The Inorganic Spin-Peierls Compound CuGeO3

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Submitted on 1 Jan 1996

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J. Boucher, L. Regnault

To cite this version:

J. Boucher, L. Regnault. The Inorganic Spin-Peierls Compound CuGeO3. Journal de Physique I,

EDP Sciences, 1996, 6 (12), pp.1939-1966. �10.1051/jp1:1996198�. �jpa-00247291�

The Inorganic Spin-Peierls Compound CuGe03

J-P- Boucher (~~*) and L.P.

Regnault (~)

(~) Laboratoire de

Spectrométrie Physique (**),

Université

Joseph

Fourier Grenoble I, BP 87, 38402 Saint Martin d'Hères Cedex, France

(~)

Département

de Recherche Fondamentale _sur la Matière

Condensée,

Service de

Physique Statistique, Magnétisme

et

Supraconductivité,

Laboratoire de

Magnétisme

et Diffraction

Neutronique,

Centre d'Etudes Nucléaires, 38054 Grenoble Cedex, France

(Received 10

June1996,

revised 18

July1996, accepted19 August 1996)

PACS.64.70.Rh Commensurate-incommensurate transitions

PACS.75.40.Gb

Dynamic properties (dynamic susceptibility,

_{spm waves,}

spin

diffusion, dynamic

scaling,

etc.

Abstract. A _review of recent

experimental

results obtained _on the

inorganic spin-Peierls compound

CuGe03 is

proposed.

As the

spin-Peierls phenomenon

results from trie

interplay

between lattice and

magnetic (quantum) fluctuations,

the

presentation

focuses _on the diflerent

dynarnical

aspects ^{of the}

problem.

With

CuGe03,

_many

points

have been clarified and _new results

acqmred.

However, ^it remains open questions which, due to the

high quality

of the

available crystals, _can be

expected

to be solved in the future.

1. Introduction

Since the

pioneering

work of Hase et ai. in 1993

[ii,

_a lot of

works,

bath theoretical and

experimental,

has been devoted to the

compound CuGe03.

It is _now well established that this

inorganic

material

provides

_{a very}

good example

Dia

"spin-Peierls system".

Such _a

system

can

be defined _as follows: it is _a

spin

system which

undergoes

Iattice distortions under the eifect of

magnetic quantum

fluctuations. This remarkable

dynamical magneto-elastic phenomenon

gives rise to a rather universal

phase diagram

as a function of field H and

temperature

T.

such _a behavior _was

predicted

to _occur in one-dimensional

(ID) HeiseùJerg

or XY

antiferromagnetic (AF)

s =

1/2 spin

chains

[2], where,

_as T _-

0, large _quajtum

fluctuations

are known to

develop

in a broad continuum of excitations

[3].

^{The first}

obiervations

_of

_spin-

PeierIs

(SP

transitions _were obtained _{on organic} mater1als

[4j, which,

in the 70's, _were found to

provide good examples

of

quasi-ID conducting

and

for isolating spins systems [Si.

^{The recent}

discovery

of

CuGe03

_{as a}

spin-Peierls _system

has renewed the interest in this

fascinating

phenomenon. Large single crystals

of

high quality

_{are now} available,

allowing experimentalists

to

develop

measurements which could net be done before. In the Iast years, many

questions

have been

solved,

new have occurred and _some remain _open. This

explains

that the research _on

(*)Author

for correspondence

(e-mail: [email protected])

(**)

Unité Mixte de Recherche N°C5588 du CNRS

Q

Les

Éditions

_{de Physique 1996}

1

i~

(L) ~

12

~~

. Hllc

_q ~ ^A Hl/b

~

. Hlla

6

~

D

4 6 8 10 12 14

Temp

/K

Fig.

I.

(H,T) phase diagram

of the spin-Peierls

compound

CuGe03 (19, 20]

showing

the three dilferent

phases:

uniform

(U),

dimerised

(D)

and incommensurate

il).

The sohd and dashed lines represent ^{second and first order} transitions

respectively,

and

(L)

the Lifschift

point.

CuGe03

is still _very active. In the

following,

_{a review} of recent

experimental

results obtained

on this

compound

is

presented.

Trie basic

properties

of the materai _are described in Section 2. The

(H, T) phase diagram

is shown to

correspond quite

weII _to the theoretical

predictions

for _a

spin-Peierls

_{system [6]:}

the charactenstic three diiferent

phases

_are weII identified

(Fig. l).

At

high temperature,

there is the "uniform" U

phase,

where the

system

is

usually

considered to be made of

simple inagnetic

chains

(they

_are defined with _one Iattice

parameter

_c, and _one

exchange coupling Jc

between

neighboring spins).

As the

temperature

^is

decreased,

_a first structural transition

is achieved at Tsp(+w ^{14 K in}

CuGe03).

In moderate

field,

this transition

corresponds

to a dimerisation of the Iattice. In that "dimensed" D

phase,

t>vo Iattice parameters and two

exchange couplings Jci

and

Jc2

_are then needed _to define the

magnetic

chains.

Increasing

the

magnetic

field from the D

phase yields

_{a new} transition

occurring

at a

specific

value

Hc

of the field

(Hc

_+w 12.5 T in

CuGe03 _).

This field-induced transition

corresponds

to a new deformation of the Iattice. Above

Hc,

the Iattice becomes mcommensurate

(with respect

to the uniform aiid

the dimensed

chains).

In this "mcommensurate" I

phase,

the Iattice deformation _is

expected

to _increase with the

applied magnetic

field until the saturated

paramagnetic

structure of the

commensurate

phase

is re-obtained

(for

H

+w

Jc /g/~B (6-8].

The

magnera-elastic coupling

which _govems the dilferent Iattice distortions _is

generally

_con-

sidered under the

simple

forai of _a Iinear

coupling

between

spins

and

phonon operators [6-8].

Such _a model

predicts

the diiferent structural transitions to be driven

by

_a weII defined "soft mode" of the

phonon spectrum,

the

softening being directly

mduced

by

the

magnetic

quantum

fluctuations.

Though

it is _a crucial

point

in the

problem,

such _a soft mode has _never been observed in the past [4]. ^The

expenmental

^studies conceming the Iattice and the

phonon

_spec-

trum of

CuGe03

_are

presented

in Section 3. The

crystallographic

structure of this niatenal is

CU

chain

1

Fig.

2.

Representation

of the

crysjallographic

structure for CuGe03.

sho>vn to

depend appreciably

_on bath temperature ^{and field. The diiferent} Iattice distortions dimerisation and

incommensurability

have been

clearly identified,

and the associated

critical,

and

pre-critical,

behaviors _are

compared

with the

predictions

of current models.

The

dynamical properties

of

isotropic antiferromagnetic

chains have

always

been the

subject

of many

propositions

and discussions. For

spins

_{s =}

1/2,

the

prediction

that, _at T ₌ 0, there exists _a continuum of excitations

starting

frein the

ground

state was

given

in 1931

(the

"'Bethe

ansatz")

_[9]. For

integer

_spins

ii.

_{e.. s}

= 1 for

instance),

_a

completely

diiferent

prediction (the

"Haldane

conjecture"

_was

presented

in 1983

[loi

an energy gap should exist between the

ground

state and the

elementary

excitations. In the fonner _case,

Iow-energy

fluctuations _are

expected

to

develop

_as T _-

0,

while

they

_are

suppressed

in the latter _case. The

spin-Peierls phenomenon,

which is _a direct consequence of these

Iow-energy

fluctuations _as

they

create instabilities in the whole system can

only

be observed in the quantum spin case. The distortion which _occurs at the SP transition

yields

_an immediate stabilization of the

system,

since _in the

case of dimerised

magnetic chains,

_as in the Haldane

conjecture,

_{an energy gap} A is present ⁱⁿ the excitation spectrum

[1ii.

The rote of the

magnetic

excitations and fluctuations which _are

so essential in the

spin-Peierls phenomenology

wiII be considered in Section 4.

They

wiII be

analyzed

in the dilferent

phases,

with _a

particular

interest on their

Iow-energy

contribution.

The

experimental investigation

_on

CuGe03

_can be

predicted

to remain very active _in the

near future. Dilferent points, which

question

the usual basic

spin-Peierls phenomenology,

_are

still unsolved. These points are

briefly

reviewed in the conclusion where _a sketch of recent studies _on

doped samples

is aise

given.

2.

CuGe03

Germanate

CuGe03 crysta1Iizes

within _an orthorhombic structure of space group Pbmm. The Iattice

parameters

at _room temperature are: a = 4.81

À,

b

= 8.43 and _{c =} 2.95

À.

The

crystallographic

structure of this

compound

is

reproduced

in

Figure

2

[12].

^It can be descnbed

as a

staking

of

Cu02

chains and

Ge04

chains

sharing

_{one oxygen} atom. The chains _are

aligned

single-crystal CUGeO~

Bonner and Fisher

j

^J = 88 K

fl

_O H

II a

à

~ H ^I b H ₌ T

(

a H ^I _c (a)

ce

T

~i2.0

é

single-crystal CuGe03

E

3 ~A.~

i

_H=1T

a

O H _II a

[

. H

II b

& a H _II c

3

)

y=o,71

)

(b)

ce

Fig.

3.

Magnetic susceptibility

of CuGe03, from

[ii.

In

ai

the solid line

corresponds

to the prediction for

Heisenberg

AF quantum

spin

^chains _[16] with Jc

= 88 K.

along

the _c axis and the unit ceII contains _two unit formula. The Cu-O-Cu

bonding angle (responsible

for the super

exchange

intrachain

couplings)

is very near

90°,

_a value which should

imply

_a

strong sensitivity

to distortions of the

Cu02

_groups. Neutron diffraction measurements

as a function of

temperature

^down to 20 K

[13] recently

revealed _a

quite

sizable and continuous structural

deformation,

which _can be viewed _{as a}

twisting

of the

O(2)-O(2)

octahedron

edges accompanied by

_a translation of the tetrahedron.

The

specificity

of

CuGe03

has been

early recognized

from the

quite intriguing

behavior observed at Iow

temperature

on the

susceptibility x(T). Figure

3 shows the first results oh- tained for

x(T), by

Hase et ai.

iii.

The most remarkable feature _coiicems the

rapid drap

which is observed below

+w 14 K for _any

crystallographic

directions _a, b and _c. Such _a Iow-T behavior is

quite

reminiscent of that observed _on the

prototype spin-Peierls _systems,

Iike e.g.

TTF-CUBDT [14] or

MEM(TCNQ)2 _[15],

and it _was

immediately proposed

that

CuGe03

is the first

example

of _an

inorganic spin-Peierls compound (with

_T~p

+w

14

K) iii.

Above

Tsp, x(T)

is

essentially

characterized

by

_{a maximum} at TM

~

60 K

(the

small

anisotropy

is _at- tributed _to the

gyromagnetic

factor _g of the CU

ions).

Such _a maximum _in

~(T)

is

actually expected

for _a Iow-dimensional

Heisenberg

AF

spin

system. ^The

comparison

with the

quantum (s

=

1/2) spin

chain model

(TM

_"

0.64Jc) _[16], yields

for the

nearest-neighbor (nn)

intrachain

exchange

interaction _in the U

phase

the

following

evaluation:

Jc

+w 94 K.

However,

the _agree- ment between the observed

x(T)

and the Bonner-Fisher

prediction _[16]

_is rather poor. The deviation from this Iaw _{coeurs at}

relatively high temperature, typically

belo~v 200 K. Such _an

"anomaly"

is net

unique

and has

already

been observed in other

spin-Peierls

systems ^Iike _e.g.

,,,,<,,,,,,,,,<,<>«<,,

"'

Pi _<,,,

~/ _--~~

~ o

a3

° 5.OT

é~

. 8.OT

C

v 10.0T

8

o 11.0T

lô

~ 125T

k

2.8T

~j

_~ _ÎÎ~Î

~

"~,~/~

.ooo ~~

Temperature (K)

Fig.

4.

Magnetization

_{as a} function of temperature

MIT)

for different fields

(H

_ii

ai

[19].

(BCP-TTF)~X (where

X

=

PF6

or

AF6) _(17].

It may find its

origin

either in the existence of

relatively important magneto-elastic

^elfects,

starting

weII above

T~p,

or in the existence of _a

non-negligible

next-nearest

neighbor (nnn)

intrachain

exchange coupling.

^As _a

support

^of the former

assumption,

it

might

be

interesting

to compare

x(T)

with the T

dependence

observed

on the Iattice parameters

(cf.

Seat.

3j.

Within the latter model, it has

recently

been shown that the observed

~(T)

could be weII

explained

if the ratio between _nn and _unn

couplings

is of the order of

J(/Jc

+w 0.2 with

Jc

+w

150 K

[18]. Magnetization

measurements

M(T)

hâve been

performed

for dilferent field values

[19].

^{A few}

examples

of such data _are shown in

Figure

4

(for

H

applied

in the _a direction

).

As for

x(T),

the

drap

in

tif(T)

observed between 14 and 10 K characterizes trie

spin-Peierls

transition: _as

expected (see Fig.

10 in Sect.

3), _Tsp

is _seen to de-

crease

slightly

~N.ith H

increasing.

In the _narrow field _range 12.5-13.5 T _a noticeable _re-entrant

elfect is aise observed at Iow

temperature.

^That increase of

M(T)

observed _at the Iowest T

corresponds

to the

crossing

of the D-U transition Iine. It is observed

because,

in

CuGe03,

the critical field

Hc

decreases

slightly

with T

(see Fig. il. Defining _Tsp

_as the

temperature

where x +w

ôfif/ôT

is maximum, the

phase diagram

_given in

Figure

1 is

finally

obtained

[19, 20].

^As

shown in

Figure

5,

specific

heat measurements

Cp(T)

have aise been

performed

_{as a} function of _an

applied magnetic

field

(up

to 21

T) _[21].

For any value of

H,

the

spin-Peierls

transition is weII characterized and

clearly

_seeu to be of second order. In contrast,

according

to the

hysteresis

observed below

+w 6 K _on

M(H) _[22],

the D-I transition _is considered to be of first order. As shown in

Figure 6,

for T

+w I.S

K,

the

hysteresis

is of the order of

ôHc

+w o-1 T.

The three

phases charactenzing

_a

spin-Peierls system

are

clearly

observed in

CuGe03.

As

expected

the U-D and U-I transitions _are of second

order,

which is

represented by

the solid Iine in

Figure 1,

while the D-U transition is of first order

(the

dashed Iine in the _same

figure).

The Lifschift

(L) point

is determined for

HL

~ 13 T and

TL

~ 11.5 K. TO _Dur

knowledge,

the re-entrant behavior associated with the D-U transition

(Hc slightly decreasing

with

T),

theoretically predicted [6-8],

is observed for the first time.

35

30 ^{a H=} 0 T

j

& H=10 T

25 x H=13T

/~

Ç/

_D H=18 T ~?

cn 20

. R=21 T _o

oo°

' t

o ~o° ^~

~

,~

^~

E 15 _o ,

-

à

~

,. ^. , ^eD

o .

oe io ^O°

é

~°

u ^o x~

5

0

6 8 10 12 14 16

T

(K)

Fig.

5.

Specific

heat _{as a} function of temperature for diflerent fields

(H

ii cl [21].

160

~

4J .

ô .

E

.

~ ÎÎ

~~

~É 40

. ~

o

0

12

i~ ^{a aXlS}

- °°o. ^{" ~} ~X18

~ ^{z °Oo}

,

^{005 1 °Oo}

°~Oo

y~ °°~Oo_

~~

ù-Ù

- ( ^{~° 1°° 15° ~°0}

~/ ~ ~ ~.OO*°

" .O*

". ..W*"

~j "OOOOOOO"

~

^~l.0

O ^~

O-

Vl

~j

^~'5

~~~

^{~~ ~~}

..~'

~ ^,' ,* *

X z-o .:"

ç~~ _"O^"O

"O

~i

1.5

~.[.°

.O . b axis

£

_j, ^VOÎUme

i~ ^JO'

$~ vi

4l _vO

~ O

é' 05

o-o

o 50 ioo iso zoo

Temperature (K)

Fig.

7. Coefficients of the linear thermal

expansion along

_a,

b,

_c, and of the volume _{as a} function of temperature [23].

3.1. LATTICE DisToRTioN IN ZERO FIELD. In

CuGe03,

the

rapid drap

observed _on the

susceptibility x(T)

below 14 K

iii

is

clearly

associated with

appreciable

temperature

dependen-

cies of structural

components,

^which reveal that sizable

magnera-elastic couplings

exist in finis

compound. Figure

7 shows the temperature

dependence

of the coefficients _{aa, ab} and _oc of the Iinear thermal

expansion

for the three

crystallographic

_axes

and,

of

(aa

_{+ ab + oc} for the vol-

ume

expansion _[23]. Quite unambiguously,

these measurements

give

evidence for _a structural

phase

transition at T~p +w

14.3 K.

They

aise show that, weII above

Tsp,

^{the Iattice of}

CuGe03

is

already

_very sensitive to

temperature (it

is

interesting

to compare

Fig.

3a and

Fig. 7,

for

instance).

AIT these results _are corroborated

by X-ray [24]

^{and neutron} diffraction

[25, 26]

measurements. The

temperature dependence

of the Iattice

parameters

_a, ^{b and} c are

reported

in

Figure

^8. The

Iargest

^variation is

definitely

observed

along

the

b-direction,

where _a weII defined

drap

of the Iattice

parameter

is

clearly

_seen below

Tsp. X-ray [27],

neutron

[26-28]

^and

electron

[29]

diffraction measurements have

provided

_a

precise

determination of the structural distortion occurnng ^at

Tsp.

^{Trie first evidences of the existence of}

superlattice ^peaks

^below

Tsp

were obtained from

X.ray

_[27] and electron

[29]

diffraction measurements. These satellites have been indexed with _a commensurate

propagation

vector k ₌

il /2,1,1/2], corresponding

to out-

of-phase displacements

from the

original

atomic

positions.

^Neutron diffraction measurements

on a

single crystal

have confirmed the presence of such nuclear satellites net

only

for odd

[26,27]

é

4.ao13

o o

4.aria

o

§_o°

o

~'~~~~10

_{15 20 25 30 35 40}

iemperalure

(K)

14.7meV 10'-20'-10'-10'

Analyzec

PG(004j

Q

=

(0,0,2

°

Aclc

=

lo'~

T~ = 14.2K

~'

7.48meV 10'-10'-10'-lO'

Anal~zer:

Ge(2z0j

~

Q

= 0,6,0)

Ab/b = 10'~

m

8.

T~ = 14.2K

0 10 20 30 40 50 60

Temperature (K)

Fig.

8.

Temperature dependence

of the lattice constants

along

_{a [24],} and _c and b [26].

but aise for _even kb

components [26],

a fact which indicates that the actual

propagation

vector

m

CuGe03

is

k~p

= 11

/2, 0,1/2].

The location of the

corresponding point

in

reciprocal

_space is given in

Figure

9a.

Figure

10a shows _a

typical longitudinal

_scan

through

the satellite observed at

il /2,3,1/2],

which gives evidence for _a resolution-Iimited

peak.

The

purely

nuclear nature of these

superlattice peaks

has been established from bath their

scattenng

~N.avevector k and

temperature

^T

dependencies.

The T

dependence

of the

il /2,3,1/2]

satellite is

depicted

in

Fig-

ure lob. As _can be seen, the

Bragg-peak intensity

vanishes at

Tsp, exactly

^where the

drap

_in

a*

l12

a

k~m ifioi/z

", ' '

)

",

~

Î i/~

",

b* ',, _,/ c*

"

"

"~.~

k~

₌

[o,i,1/2j

E 13)

, ,-,

, , ^'

/ ^'

j ^'

/ /

/ '

,

, ,

1

,(

/ ~

/ Ùl G2

/ ,

j ~/

Eoi 'jj~

,

j ^{", 1'}

~~ ^{"', 1' C}~

", ~ ^l'

", GI /~

', i~~

'±

k~v =

[1,1/2]

Fig.

9.

ai Representation

of the 3D

reciprocal

_space for

CuGe031 hi

Dispersions of the elementary excitations in the D

phase.

for the two

reciprocal

directions b* and c*

(see text).

The solid _curves represent the

dispersions

observed

experimentally.

the

susceptibility ~(T)

_occurs. The observed behavior is consistent with _a critical

exponent fl

_+w 0.27

0.30,

_an evaluation far from the mean-field

prediction fl

_+w o-S

[28].

^{This small value} of

fl

however agrees with the fact

that,

above

Tsp, appreciable anisotropy

is

present

^{in the} structural fluctuations.

Although hardly

visible in the neutron

scattering

measurements

[30],

these fluctuations have been

clearly

observed

by X.ray diffraction,

_up to

+w 50 K

[27]. Figure

11 shows the

temperature dependence

of the structural inverse correlation

Iengths (~~

measured

along

the three

reciprocal

directions

a*,

b* and c*

[27, 31].

^Within

experimental

_errors,

(jl

becomes 3D _near

Tsp

^{and behaves} as

(T Tsp)~/~, whereas,

_as T

increases,

the

pre-transitional

fluctuations _{are seen,} in the _a and b

directions,

to become

successively uncoupled.

# Î

₁₄₀₀

à

^~~°° à

Î

1000

~~ ~ ~ ~ ~

( _a)

_-- HAI

kce TZK

g

^{800 H~'~ T~25K}

é

₆₀₀

400 200

1 Î

~

0.06 -0.04 -0.02 0 0.02 0.04 0.06

q

(r.l.u.)

1

₇₀₀

(

~oo

Î

'~

CUGeO~

E .

é ~~~ ^' o=(l12,3,l12)

E

Î bj

400

~°~

é

300 ^{~ H~ km}

~§

* '~"8.~ ~"

(

200 o~

~

g

_ioo 8.G.

~

)

~ ~

0 5 10 15 20

Temperature

(K) 15

CUGeO~

'~ W(l12,3,l12)

q

¹³

~~

~ ₁₂

_cj

11

10

0 20 40 60 80 100

H

(koe)

Fig.

10. Neutron scattering [28]:

a) Longitudinal

_scan

through

the

super-lattice

peak ₁₁

/2,3,1/2];

hi Temperature dependence

of the _maximum intensity of this

peak.

for H

= 0 and H

= 9.85 T:

c)

Field dependence of Tsp determined from such measurements.

An _accurate determination of the

crystallographic

structure of the dimerised

phase ii-e-,

for T _<

Tsp)

^{has been obtained from} neutron diffraction measuremeiits

performed

_{on serres}

of satellites

[13, 27]

The

corresponding

Iattice distortion is

reported

iii

Figure

12.

According

0A

Tco ^TCO

0.3 *

_

/~

_

_a~Î j/~

OE

~ ~'~

~'~

~

^{14 15 16 17 18}

UP

j~

O.l -e- a*

+~

b*

+- c*

O.O

14 16 18 20 22 24 26 28 30 32 3436

Temperature(K)

Fig.

ii. Thermal

dependence

of

(~~ along a*,

b* and c*. Tco is the temperature at which

(jl 1la. (/~

and

(j~

close to T~p are shown

m the _mset [31].

CuGe03 Q

_Cu O,1l2z

~

_{Ge l14,314}

. O(1) o,l12

. O(2) l14,3l4

aÎ

~

z=l12

~=o

Îc

Fig.

12. Schematic

representation

of trie

low-temperature

structure of CuGe03. Arrows and signs indicate the directions of atoniic displacements

[26,

13].

~~~~~~ ~ ~~~~

CuGe03 T=300K

THz

~~

5 ^~

~

4

,

3 ~

~

i

o _o

0 .00 0.20 0.40 0.00 0.20 0.40

~)

^{q DIRECTION [0 0 1]}

~)

q DIRECTION Il 0 1]

Fig.

13.

Dispersion

relations of

phonons

_m the directions [0 ⁰

ii

and

il

0

il

at _room temperature [33].

to that

model,

the

Iargest displacements

_are observed for the Cu-atoms which _move

along

the _{c axis,} and for the

O(2)-atoms

which _move in the

(a, b) plane,

however with _very small

relative values

[13]: u[~/c

+w

0.0020, u[j~j la

+w 0.0018 and

u[~~j16

+w 0.0008. The

resulting

Iattice distortion _can be described _{as an}

altemating

rotation of the

Ge04

_groups around the Ge atoms [27] or around the

O(1)-O(1)

axis

[13],

^which

altemately

induces

positive

or

negative displacenients

of CU atoms

along

_c, and

eventually

_a small

displacement

of Ge _atoms

along

b

[13].

^{Such sma1I}

displacements explain,

_even

quantitatively,

how dillicult is the detection of

pre-transitional

structural fluctuations from neutron

diffraction, except

_very near

Tsp [30].

For

the _sanie reason, and

despite

_very careful measurements

[25,32-36], performed

in

particular

in the

vicinity

^of

ksp,

it has _net been

possible

_so far _to observe _any

phoiion softening

when

approachiiig _Tsp. Examples

of

phonon dispersion

_curves measured in the [0 ⁰

ii

and the _{[1 0}

ii

directions [33] ^at room

temperature

_are shown _m

Figure

13.

Only

_very weak

changes

_are

observed _as T

decreases,

_even for T _<

Tsp (after

corrections due to the usual Bose

factor).

No

phonon softemng

has

yen

^been detected in

CuGe03.

This

negative

result _may be attributed either to trie weakness oi trie relevant

phonon

_{intensity or to} trie _nature of trie

phase

transition itself

(see Conclusion).

3.2. LATTICE DisToRTioN _{IN A} FIELD. In the D

phase,

the structural

properties

are

expected

_to be httle alfected

by

the

application

of _a

magnetic field,

at Ieast _up to the cnt- icaI value

Hc,

above which

begins

the incommensurate I

phase. According

to the usual

descriptions, Hc

_is

directly

related to the transition

temperature Tsp

^{and the}

spin-gap

A _ex-

pected

to characterize the

magnetic

excitation

spectrum

^{of dimerised chains}

[11] (cf.

^sect.

4):

Hc

+w1.48

kTsp/g/~B

~ 0.84

A/g/~B, and,

in Iow fields,

Tsp

^{should decrease}

quadratically

with H

[7, 8]:

ATsp/Tsp

+~

-tlg/tBH/l2kTspl0lll~

Dilferent

techniques including K-ray [24], magnetization [37],

^{ultrasonic studies}

[38, 39]

^and

neutron

scattering _[28]

have shown that such _a behavior is weII observed in

CuGe03 Figure

lob

gives

the evolution with

temperature

of the maximum

intensity

of the satellite

[1/2,3,1/2],

for

two values of the

magnetic

field. H

= 0 and H

= 9.85 T. As

expected. T~p(H) displays

_a

shght

decrease. of about

13%

in this field _range. The

corresponding experimental

data _are

summarized in

Figure

10c.

They

are weII

reproduced by

the above

quadratic

relation, but with

a

pre-factor

t

+w

o-S,

slightly Iarger

than the theoretical

evaluations,

t

+w 0.36 0.44

[7, 8j.

^This

discrepancy

_can be attributed _to the precursor Iow-D structural fluctuations

(Fig.

ii

),

which _are

neglected

in the usual theoretical

approaches

based

essentially

_{on mean} field

approximations.

In _a

field,

the most

interesting

^feature is

expected

to _occur above the critical field

Hc,

in the I

phase.

The Iattice

incommensurability characterizing

that

phase

has been

proposed

to be

described

by

_a soliton-Iattice model

[40-43],

associated with _a

field-dependent

incommensurate

wave vector

k~p(Hl.

In the

simplest

case, trie lattice distortion _con be viewed _{as a}

staking

of dimenzed

regions regularly spaced by

_a 3-dimensional _array of demain watts

ii-e-

the

"solitons"

carrying

each _{one a} spin

1/2.

The

magnetization

recovered above

Hc

is then

directly

related to trie number of solitous. The cell parameter ^{L of} trie soliton lattice

(representing

two times the soliton-soliton

distance)

is

directly

related to the

departure

from the commensurate

wavevector

ksp

=

k~p(0), namely:

jk~~iHj k~~joj

_r~ 2~

IL

_c~

MjHj

This

quantity

would be _an

increasing

function of

field,

whereas trie soliton half-width r should be

weakly

field

dependent [40-43]. Moreover,

trie Fourier transform of trie Iattice distortion _is

expected

to contain

only

odd harmonics

(+3 ksp,

+5

k~p,.. ),

with

rapidly decreasing ampli-

tudes

[43]:

^{the Iattice modulation should be}

nearly

sinusoidal.

X-ray

diffraction measurements

[44, 45]

^bave

recently

confirmed trie incommensurate nature of trie

I-phase

in

CuGe03. Figure

14a sho>vs _serres of wavevector _scans

through

trie

là /2,1,5 /2]

satellite

performed

in trie

il

0

ii direction,

for fields below and above trie cntica1fieId

Hc.

At Iow

field,

_a

two-peak

structure is

observed,

which is due tu trie _use of _an incident

X-ray

beam

coiitainmg

two dilferent

wavelengths.

Above

Hc,

each

peak

is _seen to

split

into two

satellites, giving

_use

finally

to a

four-peak

structure. For these

satellites,

the

component

^of

k~p(H) along

the chain axis is _seen to become mcommensurate. The

intensity

of bath the commensurate and incommensurate reflections _are

given

_{as a} function of field in

Figure

14b.

Two

important

features of the D-I transition emerge from the

present

data obtained _{on pure}

CUGe031

the

step-Iike

behavior at

Hc

and the

relatively

weak

hysteresis ôHc

+w o-1

T,

the

latter elfect

being

aise

reported

from

magnetization

measurements

(see Fig. 6) [22].

Bath results _are

signatures

of the first-order character of the

phase

transition at

Hc,

which would suppose a

"pinning'

of the solitons. The

mcommensurability along

the chain _is observed to

increase with

H,

which, _m the soliton

model, corresponds

to a

decreasmg

soliton distance.

The recent

observation, by X-ray

diffraction

[45],

^of a

tiny

third-order-harnionic satellite

(with

relative

intensity

13

Iii

~

il (100-150) strongly

_supports the soliton-lattice model for

CuGe03

1000 ~~°~

£

750 ~

qp

^H=12.5T

~j

oJ ⁷⁵⁰

Îi

_ai

~

₂₅₀

Îà

o

à

500

Ù

400

aé

Zoo

fi

H=12.6T

~fl _~

500

o

400 300 zoo

ioo H=iz.95T

~2.48

_{2.49 2.50 2.51 2.52}

1(r,Î.u.)

zsoo

.

~j

500

à

É

(

~

2.0 12.2

0

2

Fig.

14.

ai

Scans

through

the [5

/2,1.5/2]

satellite _m the

il

0

il

direction, at 5 K,

showing

the

occur-

rence of _an incommensurate phase above Hc

+~

ii-fi T [44];

hi

Field

dependence

of the commensurate

(closed symbols)

and incommensurate

(open symbols) showmg

the

step-like

behavior at Hc [44].

A soliton width could be evaluated.

Along

the

chain,

the relative half-width is of the order of

r/c

+w 10

-15,

which

implies

_a

non-negligible overlap

of the demain watts.

Finally,

in the Iimited

explored

field _range

(between Hc

and 13

T),

r is observed to be

practically

field

independent,

_as

expected.

4.

Magnetic

Excitations and Fluctuations

4.1. THE DIMERISED D PHASE. The

investigation

of the

magnetic

excitations in the D

phase

is

important

for _{two reasons.} As

explained

in the

introduction,

_{an energy gap} ~l should be _seen in the energy spectrum

[11] and,

ⁱⁿ such a dimerised

phase,

the elfect of _a

magnetic

field should reveal _a very

peculiar

behavior. This latter

point

^is a

general

feature of the _so- ca1Ied

"spin-Iiquid systems" [46].

^{whose dimensed and Haldane}

spin

chains

belong

to. In such

systems,

the

elementary

excitations _are

actually

defined with _an additional

quantum

number S =

1,

where S

represents

the total _spin operator. ^Due to this

property,

the

application

of _a

magnetic

field should result in _a Zeeman

splitting

of the

elementary

excitation

spectrum, and, additionally, specific Iow-energy

fluctuations should

develop

in the

spin

system.

In the D

phase

of

CuGe03,

weII defined excitations have been observed

by

neutron inelastic

scattering (NIS)

measurements

[28, 47].

^{For H} = 0, the

corresponding dispersion

_{curves are}

shown in

Figure

là. In that

figure,

the value _q

(or

_{qb or}

_q~)

= 0 refers _to the

point [0,1,1/2]

of the 3D

reciprocal

_{space given} in

Figure

9a. It

corresponds

to the AF wavevector for the

spin

system: kAF

"

(0,1,1/2]. Dispersive

elfects _are

clearly

observed in trie three

crystallographic

directions. From these _{curves. a} determination of the

magnetic couplings

bath

along

and

perpendicular

to the chains _con be made

[28, 47].

In

Figure lsb,

the data obtained

along

c*

are

compared (the

^fuII

Iine)

with the usual

expression

for dimerised chains

(with magnetic

altemation _a

=

Jc2/Jcil _[11]

Eq

= [~l~ +

(El El) sin~(2~qc)]~/~

where A

[+w 1.05

Jci(1- a)~/~]

is the

expected

_{energy gap}

_[48]

and

EM

_"

~Jci(1+ a)/4

represents

the _maximum energy in the

dispersion: EM

+~ là mev

(+w 170

K)

K. For

Jci

and _a,

one then obtains the

following

evaluations:

Jci

+~

122 K and _a

+~

0.92

[28].

^{For small values} of _qc, the

agreement

^{between that model} and the data is however

only approximate.

The

dashed Iine shown in the _same

figure

would better evaluate the effective

velocity iv

+w là?

K)

of the

elementary

excitations. ~vith _u

=

~Jc /2,

_as for uniform chains

[3],

one would obtain _an

"apparent" exchange coupling Jc

+w 100 K

[28]. Finally,

it is worth

mentioning that,

if _a next-

neighbor

interaction

(J)i) along

the chain is taken into

account,

the

slight

misfit observed _at Iow values of _qc is reduced. Within _a

simple

Holstein-Primakoif

procedure,

_a

good agreement

with the data _con be obtained for

J(i /Jci

~ o-1?

[49].

^{The value of this ratio} compares weII with that

(J(/Jc

+w

0.2)

of the recent model

proposed

for

analyzing

the

susceptibility

in the U

phase (see

Sect. 2 and

[18]).

For the

dispersion along b*,

the neutron data _are showu in

Figure

lsc.

They

_are

compared

with _a standard

"spin-wave"

model

(fuit fine),

which

yields,

for the

exchange coupling

_in the b

direction, Jb

~ 10 K. similar

analysis performed along

a*

grues

Ja

+w1 K

[28, 34].

Due to these interchain

couplings,

several gaps can therefore be observed in the whole 3D

reciprocal

_space. However,

neglecting

the rather small

dispersion along a*, essentially

two gaps have to be considered. The lowest energy gap,

EGI

= 2 + 0.05 mev

(=

23 + 0.6

K).

occurs, in

particiilar,

at the

antiferromagnetic

wavevector

kAF

_"

[0,1,1/2j,

and the

largest,

EG2

_" S-1+ 0.25 mev

(=

66 + 3

K),

at the _center of the Brillouin _{zone, i.e.;} at ko "

[o, 0, 0].

^A

sketch of trie

dipersion

_curves with these dilferent _gaps is given m

Figure

9b. Trie

spin-Peierls

20

t₌ 0.75

15 c*

~

) a)

~~

20

É~

~~~~°3

~ b)

ç

^{15 T=1.8K}

b* k=0

j

5

Q

10

a* h=

lj

^wp ₅

~

0 o-S ' 5 ~

0 O.1 0.2 0.3 0.4 0.5

q

(À')

~c (~~.~')

CUGeO~

T=1.8K

~i

Q=(0,-1+q~,l12)

(

5

~

E~

cl

LU

~0

_0.2 0A 0.6 0.8

q~(r.l.u.)

Fig.

là.

Dispersion

relations of the

elementary

excitations in the D

phase: along

the 3 directions a*, b* and c*, from [34], and

along

c* and

b*,

from [28].

gap A of the usual ID models _is identified to the Iowest energy gap

EGI,

1-e-; in

CuGe03,

ùh e

EGI

+~ 23 K.

Raman

scattenng

measurements bave been shown to olfer _an

interesting

_way of

probing

the

magnetic

fluctuations _in

CuGe03 [50].

Thon

technique

is

basically

sensitive to the

deiisity

of

states

and, accordingly,

_any maximum _{or minimum}

present

ⁱⁿ the excitation spectrum should

result in _a

"peak"

_in the observed Raman

intensity.

For the dimerised D

phase,

the Raman data _are shown _in

Figure

16a. With

respect

to NIS

data,

_a factor two occurs in the _energy scale: _it results from the fact that

4-spin (and

non

2-spin)

correlation functions _are

probed

in a

magnetic

Raman _process

[51].

^Peak

I,

_at E

+~

32

cm~~

(+w 46

Ii)

is therefore _seen to

correspond

_very well to the lowest _{energy gap}

EGI (2EGi

₌ 46

K).

Peak 2 _~N-as attributed to _a "Fano" mode [52]

resulting

from _a

strong couphng

between _a

phonon

and the

magnetic

excitation

continuum,

rather than _to the

highest

_gap

EG2,

which due this elfect is net

easily

visible. Peak

3, however, occurring

at _+w 230

cm~~

(+w 330

K)

is

dearly

the

signature

^{of the}

T

(K)

, ,

, 80

~

",

d) _{20 T}

b ..~]~_,

i _b)

' 60

1

3

^*4

~

17 ~Î

~fl

~ _§~

£~~j_j """ (

~

2 9

~-

0 100 200 300 400 500 200 300 400

Raman shift

(cm

_~) Raman shift _cm

Fig.

16. Raman scattering intensitj, [50, 66]_:

a)

In the D

phase (peaks

1 and 3 correspond to the gap

EGI and trie _maximum EM of the

magnetic dispersion curves); b)

In the SRO

regime

of the U phase

(trie

_arrow shows the peak associated with the

maximum

El

of the

magnetic

_{spm wave}

continuum);

ci

In the HT

regime

of tbe U

phase showmg

^the

development

of

low-energy

fluctuations _as T increases;

d)

At T

= 4.2 K for H

= 1 and 20 T, _i.e., in the D and I

phases respectivelj, (as

discussed in the text,

the

peaks

shown

by

trie _{arrow are} the

signature

of

(quasi) propagative elementary excitations).

In all these

figures,

the other peaks _are associated with

phonons

[50].

maximum

EM (2EM

~ 340

K)

of the

magnetic dispersion

_{curves as}

they

_are observed in NIS measurements.

Due to the additional

quantum

number S

= 1 mentioned above, one

expects

the

application

of _a

magnetic

field _to result in _a Zeeman

splitting

of the

elementary

excitation branches. The first evidence of such _an elfect _was obtained

by

electron

spin

resonance

(ESR)

measureinents

[22].

^"ESR transitions" _are defined _as transitions associated with _a

change

Am

= 1 of the

magnetic quantum

^{number, but with} no wavevector

transfer,

_{i. e.,}

Aq

= 0. In dimerised

chains,

two kinds of such transitions _con be

induced,

between excited states and from the

grouiidstate.

Transitions between excited states _con be realized in any

points

^{of the} Brillouin _zone and, in

particular,

at the lowest gap

positions.

As shown

previously

for Haldane

spin

chains

[53],

such transitions

correspond

to the "standard" ESR

signais

observed at the Zeeman

frequency (for isotropic systems

as

CuGe03,

_u

+w

gpBH) _[54].

The

temperature dependence

of such ESR

signais

_is charactenstic of _an activated _process.

Assuming

_a Boltzmann distribution

betweeii the Zeeman

split

states, the data for the

integrated intensity

of this "standard" ESR fine _are well

explained by

this model

(the

fuit fine _in

Fig. 17a) [20j.

^{An evaluation of the}

Iowest _{energy gap} of the

system

can then be obtained: £h

+w 23.5

K,

which is in remarkable

agreement

with the NIS determination for

EGi Since,

in dimerised

chains,

the

groundstate

_is

a S

= 0 state, ESR transitions _con aise be induced from the

ground

state, at Ieast if _m

= +1

excited states _are aise

present

at the Brillouin _zone center

(ko

_"

[0,0,0]).

This is

actually

the _{case in} dimerised chains

[11].

^{A few}

examples

of such ESR

signais

observed in

CuGe03

are shown in

Figure

17b. The

extrapolation

to zero field

provides

_a direct evaluation of the gap ^at

ko.

The obtained value

+~ 1340 GHz _{(+~ 64}

K)

_agrees weII with the NIS determination of the second energy gap

(EG2

~ 66

K).

This ESR

investigation

confirms the

representation

of the

elementary

excitations given in

Figure

9b. It _proves aise

that,

_{in a}

field,

_a Zeeman

iaoo

T = 4 K

Î

@@

Î

= ~

b)

q

~

¹⁴⁰⁰

q§

--

1397 GHz

~'

ffi

^~ ₁₃₀₀

1267GHz

1200

~)

l1DD

',,

^{~~~~ ~~~}

',,

0 5 10 15 20 0 2 4 6 8 10 12 14

T ~J~) B fresla]

3.5

CUGeO~

3.0 _T=6K

HJJ(6,-1,0)

Cl Ç_w 2,5 g=2 18

E

~ 2. 0

j

p _5

,o

0.5

0 20 40 60 80 100

H

(koe)

Fig.

ii. Elfect of _a

magnetic

field _on the

elementary

excitations

m the D phase:

a) Integrated

intensity ^{of the} "standard" ESR line

(see text)

[20];

b)

Zeeman

splitting

of the miiform mode at the Brillouin _zone center: ko

= (0, 0. 0] (22];

c)

Zeeman

sphtting

of the AF mode at kAF

=

(0,1,1/2]

[28].

sphtting

does _occur at the Brillouin _zone center

(1.e.,

at

ko

_"

[0, 0,

0]

[22]. Directly

observed

by

VIS measurements

[28, 55],

a similar Zeeman

sphtting

has been shown to

develop

at the

antiferromagnetic point kAF

_"

(0,1,1/2].

Such data obtained _up to about 10 T

[28],

are

displayed

ⁱⁿ

Figure

17c.

The additional

Iow-energy

fluctuations associated with the S

= quantum number _were first

predicted

for Haldane _spin chains

[56, 57].

Associated with _two

elementary

excitations of _energy

Eqi

and

Eq2, ^they

^{result from} transition processes

involving

the energy dilference

Eqi -Eq2

For that _reason,

they

form _a

Iow-energy continuum, which,

in _zero

field, spreads

around E

+w 0.

In the dimensed

phase

of

CuGe03,

these fluctuations have been shown

[58]

to contribute

dominantly

to the nuclear relaxation rate

(1/Ti)

of the CU nuclear

quadrupole

_resonance

(NQR)

_[59]

(see Fig. 18).

Due to these _processes,

1/Ti

is

expected

to decrease

exponentially

as a function of the _gap ~l and T

according

to the

general

Iaw

+~

exp(-A/T) _[56, 57].

Such behavior

explains

rather well

[58]

^the

NQR

results measured in the dimensed

phase

of

CuGe03