Transport properties of the isostructural organic conductors Cu(L)I with itinerant charge carriers strongly coupled to Cu2+ localized spins

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Transport properties of the isostructural organic conductors Cu(L)I with itinerant charge carriers

strongly coupled to Cu2+ localized spins

G. Quirion, M. Poirier, C. Ayache, K. Liou, B. Hoffman

To cite this version:

G. Quirion, M. Poirier, C. Ayache, K. Liou, B. Hoffman. Transport properties of the isostructural organic conductors Cu(L)I with itinerant charge carriers strongly coupled to Cu2+ localized spins.

Journal de Physique I, EDP Sciences, 1992, 2 (5), pp.741-751. �10.1051/jp1:1992177�. �jpa-00246580�

Classification

Physics

Abstracts

72.20M 72.15Q 75.20E

Transport properties of the isostructural organic conductors

Cu(L)I with itinerant charge carriers strongly coupled to Cu2+

localized spins

G.

Quirion (I),

M. Pointer

(I),

C.

Ayache (2),

K. K. Lieu

(3)

and B. M. Hoffman

(3)

(')

Centre de Recherche _en

Physique

du Solide,

D6partement

de

Physique,

Universit6 de

Sherbrooke, Sherbrooke,

Qu6bec,

JlK2Ri, Canada

(2)

D6partement

de Recherche Fondamentale de la Matibre Condens6e, Laboratoire de

Cryophysique,

C-E-N-G., 38041 Grenoble, France

(3)

Department

of

Chemistry

and Materials Research Centre, Northwestem

University,

Evanston, Illinois 60201, U-S-A-

(Received

16 October J991,

accepted

in

final form

J3 January 1992)

Abstract- We report ^{the microwave and} transport

properties

of the isostructural

organic

conductors

Cu(L)I

(L ₌

phthalocyanine ~pc), tetrabenzoporphyrinato (tbp), triazatetrabenzopor- phyrinato (tatbp)).

In these

compounds

the

magnetic

moments (S

=1/2)

of the Cu2+ ions are

found to be

strongly coupled

to the conduction electrons which results in dramatic effects _on the transport properties. Whereas the conductivity at room temperature ^{is found} to be metallic, it decreases

by

several orders of

magnitude

below 100 K and shows _a

large positive magnetoconduc- tivity.

These effects _are discussed in terms of

scattering

of the free carriers

by

the localized

spins (Cu2+,

S =1/2). At low temperatures

(T«10

K), _we have also observed that the microwave

conductivity

is enhanced

relatively

to the dc _one and it

generally

decreases with the

magnetic

field _{; over} the _same temperature range the dielectric constant increases with the field. These effects at low temperature are rather believed to be related to a new relaxafiion mechanism between the chain of localized and the itinerant

spins.

I. Introduction.

The

study

of

quasi-one-dimensional organic

^{conductors has revealed} a wide

variety

of

interesting

features in the

past

^few years

(Peierls distortion,

CDW and

SDW).

Another

major

advance in

organic

metal research _came with the stabilization of _a

superconducting

state in the

(TMTSF)2X

salts

(X

=

PF~, ASF~, Cl04, etc.) [Ii

and _more

recently

in the

organic family (BEDT-TTF)~X (X

₌

Re04, _I~, Cu(SCN)2) 12-4]. Although

the search for

high

critical

temperature (high-T~) superconductors

is the main

goal

in the

investigation

of

organic conductors,

it is worthwhile to draw attention to

organic

conductors which exhibit _some unusual

properties. Among them,

the

(perylene)~ M(mnt)~ (with

M

=

Pt, Pd) family [5, 6]

has got its own

reputation

due to the

possibility

of

having

_a ID electron gas

coupled

to a chain of localized

spins (S

=

1/2).

In these

compounds,

it has been

proposed

that the

spin-Peierls

distortion observed _on the

M(mnt)2

stacks induces _a metal-insulator

phase

transition _on the

perylene

stacks.

Cu(pc)I (copper phthalocyanine iodide) [7]

is another

example

of _a ID electron gas

coupled

to a chain of local moments

(S

=

1/2).

The main difference between this

compound

and the

perylene

^salts is that for

Cu(pc)I

^{the itinerant and localized}

spins

_are both _on the _same stack.

Although

the

magnetic

and EPR measurements

[7-9]

have revealed that the local

spins

_on ^the

Cu2+ sites _are

strongly coupled

to the conduction holes associated with the pc

ring,

_no metal- insulator

phase

transition is observed. However this

strong coupling

seems to have dramatic effects _on the transport

properties

whereas the

conductivity

is found to be metallic down _to 100

K,

it decreases

by

several orders of

magnitude

at lower

temperatures II 0]. Moreover,

the

positive magnetoconductivity

observed at low

temperatures suggests

^{that this}

huge

conduc-

tivity drop

results from _a

magnetic scattering

_process

involving

the local _moments. This assertion is also

supported by

the

conductivity

measurements realized _on the

Cu~Nii _~(pc)I alloys ill -13].

In these

compounds,

where a fraction of the

paramagnetic

Cu2+

(S

=

1/2)

ions

are

replaced by diamagnetic

^N12+

(S

₌

0) ions,

it has been shown that the

conductivity

maximum is shifted toward lower temperatures as the local moment concentration _x is

reduced. In these unusual

conductors,

_{new types} of

phenomena

_are also observed at lower

temperatures (T~BK).

For

example,

the

disappearance

of the EPR

signal

without any associated loss of

paramagnetism [8]

coincides with the enhancement of the microwave

conductivity (16.8 GHz)

relative to the dc measurement

[12].

These anomalies have therefore been ascribed _{to a new}

type

^{of relaxation mechanism between the free carriers and} the local

moments mediated

by

the RKKY interaction

(Ruderman-Kittel-Kasuya-Yoshida).

Although

_we

already

know that

Cu2+

_{local moments are}

responsible

for the

peculiar physical properties

observed for

Cu(pc)I

and

Cu~IQij _~(pc)I ill, 12],

_more information is needed to characterize the

physical

_parameters involved in these

phenomena.

In

particular

it

would be

interesting

to estimate the relevance of the Cu-Cu

spacing

_on the observed

properties.

This has been

partly

done in

CujNii _~(pc)I compounds [I1, 12]

where the _mean Cu-Cu distance could be

easily

varied upon

doping.

Another

possible

_way of

doing

this is _to

study

isostructural

compounds

^like

Cu(L)I

in which the lattice

parameters

can be

changed

via the modification of the

ligand (L). Fortunately,

the chemical

flexibility

of the

porphyrin macrocydes provides

this

opportunity. Up

to now, three variants of the

porphyrinic

skeleton have been examined for this purpose,

tbp (tetrabenzoporphyrinato),

_pc

(phthalocyanine)

and

tatbp (triazatetrabenzoporphyrinato) macrocycles [14, 15].

In this paper ^we report ^the

transport properties (thermoelectric

_power, dc

conductivity

and microwave

conductivity

16.8

GHz)

of the isostructural

compounds Cu(L)I (L

=

tbp, tatbp, pc)

_{as a} function of

temperature.

We also present ^{the microwave}

conductivity

and dielectric

constant as a function of

magnetic

field.

Although

that _some of the results obtained for

Cu(pc)I

and

Cu(tatbp)I

have been

published

in _some extent

previously [10-13,

17,

27],

its inclusion in the present paper is suitable _{as we} wish _to present a survey of the transport

properties

within the

family.

The results found in these isostructural

compounds

^reinforce the trend found

previously

^{in the}

Cu~Nii_~(pc)I alloys [I Il.

The metallic character of these

compounds

is

clearly

established and the

magnetic scattering

of carriers

by

local moments is confirmed. A

large positive magnetoconductivity

is measured for all

compounds

and

frequency

effects are observed at low

temperatures.

As for the

Cu~Nii _~(pc)I alloys [I II,

these

peculiar properties

_are discussed in terms of itinerant-localized

spins

interaction and indirect

exchange

interaction between local moments which _seems to be

extremely

sensitive to Cu-Cu distance.

2. Structural and

magnetic properties.

The

magnetic properties

of the

Cu(L)I organic

conductors

~L

_{= pc,}

tbp

and

tatbp)

_are

already

well documented

(Nuclear Magnetic

Resonance

NMR,

Electronic

Paramagnetic

Resonance

EPR, magnetic susceptibility) [7-9, 16, 17]. Here,

_we summarize the earlier structural and

magnetic analyses

realized

by Ogawa

et al.

[7-9]

and Liou _et al.

[17]

in order to

help

the discussion of the transport

properties.

All

Cu(L)I compounds presented

here have been found to be isostructural the

nearly planar Cu(L)

molecules form linear metal-over-metal stacks

separated by

linear chains of

Ii

ions.

Here,

the iodine chains

provide

the

partial

oxidation

(1/3)

of the

Cu(L)

stacks to ensure a metallic character. The

charge

carriers

belong

to the _gr molecular orbitals of the

ligand ring (L

₌

tbp, tatbp, pc)

and the

resulting

band

filling

is

5/6.

The

peculiar aspect

^of these

compounds

_comes from the fact that the center of the

ligand (L)

is

occupied by

the

pararnagnetic

Cu2+ ion

(d9,

S ₌

1/2),

which

gives

rise to an

array of localized

spins coupled

to ID electron gas. The coexistence of the itinerant and localized

spins

is confirmed

by

the

magnetic susceptibility

measurements which show _a Curie-

Weiss contribution associated with the localized

spins

and _a

temperature independent

component

(Pauli-like)

_X« associated with the itinerant carriers. Down to 10 K the results _are

normally

well-fitted _to

x(T)

=

~~§

_~ ^{+ x«.}

⁽¹⁾

The deduced Curie constant C confirnls that there is

effectively

_one S

= 1/2

spin

_{per copper}

ion. The Weiss

temperatures

^{o which}

provide

_an estimation of the Cu-Cu interaction _are

respectively (-

4.0 _± 0.I

K)

and

(-

6.9 ± 0.3

K)

for

Cu(pc)I

and

Cu(tatbp)I. Moreover,

the NMR

spin-lattice

relaxation measurements

[9]

indicate that direct

exchange

interaction

between Cu

spins (J/k~

_~ 0.3

K)

is _an order of

magnitude

less than that inferred from the

susceptibility

measurements.

Consequently,

it has been

suggested

^that this

large

Cu-Cu interaction arises

primarily

from indirect

exchange coupling

of the RKKY

type.

^{This result is}

supported by

the EPR

spectrum [12]

which exhibits _a

single axially symmetric

line that

possesses a temperature

dependent g-value (bottleneck regime).

All the

magnetic

_measure-

ments discussed here

clearly

indicate the existence of _a strong

coupling

between local and

itinerant

spins

in the

Cu(L)I compounds.

3.

Experimental

and results.

3.I THERMOELECTRIC _POWER MEASUREMENTS. -The thermoelectric power data _were

obtained

using

_{an apparatus} similar to the _one described

by

Chaikin and Kwak

[18].

The

samples

were mounted _on 17 _~Lm pure

gold

wires and contacts were made

using gold paint.

A slow

altemating

temperature

gradient

with _a maximum

temperature drop

^of I K _was

applied along

the easy conduction axis. The

temperature gradient

was measured with standard

Chromel-Au

(0.07-at.f6 Fe) thermocouples.

With this

apparatus,

we

directly

obtained the

thermoelectric power S of the

sample,

the small contribution of the

gold

leads

(SA~ w I

~LV/K ) [26] being neglected.

As shown in

figure I,

the

temperature dependence

of the thermoelectric power of

Cu(tatbp)I

and

Cu(tbp)I

are very similar _; it exhibits two distinct

quasi-linear regions

for T above _or below 60 K. For

Cu(pc)I,

a linear

region

is also observed at

high temperatures

but contrary to the others it is almost constant below 150 K. We believe that this difference is _not intrinsic to the material but

likely

related _to the poor

quality

of the

Cu(pc)I crystals.

^Visual

inspection

of these

crystals frequently

revealed

purple

reflections

indicating

the presence of

an

insulating phase Cu(pc).

60

tatbp 50

40 tbp

q~

~ 3Q

w PC

~a

20 p

a a

lo

~ o o

O

loo 200 300

T(K)

Fig.

I. Thermoelectric power as a function of temperature ^{for the} isostructural

organic

conductors Cu(L)I.

Cu(pc)I

(D),

Cu(tatbp)I

(Zi) and

Cu(tbp)I

(Q).

According

to the

tight-binding

band

model,

the thermoelectric power of _a one-dimensional metal may be derived from the Boltzmann

equation

_:

gr~k(

T

cos

(~rv/2) r,(g)

~

3 _e 2

tjj

sin~ ₍

w v/2

)

^~ T

(8 )

t~

~~~

where tj ^is the transfer

integral (4

_tj is the

bandwidth), k~

and _e

respectively

the Boltzmann constant and the electronic

charge,

_v

=

2 _p the number of conduction electrons per site

and _p the

degree

of oxidation

(p =1/3). Finally, r(8)

and

r'(8)

_are

respectively

the

scattering

time and its energy derivative. The

thermopower

data

clearly

indicate that the band

structure is similar for the three

compounds,

moreover a

positive

S value is

compatible

with _a

5/6 filling

of the

gr molecular band. If _we

neglect

the contribution from

scattering

(r'Iv ),

a linear fit above 100 K

(200

K for

Cu(pc)I) yields

for the

longitudinal

^bandwidth 4 tjj ⁼ 1.2 _± 0.I

eV,

_a value

commonly

found in

organic

conductors. For the moment, the

change

of

slope

observed around 60K is attributed to the contribution

arising

from the

scattering

_{processes r} '/_r

(

_e

).

3.2 MicRowAvE CONDUCTIVITY. -The microwave

conductivity technique requires

_no

electrical contact to the

crystal

and is

exceptionally

well

adapted

for

needle-shape samples.

These measurements were carried out

using

the standard

cavity perturbation technique [19].

A

rectangular cavity operating

at 16.8 GHz is used in _a

TEio2

transmission mode. The

sample

is located in _a

region

^of maximum electric field with the needle axis of the

sample parallel

to the field. The _resonance

frequency

shift

Af/f

and the variation of the

quality

factor

A(1/2 Q) following sample

insertion _are used to determine the microwave

conductivity

and

dielectric constant

according

to the

quasistatic approximation applied

to _an

elongated ellipsoid sample [20]. Sample's geometry

^{and absolute}

conductivity

value _ensure that the skin-

depth regime

_was never reached for these three

compounds

at all

temperatures.

In

figure 2,

the

temperature dependence

of the microwave

conductivity (16.8 GHz)

is

presented

for the three

Cu(L)I crystals.

The absolute values at 300 K _are

given

in table I _; the lower

conductivity

of

Cu(pc)I

^is

again

believed to reflect the poorer

quality

^{of this}

^compound.

Nevertheless, ^the

temperature dependence

is very similar for all

compounds

: from 300 K down to a

temperature T~,

where _a broad maximum is

observed,

the

regime

is metallic

below

T~

the

conductivity

decreases

by

orders of

magnitude

down to a

temperature

Tp

below which the

conductivity

is

nearly

constant. In the _same

figure,

the full line

corresponds

to data obtained with _a

magnetic

field of 8 Tesla

applied perpendicular

to the

conducting

axis

(transverse magnetoconductivity).

For _{now on,} the

subscript

M and P

respectively

refer _to the maximum of

conductivity

and the

apparition

of _a

plateau

on the

conductivity

at low temperatures. ^{In the metallic}

regime (T~ T~),

_no measurable mag-

netoconductivity

is observed for

Tp

_~ T

~

T~,

_a

positive magnetoconductivity

is observed with _an

increasing amplitude going

from

Cu(pc)I

to

Cu(tatbp)I

and to

Cu(tbp)I.

For

Cu(pc)I

the

magnetoconductivity

at 10 K is

only

2 fib, ^{this is}

why

it is not visible in

figure 2, compared

to 15 fib for

Cu(tbp)I.

Below

Tp,

the

magnetic

field

depresses

the

plateau

and shifts it to lower temperatures ; as it will be shown

further,

the

magnetoconductivity

reveals many structures for this

temperature

range.

~3

~2

I

~

~~ i ^u

I 'i

U 10°

cZ

d io~~ _T

P

~~-2

~~-3

lo loo 400

T(K)

Fig.

2. Microwave

conductivity

(16.8 GHz) _{as a} function of temperature ^{for the} isostructural

organic

conductors Cu(L)I at two

magnetic

field

amplitudes

H

=

0T

(symbols)

and H

=

8T (full line).

Cu(pc)I

(D),

Cu(tatbp)I

(Zi) and

Cu(tbp)I

(Q).

3.3 DIELECTRIC CONSTANT.-Tl~e dielectric _{constant may}

only

be measured _at low

temperatures

^{when the}

conductivity

has

sensibly

decreased. This is

why

the data shown in

figure

³

give

^the temperature

dependence only

below 20 K. As for the

conductivity,

the dielectric constant decreases with

decreasing

temperature ^and a

slope

variation is observed around

Tp.

When _a

magnetic

field of 8 Tesla

(solid

line in

Fig. 3)

is

applied,

the dielectric constant increases for the three

compounds.

Its appears also that the absolute value of _e scales with the

corresponding conductivity (see Tab.1).

Table I. Various parameters extracted

Jkom

the temperature

dependence of

the microwave data

for

the isostructural

organic

conductors

Cu(L)1.

cu(pc)I cu(tatbp)I cu(tbp)I

Cu-Cu 3.213 ± 0.002

distance*

«~oo~ 67 _± 310 _± 10 220 _± 10

«~~ 0.21 _± 0.01 0.75 _± 0.02 1.3 _± 0.I

e~~ 180 _± 10 630 _± 5 300 _± 100

T~

^{150±20 90±5 83±5}

Tp

8.0 _± 0.2 6.5 ± 0.2 3.3 _± 0.2

TJpR

^{8 6} _~ ⁵

* See OGAWA M. _ei al., Phys. Rev. B 39 (1989) 10682.

4000

/ 1'

a

/~ y

f

l000 ~f

~Afli

I &A~

~P I'

O

AA /

~

'i / G(

o°~l'

/y

nn° / Tp

n

II

loo

I lo 40

T(K)

Fig.

3. Microwave dielectric constant (16.8 GHz) as a function of temperature ^{for the} isostructural

organic

conductors Cu(L)I at two

magnetic

field

amplitudes

H

= 0 T

(symbols)

H

= 8 T (full line).

Cu(pc)I

(D),

Cu(tatbp)I

(Zi) and

Cu(tbp)I

(Q).

3.4

FREQUENCY

EFFECTS. -In order to understand the nature of the microwave conduc-

tivity,

we compare in

figure

4 the

temperature dependence

of the dc and microwave conductivities of

Cu(tatbp)I

obtained at 13.5 GHz

[from

Ref.

[27]]

and 16.8 GHz. Between

~~ 3

lo ~

Cu(tatbp)I

) iol

~i

e 10° '

~

10~l '

l

lo-2

lo loo 400

T(K)

Fig.

4. Normalized

conductivity

_« (T)/« (300 K) of

Cu(tatbp)I

_{as a} function of temperature at tllree different

frequencies. f

=

27 Hz (---), 13.5 GHz ) and 16.8 GHz (D).

10 K and 300

K,

the two sets of data remain in

good

_agreement. However _as the

temperature

is further decreased _a

large

deviation is observed: the microwave

conductivity nearly

saturates whereas «~~ continues to decrease down to 2 K. The saturation of the microwave

conductivity

is

clearly

_a

frequency effect,

the

higher

the

frequency

the

higher

the

conductivity (see Fig. 4).

Similar

frequency

effects _are also observed in

Cu(pc)1 [12]

and

Cu(tbp)I

and

they

have also been observed in the

Cu~Nii_~(pc)I alloys.

In all these

compounds

the

sharp

departure

of the microwave data from the dc _{ones occurs}

approximately

at the temperature

Tp.

It is worthwhile _to mention here that the anomalous behavior observed in this

temperature

_range is also visible _on the EPR linewidth which

diverges [12, 17]

at _a

temperature T~pR

^close to

Tp.

In table

I,

both temperatures

Tp

and

T~pR

are listed for the

Cu(L)I compounds.

All these results

clearly

establish that the

conductivity

maximum is

effectively

related to a transport process for which

my «

I,

whereas the

conductivity

enhancement observed below

Tp

is ascribed to _some

frequency dependent

mechanism. For

these _reasons, the data will _now be discussed

according

to the two relevant

temperature

ranges, T

~

Tp

and T

~

Tp.

3.5 MAGNETIC _{MELD EFFECTS.} The microwave

conductivity

has been measured at fixed

temperatures

as a function of the

magnetic

field up ^to 10 Tesla. For the temperature range T ~

Tp,

the

magnetoconductivity obeys

_a

H~

power law for the three

compounds.

An

example

of this is

presented

in

figure

5 for

Cu(tbp)I.

This

compound

has been chosen because it shows the

largest positive magnetoconductivity.

The data _can be well fitted

(solid

line in

Fig. 5) by

the relation

~"~~~

=

(l

^+A

~~j ⁽³⁾

"

(0)

_TY

where

y =

2.1 _± 0.I and A

=

0.24 _± 0.01 K

~/T~.

o.6

o.5

O.4 Cu(tbp)1

(

' O.3

~

$

0.2

o-I

O-o

0 20 40 60 80 loo

H~(Tesla)~

Fig.

5.

Magnetoconductivity

Am (H)/« (0) of

Cu(tbp)I

as a function of H~ _{at selected} temperatures.

T

= 12 K (D), 10 K (m), 8 K (Zi) and 6 (A) the solid lines represent ^{the fit} obtained from

equation

(3).

We must recall that _a similar field

dependence

has been observed for the

Cu~Nii_~(pc)I alloys [I Ii-

For T~

Tp,

^the

magnetic

field

dependence

of the

conductivity

is not so

simple

since it

seems to show many

components.

^For

example,

in

figure 6a,

the

conductivity

of

Cu(tbp)I

at

2 K increases at low

field,

decreases

slowly

for H

~ 4

T,

reaches _a minimum and increases

again

at

higher

fields. The minimum decreases in

amplitude

and shifts to lower fields _as the

io.o

a) Cu(tbp)I

t

b

i.o

O

b) i

% f ~ o So

# aw

2 4 6 8 lo

~esla)

Fig.

6. -Microwave

conductivity

(a) and dielectric constant (b) of

Cu(tbp)I

_{as a} function of H _at selected temperatures. ^T = 1.9 K

(D),

3 K (m), ⁴ K (Zi).

temperature

^{is increased. The minimum} seems to be the result of _two

competing mechanisms,

the

positive magnetoconductivity varying

with

H~

as it is observed for T

~

Tp

and _a

negative

one at low fields _; the

negative component

is

progressively depressed

either

by increasing

the

temperature

or the distance between Cu

neighbors. Effectively,

this minimum is observed _at

higher

field in

Cu(pc)I

and

Cu(tatbp)I

where the lattice distance is shorter. In

figure 6b,

_we also compare the field

dependence

of the dielectric constant. We observe that the dielectric

constant starts to be field

dependent approximately

at the _same field _as the

conductivity

does.

This indicates that the microwave data _are

probably

not related _to ohmic losses _as it _was

already pointed

out

by

the observation of

frequency

effects in this

temperature

range.

4. Discussion.

Conductivity

and thermoelectric _power measurements indicate that the

Cu(L)I compounds

have the _same band structure. The fact that the

conductivity presents

a non-metallic character

below

T~

cannot be related _{to a}

phase

transition. The temperature

dependence

of the

conductivity

is rather similar to that found in

organic

conductors like

Qn(TCNQ)2

and NMP-

TCNQ 129]

where it has been

convincingly

demonstrated that disorder induced localization

leading

to non-metallic

conductivity

at low

temperatures. However,

_we have to

disregard

this

type

^of localization _as it cannot

explains

the observation of

large positive magnetoconductivity

in these

compounds.

We rather believe that this non-metallic behavior is related to the

scattering

of free carriers

by

Cu~+ local _moments

(S

=

1/2) along

the chain. The maximum in the

conductivity

^{would then} result from the

competition

between

phonon

^diffusion and

magnetic scattering,

^this last mechanism

being

dominant _as the thermal fluctuations _are

reduced. This assertion is

supported by

EPR and NMR measurements

[7-9]

^which showed _a

strong coupling

between free carriers and localized

spins. Moreover, conductivity

measure-

ments realized _on the

Cu~Nii _~(pc)I alloys

have shown that the

conductivity

maximum is

effectively

related _to the concentration _x of local moments ; the maximum is

pushed

to lower

temperatures

as x is reduced

[11-13]. Although

the Cu-Cu distance in

Cu(tbp)I

is not

available,

the _same trend is also observed in the

Cu(L)I compounds

_;

T~

decreases _as the

mean Cu-Cu

separation

is increased

(see

Tab.

I).

^If this result is

valid,

_{we can expect} that the lattice parameter

along

the chain in

Cu(tbp)I

is

longer

then the _one in

Cu(tatbp)I

and

Cu(pc)I.

The

magnetic scattering

is also confirmed

by

the observation of _a

positive magnetoconductivity;

^{for this} case an extemal

magnetic

field

partially

freezes the

spin degrees

of freedom and therefore reduces the

scattering

rate. As shown in

figure 2,

a

magnetic

field of 8 Tesla has _a

decreasing

effect

going

from

Cu(tbp)I

to

Cu(tatbp)I

and to

Cu(pc)I.

^This

clearly

indicates that the

strength

of the

magnetic scattering

mechanism between itinerant and localized

spins

is

strongly dependent

_upon the Cu-Cu

separation.

It is very

tempting

to invoke _a

Kondo-type

mechanism in order to

explain

the observation of _a

positive magnetoconductivity. However,

neither the

logarithmic temperature dependence

nor the

magnetic

field

dependence (HIT

)~ for the

magnetoresistivity generally

associated to

impurity

Kondo

[21, 22] scattering

_are observed in these

compounds.

In fact the Kondo

impurity scattering

should _not be used to fit _our data _{as we are}

dealing

^with concentrated

magnetic

systems.

Moreover,

the «localization» of the free carriers

by

the presence of localized

spins

must be understood in relation with the

dimensionality

of these conductors _: one-dimensional

systems

are

naturally

unstable and RKKY

interaction,

which is inferred from the EPR linewidth

II 2],

is

expected

to be _more

singular

in _one dimension that in three

dimensions. For the moment, even if _some authors

[23-25]

have studied the

coupling

between localized

spins

and conduction

electrons,

_no theoretical result could be used in order to

analyze

_our

conductivity

data.

At the lowest temperatures

(T

_~

Tp),

the microwave

conductivity

is

frequency dependent.

Following

the

rapid

decrease of the

conductivity

due to

magnetic scattering,

_a

frequency dependent plateau

is observed for all

compounds.

^{As it has been shown}

^again

^for

CujNii ~(pc)I alloys

II

-13],

this

plateau

_seems also to be related to the

strength

of the

spin- spin

interaction _or to the average Cu-Cu

separation (Tp

decreases with

x)

here the _same

trend is also observed in the

Cu(L)I compounds (Tp

decreases _as the Cu-Cu distance is

increased,

_see Tab.

I).

In order to

explain

this

frequency

^{effect in close relation} with the presence of localized

spins,

we invoke the

opening

of _{a new} relaxation channel for the free and localized

spins

below

Tp.

We _may then argue ^that an efficient energy transfer between both

magnetic _systems

will

give

rise to this relaxation mechanism. Such _a mechanism would then

explain why

the

conductivity

and the dielectric constant _are

highly magnetic

field

dependent.

This relaxation effect could also

explain

the anomalies _seen in EPR

[12],

I.e. the

broadening

of the linewidth below

Tp

and the

frequency dependence

of the g factor. The fact that the EPR linewidth is broaden without any loss of

susceptibility

indicates that the localized

spins

transfer their energy ^to the free

spins through

this relaxation channel. If this relaxation

mechanism _can

explain

the anomalies observed in EPR and microwave

conductivity

measurements for T~

Tp,

we can expect ^{that the} characteristic

frequency

of this relaxation

mechanism must be in the

gigahertz

_range

(frequency

at which both measurements are

realized).

5. Conclusion.

The

physical picture

that

emerged

from these results is that the localized

spins play

_a

dominant role _on the

transport properties

of these

quasi-one-dimensional

conductors.

Although

these

organic

conductors retain their

quasi-one-dimensional

character down to 2

K,

the free carriers _are, in _{a sense, «} localized _»

by

the local moments array ; this is confirmed

by

the very

large positive magnetoconductivity

observed. In

fact,

if _one could

apply

_a

strong enough magnetic field,

_one should be able to restore the metallic

conductivity.

Such _a

spectacular

and unusual

conductivity

enhancement

by

_a

magnetic

field is believed to be related _to the

dimensionality

of the system. ^{It is} also

conjectured

that this strong

coupling

between the _two

spin

_systems is

responsible

for the

opening

of _{a new} relaxation channel for temperatures ^below

Tp.

This relaxation channel

probably

mixes the response function of both

spin systems

^which

gives

rise _{to an} additional _energy

absorption

ⁱⁿ the microwave and EPR measurements at the

temperature Tp.

The results

presented

here also indicate that these _new

scattering

and relaxation mechanisms _are both

extremely

sensitive to the Cu-Cu distance.

For the moment, few

things

are known about the

transport properties

of one-dimensional Kondo lattice

[23-25]

_system. We believe that the

magnetoconductivity

results

presented

here

reinforce the trend found

previously

in the

Cu~Nii_~(pc)I alloys, giving strengthened

evidence for _an unusual effect in this

family

of

organic conductors,

that _must drive the attention of theoreticians.

Acknowledgements.

The authors

acknowledge

fruitful discussions with C. Bourbonnais _as well _as his

helpful suggestions,

we are also

grateful

to M.

Castonguay

for technical support. ^{This work} was

supported by

the Natural Sciences and

Engineering

Research Council and Fonds de Formation de Chercheurs et d'Aide h la Recherche and

by

the Solid State

Chemistry Program

of the National Science Foundation Grant No. DMR 8519233.

References

[I] JtROME D. _et al., J.

Phys.

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[2] PARKIN S. S. P, et al., Phys. Rev. Lett. 50

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[3] URAYAMA H, et al., Chem. Lett. 55

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[4] YAGUBSKII E. B, _et al., JETP Lett. 39 (1984) 12.

[5] HENRIQUES R. T. et al., J.

Phys. Colloq.

France 45 (1984) C17-5197.

[6] HENRIQUES R. T. _et al., J.

Phys. Colloq.

France 47 (1986) C19-4663.

[7] OGAWA M. et al., J. Am. Chem. Sac. 109

(1987)

II IS.

[8] OGAWA M. et al.,

Phys.

Rev. Lett. 57

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l177.

[9] OGAWA M. et al., Jpn. J. Appl.

Phys.

26 (1987) BD4.

[10] QUIRION G, et al., J.

Phys. Colloq.

France 49 (1988) C8-1475.

[I ii QulRioN G, _et al.,

Phys.

Rev. B 43

(1991)

860.

[12] OGAWA M, _et al.,

Phys.

Rev. 839

(1989)

10682.

[13] QUIRION G. et al.,

Synth.

Met. 41-43

(1991)

2653.

[14] HOFFMAN B, and IBERS J. A., Acc. Chem. Res. 16

(1983)

15.

[15] PALMER S. M, et al., Mol.

Cryst. Liq. Cryst.

125

(1985)

1.

[16] GODFREY M. R. _et al.,

Synth.

Met. 29 (1981) F51.

[17] LIOU K. K, et al.,

Inorg.

Chem. 28

(1989)

3889.

[18] CHAIKIN P. M. and KWAK J. F., Rev. Sci. Jnstrum. 46 (1975) 218.

[19] BURANOV L. I. and SCHEGOLEV I. F., Prib. Tekh.

Eskp.

2 (1971) 171.

[20] QmRION G. et al., Solid State Commun. 64

(1987)

613.

[21] KONDO J.,

Prog.

Theor.

Phys. (Kyoto)

32

(1964)

37.

[22] KONDO J., in Solid State

Physics,

F. Seitz et al., Eds. 23 (Academic, New York, 1967).

[23] DONIACH S.,

Physica

91B (1977) 231.

[24] JULIEN R., FIELDS J. N. and DONIACH S.,

Phys.

Rev. B16 (1977) 4889.

[25] CARON L. G. and BOURBONNAIS C.,

Europhys.

Lett. ii (1990) 473.

[26] BARNARD R. D., in

Thermoelectricity

in metals and

alloys (Taylor

& Francis Ltd, London, 1972) p. 192.

[27] QUIRION G, et al.,

Phys.

Rev. B 37

(1988)

4272.

[29] ZUPPIROLI L., ⁱⁿ Low-Dimensional Conductors and

Superconductors,

D.J6rome and L.G.

Caron, Eds. (Plenum Press, New York and London, 1987) _p. 307.

Mathematical Methods for Scientists and

Engineers

Linear and Nonlinear

systems

P. B. KAHN

(Wiley, 1990)

469 _pages, £ 43.65.

Le lecteur

frangais

risque d'dtre _un peu

surpris

_par ce livre aussi _peu formel que

possible

_sur

quelques

m6thodes

math6matiques

couramment (ou mains couramment) utilis6es. Si le niveau du fond de

l'ouvrage

est bien celui d'un d6but de second

cycle

universitaire _ou de

premibre

ann6e d'dcole

d'ing£nieurs,

au

premier

abord, la forme semble

beaucoup plus

d16mentaire. On peut en retirer

l'impression d'apprendre

les

math6matiques

_{« sun} le tas _» tant le _{texte est}

parsem6 d'exemples

et d'exercices _sans que l'on sache vraiment ok ceux-ci s'arrdtent et ok

reprend

le _cours. Le contenu global lui-aussi vient comforter cette

opinion.

Qu'on _en

juge.

Le livre comporte deux parties, ddd16es l'une _aux

systbmes

lin£aires et l'autre _{aux non} lin£aires. La

premibre partie,

plut6t d6structur6e, _{commence par un} bref

chapitre

de

rappels

divers,

puis

_passe h la th60rie des matrices dans le contexte le

plus simple ~pour

les d6monstrations, tout est

diagonalisable),

h la fonction Gamma, h _un peu

d'analyse

lin6aire, h I'£valuation de _sommes et

d'int6grales,

_{et se} termine

sur les

propri6t6s asymptotiques

des

dquations

diff6rentielles lin6aires du second orate.

Les choses

s'arrangent

dans la deuxi~me

partie,

nettement

plus

coh£rente, centrde _sur l'6tude des oscillateurs _non lin6aires.

Aprbs

_une introduction _sun l'incontoumable oscillateur

hannonique,

_un

int6ressant

dclairage

est donn6 _sur la notion de tenure s£culaire

qui

permet ^{de mieux}

comprendre

les m6thodes

d'approximation

£tud16es dans les

chapitres

suivants, Poincar6-Lindstedt (ch. 10), moyennage (ch. II), dchelles

multiples

(ch, 12). Le livre se termine sur une introduction h la transition _vers le chaos par doublement de

p6riode.

Compar6

_{au mot «} m£thode _», le _{mot «}

technique

_{» a} malheureusement chez nous un sens un peu

p6joratif.

Je crois pourtant qu'il serait

plus appropri6

_en tout cas d£routerait-il moins le lecteur

qui,

_au

vu du titre, pourrait s'attendre h _un texte moins _« terre h _terre

», N6anmoins, je _ne crois pas

qu'il

faille

pour ^autant « snober

» ce livre

qui,

d'une part, ^donne un £clairage 6minemment

pratique

h nombre de

questions

souvent

plac6es

dans _{un contexte} trop abstrait notamment dons le _cursus

frangais

et, d'autre part,

r£pond parfaitement

_aux besoins de celui

qui,

hors d'un encadrement universitaire, cherche h _se

former h la

pratique math£matique indispensable

_pour Waiter proprement ^{bien des situations courantes}

en

physique

et en sciences de

l'ing6nieur.

Il faut aussi rendre

hommage

aux efforts de l'auteur _pour faciliter le travail individuel, Sans revenir _sur

l'adaptation remarquable

de la forme

grin£rale

de

l'ouvrage

h cet

objectif,

_nous noterons par

exemple

que dons la table des matibres,

aprbs

le tide de

chaque chapitre,

il _a

plac6

_un court r6sum£ des motivations _et des r6sultats

qui

_y sont

d6velopp6s,

_ou

dons la

bibliographie

les ouvrages mentionn£s sont comment£s si bien que l'on salt leur niveau et le type de

renseignement qu'on

_{peut y} trouver pour

compl£ter

_sa formation.

Paul MANNEVILLE.

Journey

into

light.

Life and science of C. V. Raman

G. VENKATARAMAN

(Indian Academy

of

Sciences, Bangalore, 1988)

570 _pages,

photographs (black

^{and white and}

colour).

It is _{a rare}

pleasure

to have in your hands _a book like this _one,

providing

_a

thorough

and

passionate

description

of the life and work of _one of the _most

outstanding physicists

of this century, ^{Sir C.} V.

Raman. The controversial temperament of Raman

gives

_a

piquant

flavor _to the book, and its beautiful presentation ^makes it very attractive to read,

The book starts with _a brief historical

description

of the birth and

growth

of Westem Science in India, until the second half of the XIX century, followed

by

_{a summary} of Raman's

youth,

He _was bom in 1988, in the town of Tiruvanaikkaval, in South India. In his

early

days, ^he

proved

to be

a very

bright

student,

winning

several awards. He spent ^four years ^at the

Presidency College

of Madras, where his flare for

physics

started to

develop.

It _was also at this

College

that he

published

his first _paper,

on the

subject

of

unsymmetrical

diffraction of

light,

thus

starting

_{on one} of the fields which would remain of his

primary

interest

throughout

his life.

Chapter

2 of this book describes these

early

_years of

Raman's life,

including

his marriage, in _a

light

and

pleasant

tone, which is also utilized in many other parts ^{of the} text, as in

Chapter

3, where his _access and stay at the Indian Association for the Cultivation of Science (IACS), in Calcutta, _are sketched,

Chapter

4

extensively

describes Raman's vast fields of work

during

his stay at Calcutta,

starting

with vibrations, musical instruments (violin,

piano,

and Indian instruments, like the mridangam, tabla, tambura and veena), and

moving

on to

Optics (oblique

diffraction, curvilinear apertures, coronae and halos), and then

gradually switching

into _more

spectroscopic subjects,

like

optical anisotropy

and Kerr effect, There is _a mathematical

description by

the author _{on some} of the processes mentioned above, which,

although

of interest _to

specific

readers, breaks _a little the lead and

rhythm

of the story ^{for the}

non-specialist.

However, these mathematical sections, which appear also in later

chapters

of the book,

are

tagged

with _a

symbol

(*) at

beginning

and end, to facilitate their

skipping by

readers not interested in them,

A good

opportunity

^is

provided

in this

chapter

_to remark the

changes

in scientific

jargon,

from those days till _our present communications. One of Raman's

colleagues,

Chuckerbutti, in _a paper

describing

the diffraction effects which _are

responsible

for colours of heated metals, writes _« colours _{start at} about _a reddish _or violettish tint,,, On still further

heating,

rather at a

high

temperature, ^the colour is almost white.,, The colours exhibited at this

repetition

are very rich and gorgeous.,. », This

gives

such _a

pleasure

to read, that the author of this book is warmly thanked for

picking

out such pieces of text. A

feeling

of thrill and wonder also arises from the

description

of _some of Raman's

laboratory experiences

:

they

carried out

apparently simple experiments, by

means of all sort of ready at hand

equipment

: spare parts ^of a

bicycle,

_a

piece

of wire and _an

electromagnet, sunlight

illumination of

optical

setups. ^And yet he _was able _to draw

important physical

conclusions,

explain

facts _not yet understood, and make clear

advances in the field.

Chapters

5, 6 and 7 _are

entirely

dedicated to the Raman effect. The

laboratory experiences

that led to the

discovery

of this

feeble scattering,

or scattering with _a

frequency shift,

_as it _was first called, _are narrated _as extracts from the diary ^{of Raman's} student (at the time), K. S. Krishan, and _are very

thrilling

to follow. The author has selected _a

moving description by Lady

Raman of the Nobel Prize award _ceremony in Stockholm, in December, 1930.

Whereas the basic

physics

of the Raman effect,

given

in

Chapter

6, _seems to appear a bit short _on the quantum ^mechanical basis, and the

polarization

effects remain somewhat unclear, the _new

phenomena

that have _{come up} after the advent of lasers _are very

neatly pictured

in

Chapter

7.

Although they

are

well known, it is worth

recalling

_some of the techniques ^based on the Raman effect when excited by

means of

high

_power lasers _: non linear

techniques,

like CARS _or SRS (Stimulated Raman

Scattering),

Raman laser, Raman

microprobe,

and _more.

Roman's life was never easy. Soon after his great success at the Calcutta IACS, he _was forced to leave this institution,

mainly,

_as it _{seems, as a} result of the envy he raised _{on some} of his

colleagues,

with

whom he never

compromised

to avoid confrontations. He then moved to

Bangalore,

where he _was

appointed

Director of the Indian Institute of Science

(IISC),

_{a cosy} and easy

going

Institute, where little research was

being

done at the time. He _was

immediately

set for

changes, aiming

to convert the IISC into

a center

for

excellence. This led him into several troubles, like the

resignation

of two Professors, _{a severe}

shortage

of funds, and the

opposition

of the establishment, all of them

finally giving

rise to the creation of _a Committee, intended

originally

to review the situation at IISC, but which in

practice

acted with the

obvious purpose of

forcing

Raman out. This _was

eventually accomplished,

since four years after his

appointment,

Raman

quit

the

Directorship

of the Institute, to continue with his _own research _as Professor of

Physics.

All this is described at

length

in the first part ^of

Chapter

8_; the second part ^is

endeavoured to the research that he carried out

during

^his stay at IISC, until his retirement at 60 years of age.

Chapters ⁹ and 10 describe in detail the Raman-Nath theory, Raman's most

outstanding

research contribution from his

Bangalore

times, and the controversy ^{that confronted him and} Bom, based _{on a} different theoretical

approach

to lattice

dynamics,

in which Raman stood _on the wrong side.

Chapter

II is _a short _one, dedicated to the Indian Academy of Sciences, founded

by

Raman, which has _so grown with time _as to become _a successful scientific institution

today,

where _a

large

deal of Indian research

contributions _are

published

in ten separate ^theme

joumals.

After retirement, he created his _own Institute, the Raman Research Institute, also in Bangalore, where he could dedicate himself to research _on his favourite

subjects. Unfortunately,

he did not appear to be able _to

enjoy

this situation all the time, _as his moods

changed dramatically,

from _a

complete

dedication to science, at the

beginning,

to a stage ^{of reclusion and almost}

hostility

to the world at

large,

to

finally

a new change ^that

brought

him back full of zest to the task of

educating

_young students and

stimulating

them to do science. In this respect, ^the book collects _some excerpts from Raman's radio broadcasts, which touched _{on many} different

subjects

_:

physics

for the

layman,

soil, _{water, sea} shells,

etc. The

reading

from these broadcasts is very

exciting,

and _once

again

the author is to be

praised

for his

intelligent

selection.

Raman _was cremated in the

gardens

of his Institute, which he had himself

designed,

and that he loved

dearly.

A

single

tree,

pictured

in _one of the beautiful colour

photographs

of the book, marks the

place

of his cremation, _{as was} his wish.

One of this book's

highest

values lies in its constant

pledge

in favour of basic research, _a

subject

which constitutes _a permanent struggle between

politicians

of almost any time and country, ^{and the scientific}

community.

The book includes several pages of Notes, full of anecdotes, which contribute _to enliven the text, as well _as the many

photographs

and pictures that are

interspersed

in its pages.

Rafael ESCRIBANO.