“Nearly-commensurate” charge-density wave in linear-chain compounds

Synthetic Metals, 29 (1989) F 3 1 3 - F 3 2 0

"NEARLY-COMMENSURATE"

V.B.

CHARGE-DENSITY

Preobrazhensky,

Kurchatov

A.N.

Institute

F313

WAVE

IN L I N E A R - C H A I N

COMPOUNDS

Taldenkov

of A t o m i c

Energy,

Moskow,

123182,

USSR.

ABSTRACT The e x p e r i m e n t s nity to trace systems

under

the e v o l u t i o n

w h i l e the

orthorhombic

existent chain

of e l e c t r o n i c

data

shows

that

almost

are o r i g i n a t e d

from c o m m e n s u r a b i l i t y

with

properties

of C D W - b e a r i n g

at present

are r e v i e w e d

all specific from a small

way

for

w i t h the aim

The analysis

properties departure

crystal

opportu-

in a c o n t r o l l a b l e

a kink model.

with underlying

a unique

is a v a i l a b l e

experiments

CDW model

offer

is changed

set of results

(o-)TaS 3 . These

a sliding

compounds

deformation

incommensurability

A most c o m p r e h e n s i v e

to compare

strain

of

of linear-

of CDW p e r i o d

lattice.

INTRODUCTION The Fermi structural

surface

is a c h a r a c t e r i s t i c The very mary

unusual

lattice.

rest

uniform

of

2/.

compounds

k = h/pf,

state,

[S],

0379-6779/89/$3.50

quasi-iD

compounds

type

wave

(CDW)

conductors.

are o r i g i n a t e d

the CDW

al<
of c o m m e n s u r a b i l i t y ) ,

in w h i c h

becomes

wave-length,

is i n c o m m e n s u r a t e

"nearly-commensurate"

At a s u f f i c i e n t l y

ground

into domains

inorganic

of these

parameterl6J=J( k - N a)/N

N - the order

/i,

of m o s t

w i t h a Peierls

of c h a r g e - d e n s i t y

pri-

of CDW.

momentum

The case

surability meter,

feature

of l i n e a r - c h a i n

ed by a Fermi

associated

and a f o r m a t i o n

properties

from e x i s t e n c e

In m o s t

instability

distortion

CDW,

when the

- in-chain

incommen-

lattice

para-

is of a p a r t i c u l a r

inte-

small 6 the f o r m a t i o n the i n c o m m e n s u r a t e

always

determin-

with u n d e r l y i n g

energetically

of space non-

CDW is b r o k e n

favourable.

In this

© Elsevier Sequoia/Printed in The Netherlands

F314 state CDW w i t h i n each d o m a i n tal

lattice,

is l o c a l l y c o m m e n s u r a t e w i t h the crys-

g i v i n g a gain of c o m m e n s u r a b i l i t y energy,

w h i l e an

abrupt c h a n g e of CDW's p h a s e occurs

at d o m a i n b o u n d a r i e s

a d j u s t the a v e r a g e d CDW w a v e - l e n g h t

to its a p p a r e n t

meaning.

The r e g i o n s

or kinks

- b e a r an excess charge.

pinned,

is i m m o b i l e

of a b r u p t CDW p h a s e c h a n g e

its t h r e s h o l d meaning. properties

effects

Meanwhile,

the d c - i n d u c e d v o l t a g e o s c i l l a t i o n s

external

(VO) and states

-

fields. - a sli-

5] - is also c a p a b l e to d e s c r i b e s p e c i f i c p r o p e r -

rence b o t h m o d e l s p r e d i c t v e r y

D e s p i t e an o b v i o u s p h y s i c a l similar behaviour

w h e r e a k i n k model

forecasts

diffe-

of CDW s y s t e m s

e x c e p t the r e g i o n n e a r the c o m m e n s u r a t e

transition,

specific

an a l t e r n a t i v e and d i s t i n c t l y d i f f e r e n t model [4,

fields,

exceeding

and f r e q u e n c y

a s s o c i a t e d w i t h e x i s t e n c e of m e t a s t a b l e

ties of l i n e a r - c h a i n compounds.

all cases,

all

- the n o n - o h m i c

of a k i n k array w i t h

being

electric

s t r o n g fields,

A c c o r d i n g to a k i n k model

arise from i n t e r a c t i o n

d i n g CDW model

available

in s u f f i c i e n t l y

of l i n e a r - c h a i n c o m p o u n d s

d e p e n d e n t conduction, numerous

"incommensurate"

- discommensurations

W i t h i n this p i c t u r e CDW,

in any e x p e r i m e n t a l l y

while kinks are d i s l o d g e d

so as to

for

- imcommensurate

an a n o m a l o u s b e h a v i o u r

sin-

ce the k i n k c o n c e n t r a t i o n v a n i s h e s n e a r the c o m m e n s u r a b i l i t y point. The e x p e r i m e n t s u n d e r u n i a x i a l ed here, le way,

in w h i c h the

strain d e f o r m a t i o n to be d i s c u s s -

incommensurability

are b e l i e v e d to be c r u c i a l

is c h a n g e d in a c o n t r o l l a b -

in d i s c r i m i n a t i o n b e t w e e n a k i n k

and a s l i d i n g CDW model. At

present

a

most

i n f l u e n c e of u n i a x i a l perties

of

mentional"

(o-)TaS3, member

Its a v a i l a b i l i t y

set of r e s u l t s

is g a t h e r e d on the

strain d e f o r m a t i o n on v a r i o u s e l e c t r o n i c proa representative

and,

in a f a m i l y of i n o r g a n i c

perhaps,

a most

linear-chain

in a form of v e r y p e r f e c t t h i n w h i s k e r s

beneficial opportunity ties at e x t e m e l y

complete

"one-di-

compounds. offers a

to trace the e v o l u t i o n of e l e c t r o n i c p r o p e r -

large r e v e r s i b l e d e f o r m a t i o n s

exceeding

1.5 %.

RESULTS Two e s s e n t i a l l y in p r e s e n t

study::

E t ~ 20 ÷ 25 V / c m

d i f f e r e n t types

of o-TaS 3 s a m p l e s have b e e n u s e d

a material with relatively high threshold field

(at 90 K) and h i g h p u r i t y s a m p l e s w i t h E t a 0 . 3 V/cm,

grown at C R I P in Budapest.

The c o n s i s t e n c y of the m a i n r e s u l t s

b o t h types of so d i f f e r e n t

samples

essential

for this m a t e r i a l

on

show the p h e n o m e n a o b s e r v e d are

i r r e l e v a n t of its purity.

F315

L o w - f i e l d c o n d u c t i o n and t h e r m o p o w e r . Since the c o n d u c t i o n

of o-TaS~

is field

the full c o n d u c t i o n p h e n o m e n o l o g i c a l l y

i n d e p e n d e n t for

can be d e c o m p o s e d

low E,

into two

parts: o(S,E,T) where

a I stands

conduction, uniaxial

gnl-

i n d e p e n d e n t at E < E t

n o n - l i n e a r part,

part

of

equal to zero for E < Et;

linear

S -

strain deformation. shown r e c e n t l y

[6,

7] that in

a

(65 K < T < Tp) the l o w - f i e l d c o n d u c t i o n

as believed, has

+ Onl (S,E,T)

for a field

and

It has b e e n range

= 01 (S,T)

from one-particle

a strong non-monotonic

ly a g a i n s t u n i a x i a l

excitations

broad

in o - T a S 3 ,

across

s t r a i n dependence,

temperature

a

derived,

Peierls

g r o w i n g first

gap,

linear-

s t r a i n d e f o r m a t i o n S, w i t h a s u b s e q u e n t d r o p at

large S. For the p u r p o s e of f u r t h e r d i s c u s s i o n we d e n o t e a t e m p e r a ture d e p e n d e n t

c r i t i c a l v a l u e of a s t r a i n at w h i c h for any p a r t i c u -

lar T a m a x i m i m of Since the gap

a1

a g a i n s t S is r e a c h e d as S c

(as d e t e r m i n e d

from

ig ~1 vs

fixed S) r e m a i n s p r a c t i c a l l y u n a l t e r e d by stress, dependence bility

of

a

(T). I/T d e p e n d e n c e s anomalous

strain

s h o u l d be a t t r i b u t e d to the c h a n g e of c a r r i e r mo-

1 r a t h e r t h a n to v a r i a b i l i t y

of c a r r i e r c o n c e n t r a t i o n .

i m p o r t a n t c o n c l u s i o n o u t l i n e d f r o m the c o m p a r i s o n b e t w e e n pressure

at

dependences

of l o w - f i e l d c o n d u c t i o n

v e d are b r o u g h t a b o u t p r i m a r y by t r a n s v e r s a l p r o d u c e d by u n i a x i a l

strain

Another

s t r a i n and

is that c h a n g e s

obser-

c o n t r a c t i o n of s a m p l e s

r a t h e r t h a n by i n c r e a s e of i n t r a c h a i n

i n t e r a t o m i c distances. These results,

obtained first

in

[6] on s a m p l e s w i t h r e l a t i v e l y

h i g h E t , a r e n o w s u p p o r t e d by m e a s u r e m e n t s presented

in a n o t h e r p a p e r

(this issue)

The t h e r m o p o w e r m e a s u r e m e n t s v a l u e of S c some p e c u l i a r i t i e s thermopower

a(S)

show

on h i g h - p u r i t y

samples

along with thermopower

that

on s t r a i n

at

the

dependences

and

data.

same

critical

of

absolute

are o b s e r v e d as well.

H i g h - f i e l d conduction. The n o n - o h m i c in

[8] and

[9].

conduction

These r e s u l t s

racteristic

of o - T a S 3 has b e e n

studied thoroughly

in a r e s t r i c t e d range of e l e c t r i c f i e l d s n e a r E t a l s o are n o w c o n f i r m e d on h i g h p u r i t y specimens.

strain dependences

dc-measurements

shown

in fig.

of h i g h - f i e l d

in

Cha-

c o n d u c t i o n o b t a i n e d by

i. T h o u g h the g r o s s f e a t u r e s o b s e r v e d

are c o m m o n for t h e w h o l e t e m p e r a t u r e

range

(T < Tp),

for the p u r p o s e

F316

,' ~ m j ~ ' ~ . . .

r C,'Y I-.-

i

+1+

"I

]

I

I

I

I

I

# i 3HF

o.li

I

0.23 ~--~._.~--~+-

\

£TI

.~:=0

i

/

//

\\

_ 45

"2"-

....

" '~'

= 0.8V,'c,, / 30.

/

,y_1- G ,.~.-:,

-.

J. 45

l

"

. ............

"++~-

20

+

,,,

// ,,+,-I /

I

i

S Fig. Fig.

i

T

I

I

0.4 R

~

0.8

N

O,

7;:i

I

0.6

I

55

1.0

( Z )

~"

[

i. -E

i' (~

I

r'.

2.5

, i

Ctjl

I. S t r a i n d e p e n d e n c e of h i g h - f i e l d c o n d u c t i o n at f i x e d fields. 2. The d e p e n d e n c e of b r o a d b a n d n o i s e a m p l i t u d e on the field at f i x e d v a l u e s of d e f o r m a t i o n . S t r a i n is s h o w n in %, s a m p l e 13HF, S c = 0.55 %.

of c l a r i t y
fig.

mation

we

shall

where

A most from

concentrate

Onl b e h a v i o u r

prominent

feature

1 is that,

Onlin h i g h

it drops mum

i

0.2

n.

i0

I //

4

0

O. 5'2

at l e a s t

while

fields two

on the

is m o r e disclosed

at small

exceeding

orders

low t e m p e r a t u r e

region

(70K<

simple. in this

study

and r e a d i l y

S and at e x t r e m e l y many

times

of m a g n i t u d e

the

at So,

large

linear

seen

defor-

conduction,

just w h e r e

a maxi-

of o I is o b s e r v e d . A key p o i n t

depletion

in r a t i o n a l i z i n g

of n o n - l i n e a r

is i n c o n s i s t e n t

with

near

S c is e x p e c t e d

some

reasons

rease

this

model

of c o n d e n s e d S e with

are p r o v e d

near

in t w o

the

invalid.

is an a l m o s t

a behaviour

full

of

'onl Onl

Indeed,

a drop

of

cases:

either

if f o r

Sc with

electrons,

a result

to be

data

at S c . S u c h

C D W model.

is d e s t r o y e d

as S r e a c h e s

assumptions

sliding

within

CDW

of a f r a c t i o n

enhanced Both

the

the

the presented

conduction

or

an a p p r o p r i a t e if E T

CDW Really,

is

become

dec-

strongly immobile.

it has b e e n

shown

F317

in

[6]

by l o w - f i e l d

is a l m o s t royed.

The field

xed values CDW

does

gives

Near

obtained~

Sc , w h e r e

been

used

in p r e s e n t of t h e

that variations

study

with

field

the

evidence

against

reason

an

for

The

a two

strain show

order the

to d i s r u p t i o n

of C D W

mehave

3 clearly

Sc . T h e r e b y

neither

li-

this method

one.

in fig.

near

from

characteristics

of

drop

the transport

of

of CDW,

at S = S c s e e m s by sliding

T=170 K

•

fi-

that

independent

a traditional

immobility

proof,

I-V-curves

to account

of S c is a t t r i b u t e d

dest-

of S c as well.

noise

conduction

gap

is n o t

at d i f f e r e n t

another

of

presented

small

CDW

is v e r y weak,

For this

along

are too

of E t . T h u s

a direct

I-I

a vicinity

a departure

from broadband

of n o n - l i n e a r

Onl in a v i c i n i t y provide

error.

threshold

of F~

drop

from

the Peierls

noise

2, g i v e

the non-linearity

systematic

of E t d e t e r m i n a t i o n

nor to raise

in fig.

that hence,

of a b r o a d b a n d

shown

thod

dependences

measurments

deformation,

at any S including

a large

magnitude

strain

dependences

usually

nearity.

by

of a strain,

exist

E t is

conductivity

unaffected

to

CDW.

o-Ta$.~

N

-r

2.3 ',//,;:,. T = 9 0 k

[ 2;Oj,,.

°,_, • •

iii

~

go

L1

t

E-0.4 o

-=..

T=131 K

_.J

~"

-0.._-3,

"

.0.2

.-.

:,-0.3

•

• OoQ

• oo oOo

I

•

•

•

•

•

i

~0.03

1.0

'" "r ~--

T=91 K

ooo

C<,

o

1.E;

o

1.4

O. 1

i

_J CJ

-r

"~

•

8

#13HF

I

r:

"~_: 4n

OQ

}

o

o

o

o

\ t°°

o

V

°

o o

o

o

°

%

,7~-T,3:~::.-:

.1.2., oo 6 O0 °8 0.2 .4 f

I

T

Fig.

Fig.

0.8 I

L-Z.~; I.L]

I

~'

o "o • t

R

I

I

N , Z

1.2 I

,= 2:" .....

20 I-I

O. 25

r-i._

i

i

S T K'. A I N

O. 75 i

':X)

3. T h e s t r a i n d e p e n d e n c e of t h e t h r e s h o l d f i e l d c h a r a c t e r i s t i c for d i f f e r e n t t e m p e r a t u r e r e g i o n s . (.) - f r o m b r o a d b a n d noise characteristics, (o) - f r o m I - V - c u r v e s ; s a m p l e 13HF. 4. S t r a i n d e p e n d e n c e of m a i n h a r m o n i c f r e q u e n c y at f i x e d v o l t a g e s (top) a n d t h a t of 7 = J n l / v (bottom), s a m p l e 39H.

F318 The b e h a v i o u r natural

of h i g h - f i e l d

explanation,

i) The strain produces the CDW to b e c o m e deformation

conduction

a variability

commensurate

S = Sc

under

strain

receives

a

if we put for two hypothesis:

(T)

(where

in CDW wavevector,

with underlying all e l e c t r o n i c

lattice

leading

at critical

properties

exhibit

so-

me peculiarities). ii) The n o n - o h m i c tion,

conduction

than from d i s l o d g e m e n t

According against which

to above

the strain

increased

causing

within

of n o n - l i n e a r

as

follows.

limited

tively high. tion grows, reduces

As one moves

# . A theory

dc-induced

in

dc-induced

is

carrier m o b i l i t y

scattering,

mechanism

of free c a r r i e r

mobility

in p r e s e n c e

oscillations

first

is rela-

which of kinks

(VO).

- band noise"

in [ii].

of f r e q u e n c y

Jnl and

in a wide

is found

the r e l a t i o n

7 = Jnl / Y

temperatures

and values

striking

4).

range

remaining

the

unaltered

if Jnl

characteristic

of a p p r o p r i a t e

voltages),

occurs

near

6). A most p r o b a b l e

in a v i c i n i t y

dist a n c e

becomes

a result

that the kink

densities within

the

follow

relationship

of current

cation

(fig.

deformed applied

main h a r m o n i c s

A linear

is that,

Sc

voltage

between

(fig.

5),

30 % for all

of a strain.

phenomena,

even

v of

(fig.

in uniaxial

For co n s t a n t

study,

is that

concentration

the free

phonon

explained

scattering

current

fect

kink

be

up or down from S c, the kink concentra-

- VO or "narrow

studied

dependence

A most

and/or

can

an a d d i t i o n a l

that of n o n - l i n e a r v

the Sc,

deis

[i0].

voltage

o-TaS 3 was strain

only by impurity

providing

is d e v e l o p e d

point

charge

conduction.

conduction

Since

S c,

At h i g h e r

an o p p o s i t e

of n o n - l i n e a r

of l o w - f i e l d

decreases

point

conduction.

of kinks h a v i n g

small near the c o m m e n s u r a b i l i t y be i n g

the kink c o n c e n t r a t i o n

the r e s t o r a t i o n

dependence

this model

from kink mo-

going to zero at a c o m m e n s u r a b i l i t y

the c o n c e n t r a t i o n

The strain

rather

of CDW as a whole.

assumptions

leads to d i s a p p e a r a n c e

formations

is o r i g i n a t e d

is m a i n t a i n e d

an inchain

lattice

in a k i n k

lattice

herent

and the

individual

full

comes

explanation

coherence

point

under

(by appliof

VO

for this efthe i n t e r k i n k

lenght

to be destroyed.

leads the o s c i l l a t i o n s lines

samples

depression

of a c o m m e n s u r a b i l i t y

larger than

order

an almost

for all

to be c o n s t a n t

~ FLR,

The

with

loss of

turn out to be inco-

in VO spectra to disappear.

F319

o-ToS3,SOK !

!

N

~= o.s! " O - 0 . 1 & %

.,*

v

-0.27/, • -0.55:/.

+ DO

" -0.66,'/,

O.

PEFERENCE\

"~

'

•

•

•

~_.~_.51 _

#.i

,,,'~..,j

,

~w el:

-

,,~S=SC/.._

,o %"

0-0.827.

z

.70 +

|

•

•°e~,

ILl

c~0.2

iooh l

:*a"

w

:'~ W"

¢v

o Fig. Fig.

,,ql,

•cA,

;' .: .. ¢,~ •

s@ ~.~.. "I.t O0 I

I

p.o5 o.i NONLINERR CURRENT (FR)

o

o:2 o14 o:s F R E 0 U E N C Y (.Hz)

o.e

5.

The d e p e n d e n c e of m a i n h a r m o n i c f r e q u e n c y on n o n - l i n e a r c u r r e n t f o r s e v e r a l f i x e d S, s a m p l e 20H. 6. The e v o l u t i o n V O s p e c t r a u n d e r u n i a x i a l s t r a i n at c o n s t a n t Jnl = 20 A/cm ~ s a m p l e 14H.

Hysteretic

behaviour

The u n i a x i a l states

and

strain

produced

switching.

deformation

by thermal

T < 130 K a s t r a i n

cycling

deformation

by

hysteresis

in l o w - f i e l d

hysteresis

especially

clear

indicative

of a p h a s e

transition

Among strain

more

than

in o n l y

The magnitude

one

cut

30 s a m p l e s

effect

at S c in a c c o r d a n c e

rability

point.

it w a s

never

low frequency

observed

S

in a v i c i n i t y occurring

with

switching

was

have

lowered

found

of S c . A t

been

found

to

be

deformation

observed

seen

that

This

seems

was

at

pronounced

as well.

of S c

is c l e a r l y

a proposal

in a v i c i n i t y

oscillations

a well

at a c r i t i c a l

switching

effect

metastable

[12] ~, m e a n w h i l e ,

and thermopower

is p r o g r e s s i v e l y

vanishes

At high

of a s a m p l e

studied

This

to d e p r e s s

its o w n p r o d u c e s

conduction

sample.

of t h e

is s h o w n

at

in fig.

with

S and

zero 2. it

S c is a c o m m e n s u -

in m a n y

samples,

but

S > Sc i n t e r m i t t e n t

in m a n y

samples.

CONCLUSIONS At present

there

incommensurability

are no direct with

riments

under

ties

linear-chain

of

discussion

re of C D W p e r i o d

from

a strain. show that

compounds

are

measurments Meanwhile,

showing the

analysis

(i) a l m o s t

all

originated

from

commensurability

and

(ii)

a change

specific

the

a small strong

of

of e x p e properdepartustrain

F320 dependence of all electronic properties in these materials is consistent with the kink model,

while incompatible with the sliding

CDW model. ACKNOWLEDGEMENTS We are indebted to S.A. Brasovskii for many fruitfull discussions and to A. Janossy and his collaborators for high quality samples. REFERENCES 1. P. Bak, V.J. Emery,

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217