Rb1C60 under Pressure: an NMR and ESR Study

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Rb1C60 under Pressure: an NMR and ESR Study

P. Auban-Senzier, D. Jérome, F. Rachdi, G. Baumgartner, L. Forro

To cite this version:

P. Auban-Senzier, D. Jérome, F. Rachdi, G. Baumgartner, L. Forro. Rb1C60 under Pressure:

an NMR and ESR Study. Journal de Physique I, EDP Sciences, 1996, 6 (12), pp.2181-2190.

�10.1051/jp1:1996214�. �jpa-00247306�

J.

Phys.

I France 6

(1996)

2181-2190 DECEMBER1996, PAGE 2181

RbiC6o under Pressure:

_an

NMR and ESR Study

P. Ruban-Senzier

(~),

D. Jérome

(~~*),

^{F. Rachdi}

(~),

G.

Baumgartner (~)

and L. Forro

(~)

(~) Laboratoire de

Physique

des Solides

(**),

Université Paris-Sud, 91405

Orsay

Cedex, France (~) ^{GDPC. Université} Montpellier II, Place E. Bataillon, 34060 Montpellier, ^France

(~) Ecole Polytechnique Fédérale de Lausanne, 1015, Lausanne, Suisse

(Received 29

July1996,

received in final form and

accepted

30

August 1996)

PACS.61.48.+c Fullerenes and fullerene-related-materais PACS.76.60.Es Relaxation eflects

Abstract. We report ^{the results of}

magnetic

measurements _on the orthorhombic alkali-

metaI fullende RbiC6o. Measurements of the NMR relaxation Ti and ESR _spin

susceptibility

under _pressure

(P

< 5

kbar) provide

clear evidence for the importance ^{of electron} correlations

m this

phase

at _variance with

superconducting phase

3 fullendes. We show that spin fluctu- ations

(ferromagnetic) persisting

_up to _room temperature ^order

antiferromagnetically

at Iow

temperature ^and

give

rise to

long

_range order below 15 K. These results support ^{the bond} struc- ture calculation

describing

this

polymerised phase by

_a three-dimensional model. The

magnetic ground

state _is

suppressed by

_{a pressure}

exceeding

_Qe 6 kbar and

gives

rise to _a

conducting phase

at 12 kbar whose

susceptibility

_is still

possibly

enhanced

by magnetic

fluctuations.

Alkali-metal fullerides

A~C60

with A

=

(K,

Rb and

Cs) belong

to _a rich

family

of molecular solids which have

provided

_a wealth of

physical properties. Up

to _now, the existence of rive stable

phases

with _x

=

0,

1,

3, 4,

^{6 is well} established. The _x

= 3

phase

is the most

popular

since

superconductivity

has been stabilized _up to

temperatures exceeding

the maximum cntical

temperatures

^of

organic

_as well _as

regular inorganic superconductors.

The conduction band of these matenals derives from the LUMO of the

C60

^{molecule which is}

a three-fold

degenerate

tiu level of the molecule with the icosahedral

symmetry.

The

insulating

character of

phases

x ₌ 0 and 6 is easy ^to understand _as it

corresponds

to the tiu level

being

either

empty

_or filled. The _z

= 4 is _more

interesting

_since the conventional band

theory predicts

a

partially

filled conduction band whereas various

expenmental

data have revealed that the

A4C60 compounds

_are

insulating (or semiconducting).

The

insulating

to semimetalhc

transition which is observed in

Rb4C60

under _pressure is related to the

pressure-induced overlap

between the lowest two-fold

degenerate

and the upper Jahn-Teller

splitted

subbands

iii.

The

phase AiC60

is also _a remarkable

system

since

compounds

with A

=

K,

Rb and Cs

undergo

_a first order structural

phase

transition around 350 K

[2],

^between a fcc

phase

at

high- temperature

^and an orthorhombic

phase

at

low-temperature

_[3]. The orthorhombic

phase

_is

particular

_in that the center to center distance between

C60

ions is shorter

along

_one direction than

along

_any other directions. This feature gives use to a

polymerized

structure.

(*)

Author for

correspondence (e-mail: jerome@Ips.u-psud.fr) (**)

associé _au CNRS

©

Les

Éditions

_de

_Physique

₁₉₉₆

The existence of

polymerised C60

chains is

strongly supported by high

resolution

~~C-NMR spectra showing

the existence of four-fold coordinated

sp~

carbons

taking part

in _a

cyclo-

addition reaction between _near

neighbouring

molecules in addition to the usual

sp~

carbon site

[4,5].

Chauvet et ai-

[6,

7] have

proposed

that the

single

alkali electron results in

half-filling

the lowest Jahn-Teller

splitted

subband in the tiu manifold- The

quasi

one dimensional

(Q-1-D)

character of that band could in turn

explain

the

development

of _a

niagnetic

modulation at low

temperature beanng

_some resemblance with the

properties

of

Q-1-D organic compounds

such

as

(TMTSF)2X

_[8]. The influence of electron-electron correlations in the

magnetic properties

of the

polymeric phase

has been

suggested by

the observation of _a nudear relaxation time

Ti being

almost temperature

independent

_[9] thus

ruling

out both _a normal metallic

(Kornnga-like)

_or

a

semiconducting

behaviour.

Since

high

_pressure has

already proved

to be _an

important

parameter

governing

the _super-

conducting

_or the conduction

properties

of

A3C60 (10, iii

and

A4C60 Ill respectively,

_a NMR

study

of

AiC60

has been undertaken

using ^~~C-NMR

in

RbiC6o.

The results of this

preliminary study emphasize

the

importance

^of electron correlations in

AiC60

and show that the

magnetic instability

which is

quickly suppressed

under pressure

gives

rise _{to a}

conducting ground

state-

Furthermore,

the relation between

Ti

and the

spin susceptibility

_{as pressure} is varied

suggests

the existence of

strongly developed

uniform

spin

fluctuations _{up to room}

temperature

which _{cross over} to critical

antiferromagnetic

fluctuations below 50 K

leading subsequently

to the 3-D ordered

antiferromagnetic ground

state around

TN * 10 là K at P

= 1 bar-

NMR measurements have been

performed

_on the

~~C

nudei of _a

~~C

enriched

RbiC6o (10%

enrichment)

at a Larnior

frequency

of 100 MHz-

The

~~C-MAS

NMR spectrum ^contains

eight

lines under ambient conditions which _are at- tributed _to the

polymeric RbiC6o Phase plus

_{a narrow one} which is related to the

coexisting

fcc

phase.

In wide band

NMR,

the

eight

lines cannot be

separated

and the

lineshape

is

spread

over m 50 kHz

(500 ppm)

between -100 and +400

ppm/TMS.

Two _narrow transitions _are

superimposed

to the broad

spectrum;

one at 143

ppm/TMS

is related to a few

percent

^of re-

maining C60 Phase

and the other at 183

ppm/TMS

_comes from the fcc

Rbi C60 phase.We

have noticed that traces of the

coexisting

fcc

phase

_are

totally

removed from the NMR spectrum at T

= 300 K when P exceeds 2 kbar- The

polymeric phase

is thus stabilized under _pressure.

Furthermore,

_an additional line at 26

ppm/TMS

has been identified _{as coming} from the

liquid

pressure medium. This spurious

signal

with

Ti

_{* s} under ambient conditions is _no

longer

visible at low

temperature

or

land)

under pressure as

Ti quickly

_increases when the medium becomes frozen.

Ti

has been measured with the

saturation-recovery technique, fitting

the recovery of the

integrated

NMR

signal by

_a

single exponential

function. This time

dependence

_is not followed very

accurately

at low temperature

(T

_< 30

K,

^P ₌ 1

bar),

diflerent

types

^of

fitting procedures leading

to diflerent values of

Ti However,

the T

dependence

of

Ti

_is not

senously

aflected

by

the choice of the

procedure.

Figure

1

displays

the

temperature dependence of1/Ti

at diflerent _{pressures up to} 12.6 kbar. The ambient _pressure data _{are in} close agreement ^{with the} literature. What is clear

in

Figure

1 is the suppression of the low

temperature

rise

of1/Ti

ascribed _to the onset of

a

magnetic ground

state. Under 12.6

kbar,

the data

of1/Ti

_uers~ls

T,

is

approaching

the canonical

Kornnga

behaviour

la 30%

increase of

(TIT)~~

is noticed between 300 and 4.2

K)-

6 kbar _{is an} intermediate pressure ^at which _no

magnetic long

_range order _can be stabilized down to 9 K

although

the behaviour

of1/Ti

_us- T is far from what is

expected

in _a

regular

conducting regime-

N°12 RbiC6o UNDER PRESSURE: AN NMR AND ESR STUDY 2183

4

~ §§

~~~~~~ ^~~~

Î~ ~~~~

o

~

3

~

O

~

o

<

^O

o

~ P=lbar

4 2

lO 20

°

Temperature (K)

O

_

O ~ o

~

~

~$

3 C£©

~ ~

~~~~~~

É

~ P=6kbar

v w

~

?

P=12.6kbar

qv

~ .

, w

~,w

O 50 OO 150 200 250 300

Temperature (K)

Fig.

l.

Temperature dependence

of the ~~C

spin-Iattice

relaxation rate at different

applied

_pres-

sures. Insert:

Temperature dependence

of the _spm-spm relaxation rate at Iow temperature ^{and ambient}

pressure

reveahng

_a

drop

belo~v 9 11.

Figures 2a,

b show the _room

temperature

_pressure

dependence

of the _spm

susceptibility

obtained from ESR expenments under _pressure [12] ^and

of1/Ti

Combining

the data of

Figures

2a and 2b, _a relation between

1/Ti

and the

spin susceptibility

can be

derived,

as shown _in

Figure

3- Since the

scattenng

of the ESR _raw data _is rather

large

we have

performed

_a least square fit with the law

t(P)/x(1 bar)

= 1-

aP~ giving

_{a =} 0.0924 and b

= 0.74 with P in kbar _as shown _in

Figure

2a. The value of the

susceptibility

_given

by

this fit at pressures

corresponding

to the NMR expenments has then been used to

generate

the

plot

in

Figure

3.

According

to the data _in

Figure 2a,

the initial pressure coefficient of the

susceptibility

amounts to -9%

kbar~~

_This value is

admittedly

much

larger

than the _pressure

depen-

dence of

susceptibilitv

which has been

reported

in

A3C60, namely -1% kbar~~

_for the _pressure

Rb~C~~

É

~ . O.g

~' . .

~

'

il4

~ O.7

O

a) kbar)

4

Rb~C~~

~ .

T=290K

~

Vl ^.

~' .

~ 2

~

. ~

' .

i

O

~~

Fig.

2.

a)

Pressure dependence of the ESR _spm

susceptibility

normahzed to its value under ambient conditions. The continuous Iine is _a fit to the data of trie form:

x(P)/y(1bar)

= 1-

aP~

_with

a = 0.0924 and b

= 0.74 and P in kbar

b)

Pressure dependence of the ~~C

spin-Iattice

relaxation rate at _room temperature.

dependence

of the

Knight

shift

(susceptibility) il _Ii

_or

-2% kbar~~

_{from ESR}

experiments

_un-

der _pressure in

K3C60 (12].

^{Even if it is} not

fully justified

to compare

RbiC6o

and

K3C60,

_we

are

fairly

confident that the

large

_pressure coefficient of the

polymeric Rbi C60

can be ascnbed to _an

exchange

enhanced

susceptibility.

The Stoner enhancement factor could well be of the

order of 3 _{or so} under ambient conditions. The

predominance

of electron-electron

repulsions

in

phase

_as

compared

to

phase

3 is in

agreement

^with a calculation of the correlation _energy due to the molecular Jahn-Teller distortion _in bath

phases _[13].

This model shows that the

N°12 RbiC6o UNDER PRESSURE: AN NMR AND ESR STUDY 2185

4

Rb~C~~

3

1

62 1

X

in a Mott-Hubbard _{state i.e. a} 1-D localized

antiferromagnet _[18].

Brouet et ai.

[15]

^have

conduded, fitting

the

temperature dependence

of

~~C il /Ti)

between 100 and 300 K

by

the 1-D

law, equation il),

that

Kp

m 0.2 _{or even} 0.05. In the limit where

2kF spin

fluctuations

contribute

predominantly

to the

relaxation, 1/Ti

becomes

T-independent

but _a functional relation between the

susceptibility

and the relaxation rate _can be

anticipated _[19]. Therefore,

a functional behaviour such _as

1/Ti

_{cc xs} is

expected

when both

1/Ti

and _{xs are} modified

by

the

application

of _a

high

_pressure.

The

plot

in

Figure

3

gives 1/Ti

_cc

(xs)~

_as P is varied at _room

temperature-

The exponent

a = 1 does not agree with the data in

Figure

3 and _we think this is

beyond

the

experimental

accuracy.

Instead,

_a

=

3/2 (or 2)

_{are more} realistic values for the functional relation between

1/Ti

and _ts.

It should also be reminded that _{a power} law exponent

Kp

_m 0 _1.e, the

strong coupling limit, implies

that the carriers _are localized

along

the

polymer

chains

[20].

^The structure of the

polymer phase [î]

as well _as the

expenmental

data do not corroborate this

picture

_[21]

(see

the Note Added in

Proofs).

The other model ~vhich has been

proposed

is that of

strong ferromagnetic

fluctuations _per-

sisting

_up to _room

temperature

_[22] In the _case of _an

incipient ferromagnet, 1/Ti

reads

[23],

1/Ti

_cc

T(xs)~~~

_or

T(~s)~ ₍₂₎

at 2 or 1-D

respectively-

In the

high

temperature

regime,

_our data show that the temperature ^{and the} _pressure

dependence

of both

1/Ti

and _xs would be in

agreement

with

equation (2)

and with the existence of uniform

spin

fluctuations.

At lower

temperature

and ambient _pressure the AF

couphng

between

ferromagnetic layers

drives the onset of _a 3-D ordered

ground

state- Hence, AF critical fluctuations _govern the tem- perature

dependence

of the relaxation in the

vicinity

of the

phase

transition with _a contribution going like

[24],

~~~~~~~

~

(j'_~~)l/2

^~~~

This cntical

regime

has been observed above the onset of the SDW

ground

state in

organic

conductors

[25j. Figure

4 shows that

equation (3)

_is

obeyed

for

RbiC6o, taking

TN

= II.ô K.

The

finding

of such _a low value for the cntical temperature ^{of the}

magnetically

ordered state is indeed in

good agreement

with other

experimental investigations

of the _same

system

at low

temperature-

^The

magnitude

of the internal

magnetic

^field measured

by

_{muon spin} relaxation at _zero external field exhibits _a

sharp

increase below 20 K

[26, 2î]-

The

spin-spin

relaxation time T2 which has also been measured in the present

investigation

reveals _a

drop of1/T2

below II

K,

_see the insert of

Figure

which _can be attributed to the

spins of close

neighbour ~~C

nudei

becoming decoupled by

the _use of the internal

magnetic

field at the onset of the

magnetic

transition

[28]

The consequence of

magnetic ordering

on the electronic

properties

of

Ai C60

has been _con- sidered

by

Erwin _et ai. [22] ^Three dimensional

antiferromagnetic

correlations contribute to stabilize _a semimetallic

(or

_even

semiconducting) antiferromagnetic ground

state with two sub- lattices such that the spin

polanzation

alternates between _corner and

body-centered

sites of

the

body

center orthorhombic _structure

[29].

^The

temperature

_region between 20 and 50 K is

dominated

by

_precursors eflects-

Magnetic

_{precursors are} observed and give use to the diver- gence

of1/Ti

while the opening of _a

pseudo

_gap at the Fermi level _is

supported by

the

drop

of the

spin susceptibility

and of the

conductivity

belo~v. 50 K

I?ii

At _a pressure of 6 kbar _no 3-D

ordering

_is observed from the NMR data down to 9 K.

However,

_{even in} the absence of _any

phase

transition

strong

AF fluctuations _remain

in the

N°12 RbiC6o UNDER PRESSURE: AN NMR AND ESR STUDY 2187

13

~

~~i~60 ^~

(

^°°~

_P=lbar

ÎÎ

~

/

O.2

~

O ~

O.o

20 40

Temperature (K)

a)

~~l~60

2

P=6kbar

- ~

~w

Vl

~

~

' O

O

b)

Table1. Va1~les

of (TIT)~~

at iow

temperat~lre

m the

conducting

state

of

_uario~ls

f~liierides.

Pressure

(TIT)~~

Reference

(kbar) 10~(K s)~~

KiC60

0.001 3 [15]

RbiC6o

12.6 9.5 this work

K3C60

0.001 à-à

[loi

Rb3C60

0.001 9.5

iii

Rb4C60

12 5.2

[Ii

Finally,

under 12

kbar, Rbi C60

is

approaching

the situation of _a

regular

metallic state with _a

remaining

enhancement of

(TIT)~~

at low

temperature

due to uniform

spin

fluctuations. Table I summarizes the values of

(TIT)~~

which have been measured in diflerent

compounds

of the

Rb~C60

and

A~C60

series ~v.henever the metallic state can be stabilized at low

temperature-

Since the

hyperfine coupling

for

~~C

nuclei _is

expected

to be

independent

of bath the alkali atom and pressure, companng

(TIT)~~

values amounts to _a

comparison

of the

spin susceptibil- ity-

The

similarity

^between the

conducting

state of

RbiC6o

stabilized under _pressure and the

ambient _pressure

conducting

state of

Rb3C60

_is indeed very

striking.

This behaviour

supports

a

picture

of

Rbi C60 evolving

towards _a

regular

conductor at

high

_pressure

(with

_a limited eflect of

magnetic

fluctuations _on the enhancenient

of1/Ti).

The _case of

Rb4C60

is

slightly

diflerent

as the role of _pressure in this Jahn-Teller

compound

is to stabilize _a semimetallic state

through

the

overlap

between Jahn-Teller

splitted

subbands. A further increase of

(TIT)~~

above 5.2

can still be

expected

at P _> 12 kbar. As far _as

K~C60 compounds

_are concerned

K3C60

shows

a value of

(TIT)~~

which is smaller but

approaching

that of

Rb3Côo.

The remarkable _narrowness of the ESR linewidth in

polymenc phases

_as

compared

to the

phase

3 remains _an important

problem

which

requires

^further clarification. The dramatic

reduction of the linewidth from 600 G in

Rb3C60

down _to 6 G in

RbiC6o

under anibient conditions has been taken _{as an} evidence for the 1-D _nature of the

conducting

electron _{gas in} the

polymer phase

_{[6] as} for 1-D

organic

conductors [8]. ^Such an

interpretation

would however

require the existence of _a

large anisotropy

between intrachain and interchain

couplings- Keeping

the _same electron

scattering

time in bath

compounds,

the 1-D

interpretation

for the _narrow line~v.idth would

require

the

couplings

to be

anisotropic by

_a factor 10

(at least)

_[8]. Present

band structure calculations _{are not able to} support ^this extreme situation [22]

The

possibility

for

superconductivity

in the

polymeric phase

under _pressure needs also _some

comments. If _one takes the numbers for

(TIT)~~

in Table I at face

value, superconductivity

could be stabilized in

RbiC6o

at P

= 12 kbar.

However,

the NMR data of

1/Ti

_uers~ls

temperature, Figure

1 have failed _to show _a sudden

drop

belo~v.

Tc

which _can be attributed to the

opening

of _a

quasipartide

_{energy gap.} The absence of

superconductivity

_is still not

entirely

condusive _as the expenment was conducted

in a

magnetic

field of 9.4 T and at a

temperature

not lo~v-er than 4-2 K-

However, following

the

empincal

relation bet~veen

Tc

and the fcc lattice

parameter,

^which has been established for

Phase

3

fullendes,

it may be

argued

that

RbiC6o

with _a fcc lattice parameter of14.08

À

_at ambient _pressure should not reveal any

superconductivity

_[30]

In

conclusion,

the

expenmental study

of the orthorhombic

polyinerized phase

of

RbiC6o

by ^~~C-NMR

under pressure has revealed the

importance

of electron correlations. Unlike the _case of

Rb3c60

where _a

fairly

weak value of the _on-site

repulsion

to electron bandwidth

N°12 RbiC6o UNDER PRESSURE: AN NMR AND ESR STUDY 2189

ratio

(U/W)

is

required

to

explain

the _pressure

dependence

of the

superconducting

critical

temperature, U/W

_may be

large

_in

RbiC6o land Csi C60)

in order to

explain

the

strong

_pressure coefficient of the

spin susceptibility

and

~~C spin-lattice

relaxation rate. The

strength

of the

correlations in this Fermi

liquid

is

large enough

to drive the onset of _an

antiferromagnetic

non-metallic

ground

state below 15 K _{or so} under ambient pressure.

Although

the

persistence

of

strong spin

fluctuations _{up to room}

temperature

cannot be

disputed,

the daim of1-D

antiferromagnetic

fluctuations _up to _room temperature ^{should be taken} with _a

grain

of sait.

The companson between the _pressure

dependence of1/Ti

and _,is favours the existence of 2

or 1-D

spin

fluctuations. This

finding

is in

agreement

with the band structure calculation

induding

the role of electron

repulsions predicting ferromagnetic

fluctuations

along

the chains and

antiferromagnetic coupling

between nearest

neighbour

chains. The

magnetically

ordered

ground

state is

suppressed

under pressure but at 6 kbar

remaining

3-D

antiferromagnetic

fluctuations _are still observed in the low

temperature

regime

according

to the

T-dependence of1/Ti

_even in the absence of any

long

_range

ordenng

above 9 K.

A

conducting phase

_is stabilized at low

temperature

under

high

_pressure.

However,

_even

if the value of

(TIT)~~

for

RbiC6o

_is the _{same as} for the

compound Rb3C60

it is not clear

yet

^{whether the bare values}

~T(EF)

are also of the _same

magnitude

_or there exists a

large

diflerence between the t~vo

phases

_as far _as

spin

fluctuations _are concerned- This _may be _an

interpretation

for the absence of

superconductivity

above 4.2 K in

RbiC6o

under pressure.

A determination of the _pressure

dependence

of the structure of the

polymeric phase together

with the related band structure calculation should be _very useful for _a further

understanding

of the electronic

properties

of this

compound-

Acknowledgments

We

acknowledge

fruitful discussions ~v.ith M- Héritier and B-

Coqblin

and the

cooperation

of M. Nardone. H.

Mayaflre

and P. Wzietek for their

help

_in various

expenmental

aspects ^{of this} work and A. Sienkiewicz for his

help

in the EPR

experiments-

Note Added in

Proofs

The

~~C

relaxation rate of

RbiC6o

does not reveal _any field

dependence

between and 9-4 Tesla at _room

temperature.

This behaviour is _at uariance with the field

dependence

which has been

reported

in matenals

exhibiting

one-dimensional

dynamics (m ^H~~/~

of

long wavelength

spin fluctuations at fields above _{a cross-over} value related to the interchain

hopping

rate.

In

TTF-TCNQ (~)

^and

(TMTSF)2Cl04 (~)

^the cross-over fields _are about o-à and 5 Tesla

respectively.

It _can be infered from these values that the interchain

hopping

rate

land

also the interchain

band~v.idth)

is _even

larger

in

RbiC6o

than for the

Q-1-D Bechgaard

conductors

(unless

the intra-chain fluctuation life time _is

unexpectedly

_very

large).

This feature supports

a

dimensionality higher

than _one for the

spin

fluctuations at _room

temperature.

~

see reference [8j

(~) ^{Carretta P. et} ai., in

"Physical

Phenomena at

High llagnetic Fields",

Z- Fisk et ai. Edq.

(World

Scientific,

1996)

_pp. 328-333

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