Evidence from 1H-NMR for a Crossover from “Local-Moment” Antiferromagnetism to Spin-Density Wave in (TMTTF)2Br with Application of Pressure

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Evidence from 1H-NMR for a Crossover from

“Local-Moment” Antiferromagnetism to Spin-Density Wave in (TMTTF)2Br with Application of Pressure

B. Klemme, S. Brown, P. Wzietek, D. Jérome, J. Fabre

To cite this version:

B. Klemme, S. Brown, P. Wzietek, D. Jérome, J. Fabre. Evidence from 1H-NMR for a Crossover from “Local-Moment” Antiferromagnetism to Spin-Density Wave in (TMTTF)2Br with Application of Pressure. Journal de Physique I, EDP Sciences, 1996, 6 (12), pp.1745-1752. �10.1051/jp1:1996186�.

�jpa-00247279�

J.

Phys.

I France 6

(1996)

1745-1752 DECEMBER1996, PAGE 1745

Evidence from ~H-NMR _for

a

Crossover from "Local-Moment"

Antiferromagnetism to Spin-Density Wave in (TMTTF)2Br with

Application of Pressure

B-J- Klemme

(~),

S-E- Brown

(~,*),

^P. Wzietek

(~),

^D. Jérome

(~)

and J-M- Fabre

(~)

(~)

Department

of

Physics

and

Astronomy, University

of California, Los

Angeles,

CA 90095, USA

(~) Laboratoire de

Physique

des

Solides,

Université de Paris-Sud, 91405

Orsay Cedex,

France

(~) Laboratoire de Chimie

Organique

Structurale, Université des Sciences et

Techniques

du

Languedoc,

34060

Montpellier,

France

(Received

27 June 1996, revised in final form 26

August

1996.

accepted

27

August 1996)

PACS.72.15.Nj

Collective modes

(e.g.,

_in one-dimensional

conductors)

PACS.75.30.Fv

Spin-density

_waves

PACS.75.40.Gb Dynamic properties

(dynamic susceptibility,

_{spin waves, spin}

diffusion,

dynamic

scaling, etc.)

Abstract. We have made measurements of the proton

spin-lattice

relaxation in the low-

temperature

antiferromagnetic ground

state of

(TMTTF)2Br

at different pressures. Ai ambient

pressure, the relaxation rate

1/Ti

is

peaked

at the transition temperature ^with isotropic critical

fluctuations apparent _over a wide temperature _range.

l/Ti

declines

monotonically

_as the tem-

perature is lowered.

Application

of

hydrostatic

_pressure results _in additional relaxation, _very hkely from collective excitations, in the ordered phase. The results taken

together imply

the system is driven from

commensurability

at _a very low pressure

(<

4

kbar).

The behavior _is

summarized in _a P T

phase diagram.

The

family

of molecular conductors known _as the

Bechgaard

salts _are remarkable in the

variety

^of

physics

associated with electronic correlations

Ill.

To _a

great

extent, this _is be-

cause the effective

dimensionahty

of trie conduction electron orbital motion is

easily

tuned _ma

relatively

small

changes

_m

temperature,

pressure or

magnetic

field. The

ground

states _acces- sible

through changes

of _pressure and

magnetic

^field include

Spin-Peierls, antiferromagnetic (spin-density wave-SDW), superconducting,

and

magnetic

field-induced SDW states.

The materials _are based _on trie

planar

donor molecules

tetramethyltetraselenafulvalene (TMTSF)

_or -thiafulvalene

(TMTTF),

which stack _{one on}

top

of the other.

Adjacent

molecu- lar stacks form

planes

which _are

separated by layers

of counterions, ^such as

Br~, PFj, CIO[,

etc. For reference _to trie discussion

below,

trie stack direction is _a,

perpendicular

to _a m trie molecular

plane

_is

b',

and normal to trie

plane

_is c*. The electromc conduction band is half-

filled,

_{as one} unit cell contains two molecules and _one counterion- The ratio of transfer

integrals

ta » tb » tc

(la:1:o.03)

leads _{to a} Fermi surface that is

àpen along

trie b' and c* directions and

(* ^Author for

correspondence (e-mail: brownslphysics.ucla.edu)

©

Les

Éditions

de

Physique

1996

1746 JOURNAL DE

PHYSIQUE

I N°12

thus

susceptible

to

nesting

eifects such _as the formation of

density

_waves. The most familiar

example

is

(TMTSF)2 PF6 (Se-PF6),

which has _a

strongly temperature-dependent

metallic

conductivity

before

undergoing

_a metal-insulator transition to _an incommensurate SDW _state at 12 K and ambient _pressure

[1,2].

By

contrast, identical salts made from the sulfur-based TMTTF molecule tend to have _more localized electrons

[1,

3]- ^{It is}

generally

believed that the

important

diiference from TMTSF materials is the amount of effective dimerization of the _two molecules _m the unit cell

(it

is

significantly greater

for TMTTF

systems),

which leads to two transfer

integrals

in the stack direction. The result is _an enhanced two-electron

Umklapp scattering

and thus _a Mott-Hubbard

(MH) charge

_gap

Ap [4].

^Two consequences of the MH gap are

first,

the

suppression

^of coherent interstack

single-partiale

motion and

second,

_a

separation

of the

charge

and

spin degrees

of freedom

(there

is _no

accompanying spin gap).

In the _case of extreme dimerization the

ground

state is

Spin-Peierls (e.g., (TMTTF)2PF6 là,

_fil

),

and in intermediate _cases the

ground

state is

antiferromagnetic

but commensurate with the lattice

je.

_g.,

(TMTTF)2Br [7-9]).

Transport

studies of

(TMTTF)2Br (S-Br)

showed

interesting

eflects of

high-pressure

_on

the

ground

state

[10,11j.

The

antiferromagnetic

wavevector at ambient pressure is low-order commensurate with the lattice. When the

applied

_pressure exceeds 10

kbar,

nonlinear

transport

reminiscent of the

depmning

of incommensurate

density

_waves is _seen,

just

^{like that} observed for

(TMTSF)2PF6 _(12].

These results _were

interpreted

_as the eflect of _a

dimensionality

_crossover in the

single partiale motion,

which _occurs because trie relevance of trie MH

charge

_gap is

rapidly

diminished with

application

of

only

r- 5 kbar of

hydrostatic

_pressure. At lower pressures,

dTN/dP

_> o follows from trie

expected

increase in interstack

exchange

with _an increase in trie ratio

tb/Ap.

At _pressures P _> 5

kbar, dTN/dP

_< o results because trie

imperfectly-nested

Fermi surface bas been restored. And

finally, just

as for

(TMTSF)2PF6,

trie

imperfect nesting

leads to

incommensurability

and _a "turn-on" of collective

transport. Although

this

picture

is

probably

somewhat

idealized,

it is _a useful

starting point

for discussion.

Here _we

report

on measurements of

~H spm-lattice

relaxation _rate

(1/T~)

at four pressures:

ambient,

4.5

kbar,

6

kbar,

and 10 kbar.

By conducting

NMR

experiments,

we

hoped

not

only

to find microscopic

support

for the

general

scenario laid out

above,

but also to

explore

_{m more}

detail the _pressure

/temperature phase diagram

_up to where non-ohmic

transport

was first _seen at 10 kbar. In

principle,

NMR _can be used _{as a} tool to answer

questions

related to issues of

commensurability, particularly

at

magnetic

fields below the

spin flop

field

(Bsf

_r- o.4 T

[13]).

It is also _a sensitive

probe

of

low-frequency

fluctuations of the order parameter, such _as

phase

fluctuations in _an incommensurate

density

_wave. Dur focus _{is on} the

spin-lattice

relaxation _rate

(1/T~),

which

probes

the

spectral density

of fluctuations _at the Larmor

frequency.

Previous results from

~H

_{NMR at P}

= 13 kbar _on

powdered samples

showed _a

temperature-independent

rate below TN

(14].

Dur

experiments

also indicate that

1/Ti

at ambient _pressure is

qualitatively

and

quantitatively

diiferent from

1/T~

at

higher

_pressures. We find that the latter is very close to what is observed in trie SDW

phase

in

(TMTSF)~PF6 [15,16j.

At intermediate _pressures,

there _{is a} contribution which _we

interpret

as a result of collective fluctuations. No evidence for

a

commensuratelincommensurate

transition is observed with trie

NMR, leading

_us to

suggest

that trie

system approaches plane-wave incommensurability

in _a continuous _manner. Even at P = 10

kbar,

the

hneshape

_appears to be diiferent from the

Se-PF6

material

[17j.

The

crystal

chosen for this

study

_was made at

Montpellier using

the standard

electrolysis method,

_{as m our previous} work _on the

transport properties.

Its _{mass was} about 280 pg and the face

defining

the

plane

normal to c* _was well-defined. NMR measurements _were carried out at low

magnetic

fields

Bo

_<

Bsf,

varied in the b'- c*

plane

_{so as} to

exploit

the full

anisotropic

character of the

antiferromagnetic

_state

(the

_easy and intermediate _axes at ambient _pressure

are known to be close to b' and

c*, respectively [18j).

Pressure _was

applied

in _a standard

N°12 ANTIFERROMAGNETISM IN

(TMTTF)2Br

1747

~~ . l bar

A~~

~ A la kbar

ç'~

₆ 6

~~~ _~~~

~i

.

"~

°

..

~ . ~

$

_{. 66}

~~

ù-1

ù-o

T/T~

8

_- 'ce

~4

2~ iso

§

1î48 JOURNAL DE

PHYSIQUE

I N°12

where _T is trie

delay

after _a saturation sequence. Then

Tp~

e T is a characteristic time of trie

system.

At ambient _pressure,

fl changes slowly

from

unity

for T _> TN to about o-fi at trie

lowest

temperatures

^measured.

fl #

1 _{can occur} for _{many reasons-}

Among

these at least two may

apply

here: _more than _one contribution in the

integration

window for the

magnetization

evaluation, and

spin-diffusion-limited

T~ _processes.

Trie contrast of trie ambient _pressure data to that from 10 kbar is substantial. The transition

region

becomes

extremely

_narrow, with trie

signature

of _a

peak

from

ordering only

about K wide. A

large

temperature

mdependent

rate

develops

below trie transition and extends to

temperatures

as low _as 6

K,

followed

by

_a

_strong

maximum centered at about 5 K.

All of trie features of

Tp~(P

= 10

kbar)

_{are common} to trie

prototypical

mcommensurate

system, (TMTSF)2PF6 115,16].

In

particular,

trie

large, relatively temperature mdependent

part ^for

Se-PF6

is

commonly

attributed to slow fluctuations related to trie SDW

phase

at trie

nuclear sites. These fluctuations _are at _a low energy because of trie

system's

incommensura-

bility.

While the association of the

peak

itself to a

particular

mechanism remains controversial

[15, 19],

^{it is} _very

hkely

also attributed to

phase

fluctuations _m both

Se-PF6

and _our system. ^For one

thing,

there _{is a}

large angular dependence

to the

strength

of the

peak

and to the

temperature independent

_part; both _seem to be related to the

angle dependence

of the linewidth. We

observe that the minimum

broadening

is for the de

magnetic

^field near to the c*

direction, just

_as for

Se-PF6.

The

broadening

arises from two sources, the

hyperfine

scalar interaction

and the

dipolar

interaction. If the scalar

part dominates,

then the

broademng

_{varies as}

cos(çi) (çi

= o for

Bol16'). Dipolar coupling

to the electron

spin

^leads to deviations from the sinusoidal

dependence, including

_nonzero

broadening

^for

alignment

^{of the de field with} c~ In

Figure 1b,

we show the

angular dependence

of

Tp~,

for the _{same cases} of P

= o and 10 kbar. The solid line

through

the data taken at P

= 10 kbar is

given by

the function

Tp~(çi)

₌ A ₊ B

cos~(çi),

with çi ^measured from the c* axis and A

= 3

s~~

_{and B}

= fi-à

s~~.

As fluctuations of the local field

orthogonal

to the axis of the de field _are

Ti

_Processes, the data _are consistent with _some type ^of

low-frequency phase

fluctuation

although

_no

proof

has been oflered that the

system

is mcommensurate at 10 kbar-

Completely

absent is any measurable

anisotropy

at ambient

pressure where the

system

^has been shown to be commensurate

[7,8].

To examine _more

closely

the

temperature dependence

of the

amsotropic part (including

the

Peak),

in

principle

_we would have to find the diiference

ATp~

=

Tp~(BOÎÎC*) Tp~(Bo((b')

to

give

the functional form for the contributions

originating

from what _we consider _to be the

phase

fluctuations.

However,

at 10

kbar,

the

anisotropy persists nearly

_over the entire tem-

perature

_range, hence _no subtraction _{is necessary}

(trie justification

for this

procedure

is that the

isotropic,

critical part ^is

msignificant

_{except very} close to

TN ). Figure

2 shows T~~~ for two

frequencies,

_UJN/27r

= 8 MHz and 28 MHz with the field

along

c*. The

peak

is

typical

for fluctuations with _an effective activated correlation

time,

where trie characteristic time grows

long enough

to pass

through

trie

probing frequency.

Similar behavior _is

ubiquitous

_{to measure-}

ments of trie dielectric relaxation _in

density

_wave

systems weakly pinned by impurities,

and

are believed to result from trie existence of many

low-lying

metastable states. In that _{case, a} dielectric

susceptibility

with _a distribution of characteristic time scales _is used to describe trie observed behavior

[20]-

^The distribution _is often

represented using

trie form

~~~~

l +

ÎÎTC)"

^~~~

for trie _q

= o dielectric

susceptibility,

where _{a is}

typically

_near o-î and _Tc

= To

exp(ih/2kBT)

with A trie

quasiparticle

_gap.

N°12 ANTIFERROMAGNETISM IN

(TMTTF)2Br

1749

1o

P=10 kbar 8

_- ~ A/

k~=26

^K

w o

É ~~=48

ps

©

₄ ^°

,'~'

.

/

2 ,'

~ ~

,,'

o

0 ^"

0 2 4 6 8 0 2 4

temperature (K)

Fig.

2. Proton

Tp~

_w.

T(K)

at 10 kbar for

wN/2~

= 8 MHz

(filled circles)

and 28 MHz

(open circles).

The sohd fine _{is a} fit to the lower frequency date _using equation

(2)

and _an activated correlation

time with energy A

= 26 K. Insertion of

UJN/2x

₌ 28 MHz into the _same formula

gives

the dashed hne.

Thermally

driven fluctuations between metastable _states will also influence

Ti

because of trie associated

magnetic

^field fluctuations

[21, 22j.

In related work _on mcommensurate dielectrics

[21]

^trie

fluctuation-dissipation

theorem _was

applied

_to relate trie

phase

fluctuations to an

overdamped susceptibility

similar to

equation (1)

but with _o

= 1, and with trie diiference that it is

appropriate

^{for trie NMR}

Ti

measurements to include _a summation _{over q-}

Thus,

_we bave

ôq(u~)~

r~

~[~'xi(u~), ⁽³⁾

where

çiq(uJ)

^{is the}

spectral component

^{of trie}

phase displacement

at

frequency

uJ and wavevector q

[22].

^{Insertion of}

equation (2)

into

equation (3)

with _Tc

independent

of _{q will} lead to _a

peak

in

1/T~

when _UJT

~- 1.

Setting

a = 1 is

equivalent

to

ignoring

_any distribution of time scales [20]

and leads to lits like that shown in

Figure

^2. Trie solid line

represents

trie fit _to trie

overdamped

mortel with A

= 26

K;

it is _a

relatively

small value for trie

expected

uh

(mean-field theory

would give A

= 1.î

kBTN,

where

TN

= 1î K. An obvious

problem

is that trie

height

of the

peak

scales

more

slowly

than

1/UJN. Setting

o diiferent than

unity,

^which better describes the dielectric

data,

doesn't elimmate the

discrepancy,

but at least

points

to a smaller activation energy than the _mean field

prediction.

Since the

assignment

of the

low-temperature peak

to a

dynamical

_{crossover is} not

entirely straightforward,

it is

important

to

emphasize

that this _is not the

only interpretation

described in the literature. Takahashi et ai.

[16],

^have

presented

the

peak

_as evidence of _a

phase

transition to another SDW

phase

_m

Se-PF6.

In fact,

specific

heat and dielectric measurements show

anomalies at about trie _same temperature ^and are attributed to trie onset of _a

low-temperature glass phase

of trie SDW state

[19]

^The

peak position's dependence

_on trie nuclear Larmor

frequency

observed here and for

Se-PF6

would be consistent

if,

for

example,

the onset of the

glass phase

_is

strongly

^field

^dependent [23].

1750 JOURNAL DE

PHYSIQUE

I N°12

P=4-5 kbar

,

eÎ'é

, o .O

~

~

,

^.O

~

.@

.

~ O ^. _~

f

o

~O

j _o

~ OO

~

ù-1

~ ~oe ₈

~ O 7

~

4

é

₀

~ _{o 4 8}

P (kbar) 0.01

0 5 10 15 20 2 5

temperature (K)

Fig.

3.

Tp~

_w.

T(K)

for P

= 4.5 kbar for fields

along

c*

(closed circles)

and b'. The inset shows the

height

of the

peak

in the relaxation rate for different _pressures, which appears ^to vanish for low

pressures when the peak _moves into the critical regime.

ATp~

is the difference between the rates for

the

applied

field

along

c* and b'.

Given these diiferent

interpretations,

it is

interesting

to note how trie

peak

evolves with

application

of _pressure. For this _{purpose, we} show in

Figure

3 trie relaxation _rate with trie field

applied along

c* at 4.5

kbar,

and

along

^b' for trie _same pressure. Trie

height

of trie

peak

grows with pressure; in

addition,

it _{moves to}

progressively

lower

temperatures

with

higher

pressure. In each of trie _cases 4-5 kbar, 6

kbar,

and 10

kbar, Tp~

is

isotropic

_m trie

temperature

range around trie

phase

transition where what appear to be critical fluctuations dominate trie

behavior. It suggests ^{that when the} temperature is

sufliciently

close to the

transition,

the

phase

fluctuations that lead to the

anisotropy

of

Figure

1b _{are not a} well-defined excitation of the system ^and the critical fluctuations _{are more} important. The critical regime becomes

narrower as the pressure is mcreased and

eventually

the

phase

excitations _are

prevalent nearly

to the

phase

transition

(as

for P

= 10

kbar).

In the inset, _we demonstrate how the

height

of the relaxation

peak

vanishes for lower

pressures. To separate ^the

anisotropic

part from the

isotropic

part, ^the diiference

~lTp~

=

Tp~ (Bo

_Îc*

Tp~ (Bo Î16')

is shown at the

peak

maximum for each of the three _pressures. The

magnitude

vamshes _as the

temperature

where it _occurs becomes close to the critical regime,

consistent with the

dynamical

_crossover scenario. Still to be

explained

is that the

magnitude

of the

peak

does not _seem to saturate with

increasmg

_pressure; neither does _a saturation _occur

in the experiments

reported

in reference [16]

We _can combine much of _our results into _a

phase diagram

_as shown _m

Figure

4.

There,

we

start with the

phase diagram

described

previously

_usmg

transport

data

[10]:

At low _pressures

(P

< 5

kbar)

_we have

dTN/dP

_>

0,

whereas

dTN/dP

_< 0 at

higher

_pressures. The _crossover between the two regimes is coincident with the

vamshing

of _a

charge

_gap

Ap-

The latter is

presumed

to scale with the temperature

Tp

at which the

resistivity

is _a

minimum,

and it is trie measured values of

Tp

^which we

plot.

For P > 10

kbar,

nonlinear

transport

_was observed

as is often associated with incommensurate

systems

hke

(TMTSF)~PF~.

The

positions

of

N°12 ANTIFERROMAGNETISM IN

(TMTTF)2Br

1751

100

1

. AF

phase boundary

.

Tp

RH T~~~~

o o

é .

~

10

OO 0

1752 JOURNAL DE

PHYSIQUE

I N°12

Acknowledgments

We would like to thank W-G-

Clark,

K-

Holczer,

and M.E. Hanson for many discussions and

support regarding

the

experiments

and the

results,

and S. Kivelson for

helpful

comments- This work _was

supported

in part

by

the National Science Foundation under Grant _nos. DMR-

9412612 and

INT-9314246,

and

by

the CNRS.

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D.,

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