Dielectric Voltage Response in Spin-density Wave of (TMTSF)2AsF6 at Low Temperature

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Dielectric Voltage Response in Spin-density Wave of (TMTSF)2AsF6 at Low Temperature

Mitsuharu Nagasawa

To cite this version:

Mitsuharu Nagasawa. Dielectric Voltage Response in Spin-density Wave of (TMTSF)2AsF6 at Low Temperature. Journal de Physique I, EDP Sciences, 1996, 6 (12), pp.2135-2140.

�10.1051/jp1:1996208�. �jpa-00247301�

Dielectric Voltage Response in Spin-Density Wave of (TMTSF)2AsF6 _at Low Temperature

Mitsuharu ~agasawa (*)

Department

of

Physics,

Hokkaido

University, Sapporo

060,

Japan

(Received

26

April

1996, revised 19

August

1996, accepted 20

August 1996)

PACS.61.66.Hq Organic

_compounds PACS.75.30.Fv

Spin-density

_waves

PACS.72.15.Nj

Collective modes

le-g-,

_m one-dimensional

conductors)

Abstract.

Voltage

_response to constant unipolar puise current in the spin-density _wave

(SDW)

state of

(TMTSF)2AsF~

_was studied. Below 3 K,

Ieading

and

tailing edges

of the

voltage

response are rounded at Iow electric field. The time dependent

charge density

accumulated in the Iattice

was estimated from the

voltage

profiles. It

con be fitted

by

_a stretched exponential

formula; q(t)

_{cc qo} (1-

exp(-(t/Ti )~)).

With

increasing

field _qo increases and shows

a maximum

at the threshold electric field for

depinning.

In the pinned state, the relaxation time _Ti increases with

decreasmg

temperature and its activation energy is

approximately

equal to that of ohmic

conductivity.

The index

fl

is _a

hnearly decreasing

function of temperature and it is

extrapolated

to _one at 0 K.

Screemng by

normal carriers becomes imperfect and

couphng

between

density

wave domains becomes stronger on

cooling.

1. Introduction

In varions

(TMTSF)2X

salts which _are

quasi-one

dimensional

organic conductors,

the

ground

state of the electronic

system

is the

spin-density

_wave

(SDW).

The

phase

transition from metal

to

insulating

SDW is observed

commonly

at _mJ 10 K. In the SDW

phase,

the

conductivity

is ohmic _at low field but increases with field above the "threshold electric field

ET"-

From

companson with the

charge-density

_wave

(CDW) _systems,

_{it has been confirmed that the}

nonlinear conduction above

ET

is due to the

sliding

SDW

depinned by

field.

In

(TMTSF)2PF6

sait and at T

mJ 3

K,

anomalies in

~H-NMR

_{relaxation time}

iii

and in heat

capacity

_[2] have been observed. It has been

proposed

that the anomalies _are related to _a

phase

transition from "SDWI" to "SDW2" _on

cooling

below

mJ 3 K

il,2j. However,

the nature of that transition has not been clarified. In the

previous study,

_we have

reported

that the

SDW

dynamics

also shows anomalies at _mJ 3 h in

(TMTSF)2AsF6

sait [3]; ^both temperature

dependence

of

ET

and the ratio of nonlinear

conductivity

at low field to the ohmic component show breaks at that

temperature.

We

proposed

that these anomalies _are indicative of _a

phase

transition, presumably sharing

_{a common} mechanism with

(TMTSF)2PF6. Furthermore,

_we have shown that the _narrow band

voltage

_noise under DC current and transient

oscillatory voltage

_{response can} be observed above

ET only

in the low

temperature

"SDW2"

phase

_[4,

_5].

(*)Present

address: Natural Sciences,

Faculty

of

Engineering,

Tokyo Denki

University, Muzaigakuendai 2-1200,

Inzai Chiba 270-13,

Japan (e-mail: nagasawafichiba.dendai.ac.jp)

@

Les

Éditions

_de

_Physique

₁₉₉₆

2136 JOURNAL DE

PHYSIQUE

I N°12

Below

ET

~v-here the SDW is

pinned,

the

voltage

response for constant

puise

current is different between in the "SDWI" and in the "SDW2"

phases.

In the "SDWI"

phase,

the

voltage responds instantaneously

to the

applied rectangular

current

puise.

On the other

hand, edges

of the response

voltage

_are rounded for the

puise

in the "SDW2"

phase.

The time until the

voltage

becomes constant increases with

decreasing temperature [3,4].

^Neither

temperature

nor field

dependence

of this "dielectric

voltage response"

has been

investigated,

however.

A similar rounded

voltage

_response has been

investigated by Fleming

^and

Schneemeyer

_[6]

in the CDW of

Ko.3Mo03.

When current

puise

for field above

ET

^has the _same

polarity

_as the

preceding

_one, the

voltage responds instantaneously

to the

puise.

On the other

hand,

when current

puise

has the

opposite sign

to the

preceding

_one, the

voltage

_{response curve} is rounded.

This is the so-called

"puise-sign

_memory effect". Parker and Zettl I?i ^have used the

puise-sign

memory effect to

investigate

the metastable

pinning configuration

in the CD~V of

NbSe3.

Recently,

Kriza et ai. [8] observed the _same effect in

(TMTSF)2PF6. They

showed that this

anomaly

_can be detected at E »

ET Mihaly

et ai. _[9] measured the

low-frequency

dielectric

response of

(TàITSF)2PF6

below

ET

and at 2 K

by

real-time relaxation

technique. They

showed that the

polarization

relaxes with

long

time in this

regime.

It _seems that the

origin

_is the

same as that of the behavior observed

by

_us at low field in the "SDW2"

phase;

^{these dielectric}

phenomena

_are due to the elastic deformation of the

pinned

SDW. While discontinuons

changes

are

expected

in the dielectric behavior at

ET

because the SDW is

depinned by

field above

ET,

such

changes

at _mJ

ET

have not been clarified

yet.

In the

present study,

_we

report

on the time

dependent

accumulated

charge density

which

is estimated from the

voltage profiles

and discuss the relation between field _response of the

pinned

SDW and functional formula of the

charge density.

2.

Experiments

Single crystals

of

(TMTSF)~AsF6

_{were grown}

by

the standard electrochemical method. The electrical leads of annealed

gold

wires of10 _~lm diameter _were attached with silver

paste

to

gold pads evaporated

on the

sample.

The whole _areas of both ends of the

sample

were covered

by

silver

paste

^{for uniform current}

density.

At _room

temperature

^{and ambient} pressure, the

conductivity

_{a was} about 400

Q~~cm~~.

The

sample

_was

slightly pressurized

in a

clamp- type

^bomb to avoid resistance

jump.

^{The actual} pressure at low temperature was lower than 0.1 GPa. The resistance

jump

was not observed

dunng applying

_pressure and

cooling.

Constant

pulse

current _was introduced

along

^the

^conducting

^{axis and the} response

voltage

_was measured.

The

repetition

rate of

pulse

current with

mJ 1 Hz _was

carefully

chosen to avoid effect of Joule

heating.

In order _to reduce

background

_noise, both

voltage

and current

profiles

were recorded

repeatedly

and

averaged.

3. Results and Discussion

At low field and below 3

K,

the

voltage 1'(t)

increases

gradually

with time t

during

the

pulse

width,

although

constant current is

apphed. Figure

1 shows _a

typical profile

of the

voltage

response ^to

rectanguiar

current

pulse

at 1.2 K.

Voltage

tail is also observed after the current is turned off. The

voltage profile

cannot be fitted to a

single

_{nor a} stretched

exponential

function.

We introduce a

parameter tm,

^{which satisfies the relation}

[V(tm) V(tm/2)]/V(tm)

₌ 0.01.

To calculate the

conductivity

we use

l~(tm)

_as the saturated

voltage Vit

=

cc),

because the

puise

^width _was rather limited to avoid Joule

heating. Though

tm itself is determined

only crudely, V(tm)

is accurate

enough

to discuss the essential feature of the

stationary

current-

voltage relation,

in which the ohinic region is

clearly

observed and

ET

is

clearly

determined.

Î~

$7

^0.04

E

g

t0.8

^{T=1.2K ~}

~ (

fi

^-

>

0.02l$

o

~

0 _t

(msec)

10

Fig.

1.

Typical voltage

and _current

profiles

at the

Ieading edge.

The dashed hne represents the

voltage

at tm. Inset: the entire

voltage profile.

Below

ET,

tm is rather insensitive to

field;

the

voltage profiles

below

ET

_can be nornialized

by V(tm)

into _a

single

_curve at _a fixed

temperature.

With

decreasing temperature,

tm _in the low field _range increases

continuously.

Above

ET, leading

and

tailing edges

of the

voltage

_response

become less rounded with

increasing

field. In field

higher

than

2ET,

tm becomes too short to be determined

experimentally;

trie dielectric _response is due to trie

pinned

SDW. Trie SDW is deformed around

pinning

centers _or at

edges

of

crystal by

external field. Trie deformation

accumulates electric

charge

and trie

voltage

_is rounded

during charging

or

discharging.

In trie

pinned

state, trie accumulated

charge

is

expected

to be

ensDwôr,

where _~sDw is the SDW condensed

density

and ôr is the SDW

displacement.

In this

scheme,

ôr should be smaller than the

period

of the

pinning potential

for trie SDW

ÀpIN

_r~ 7

À.

As _a model of trie present real

system,

we consider _a

parallel

circuit of _an ohmic _resistor and

a

capacitor.

The time

dependent

accumulated

charge density q(t)

is related _to the

injected

current

density j(t)

and the electric field

E(t);

~~~~

~Î~ ~~~~~~~~~'

where

a(cc)

_is

approximated by

that _{at t}

= tm. When the SDW is

pinned, a(cc)E(t)

_is the ohmic _current

density by

normal carriers while in the

sliding

state it is given

by

the _sum of the ohmic current

density

and the DW current

density. Figure

2 shows accumulated

charge

qo "

q(t

=

tm)

_{as a} function of the field

E(t

=

tm).

Kriza et ai. [8j

reported

that trie accumulated

charge

obtained from trie

pulse-sign

_memory effect shows _a

peak

but trie

peak

is not located _at

ET.

On trie other

hand,

trie _curves in

Figure

2 show breaks _at

ET

trie

peak

corresponds

to trie

depinning

of trie SDW. Trie _maximum of _qo, at E

=

ET,

_is not sensitive _to temperature ^and then trie SDW

displacement

ôr _is

mJ 0.3

À

_{which is not much smaller than}

ÀpIN

r~

7

À.

_{The result is consistent of the scheme of the SDW} deformation _in electric field.

Below

ET,

_qo increases

hnearly

with trie field. Trie ratio

qo/E(cc)

is

expected

to be _pro-

portional

to the low

frequency

dielectric constant

e(0).

From

Figure 2, e(o)

is

independent

of the field in the ohmic

region.

At 1.6

K, e(o)

₌

^10~

mJ

10~

is

obtained,

which is of the _same order of

magnitude

_as the low

frequency

dielectric constant of

(TMTSF)2PF6

at 2 K obtained

by Mihaly

et ai. _[9] With

decreasing temperature, s(0)

decreases but

ETe(0)

is

approximately

constant when trie

previously reported temperature dependent ET

_is used. It bas been _re-

ported experimentally

that

ETe(0)

bas _{a common} value _among trie _varions materials

[9j.

^{It is}

2138 JOURNAL DE

PHYSIQUE

I N°12

8

E~(i.9K)-~~

^{E~(1 7Ki}

. e 1.2 K

_

ET(1 2K) _-X- 1.7 K

~~

⁺

~.* j

^{~ l.9K}

~

1'

^x _~

~~jc

^° _,

Î _,' ~~l',

'

j

/

~ g,

é

'

Gf

(

^{" '} _,

ef o,

E

(mV/cm)

Fig.

2. Accumulated

charge

density _{qo as} a function of the field at tm. The cross-sectional _area and the distance between

voltage

contacts _are 0.285 _x 0.091 mm~ and 1.12 _mm,

respectively.

io°

T 1.2 K

10~

~ ~ ~~~ ~~_~

~~ ~~

t

(8ec)

Fig.

3. Ratio (qo

q(t))/qo

_us. time. The broken Iine is

expressed

_as

exp(-(t/Ti)~)>

where the

relaxation time _Ti and the exponent 0 _are 3.2 _ms and 0.7,

respectivelv.

confirmed that trie relation

ETe(o)

mJ con8tant 18 realized

qualitatively

at zero

frequency

^when the temperature

dependent ET

obtained in _our

previous

_{paper [3]} 18 used. Combined with the

experimental finding

that

ETe(o)

has _{a common} value among the _vanous matenals

[9],

^{it is} established that

ETe(o)

has _a universal

temperature-mdependent

value among DW materials.

In the

sliding state,

if the SDW is

depmned coherently,

_qo would be

equal

to _zero. In

Figure

2, qo decreases above

ET

but is finite between

ET

and

mJ

2ET.

It is

suggested

that _a

part

of the SDW is still

pinned

in that range due

to,

_e.g..

spatial

distribution of _pinning

potential

in the

crystal.

On the

contrary,

^above mJ

2ET,

the SDW slides

coherently

in the

large

fraction of

sample

volume because _qo

mJ o and the transient

voltage

oscillation is observed.

Finally,

we discuss the time

dependent

accumulated

charge density q(t

_<

tm)

below

ET.

As shown _in

Figure 3, q(t) obeys

the relation

q(t)

_c~

qo(1- exp(-(t/Ti)~)).

_In the entire

10~~

o

la ^l~° o.8

-

)

o

_ç

~

'~ ° X 0.6

~

~

x o o

x x

o

°~

°~

o.4 _o o

~

x

0.2

x

o.4 0.6 0.8 °

o 2

1/T

(1/K)

T

(K)

Fig.

4.

Fig.

5

Fig.

4. The relaxation time _Ti

as a function

of1/T

for two

samples.

Fig.

5.

Exponent fl

_{as a} function of temperature for two

samples.

temperature

_range, the relaxation time _{Ti is} shorter than tm and the

exponent fl

is smaller than

one.

Mihaly

et ai. [9] found that the time

dependent polanzability

of

(TMTSF)2PF6

at 2 K

obeys

the above stretched

exponential.

Both _Ti and

fl depend

_on

temperature.

With

decreasing temperature

_Ti increases

exponentially

_as

exp(ED /T) (Fig. 4)

and

fl

increases

linearly (Fig. 5).

The activation energy obtained from

Figure 4, ED

r~ 13 K is not much different from the thermal activation energy of the ohmic

conductivity

_mJ lî K. Normal carriers _screen the

inhomogeneous

electric field

by

the SDW deformation and the screening becomes

imperfect

with

decreasing temperature.

Even _in the

pinned

state, the above scheme of the

screening proposed by

Littlewood

[loi

is realized.

Therefore,

the

coupling

between SDW domains screened

by

normal _carriers becomes

stronger

with

lowering temperature.

As discussed

by Mihaly

et ai.

[9],

the stretched

exponential

formula

suggests

that the SDW

system

is

glassy. Glassy system

is

composed

of many domains with

slightly

distributed relaxation time and

fl

represents the distribution of the relaxation time. If the relaxation time is uniform within the

crystal, fl

should be

equal

to one and the

crystal

should behave _{as a}

single

domain. As shown in

Figure 5, fl

extrapolates

to _one at o K. In the "SDW2"

phase,

the number of SDW domains decreases with

lowenng temperature

due to

imperfect screening by

normal _carriers

and,

at T

= o

K,

the

pinned

SDW

system

would be

composed

of _a

single

domain.

Acknowledgments

I would like to thank Prof. T.

Sambongi

and Prof. K. Nomura for their instructive advice and continuai

encouragement dunng

this work. I also would like to thank Prof. H. Anzai

Himeji

of Institute of

Technology

for

providing tetra-n-butyl

_ammonium hexa-fluoroarseniic _and

helpful

2140 JOURNAL DE

PHYSIQUE

I N°12

advice _on the

synthesizing

^of

(TMTSF)2X crystal.

I would like to thank Prof. K. I<awabata for valuable discussions, and Prof. N. Mohri and Dr. H. Takahashi of the Institute for Solid

State

Physics

the

University

of

Tokyo

for

helpful

advice _on

high

_pressure

technique.

I would hke to thank Prof. K. Nemoto for comments on

glassy system.

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T.,

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Y.,

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