antisymmetric vs. symmetric exchange
sa sb
ra rb
d44444444444444ab a bD r r
Antisymmetric exchange is NOT possible in LiCuVO4 (!)
Ring-exchange geometry strongly intensifies the pseudo-dipol exchange!
Dzyaloshinsky-Moriya interaction Pseudo-dipol interaction
Cu
O
+Da
b
-Dab
b-axisx
y
+-
+-
++-
-
++--
dx2-y2 dxy
px
py
O
O
Cu(i)groundstate
Cu(j)excitedstate
H(T) in low-dimensional systems: LiCuVO4
Angular dependence of H
ring-exchange geometry
high symmetric anisotropic exchange theoretically expected Jcc 2K
0 60 120 1800.6
0.9
1.2
1.5J
aa = 0.16 K, J
bb = -0.02 K, J
cc = -1.75 K
H || b
H || a
H || c
T=200KLiCuVO4
H (
kOe)
angle (°)
H(T) in low-dimensional systems: LiCuVO4
CuGeO3 structure / susceptibility
0 50 100 1500.0
0.5
1.0 I
ESR
CuGeO3
I ESR
(arb
. u.
)
T (K)
0.0
0.5
1.0
1.5
SQUID
SQUID (
10-3 e
mu/
mol
)
0 5 10 150.0
0.5
1.0
mean field(0) = 22.4 K
TSP
2 Cu2+ S = 1/2 chains along c
J12 0.1 J
T > TSP: (T ) not like Bonner-Fisher
T < TSP: (T ) ~ exp{-(T )/T }
O1
O2
Cu1
x1
y1
z1z2
x2
y2
a
bc
Cu2
Cu2
+
O2-
J12
J
H(T) in low-dimensional systems: CuGeO3
Antisymmetric vs. symmetric exchange
? (yy) (Fig.a) and (xx) (Fig.b) are not negligible
Dzyaloshinsky-Moriya interaction Pseudo-dipol interaction
H(T) in low-dimensional systems: CuGeO3
• Intra-chain geometry is the same as with LiCuVO4
D ≡ 0 (zz) - dominant
• Inter-chain exchange:
ESR anisotropy in CuGeO3
90 00
200
400
600
(°)
CuGeO3
bc aa
= 0°
H (
Oe
)
0 90
100 K
120 K
=90°
(°)
90 0
60 K
80 K
=90°
(°)
intra chain contributio
n
inter chain contributio
n
H(T) in low-dimensional systems: CuGeO3
Empty
H(T) in low-dimensional systems
Model systems
LiCuVO4
Cu2+
S = 1/2 chain
J = 40 K
TN = 2.1 K
antiferromagnetic
order
NaV2O5
S = 1/2 per 2 V4.5+
¼-filled ladder
J = 570 K
TCO = 34 K
dimerization
via
charge order
CuGeO3
Cu2+
S = 1/2 chain
J = 120 K
TSP = 14 K
dimerized,
spin-Peierls S = 0
ground state
Introduction to electron spin resonance
Resonance field, g-values - local symmetry
LiCuVO4
ga= 2.07
gb= 2.10
gc= 2.31
Cu2+ 3d9: g-2 > 0
highest g-value for H || c
longest Cu-O bond
NaV2O5
ga= 1.979
gb= 1.977
gc= 1.938
V4.5+ 3d0.5: g-2 < 0
strongest g-shift
for H || c
CuGeO3
ga= 2.16
gb= 2.26
gc= 2.07
sum of two tensors
local symmetry like in
LiCuVO4
O1
O2
Cu1
x1
y1
z1z2
x2
y2
a
bc
Cu2
c
c
Introduction to electron spin resonance
Temperature dependence
0 200 400 6000.0
0.2
0.4
TCO
NaV2O
5
H || a H || b H || c
T(K)0 100 200 300
0.0
0.5
1.0
1.5
TSP
CuGeO3
H || a H || b H || c
T(K)0 100 200 300
0.0
0.5
1.0
1.5
2.0
TN
H || a H || b H || c
LiCuVO4
H (
kO
e)
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
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 occupiedH (, ): CO not linear but blockwiseH (T ): charge gap consistent with resistivity
Outlook – TiOCl, VOCl
0 100 200 3000.0
0.5
1.0
1.92
1.96
0
1
2
H || a H || b H || c
(c)
g f
act
or
H (
kOe
)
T (K)
(b)
I ES
R (
arb
. u
nits
)
TiOCl
(a)
Ti3+ (3d 1, S = 1/2) spin-Peierls A. Seidel et al., Phys. Rev. B 67, 020405 (2003)
V. Kataev et al., Phys. Rev. B 68, 140405 (2003)
J. Deisenhofer unpublished (EPV)
V3+ (3d 2, S = 1) Haldane
T. Saha-Dasgupta et al., Europhys. Lett. Preprint (2004)
ESR spectrometer
microwave
(9.4; 34 GHz)
electromagnet
(bis 18 kOe)
resonator, cryostat (He, N2: 1.6 – 670 K)
control unit
lock-in
temperature control
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
antisymmetric exchange possible in CuGeO3 and NaV2O5
but not in LiCuVO4 (!)
jiijjijiAE SSGSJS H Gij ~ ri×rj
Si Sj
ri rj
Cu
O
+Gij
-Gij
b-axis
anisotropicantisymmetric
(Dzyaloshinsky-Moriya)
~(g/g) ·J1. order
anisotropic symmetric
~(g/g)2 ·J2. order
conventionalestimate
Paths in CuGeO3 and NaV2O5
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
O1
O2
Cu1
x1
y1
z1z2
x2
y2
a
bc
Cu2
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
temperature dependence of low-lying phonon modes inCuGeO3
M. Braden et al., Phys. Rev. Lett. 80, 3634 (1998)
296 K
1.6 K
(THz) (THz)
inte
nsi
ty
Electron diffraction in CuGeO3
temperature dependence of
diffusive scattering intensity
C. H. Chen and S.-W. Cheong, Phys. Rev. B 51, 6777 (1995)
diffraction pattern of CuGeO3 at 15 K
inte
nsi
ty
T (K)
CuGeO3
Comparison CuGeO3
0 100 200 300
0.6
0.8
1.0
lin
ew
idth
ra
tio
CuGeO3
Ha/H
b
Hc/H
b
T(K)
0 100 200 300
0.5
1.0
CuGeO3
Jc
c/J
zz
T(K)
-0.5
0.0
Jx
x/J
zz
Anisotropic-exchange parameter
O1
O2
Cu1
x1
y1
z1z2
x2
y2
a
bc
Cu2
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