anisotropic superexchange in low-dimensional systems: electron spin resonance dmitry zakharov...

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


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


• 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


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


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.




• 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


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


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


• 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:


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


Outline




• 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)


• 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


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


[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


[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


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


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


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!




• 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


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


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)


→ (1): if only one interaction determines the linewidth: H (T, , ) = f (T ) · H (T , , )

linewidth ratio independent of temperature

Universal behavior of the linewidth


→(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


• 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


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!

Empty

Empty

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


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


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!


Cu

O

+Da

b

-Dab

b-axisx

y

+-

+-

++-

-

++--

dx2-y2 dxy

px

py

O

O

Cu(i)groundstate

Cu(j)excitedstate


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 (°)


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


? (yy) (Fig.a) and (xx) (Fig.b) are not negligible



• 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


Empty


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


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


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

anisotropic superexchange in low-dimensional systems: electron spin resonance dmitry zakharov...

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