Motional narrowing of the nuclear magnetic resonance line by the sliding of spin-density waves

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Motional narrowing of the nuclear magnetic resonance line by the sliding of spin-density waves

E. Barthel, G. Quirion, P. Wzietek, D. Jérome, J. Christensen, M. Jørgensen, K. Bechgaard

To cite this version:

E. Barthel, G. Quirion, P. Wzietek, D. Jérome, J. Christensen, et al.. Motional narrowing of the

nuclear magnetic resonance line by the sliding of spin-density waves. Journal de Physique I, EDP

Sciences, 1993, 3 (7), pp.1501-1505. �10.1051/jp1:1993195�. �jpa-00246809�

Classification Physics Abstracts 75.30F 72.15N

Short Communication

Motional narrowing of the nuclear magnetic

_resonance

line by the

sliding of spin-density

_waves

E. Barthel

I'),

G.

Quirion I'),

P. Wzietek

I'),

D. Jdrome

(~),

J. B. Christensen

(~),

M.

J#rgensen (~)

and K.

Bechgaard (~)

(~) Laboratoire de

Physique

des Solides, Universitd

Paris-Sud-CNRS,

F-91405

Orsay,

France

(~)

CISMI,

University

of

Copenhagen, Blegdamsvej

21, DK-2100

Copenhagen,

Denmark

(Received

18 January 1993,

accepted

4

May1993)

Abstract. We report _{on a}

study

of the electrical

conductivity

and

~~C-NMR

_in the nonlinear

conductivity regime

^{in the}

spin-density

_wave

(SbW) phase

of

(TMTSF)2PF6 (TMTSF

stands for

tetramethyltetraselenafulvalene).

The

narrowing

of the NMR line demonstrates that there is _a bulk _motion of the SDW. We find _a

qualitative

agreement between the nonlinear current

and the minimum current necessary to _narrow the NMR line in the

simplest

model of SDW conduction.

The

anisotropic organic

conductor

(TMTSF)2PF6 Ill

is in several

respect

the

prototype

mate- rial for the

study

of the

properties

^{of the} _one dimensional

(I-D)

electron _gas. A very

striking signature

of I-D

physics

^{is the}

competition

^between electron-electron and electron-hole

pairing

instabilities.

Due to the

stcechiometry

of the salt and its

crystalline structure, (TMTSF)2PF6

is

formally

a half-filled band I-D conductor. This

system

is sensitive to electronic instabilities. At _am- bient _pressure, the most stable _state is _a

ground

state

exhibiting

_a finite modulation of the

magnetization

_or

spin-density

_wave

(SDW) [2].

^The

divergence

towards the SDW state is dominant _as

long

_as the interchain

coupling

remains

sufficiently

small.

Hence,

the

application

of _a

high

_pressure, which enhances the _transverse

coupling

makes

superconductivity

the most

stable state at 9 kbar [3].

The SDW state is

phenomenologically antiferromagnetic,

_as demonstrated

by susceptibility anisotropy

_[4] data and

antiferromagnetic

resonance

[5].

^{The main difference between} a

regular antiferromagnetic phase

and the SDW

phase

lies in the _wave vector of the modulation. It _was

clearly

shown from the

analysis

of

~SR

_[6] and

proton

NMR

[7,

8]

spectra

that the _wave vector in

(TMTSF)~PFS

is incommensurate with the lattice.

One of the most

spectacular properties

of this

compound

is the

sharp

increase of

conductivity

above _a low threshold field

[9].

^{It is}

widely

believed that the incommensurate character of the

1502 JOURNAL DE

PHYSIQUE

I N°7

SDW

ground

state is at the

origin

of _{a zero}

frequency

collective

mode,

which in nonlinear response amounts to a

sliding

of the overall electron-hole condensate.

Pinning

of the SDW to

impurities

accounts for the _nonzero threshold field.

The _same nonlinear

conductivity

is found in

charge-density

_waves

(CDW).

In the NMR

spectrum,

the _presence of the CDW induces _a broad

frequency

distribution because of the

spatial

distribution of the electric field

gradient.

In the nonlinear

conductivity regime,

this line is narrowed

[10].

^This

clearly

demonstrates that the additional

conductivity

induces _a fast

modulation of the local

field,

thus

supporting

the notion of

sliding.

A

~H-NMR study

of the

sliding

SDW in the

quenched

SDW state of

(TMTSF)2Cl04

has been

reported recently [ill. However,

the

protons

are

dipolarly coupled

in four distinct

methyl

groups, and

give

rise _to

a very

complex

structure. The

'~C-NMR

_at the carbon sites at the center of the TMTSF molecule _are much better suited for these

studies,

because the

spectrum

is

simpler,

and the

coupling

of these nuclei to the SDW is

stronger

^than the

coupling

of

protons.

We demonstrated in _a

previous

_paper

[12]

^{that the}

'~C-NMR

line in

(TMTSF)2PF6

is also

considerably

broadened in the SDW state.

In this

communication,

_we

report

the

preliminary

results of _a

study

of the electrical _con-

ductivity

and

~~C-NMR

_{in the nonlinear}

conductivity regime

of

(TMTSF)2PF6. Narrowing

of the NMR line demonstrates that there is _a bulk motion of the SDW. We find _a

qualitative agreement

^{between the}

injected

current and the minimum current necessary ^to narrow the line in the most

simple

model of

sliding.

The

sample

_comes from the _same batch of

selectively ~~C

enriched

crystals [13]

we used in _our

previous

measurements

[12].

^The

occupation probability

for each of the central sites

(labelled (3)

and

(13)

in

[14])

^{is 5}

^il.

^Its size _was 3.0 _x 0.25 _x 0.3

mm~,

with _a cross-section of 6 _x

10~~ mm~

_and

a mass of 0.35 _mg. All measurements _were

performed

in the 9.3 T NMR field. For the

contacts,

we did not _use silver

paint,

because it is notorious for

cracking

_upon

cooldown,

but two

clamped

contacts

applied

_on the

gold-plated

b-c faces of the

sample.

No

jump

in the

resistivity

_was observed upon

cooldown,

and the residual

resistivity

at 15 K _was 0.9 Q. The 18 Q resistance _at 4.2 K is thus almost

entirely

due to the

sample,

in

agreement

with the _very

large

transverse

magnetoresistance

of the SDW

phase _[15].

At 4.2

K,

in the SDW

phase,

_we

clearly

observe _a threshold field of 5

mV/cm

in the current-

voltage (I-V)

characteristics

(Fig. I),

which is consistent with the usual values

[16].

We obtained the NMR

spectra (Fig. 2) by

_an ^echo _sequence with _a Bruker MSL400

spectrometer.

At 9.3

T,

the

'~C frequency

is 99.67 MHz. At _zero

current,

^the

spectrum

^exhibits two very wide

U-shaped

structures which _are

typical

of the

inhomogeneous broadening

due to the

sinusoidally spatially

modulated

magnetization.

Each _one is associated with _one of the _two

inequivalent

sites. The contribution of the other carbons is

negligible

because of the small

'~C

concentration and

long

relaxation time.

Under

current,

two _narrow

peaks

_grow out of the broad distributions. Their

intensity

in-

creases with

increasing

current.

However,

_even at I

mA,

there remains _a reminiscence of the

zerc-current

spectrum.

^{We believe this is due} to the

inhomogeneity

of the current

density

in the

sample. Therefore,

there is _a substantial fraction of the

sample

in which _no SDW current flows. We estimate this fraction _as 75

il

_at 0.5

mA,

and _as 60

it

at I mA.

At the _same

time,

the _presence of _a static fraction

clearly

demonstrates that the _appearance of the _two

peaks

in the nonlinear

conductivity regime

is not due to

heating

of the

sample

above

the

phase

transition. We also stress that if

heating

_were

involved,

the

intensity

of the NMR

signal

should decrease

by

at least _a factor of

3,

which is not observed.

These results confirm the

sliding

SDW

picture. However,

the exact nature of the

sliding

mode _can be characterized further

by

the ratio of the SDW current per

chain, jsDw,

to the local

phase

oscillation

frequency

_vj

(phase winding rate).

This

ratio,

in the

simplest

model

zo

(

~

j

~

O-S

l~ ("

$ ~

Q~ ^°'°

~

~l,oa

0 0

ectric field ^mV/cm)

Fig,

I.

Sample

resistance _{as a} funtion of electric field

(T

= 4.2

K).

Inset: nonlinear SDW current

ISDW " I

V/R(E

-

0)

as a function of the total current 1.

1=imA

i=o.5mA

1=omA

-400 400 800

shift

(ppm)

Fig.2.

NMR spectra in the SDW

phase

_{as a} function

if

_{the total sample}

current I at T

= 4.2 K.

1504 JOURNAL DE

PHYSIQUE

I N°7

[17],

^is

expected

to be:

jsDw/v4

₌ 2e

(I)

It _can be

indirectly

determined

by measuring

the

frequency

of the conduction noise which appears in the nonlinear

conductivity regime

_versus current.

Up

to now, these determinations

[18]

^have

yielded

_a ratio which is between 8 and 20 times smaller than

expected

from

equation (I). Although

it is not clear whether the noise

frequency

is

equal

to the

phase winding

rate _or twice

larger,

these data

suggested

_a

large discrepancy

with the

theory.

It is

usually

assumed that this arises _{as a}

strongly inhomogeneous depinning,

which leads to _{an erroneous} estimate of the effective

sliding

cross-section.

We estimate the SDW _current from

IsDw=I-V/R,

where R is the low electric field resistance

(Fig. I, inset). Then, using

_a chain _cross section of 100

i~

_and

a

depinned

fraction inferred from the NMR

spectra,

we find from

equation (I)

a mean

phase winding

rate of 30 kHz _at

a total current of 0.5

mA,

and 56 kHz at I mA. The simulations show that such

frequencies

_are

high enough

to

yield

_a substantial

narrowing

of the line.

Therefore,

_we cannot

exclude,

_on the basis of these

data,

that the

jsDw/vj

ratio is

considerably

smaller than

expected. However,

this is not necessary.

We conclude that there _are

large amplitude

local

phase

fluctuations in the _non linear _con-

ductivity regime

in

(TMTSF)2PF6.

This result is consistent with the

accepted picture

^of a

sliding spin-density

_wave.

Although

_a small

jsDw/vj

ratio is not in contradiction with _our

results,

it is not necessary to

explain

_our data.

Obviously,

combined conduction noise and

NMR measurements are needed _to solve this

problem.

After this work _was

performed

_we learned that W. H.

Wong

and coworkers

[19]

^{had also} observed

sliding

SDW in

(TMTSF)2PF6 by ~H-NMR

in low

magnetic

^fields.

Acknowledgments.

Useful discussions with G. Kriza _are

acknowledged.

We _are

grateful

to J. C. Ameline for

building

the NMR

probe

and

together

with G.

Tevanian,

for decisive

help

with the contact

system.

E. B.

acknowledges support

^from the Et~des Doctorales de l'Ecole

Polytechniq~e.

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Jacobsen C.

S.,

Mortensen K., Pedersen H.

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D.,

Mazaud

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Phys.

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[4] Mortensen

K.,

Tomkiewicz Y., Schultz T. D. and

Engler

E.

M.,

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[5] ^Torrance J. B., Pedersen H. J.,

Bechgaard

K.,

Phys.

Rev. Lett. 49

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881.

[fi] Le L.

P.,

Luke G. M., Stemlieb B.

J.,

Wu W.

D.,

Uemura Y. J., ^Brewer J. H., Riseman T.

M., Upasani

R. V.,

Chiang

L. Y., Chaikin P.

M., Europhys.

Lett. 15

(1991)

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[7] Takahashi

T.,

Maniwa

Y.,

Kawamura

H.,

Saito

G.,

J.

Phys.

Soc.

Jpn

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(198fi)

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[8] ^{Delrieu J.} M.,

Roger

M., Toflano Z., Moradpour A.,

Bechgaard K.,

J.

PlJys.

France 47

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[9] ^Tomid S.,

Cooper

J.

R.,

Jdrome D. and

Bechgaard

K., Phys. Rev. Lent. 62

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[10] ^{Ross J.}

H., Wang

Z. and Slichter C.

P., Phys.

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fifi3;

Nomura K.,

Sambongi T.,

Kume K, and Sato M.,

Physica

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II?;

S4gransan P., Jinossy

A., ^Berthier

C.,

Marcus J. and Butaud

P., Phys.

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[12] ^Barthel

E., Quirion G.,

Wzietek

P.,

J4rome

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Christensen J.

B., Jwrgensen M., Bechgaard K., Europys.

Lett. 21

(1993)

87.

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Jwrgensen

M. and

Bechgaard

K.

(unpublished).

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Thorup N.,

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K., Acta

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[15] ^{Chaikin P.}

M.,

Haen

P., Engler

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G.,

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M.,

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N., Sambongi T.,

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K., Nagasawa N.,

Tokumoto

M.,

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H.,

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1507-1508 JULY 1993, PAGE 1507

Corrigendum and addendum _to section 3 of "Level spacing

functions and

_non

linear differential equations"

G. Mahoux and M.L. Mehta

J.

PlJys.

I. France 3

(1993)

fi97-715.

In the above reference _we missed to note that the functions

A,

_{w, ~, u,} and

if

in

equations

(3.ll)-(3.21)

_are real for real _{r, so} that the absolute value of

ya~(T)

^is

unity

for real _T. In other

words,

if _we set ya2 "

exp(2ip), p(T)

is real for real _T, satisfies the

(non linear)

differential

equation

p"

+

~'~ ~)

^{tan p}

^p'~

^{+ 4 = 0}

^(3.28)

T

and _{near T =} 0 has the

expansion

p(T)

₌ -2T

J (T

+

o(T~)1 (3.29)

Thus

equation (3.5)

should be corrected _as

ya2 = exp

(-4iT

₊

4i(T~

₊

O(T~))

= 4iT +

4(I( _2)T~

+ 16

(

^{~~ T~} +

O(T~). (3.5')

3

Also it _was shown that each of the four functions Re

S(T),

Im

S(T), A(T), B(T)

_can be

expressed

in terms of _a fifth Painlevd transcendent

(P5),

and _one of

them, namely B(T),

also in terms of _a third Painlevd transcendent

(P3). Actually, according

to Gromak

(see

the reference

below),

each of the

remaining

three functions _can also be

expressed

in terms of _a P3. In other

words,

_as the P5 with

equation (3.5')

is related _to the P3 with

equation (3.8),

so the P5 with

equations (3.2), (3.3)

and

(3A)

_are related to the P3 with

respectively

(1)a=-I, fl=3, 1=1, b=-I;andforT«I,

Y(T)

-

-1+ ³ 1)

T +

(-I

+

<1

T~ +

(3.30)

(2)cY=-I, fl=3,1=1, b=-I;andforT«I,

y(~~ ~~~~ ^(T~

3

I $

^~

(3.31)

and

(3)cY=I, fl=I, i=I, b=-I;andforT«1,

~3 Y+(~)

_" ~~ +

(~~

j

⁺ '

(3.32)

or another

possible

choice

y_

(T)

₌

( (~

T +

(3.33)

T 3

Here _are the _necessary details. This addendum is

supposed

to be read with the

original

reference.

Consider the

couple

of

equations

~ R~

T

~~' ~)

'

~

f~1 _{~~'~ ~)} ~~'~~~

Eliminating f

_one

gets equation (3.10),

while

eliminating

R _one

gets f"

=

)f'~ ( $~

+

f(f~ _{-1). (3.35)}

Set

f

₌

1t/(1t 1),

or ~ ₌

f~/( f~ I),

_so that

'~~~ i~~1L

-~l)

^{'~~~ ~}

~~

~'~ ~~~ ~'~ ~~ ~~~

This is

again

almost _a PS with b

=

0,

and becomes _a standard PS _on

taking

T~ _as the _new

independent

variable.

Consider _now the

couple

of

equations

~

~~ ~' ~~'

^~ _TIL'

^~~1L

1)

^{~~ ~~~}

Eliminating

_{uJ, one}

gets (3.36),

while

eliminating

_{1t one}

gets

a P3 for _uJ with _cY

=

-I, fl

=

3, 1=1,

b

= -I.

In

equation (3.21)

if _one writes

f

₌

_(y~ 1)/(2iy),

then _one

gets

Y" "

~ ~

+

(y~

+

I)

+

y~

,

(3.38)

a P3 with _o

=

l~ fl

₌

I,

_{i =}

I,

b ₌ -I.

Expressing

_y in terms

off,

y+ =

it

+

-, _(3.39)

one

gets equation (3.32)

or

(3.33).

Some

one-parameter

^{families of solutions of these}

equations

are

known,

but _none of them satisfies _our conditions at _{T =} 0.

Reference

Gromak V-I-, Reducibility

of Painlevd

equations,

^Dilf. Urav. 20

(1984)1674-1683.