Wave Analysis of the Charge Density Wave Dynamics in the Molecular Conductor (Perylene)2Pt(mnt)2 (mnt=maleonitriledithiolate)

HAL Id: jpa-00247079

https://hal.archives-ouvertes.fr/jpa-00247079

Submitted on 1 Jan 1995

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Wave Analysis of the Charge Density Wave Dynamics in the Molecular Conductor (Perylene)2Pt(mnt)2

(mnt=maleonitriledithiolate)

J. Dumas, N. Thirion, M. Almeida, E. Lopes, M. Matos, R. Henriques

To cite this version:

J. Dumas, N. Thirion, M. Almeida, E. Lopes, M. Matos, et al.. Wave Analysis of the Charge Den- sity Wave Dynamics in the Molecular Conductor (Perylene)2Pt(mnt)2 (mnt=maleonitriledithiolate).

Journal de Physique I, EDP Sciences, 1995, 5 (5), pp.539-545. �10.1051/jp1:1995149�. �jpa-00247079�

Classification

Physics

Abstracts

71.45Lr

75.12Nj

72.20Ht

short communication

Wivelet _{Analysis of the Charge Density Wave Dynamics in the}

Molecular Conductor (Perylene)2Pt(mnt)2 (mut

=

maleonitriledithiolate)

J. Dumas

(~),

N. Thirion

(~),

M. Almeida

(~),

E.B,

Lopes (~),

M.J. Matas

(~)

and R-T-

Henriques (~)

(~) Laboratoire d'Etudes des

Propriétés Electroniques

des Solides

(*), CNRS,

B-P- 166, 38042 Grenoble Cedex 9, France

(~)

Centre d'Etudes des Phénomènes Aléatoires et

Géophysiques (CEPHAG) (**), ENSIEG,

B-P. 46, 38402 Saint-Martin

d'Hères,

France

(~)

Departamento

de

Quimica, ITN,

2686 Sacavem Codex,

Portugal

(Received

27

February

1995,

accepted

9 March

1995)

Abstract. A _new method based _on trie wavelet

analysis

of trie

voltage

oscillations

generated

above threshold electric field for

depmning

of trie

charge density

_wave

(CDW)

in trie molecular

conductor

(Perylene)2Pt(mnt)2 (mnt

=

maleomtriledithiolate)

bas been

developed.

This

analy-

sis method

permits

_a better time resolution of trie

frequencies

and

phases

involved in trie CDW motion than that allowed

by

conventional Fourier

analysis.

Trie results _are discussed in relation

with current models for CDW deformations.

l. Introduction

Charge density

_wave

(CDW) dynamics

_{in quasi} one-dimensional conductors lias been trie sub-

ject

of intensive studies for trie

past

^fifteen years

il, _2].

In trie CDW

state,

trie conduction electron

density

_is

given by p(x)

=

Acos(Qx

₊

_çi)

where A is trie CDW

amplitude, Q

=

2kf

is trie CDW

wavenumber,

and çi trie

phase. Depending

on trie bond

filling,

trie

periodicity

of

trie CDW _can be commensurate or incommensurate with trie

underlying

lattice. Below _a small

finite threshold electric field

Et

trie CDW is

pinned

to trie lattice because of its interactions with

randomly

distributed

impurities

_or lattice defects _or due _to

commensurability

elfects.

Above

Et,

remarkable non-linear

conductivity

due to trie motion of trie CDW with respect to trie lattice is observed. At constant current, ⁱⁿ trie non-linear regime,

quasi-periodic

volt- age

oscillations, commonly

referred to _{as narrow} band noise

(NBN),

_accompany trie current

(*)

associated with Université

Joseph

Fourier, Grenoble

(**) (URA

CNRS

346)

©

Les Editions de

Physique

1995

540 JOURNAL DE

PHYSIQUE

I N°5

flow. Trie

frequency

of these oscillations is

proportional

to trie _{excess current}

density

carried

by

trie CDW. Trie onset of CDW

sliding

is also marked

by

trie so-called broad band noise.

In trie

Fukuyama-Lee-Rice (F-L-R)

model

[3,4],

where

only

trie

phase

of trie CDW is taken into account,

pinning

results from _a

competition

beta>een trie elastic _energy of trie CDW and

preferred

CDW

phase

at

impurity

^{sites. Other models involve structural CDW}

defects,

such

as

phase

dislocations

[5], neglected

in trie F-L-R model. Trie

analogy

between

depinning

and onset of

plastic

deformations of _a

crystal

lias also been considered

[6].

^Trie

origin

of trie

voltage

oscillations is still trie

subject

of _some

controversy.

Since trie interaction energy of _a CDW with

impurities

_or with trie lattice _is

unchanged by

_a translation

through

_one CDW

wavelength,

trie

impurity pinning potential

is

expected

to be

periodic.

Trie CDW motion in this

potential

should

give

rise to

periodic

oscillations [7].

Voltage

oscillations

might

also result from

periodic

formation of

phase

vortices

required

for CDW to normal carrier conversion _near contacts _or at

strong pinning

centers [5].

These oscillations _can be observed in trie transient CDW _response to current

pulses.

At constant

current,

trie oscillations _can also be studied

by

Fourier

analysis. However,

_a

_spectrum analyser

involves time averaging, whereas trie

amplitude, phase

and

frequency

of trie oscillations may fluctuate in time. Trie wavelet

analysis presented

here _{is a}

relatively

recent method which allows time averages ^to be

drastically

reduced to a minimum and information to be obtained on short-lived events _or

intermittency.

It is

especially well-adapted

for

analysis

of trie _narrow

band noise due to trie CDW motion.

Rather than

giving

_a

time-averaged spectrurn,

trie wavelet

analysis decomposes

_a

signal

into wavelet

components

^which

depend

_on scale and time

[8-10].

^{We bave chosen Morlet's}

analyzing

wavelet

[loi

which

represents

a reasonable _compromise between time and

frequency

resolution:

il(t)

=

exp[ict t~ /2]

where _c

=

7r(2/

In

2)~/2.

With this value of trie parameter c, trie

admissibility

criterion for trie wavelet is satisfied

[9, loi. il(t)

is _a

complex

function with _an

amplitude

and _a

phase

which

represents

_a sinusoidal oscillation convoluted with _a

Gaussian,

_as illustrated in

Figure

1. Trie time and

frequency

resolution of trie wavelet

obeys

_a

Heisenberg-Gabor

relation AtA

f

₌

1/27r.

Trie wavelet transform of _a

signal f(t)

_can be written, for trie continuous case, as

2

#p~t _ii

,

j

^1~

)

)

^~ ~

'

Î

---'~

l-.----..-..---...-.

'~

5 ~ 5 0 OS

fl~~ reÔUCed ÎÉeqUeDCy

a)

_~~

Fig.

l.

(a) Analysmg

wavelet

amplitude

_{as a} function of time _m

arbitrary

umts;

(b)

Fourier tral~sform of trie

analysmg

wavelet in

arbitrary

units.

W(a, t)

₌

^a~~/~ / _f(r)il*(

~

)dr

a

where il* is trie

complex conjugate

^of

il,a

_is trie scale parameter a e

fo/f,

where

fo

is trie central

frequency

of trie

analyzing

wavelet.

W(a,t) depends

_on scale and time. If trie

parameters

_a and t _are

changed independently,

trie distribution of each

component

^of

f(r)

is obtained in trie

(a, t) plane,

that

is,

in trie time

frequency plane. Thus,

trie wavelet transform allows _a

time-frequency analysis.

Such _an

analysis

lias been

performed

in trie _case of trie

quasi

one-dimensional conductor

(Perylene)2Pt(mnt)2>

which shows _a Peierls transition at

Tp

= 8 K towards _a commensurate CDW and where remarkable

voltage

oscillations with

large amplitude

_are

easily

detected in real time

by pulse techniques

at 4.2 K. Trie CDW

dynamics

of trie Pt

compound

will be

reported

elsewhere

il1].

We bave

recently reported

trie observation of CDW non-linear

transport

in trie molecular

compound (Perylene)2Au(mnt)2,

isostructural of trie Pt

compound [12]. Sample

^and

contact

preparation procedures

_are

given

in reference

[12].

2.

Experimental

Results

The non-linear I-V characteristics and

quasi-periodic voltage

oscillations _were observed at T

= 4.2 K

using

trie _current

pulse technique [Ill.

Trie

computer-controlled arrangement

consists of _a HP 214B

pulse generator,

Tektronix A3I502

amplifiers

and _a Tektronix 2230

digital storage oscilloscope.

A non-linear I-V characteristic is shown in

Figure 2(a).

Trie onset of _non-

linearity corresponds

to a threshold field

Et

_" 9

Vcm~~. Quasi-periodic voltage

oscillations with

strong amplitude superimposed

_on trie transient

voltage

_response to

rectangular

current

pulses

and

generated

above

Et

_are shown in

Figure 2(b).

A

delayed

onset of trie oscillations with

respect

to trie

leading edge

of trie

pulse

is observed. Trie

delay

time decreases

rapidly

when trie current

pulse amplitude

is increased.

A

typical

wavelet

analysis

of trie transient

voltage

_response,

performed

at

CEPHAG/

EN- SIEG in Grenoble is shown in

Figures

3 and 4 with _a

logarithmic

scale for trie

frequencies.

Figure

3

(a)

reveals three

frequencies

_{as a} function of

time,

each with _a finite

spectral width,

for _{a current}

pulse amplitude

above threshold for

depinning.

^Trie fundamental

frequency

Fi

_+w 75 kHz is

accompanied by

harmonics

F2, F3, F4

^which _appear in

pink, red,

_orange and

yellow, respectively,

in

Figure 3(a).

A direct Fourier

analysis

of trie

voltage

oscillations reveal

6 ₇

5

~

5

fi

~

:' é ^~

> I

)

Î~

/

3

>.

~

~ ,=' 2

_f'

;"

o 0

0 0 5 5 2 0 100 200 300 400 500

1(mA) ^~'~~(PS)

a) b)

Fig.

2.

(a)

I-V _curve obtained

by

current

puise technique showing

_a non-hnearity at It _" o.18

WA;

puise

width 350 ~ls; T ₌ 4.2 K;

(b)

Transient voltage _response to current

puises

with

an

amplitude

1= 0.496

~A.

542 JOURNAL DE

PHYSIQUE

I N°5

(a)

.;.(Îi

6s5.7fi

'1,' (

'~ 3+?.ee

§

)

c lîl.à+

~

86.à?

43.48

100 15Ù -0Ll

[ma

(microsezond) (b)

W- -;<~@% ~

MS ~3~i'

.lt 0 _+r

6É'5.76

1

-,

Ùi- jL~ é-fi

~

~

Î

17~ Ù4

1 ù

aô.97

4],48

iDo isù zoo

Tirne

jrnicrosecond)

(C)

'~

Ii

ù

à

'

ç/

j j

(

^~

^~~-~~ ~~--'

~_--

~',_~ _{',_--~} ~<._,-/~ ~.._,~ ~._-~.~ ~.__--

Time microsecond)

Fig.

3.

(a) Frequency (log scale)

_{as a} function of time for 1

= 0.496 ~IA. Trie intensity of trie wavelet component increases when trie caler

changes

from black to

pink.

Trie caler

palette

_{is m a}

loganthInic

scale;

(b)

^Phase as a function of time. Trie vertical _axis is the frequency axis _m

log

scale. Trie

phase changes

from _-~ to +~ when the coter

changes

^{from black} to

pink; (c)

Transient

voltage

_{response as}

a function of time

(arbitrary ul~its).

~~) ^{-2 O 2}

6s5.76

É

-,

~'

347.88

~

~

)

_173.94

à~

a6.97

+3.4a

5o iôo iso 2ùo

rime imicr.~sacond)

(b>

fl fl@,'

-~ 0 +T

695.76

~'

1

347 88

fi

j~ ⁾

~ ^173.94

j~

(

a6 97

~ >où i~o ~oo

Tme (microsecond)

~c>

,,

Î,llll~',ll~l~l~<~lili~i,l~,,'i~ill1ll'~lifiljiiiiÎ<i~i~'«ll~«j

~ ,,

~

sa ioo

la

Time (microsecoud)

~

ÉÎ é-

§ 3~7.88

~

OE1

173.94

~~ ~~ ~~~ ~~ ~

[ma (microsecond) ^~~

fl~

Fig.

4.

(a)

Frequency

(log scale)

_{as a} function of time for1= 0.896 ~IA;

(b)

Phase _{as a} function of time.

(c)

Transient

voltage

response as a function of time

(arbitrary units)j (d) Expanded

view

showing

the

phase

_{as a} function of time _m the time interval 160 200 ps.

544 JOURNAL DE

PHYSIQUE

I N°5

not

only

these

frequencies~

but also

higher-order

harmonics with

decreasing amplitudes.

The

superimposed stripes, periodic

in

time,

which

develop

_{over a} broad _range of

frequencies,

_corre-

spond

to the

voltage spikes

in the time domain shown in

Figure 3(c),

which _{act as} Dirac

peaks

in the wavelet

analysis. Figure 3(b)

shows the time evolution of the

phase corresponding

to each

frequency Fi, F2, F3, F4.

The vertical scale is still the

frequency

scale. It _can be _seen

that the

phase

varies

periodically

from _-7r

(black)

to +7r

(pink).

Figure

4 shows the results of the wavelet

analysis

for _a current

pulse amplitude

well above threshold. Two

frequencies,

^trie fundarnental and trie second

harmonics,

_are

observed,

each with _a finite

spectral width,

_{as a} function of time. This width shows small fluctuations _as

a function of time.

During

_a short time interval

(80

_ps < t < 140

ps)

_an additional low

frequency F',

which _appears in orange in

Figure 4(a),

is

observed,

whose

spectral

width shows

fluctuations. F'

seems to increase

during

the titre interval 80 -100 ps, then to decrease in the interval

ils -140 ps. The broad structures

corresponding

to the

leading

and

trailing edges

of the

pulse

current in the real time domain _are artefacts. In contrast with the results shown in

Figure 3(b),

^{trie time} evolution of trie

phase

shows _{a more}

irregular behavior,

_as indicated in

Figure 4(b). Except

for trie additional low

frequency

F' where trie

corresponding phase

varies

monotonically, phase jumps

_are

clearly visible,

_as shown _in

Figure 4(d), especially

_neon trie end of trie

pulse

for trie

signal

with trie fundamental

frequency Fi

3. Discussion

Dur wavelet

analysis

demonstrates for trie first _time trie

possibility

^of

detecting

time resolved elfects involved in trie CDW

dynamics.

It

yields

_a resolution of structures in trie time evolution of the

frequency

and of the

phase,

net observed

by

conventional Fourier

analysis.

Another class of time resolved

experiments

involves studies of trie transient structural _response

through high

resolution

X-ray scattering.

Information _on CDW deformations _{on a} time scale of trie order of

ms lias been obtained

by

this

technique [14,15]. Temporal

fluctuations of trie NBN bave been observed under

mode-locking

conditions

[16].

Various models bave been

proposed

to describe trie

voltage

oscillations. In trie

simplest

one, trie CDW _{moves in a}

periodic potential

which has trie

periodicity

of

=

27r/Q along

trie chains. Trie CDW motion will be

periodic

with the fundamental

frequency

_v

=

Qv

where

u is trie drift

velocity

of trie CDW [7]. ^In an alternative

model, probably

_more

realistic,

trie oscillations

originate

at contacts _or at boundaries between

pinned

and

unpinned regions

[5]. ^Trie conversion of normal _carriers to CDW _{carriers occurs} at CDW

phase

dislocation

fines

perpendicular

to trie chains. Trie CDW current

changes

^rather

abruptly

whenever _a dislocation fine _is created at _one end _or annihilated _at trie other. Observation of

asymmetric voltage spikes,

shown _in

Figure 1(b),

_seems to

support

^{trie latter model.}

Figures 3(b)

and

4(b)

indicate that trie

phase

fluctuations _are

periodic _just

above threshold and show

rapid jumps

well above threshold. This

change

of

regime

_may be due to interactions between CDW

phase

dislocation lines. Trie

frequency

^F' observed in _a short time interval _may

correspond

to a transient

depinning

followed

by

a

graduai repinning

of additional CDW domains.

4. Conclusion

In summary, we bave shown that trie wavelet

analysis provides

_new data useful for _a better

understanding

of the _narrow band noise in CDW materials. This

analysis

method may open up ^a way ^to more

systematic

studies of

dynamical _properties

and metastable

phenomena

of

dilferent CDW conductors.

Acknowledgments

The authors wish to thank R. Buder for bis technical

help

and

CEPHAG/ENSIEG

for their

computer

facilities. This work _was

supported,

in part,

by

Junta Nacional de

Investigaçac

Cientifica _e

Tecnologica (Portugal)

under contract

STRDA/C/CEN/431/92

and

by

_a JNICT- CNRS

agreement.

References

iii

For _a

review,

_see: Monceau

P.,

Electromc

Properties

of

Inorganic Quasi-One

Dimensional Mate- riais, P.

Monceau,

Ed.

(D. Reidel, Dordrecht, 1985)

_p. 139.

[2] ^Grüner

G., Density

Wave _m Solids

(Addison-Wesley

Pub.,

1994).

[3] Fukuyama H. and Lee P-A-,

Phys.

Reu. B 17

(1978)

535.

[4] ^{Lee P-A- and Rice} T.M.,

Phys.

Reu. B 19

(1979),

^3970.

[5]

Ong

^N.P. and Maki K.,

Phys.

Reu. B 32

(1985)

6582.

[6]

Dpmas

J. and

Feinberg

D.,

Europhys.

Lent. 2

(1986)

555;

Feinberg D.,

Friedel J., J.

Phys.

149

(1988)

485.

[7] ^Grüner G., _m reference [2], p. 183.

[8]

Meyer

Y. and

Wavelets, Time-Frequency

Methods and

Phase-Space,

J-M-

Combes,

Ed.

(Springer, 1989)

_p. 21; Daubechies I.,

ibid.,

_p. 38.

[9] Flandrin

P., Temps-Fréquence (Hermès, Paris, 1993).

[loi

Morlet J., Arens G.,

Fourgeau

E. and Giard

D., Geophys.

47

(1982)

203.

[iii Lapes

E-B- et

ai.,

ta be

published.

[12]

Lapes

E-B-, Matas M.J.,

Henriques R-T-,

Almeida M. and Dumas J.,

Europhys.

LeU. 2T

(1994)

241.

[13] Gama

V., Henriques

R-T-, Almeida M. and

Pouget J-P-, Synih.

Met. 55-57

(1993)

1677.

[14] ^Sweetland

E.,

Finnefrock

A.C.,

Podulka

W-J-,

Sutton M., Brock

J-D-,

Dicarlo D. and Thome R-E-,

Phys.

Reu. B 50

(1994)

8157.

[15] ^Tsutsumi K., Tamegai T.,

Kagoshima

S. and Sato M.,

Charge

Density Wave _m Solids, Lecture Notes _in

Physics,

Vol. 217

(Springer, 1985)

_p. 17.

[16]

Bhattacharya

S-B-, Stokes J-P-, Higgins M.J. and Klemm R-A-,

Phys.

Rev. LeU. 59

(1987)

1849.