Charge Density Wave Properties of Quasi Low-Dimensional Transition Metal Oxide Bronzes

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Low-Dimensional Transition Metal Oxide Bronzes

C. Schlenker, C. Hess, C. Le Touze, J. Dumas

To cite this version:

C. Schlenker, C. Hess, C. Le Touze, J. Dumas. Charge Density Wave Properties of Quasi Low-

Dimensional Transition Metal Oxide Bronzes. Journal de Physique I, EDP Sciences, 1996, 6 (12),

pp.2061-2078. �10.1051/jp1:1996205�. �jpa-00247298�

Charge Density Wave Properties of Quasi Low-Dimensional Transition Metal Oxide Bronzes

C.

Schlenker (*),

^C.

Hess,

C. Le Touze and J. Dumas

Laboratoire

d'Études

_des

_Propriétés Électroniques

_des

_Solides,

_{CNRS, BP 166,}

38042 Grenoble Cedex 9, France

(Received

25 April 1996, received in final form 2î June 1996. accepted 1 Julj.

1996)

PACS.71.45.Lr

Charge-density-wave

_systems

PACS.72.15.Eb Electrical and thermal conduction in crystalline metals and

alloys

PACS.î2.15.Gd

Galvanomagnetic

and other magnetotransport elfects

Abstract. Several famines of transition metal oxide bronzes

mcluding

trie quasi _one-

dimensional

molybdenum

blue bronzes Ao 3Mo03, trie quasi two-dimensional

(2D)

Mo

purple

bronzes AMo6017 and trie _quasi 2D

monophosphate

_tungsten bronzes

(P02)4(W03)2m

show

Peierls transitions

leading

to commensurate _or incommensurate

charge density

_wave

(CDW)

states. Trie properties of trie

monophosphate'tungsten

_bronzes

(P02)4(W03)2m

_are reviewed.

These series of compounds provide _a mortel system where both trie low-dimensional character and trie average electron concentration _are function of trie

m parameter. Trie low _m compounds

(m

= 4, 6) show conventional CDW instabilities _as well

as giant positive magnetotransport and quantum oscillations _at low temperature. Detailed information _on trie Fermi surface _m trie CDW

state _is obtained from transport data, trie size of trie pockets left

by

trie CDW gap openings

being

found of trie order of1% of trie

high

temperature two-dimensional Brillomn

zone. Trie _m

= 5

compound, which _may be considered _as

an

intergrowth

of _m

= 4 and 6, shows aise instabilities with

slightly

dilferent properties. Trie absence of CDW

long

_range order affects trie properties of trie _m

= 8 member which shows low temperature properties possibly due to weak localisation elfects.

Finally,

studies _on trie 4 < _m < 14 compounds show that trie Peierls temperatures

are mcreasing with _m,

reaching high

values, _up to 550

K,

for _m

= 13. This is attributed to

a 2D character

mcreasing

with

m. Trie

mcrease of trie _room temperature

resistivity

with _{m is}

discussed in terms of enhanced

electron-phonon

_or electron-electron interactions.

1. Introduction

The transition metal oxide bronzes _are "old" matenals which have been studied since the nineteenth

century

^after the

discovery

of

NaxW03. They

_were called bronzes because of their metallic luster

[1j. Physicists

have rediscovered theni _more

recently, especially

when the

molybdenum

bronzes _were shown to be

quasi

low-dimensional metals

[2-4].

The

general

formula of these

compounds

is

A~My Dz

~vhere A is _a cation _or any group of elements

inducing

a

partial filling

of the conduction band which would otherwise be

empty

_in the transition metal oxide. The famines of bronzes of interest for this _{review are} the metallic

molybdenum

and

monophosphate _tungsten

bronzes [5].

They

have

layered type crystal

structures. The Mo

~

)Authorfor correspondence (e-mail: schlenke@lepes,polycnrs-gre.fr)

g

Les

Éditions

_de

_Physique

₁₉₉₆

bronzes include two

types

^of

materials,

the so-called blue bronzes

Ao 30Mo03 IA

₌

Li, K, Rh, Tl)

and the so-called

purple

bronzes

AMo6017 IA

=

K, Na, Tl)

_[4]. The Mo red bronzes

Ao_33Mo03

_are semiconductors and _are not considered in this review. The

monophosphate tungsten

^{bronzes have the}

general

formula

(P02)4(W03)2m

where _{m can} be varied from 4 to 14 [GI. In all ^cases, the

layered type crystal

structure leads to

quasi

low-dimensional electronic

properties,

either one-dimensional

(1D)

_or two-dimensional

(2D), depending

_on the details of the transition metal oxygen

polyhedra arrangement.

It is _now well known that quasi low-dimensional metals show two

types

^{of electronic} in-

stabilities, either _a Peierls type ^{transition towards} a

charge density

_wave

(CDW)

state or a

superconducting instability. Many examples

_can be found _among the organic low-dimensional conductors [6,

ii.

The

high

T~

copper-based

oxides

provide

an

inorganic family

^of materials where

superconductivity

is stabilized at

comparatively high temperatures.

^{In the transition} metal

bronzes,

for _reasons not clanfied at the moment, the CDW

instability

_seems to be the

dominant mechanism.

Only

_one

compound

is known _to show

superconductivity

at low tem-

perature (1.9 K):

the lithium

purple bronze, LiMo6017

_14]. In all other _cases, the existence of Peierls transitions is associated to Fermi surfaces

(FS) showing

so-called

nesting properties

in the normal

high temperature

state. These instabilities

give

rise either to metal-semiconductor

transitions,

as in the

quasi

ID blue bronze, if the Fermi surface is

completely destroyed by

the gap

openings,

or to metal-metal transitions if electron and hole

pockets

_are left _on the Fermi surface. This is the _case of the Mo

purple

bronzes and of the

monophosphate tungsten

bronzes.

In all _cases, the low

temperature

state is _a CDW state, ^with a modulation of the electronic

density

and _a related

periodic

lattice distortion of wavevector

2kF, kF being

the Fermi _wave vector of the

high temperature

"normal" metal [8]. ^The CDW

wavelength

_may

be, depending

on the

filling

of the

high temperature

^conduction

band,

either commensurate with the average

lattice,

_as in

KMo6017,

_or incommensurate _as in the blue bronze and in the

monophosphate tungsten

^bronzes.

The theoretical

description

^of the CDW instabilities has been

developed mostly

for

quasi

one-dimensional

(ID) conductors, using

mean field

theory

of the Peierls transition

[8j.

^Com-

paratively

few results _are available for 2D systems. ^{The mechanism} of the Peierls

instability

in quasi 2D conductors is in fact not

straightforward,

since it is

directly

related to the

nesting properties

of the FS. In _an ideal 1D

metal,

the FS

being composed

^of two

parallel planes

_sepa- rated

by

the vector

2kF

is

perfectly

nested and the Peierls

instability completely destroys

this

FS,

thus

inducing

_a metal-insulator transition. This _is not the _case in _a 2D metal where the FS is

quasi-cylindrical

and

normally

shows

perfect nesting

for a

given

wavevector

only along

_a

line

parallel

to the

cylinder

_axis. There is however _a

special

_case, for _a

perfect

_square lattice with _one conduction. electron per site, where the FS is

perfectly

nested for the two wavevectors

[110]

^and _[1

0j [9j.

^{Real materials}

usually

do not fit into this _case. However the

concept

of hidden

nesting (or

hidden

one-dimensionnality),

which has been

primarily developed

to _ac-

count for the

properties

of the 2D Mo bronzes

AMo6017 IA

₌

K, Na),

and oxides

(~-Mo4Oii

and

~i-Mo4Oii), applies

to other famines such _as the

monophosphate tungsten

bronzes

[loi.

The

properties

^of the low-dimensional Mo bronzes and oxides have been reviewed

recently [6,11,12].

^{Trie Mo blue bronze has been and still is the}

^object

^{of intensive studies since non}

linear transport

properties

^due to trie

depinning

^{of trie CDW had been} established

[13j.

^Recent reviews _can be found in references

[5,14].

^{This article will therefore be focused on trie series of}

trie

quasi-2D monophosphate tungsten

^bronzes,

(P02)4(W03)2m.

^These are of

special

interest

since

they

show

high

^Peierls

temperatures,

^above room

temperature

^for

large

values of _m. Also

both the low-dimensional character and the average conduction electron

density

_can be varied with trie m

parameter.

Ilb

ii_a

Fig.

l.

Crystal

structure of P4W12044

(m

= 6)

showing

trie W06 octahedra and trie P04 tetrahe- dra.

(From

Ref. [16])

In _next

section,

trie

properties

^of these series will be reviewed for trie low _m values

(m

= 4

and

6). They

_can be accounted for

by

_a conventional CDW model.

Magnetotransport

and quantum

transport provide

in these _cases detailed information _on trie CDW states. New results obtained _on trie _m

= 5

compound

are

reported

in Section 3.

They

_may not fit

perfectly

in trie usual CDW

framework, possibly

due to _a somewhat dilferent

crystal

structure. Section 4 will be devoted to trie

description

of trie

transport properties

of trie _m

= 8

compound.

In this case,

X-ray

diffuse

scattenng

studies show that CDW _are established below trie Peierls

temperatures

with

only

short range order

[15j.

^Dur recent results may indicate trie _{presence at} low

temperature

of weak localization elfects related to trie CDW disorder.

Finally,

_in Section

5,

some

properties

for

large

_m

compounds

will be

reported, including

trie increase of trie

instability

transition

temperatures

and

resistivity

with _m.

2.

Quasi

Two-Dimensional

Monophosphate Tungsten

Bronzes: Basic

Properties

and Conventional

Charge Density

Wave

Regime (m

₌ 4,

6)

2.1. BAsic PROPERTIES _AND HIDDEN FERMI SURFACE NESTING. Trie

monophosphate

tungsten bronzes,

of

general

formula

(P02)4(W03)2m

have been

synthesized

and their

crystal

structure studied _more than ten years ago

[16,lîj.

Their lattice _is orthorhombic and built

with

perovskite Re03-type

infinite

layers

of

W06

octahedra

parallel

to the ab

plane, separated by P04 tetrahedra,

_as shown

in

Figure

1. Since the 5d conduction electrons _are located in the

W06 layers,

the electronic

properties

_{are quasi} 2D. The thickness of the

Re03

blocks and therefore the _c parameter, are

increasing

with _m, while _a and b _are

only weakly dependent

on it. The number of conduction electrons _per

primitive

cell _is

always

4,

independent

of _m.

On the other

hand,

the low-dimensional character _is

expected

to

change

with the thickness of the

W06 layers.

Also, the _average number of conduction electrons _per W is

2/m,

therefore

decreasing

with

increasing

_m. The lower _carrier

density

_may

lead,

for

large

m

values,

to weaker screening elfects and therefore _to increased electron-electron interactions.

The electrical

resistivity

of the _m

= 4 and _m

= 6

members,

obtained with current in the ab

plane,

have been

reported

in references

[19, 20j.

Two anomalies in the electrical

resistivity,

3

2.5

Ê

₂

° B=6T

1.5

ÎÎ

~'"~

j

^lira

Tp2 Tpi

Biic

0.5

0 50 100 150 200 250 300

Temperature (K)

Fig. 2. Resistivity of P4W12044

(m

₌

6)

_{as a} function of temperature ^for

magnetic

field B of 0 and 6 Teslas. Trie current is

parallel

to trie _a

crystallographic

axis and the field B is

along

_c.

-9.4 y ~

É~ y.

~ w c uJ

-9.8

a)

^r

b)

Fig.

3. P4W12044

(m

=

6): la)

Band structure 16) ^{Fermi surface}

(From

Ref. [19])

indicating

the existence of two electronic

instabilities,

have been found for _m

= 4 at

Tpi

" 80 K

and

Tp2

" 52 K.

X-ray

diffuse

scattenng

studies have demonstrated that

they iorrespond

to

an incommensurate CDW with wavevector

components

in the ab

plane

_{qi "}

(0.330,0.295)

and _q2

"

(0.340, 0) [21-23j.

In the _case of the _m

= 6

phase,

these two instabilities _are found at

Tpi

" 120 K and

Tp2

" 62 K

(qi

_"

(0.385, 0)

and _{q2 "}

(0.310, 0.295)),

^therefore at

temperatures higher

than for _m

= 4. A third

instability

has also been found at low

temperature (Tp3

# 30

K) by

structural studies with _a wavevector _q3 "

(0.29,

0, ii

). Typical

^{results for the}

electrical

resistivity

and

magnetoresistivity

_are shown in

Figure

2 for the _m

= 6

compound.

One should note that _a

giant positive magnetoresistance

^{is found} at low

temperatures

for

magnetic

fields

perpendicular

to the

ab-layers.

Band structure calculations

using

a

tight binding

^{extended Hückel method in} a 2D approx- imation have been

performed

for the _m

= 4 and 6

compounds. Figure

3a shows the results obtained for the _m

= 6 member. Three bands _cross trie Fermi level. The three

corresponding

sheets of the FS _are shown in

Figure

3b

[18,19]. Nesting properties

_appear on the

resulting

FS obtained from the

superposition

of these sheets. This has been related to the so-called hidden

nesting _[10],

_or hidden

one-dimensionality,

due to the presence of infinite chains of

W06

octa- hedra

along

the _a and

la

+

b)

^{axis. In} a first

approximation,

the FS _can then be descnbed _as

ioo

80 _m=6

m fila

ù

₆₀

à

Bllc

à

^~~

_TP2

ZO

TAI

x

2°

~ 0

0 50 100 150 200 250 300

Temperature (K)

Fig.

4. Hall coefficient _{as a} function of temperature for _m

= 6. Trie current is

along

_a and trie field

along

_c.

being

due to the

superposition

of three

quasi-1D

FS'S. A similar mechanism has been invoked

to account for the existence of Peierls instabilities in the 2D

molybdenum

bronzes and oxides.

This

type

of mechanism therefore underlies the CDW

properties

of the

quasi-2D

transition metal oxide bronzes. Recent results obtained _on

NaMo6017 by angular

resolved

photoemission

spectroscopy

have confirmed _{this model}

[23].

In the _m

= 4 and 6

compounds,

the

nesting properties

of the FS combined with electron-

phonon couphng

induce _successive Peierls instabilities which

partly destroy

the FS. One should note that the Peierls

temperatures

_are

higher

for _m

= 6 than for _m

=

4,

while the normal state

resistivity

_{p300 K} is also

approximately

_one order of

magnitude larger

in _m

= 6. This

dilference in behaviour _cannot be accounted for

only by

the dilference in the calculated carrier concentration which is

expected

to be nmch smaller.

Therefore,

it has to be attributed either to a

stronger electron-phonon couplipg

in _m

= 6

compared

to _m

= 4 _{or to}

stronger

electron- electron interactions due _{to a} weaker

screening.

2.2. CHARGE DENSITY ÀiÎAVE STATE: TRANSPORT,

QUANTUM

PROPERTIES _AND FERMI

SURFACE. Hall

elfect, magnetoresistance

and

thermopower

have been

reported

for both

compounds [24, 25].

Hall elfect data _are shown _{as an}

example

^for _{m =} 6 in

Figure

4. Both Peierls transitions at

Tpi

" 120 K and

Tp2

" 60 K _are

clearly

_seen. In

pnnciple,

it is

possible

to

analyse

the

magnetotransport properties by using

the so-called two-band model. This

analysis

is valid for two-band systems ^if the

magnetoresistivity Ap/po

and the Hall coefficient follow the field

dependences

_{given in} reference

[30]: ~p/po

should _{vary as}

B~

_{in low fields.}

It should _{saturate in}

high fields, except

if the metal is

perfectly compensated. RH

should be field

independent

in the limit of low field~. In _{our case}

rlp/po

does not saturate in

high

fields

[24].

^One may therefore _{assume a} full

compensation.

One _can then evaluate the carrier concentrations and mobilities at low temperature,

assuming

the _same electron

in)

and hole

(p)

concentrations.

Figure

5 shows the results obtained in this

approximation

^for the low

temperature

CDW state.

Sharp

decreases of the _carrier concentrations _are found _below

Tp2,

as

expected

from trie CDW gap

opening:

n and p are found _to be three orders of

magnitude

smaller _in trie low temperature CDW state than at _room

temperature.

A similar

analysis

bas been

performed

for trie _m

= 4

compound.

Table I shows that _n and _{p are one} order of

35

~~ m=6

~E 25

ce

- ~ ~

@

OE E

10 ~

5 0

10

a)

Table I. Parameters

of

the _m

= 4 and 6 members

of

the

monophosphate _t~tngsten

bronzes

(P02)4(W03)2m. Tpi

and

Tp2

_are the Peieris

temperat~tres,

A is the _area at

I.fl

K

of

the Fermi

s~trface pocket

obtamed

tram

the

freq~tency of

the Sh~tbnikov de Haas

oscillations,

_n and p are the eiectron and haie concentrations at

S-É

K obtained

tram

the two-baud

anatysis of

the

transport

data.

m 4 6

Tpi

80 K 120 K

Tp2

50 K 60 K

A

(4.2 K)

6.1 _x 10~~

m~~

_{1.3 x} 10~~

m~~

n,p

(4.2 K)

40 _x 10~~

m~~

_{6 x} 10~~

m~~

1.2

m=6 0.8

c~ II a

ù

o.4 B / / _c

T=0.3 K

o

o 4 8 12 16

B

(T)

Fig.

6.

Magnetoresistance

as a function of

magnetic

field for _m

= 6,

showing

the Shubnikov-de Haas oscillations. T

= 0.3 K.

Magnetic

field perpendicular to the layers.

The

thermopower (TEP)

is shown _vs.

temperature

_in

Figure

î for _m

= 6. The

thermopower

is

highly anisotropic

_in the Peierls _state. In the

high temperature regime,

the TEP shows _a

quasi-linear

and

isotropic

behavior

along

the _a and b

crystallographic

directions. The _measure-

ment

along

b reveals _an

anomaly

at low

temperature,

around T

= 30

K, coinciding

with the third Peierls transition. Results obtained _{on m}

= 4 _are

reported

in reference

[25].

Above the

higher

Peierls temperature, the

monophosphate _tungsten

bronzes _are

expected

to behave _as normal metals below _or close to the

Debye

temperature since this temperature ^has been found _to be

approximately

280 K for _m

= 4 and 240 K for _m

= 6

[28].

^However we have found that in both

compounds

the TEP has _a

negative slope,

while the Hall constant 18

positive.

This indicates that both bronzes _are

nearly compensated

metals. Band structure calculations

predict

that _{at room}

temperature

three bands _cross the Fermi level

[19].

^The

highest

_one is

electron-like in ail

directions,

the middle _one is

expected

to be electron-like

(or flat) along

the a-axis and hole-hke

along

b, while the

opposite

^{behavior is}

expected

for the lowest band in both

compounds (Fig. 3).

The TEP is found to be electron-hke _in the normal state whatever the direction of the

temperature gradient

is. This _may therefore indicate that the

highest

band

40

VTlla

m=6

$

20

^TP2 TAI

> 0

--~---

é5

ce -20

VTllb

40

Tp3

0 50 100 150 200 250 300

Temperature (K)

Fig.

7. Thermoelectric _{power as a} function of temperature ^for m = 6. Upper _curve

(open circles):

temperature

gradient along

the _a

crystallographic

axis. Lower _curve

(filled circles):

temperature

gradient along

b.

is aswciatedlv~ith the

longer

relaxation time and

pnmarily

determines the

transport

mass and therefore the sign of the

thermopower.

On the other

hand,

the

sign

of the Hall coefficient is

determined

by

the

cyclotron properties

and

by

the electron

trajectones along

the section of the FS in the ab

plane.

Our results show that the

cyclotron

mass is

predominantly

associated with

hole-type

carriers. Similar results have been found for the

high

_T~

superconducting

oxides and attributed to the

complex morphology

of the FS

[29].

The anomalies found _at the Peierls

temperatures

^{in the} curves of the TEP _vs. T

(Fig. 7)

are due to the gap

openings

which

modify

the

density

of _states at the Fermi level and the carrier mobilities. Below

Tp2,

the Seebeck coefficient S is

clearly p-type

^{when the}

temperature gradient

is

along

the a-axis and

n-type along

b. This indicates that the CDW

pockets

induced

by

trie

Tpi

transition _are

predominantly

electrons

along

b and holes

along

_a. These results should be related to the

geometry

^{of the} gap

openings

and therefore to the

position

of the CDW satellites which _are close to

(a*

+

b*)/3) [15.21, 22].

The

hole-type

behaviour

along

a indicates that the TEP is dominated

by

_carriers left from the Fermi sheet

corresponding

to the lower band

(first

Brillouin

zone),

which have _a p-type ^{behaviour due} to the

negative

curvature

along

this direction

(Fig. 3b).

^Below

Tp2,

the TEP indicates that

hole-type pockets

are induced

by

this second _gap.

The above results show that

transport

^and

magnetotransport properties provide

detailed information _on the FS both in the normal and CDW state. In the CDW state, the _size of at least part ^{of the 2D FS is known thanks to} quantum

transport.

3.

Transport Properties

and Instabilities in

P4Wio038 (m

=

5)

The _m

= 5

compound

is different from the other members of the _serres silice the

crystal

structure _is built with altemate

layers

of

W06

octahedra of different thickness: it _can be viewed

as

resulting

from _an

intergrowth

of the

compounds

_{m =} 4 and 6

[31].

^{The band structure and} the FS have been calculated with the _same

tight-binding

2D

approximations

as for the _m

= 4

and 6 members and FS

nesting

had been

predicted _[18].

It is therefore

interesting

to

study

its

physical properties

_in order to compare them with those of the _more "conventional" members

m = 4 and 6 which have

neighbounng crystal

structures and conduction electron densities.

5

Ê

₄ m=5

o

c ~

E

à

₂

'£

.=

.1

à

fila+b

0

0 00 200 300 400 500

Temperature (K)

Fig.

8. Resistivity of P4Wio038

(m

₌ 5) as a function of temperature. ^The current is

along

the

a + b

crystallographic

axis.

l.2

_

m"5 E

o B

= 6 Teslas

Cl 0.8

E

~' 4

~ 0.6

É

Î É

E

' llc

0

0

(K)

Fig.

9. Low temperature

resistivity

of P4Wio038

(m

= 5) _{as a} function of temperature for different

magnetic

field8 B. The _current 18

parallel

to the _a + b

crystallographic

_ax18 and the field B18

along

_c.

Figure

8 shows the

resistivity

_{p us.}

temperature

measured with the de current

parallel

to the ab

plane:

_p is characteristic of _a

metal,

with _{a room}

temperature

^value

higher

than that of the

compound

_m

= 6. Two anomalies _can be _seen. The first _{one is in} the

vicinity

^of

Ti

" 100 K

and

corresponds mainly

to an increase of

slope

at low

temperature

announced

by

_a

slight

minimum around 180 K. The second _{one is seen as a} weak kink around

T2

" 30 K and is better

seen in

Figure

9

(curve

B

=

0). Figure

9 shows the

resistivity

_vs.

temperature

^under

magnetic

field

perpendicular

to the

plane

of the

layers

in fields _up to 6 Teslas in the low

temperature regime. Huge magnetoresistance clearly

_appears below

T2.

No

X.ray

diffuse

scattering

^data

are

presently

available _on this

compound.

However, it is very

likely

that the two anomalies observed in the

transport properties

_are due to CDW _{gap openings.} The

high temperature

anomaly

is

puzzhng

_since it does not appear as a clear

bump

on the

resistivity

curve: this coula indicate that the onset of CDW gap or

pseudo-gap

_opening takes

place

around 180

K,

0

m=5 -1

_

-2

oe

-5 _VTllb

-6

0

(K)

Fig.

10. Thermoelectric _{power a8 a} function of temperature ^for m = 5. Temperature

gradient

along

the b

cry8tallographic

_ax18.

with _a small decrease of the _carrier concentrations and _a

large

increase of the mobilities. This coula be due to the _presence of CDW fluctuations above

Ti

which would

anomalously

decrease the collision time and therefore increase the

resistivity.

The

freezing

of these fluctuations when the

long

_range CDW order _is established coula

explain

the

strong

decrease of the

resistivity

below

Ti,

which _{appears as a}

change

of

slope.

Similar

properties

have been observed in the

past

ⁱⁿ some

layered dichalcogenides showing

CDW instabilities

[32].

^{Structural studies coula}

corroborate this mortel.

Figure

10 shows the

thermopower

S _vs.

temperature

^{measured with the}

temperature gradient along

the

layer plane.

The two transitions _are

clearly

_{seen as} extrema in the _curve. These

extrema

correspond

to the CDW gap

openings

and indicate that the

sign

^{of the} dominant

carriers

changes

at each transition. While S is

always negative,

the

change

of

slope

below

Ti

indicates that hole

pockets

become

important

at this

temperature

^{and that electron}

pockets

are

again

dominant below

T2.

Further low

temperature magnetoresistance

data and

possible quantum transport

should

complete

this information.

4. Short

Range

Order and Weak Localisation in tl~e

Charge Density

Wave State

of

P4W16056 (m

=

8)

Diffuse

X.ray scattering

studies have been

performed

_on tl~e _m

= 8 member of the _serres

[15].

Diffuse sheets _or fines _are observed _up to _room

temperature, indicating

the _presence of CDW fluctuations. These diffuse features condense into broad satellites at

TP1

" 220 K with _wavevec-

tor qi "

(0.47.0.02,0.15)

and _at

Tp2

" 200 K with _{wavevector q2}

=

(0.19,0.03,0.06).

This

corresponds

to the establishment below the transition

temperatures

^of short range

ordenng.

This lack of

long

_range

ordenng persists

clown to the lowest measurement

temperature

^of 35 K.

The q2 short _range order modulation is also

accompanied by higher

harmonics _nq2 detectable up to n = 6. This

might

indicate that this modulation is not sinusoidal and does not

correspond

to a conventional CDW. In this context, it is

interesting

to

study

the transport

properties

_in order to find ont how

they

_are affected

by

these anomalous structural

properties.

Figure

11a shows the electrical

res18tivity

_p measured _{as a} function of temperature ^between

4.2 K and 600

K,

for current

parallel

to the ab

plane.

Above _room temperature, ^the curve18

typical

of _a metal. Below

approximately

300

K,

_p increases clown to the lowest

temperature.

2

f

^{1.8 ~~~}

o 1.6

Cl

E 1.4

3l

_1.2

°£

1 _Tp2TPi

#

'à 0.8

fila+b 0.6

0 100 200 300 400 500 600

a) Temperature (K)

1300

j~1200

^~"~

l100

~ 1000

#

900

1

800

~

~~~

£

600 fila+b

500

0 20 40 60 80 100 120 140

b) Temperature (K)

Fig.

Il.

(a) Resistivity

of P4W16056 (m ₌

8)

_{as a} function of temperature. The current is

along

the _a + b

crystallographic

axis.

lb)

Low temperature

conductivity

of P4W16056

(m

=

8)

_{as a} function of temperature.

This behaviour _may indicate weak localisation effects [33] ^{due to the disorder induced}

by

the CDW short _range

ordenng.

One may therefore

plot

the

conductivity

_a us.

temperature

in the low

temperature regime

_in order to compare ^it with results obtained _on other disordered

metals

[34]. Figure

1lb shows that _a linear

dependence

of _a is found _{up to}

approximately

60 K.

This _may be due to quantum interference effects induced

by

the CDW disorder and

giving

_use

to weak

localisation, possibly

combined with electron-electron interactions.

Magnetoresistance Ap/po

has also been measured _{as a} function of

magnetic

field.

Figure

12 shows that it is

positive

and

anisotropic, larger

for field

apphed perpendicular

to the

layers.

It

is

weak,

in the range of the at 4.2 K in fields of 6 Teslas.

Figure

13a shows that

Ap/po

follows

a law in

B~

in _a field interval

increasing

with

increasing

temperatures

(up

to 6 Teslas at 40

K).

One coula

analyse

these data either with _a two-band mortel,

assuming

semi-classical

transport,

or in relation with _a weak localisation mortel. In the first _case, the

slope

_a of

the

_curves of

Figure

13a

(Ap/po

=

aB~)

_would be _{in a} first

approximation

the _square of _an effective _carrier

mobility

_/1e~,

assuming

_a

perfectly compensated

two-band mortel with

equal

hole and electron

0.025

m=8

0.02 ~ ~~~

j0.015

^Bllc

)

O.Ol

0.005

Blla+b

0 fila-b

0 2 3 4 5 6

Magnetic

^field

(Tesla)

Fig.

12.

Magnetoresistance

_as a function of

magnetic

field for _{m =} 8, showing ^the anisotropy.

T = 4.2 K.

Magnetic

field

perpendicular

_or

parallel

to the

layers.

mobilities.

Figure

^13b shows the _curve of _{a us.}

temperature.

^{Values of} _/1e~

decreasing

from 900 to 100

cm~ /Vs

between 4.2 and 40 K _are found _on this basis. While these values _are not

unreasonable,

this mortel is inconsistent with the low

temperature

_increase ^{of the}

resistivity.

One may then invoke _a weak localisation mechanism. In this second

mortel,

the

slope

_a would be related _to the inelastic

scattering

time characteristic of the disorder

[35]

^{and therefore of}

the CDW correlation

length.

The inset of

Figure

13b shows _{a as a} function of

temperature

on

log-log

scales: _a

temperature

_power law with _an

exponent

^of

-3/2

is well

obeyed.

This behaviour coula be the

signature

of _a weak localisation mechanism. Further work is in progress

in order to corroborate this

analysis.

Thermopower

^{S has been measured} as a function of temperature ^{between 10 K and 300 K.}

Figure

14a shows that S is

always n-type

and that

Si

decreases with

decreasing temperature

except for _an

anomaly

detected in the

vicinity

^{of the}

Tpi

transition. This

anomaly

is

clearly

the

signature

of this transition which _was not detected _on the

p(T)

_curve. It may indicate that small _{gaps open on} the FS at this

temperature.

The low

temperature

behaviour of

S(T)

is

puzzling. Figure

14b shows that the _curve of

S( /T

us. T shows _a

peak

at low

temperature

^{around 30 K. Similar effects found in disordered metals} have been in the

past

^{attributed to} mass enhancement due to

electron-phonon coupling _[36].

A similar mechanism coula take

place

in _{our case.}

The _m

= 8

compound

is the

only

member of the series

showing

no

long

_range order in the distorted state. This coula be due to the

competition

between the two instabilities at

Tpi

and

Tp2

which take

place

at

neighbouring temperatures.

^{Whether the short} range order state

corresponds

to the coexistence of domains associated to _{one or} the other modulation _or to _a more

complicated

situation _is not known at the moment.

5. Instabilities in tl~e

Monopl~ospl~ate Tungsten

^Bronzes

(P02)4(W03)2m

_{as a}

function of _m

(4

< _m <

14)

Instabilities have been detected both

by transport

and structural studies in

large

_m com-

pounds [15, 37].

One should note that

high temperature

transitions _are found: for _m >

8,

these

temperatures

are above _room

temperature

^{and reach 550 K for} m ₌ 13. While most

compounds

o

;

,X'

~

~

/ ^~ a'/~ _{-~ 8(~~}

É

_{6 d}

_' ~'~ _~

^~~

j

^,

, ~ ~~~

~

. ,

-~ 40K

~ ~ '

o 4

/ ~

~ u-~a

-

~,'

R~-~"

~

~a+~'

~_~+r+ -e

o

0 5 0 5 20 2 5 30 3 5

a)

82 lTesla2)

~

m=8 ^'°°

m"~

7

'

,

6

)

^~~

''

~

, ~K

5

j ~

$

~ 4

j _oi

,oo

~'

mmpellure _lKl

d 3 4

é

2 '

- '

~

'

- -~

~ ,

0 10 20 30 40 50

b) Temperature (K)

Fig.

13.

(a)

Low temperature magnetoresistance _as a function of B~ _for

m = 8,

Magnetic

field perpendicular to the

layers. (hi

Coellicient _o defined by

àp/po

=

ceB~ as a function of temperature.

The inset shows the _same results

on a

log-log

scale.

show incommensurate modulations, another

type

^of commensurate distortion _appears for

m > 9: this

corresponds

to a

doubling

of the lattice parameter

along

_a, the related satel- lites _are

comparatively

intense and _{are not} characteristic of CDW. This modulation has been described in _terms of _an

antiferroelectric-type

distortion _in reference

[15].

^{This is}

supported by

the existence of such distortions in the

neighbounng compound W03.

Figure

15 shows the critical

temperatures

obtained from both

resistivity

measurements and structural studies _{as a} function of _m. Four types ^of transitions _can be

distinguished.

The transition

temperatures

labelled

Tci

and

Tc2 correspond

for small values of _m to

Tpi

and

Tp2

The third transition found in _m

= 6 at low temperature is labeled

Tc3

_in this

graph. Finally,

the transition

temperature corresponding

to the commensurate distortion _is labelled

Tco.

It

is clear from these results that the transition temperatures

Tci

and

Tc2

_are

increasing rapidly

with _{m up to m}

= 13.

Trie

high

values of the transition temperatures ^{and their}

rapta

increase with

m are the

most remarkable

properties

of the

monophosphate _tungsten

bronzes. One should note that for

0

-27

~ ~_

-28

~

-10

1

^~~~

~£ -15

~f

~~ vTlla _pi

>

à

-20 ^{~~° ~°° ~~°}

oe

TP2TPI

25

-30 VTlla

-35

0 50 100 150 200 250 300

~) Temperature (K)

500 ^m=8

_

~

400

~

300

t

200

ce

~~~ VTlla

0

0 50 100 150 200 250 300

b) Temperature (K)

Fig.

14.

(ai

Thermoelectric _power S

as a function of temperature for _m

= 8. Temperature

gradient along

the _a

crystallographic

axis. Trie inset shows trie

high

temperature data with

enlarged

scales.

lb) -S/T

_{as a} function of temperature

showing

^trie low temperature

peak.

large

values of _m

(m

=

13),

trie

compounds

_are close to trie oxide

W03,

since trie thickness of the

W06 layers

_is

large. However,

electronic instabilities _seen in the

transport properties

appear ^at

high

temperature

[37].

^The same

arguments

as those

developed

for trie _m

= 4 and

6

compounds

coula therefore

apply:

_{a more}

pronounced

twodimensional character would be found in the

large

_m

compounds, inducing

a more

cylindrical

FS and therefore

higher instability

temperatures.

Detailed structural studies

including crystallographic

refinements _on

large

_m

members _are

presently missing

to corroborate this mechanism. One should also note that

X.ray

diffuse

scattenng

studies show the _existence of

high

^{order harmonics of the satellites for} m > 7.

This shows that the distortion _is not sinusoidal for

large

m and therefore does not

correspond

to

a conventional CDW. This coula be attributed to

strong electron-phonon coupling inducing

a

bipolaron-type mechanism,

as descnbed in reference

[38].

Electron.electron interactions coula also

possibly

be

responsible

for such distortions.

Other related

interesting properties

^of the

monophosphate tungsten

bronzes lie in the vari- ation of the

resistivity

as a function of _m.

Figure

16 shows the _room

temperature resistivity

800 700

.

Tco

^~

600 ° Tci

/

soc ^" Tc2 ^~

~(

é

a

Tc~

o

~ ~~ /

~~~

/°~

X

100 ~D ^°

~

'>~~~

2 4 6 8 10 12 14 16

m

Fig.

15. Critical temperatures _{as a} function of

m

(see text).

Trie crossed data points correspond

to results obtained

by crystallographic

studies

only

Other data points correspond to results obtained

by

transport ^studies

land

often

by

structural

studies).

Trie fines _are

guides

to trie _eye for trie Tci and Tc2 transitions.

ioo

(

C1 10

~

.

=

-

~ ^-

~l'~ ¹

o

O

°'

/ /

~ z

~

~

~/ .

o

/

-

/

~

/ C

~

"

O,I °~

~ ~

2

4 6

8

Fig.

16. Left scale and close

symbols:

_room temperature

resistivity

_{as a} function of

m.

Right

8cale and _open

8ymbols: reciprocal

electron concentration evaluated from trie chemical formula

(2/m

_per

W

ion).

p(300 K) (log scale)

_{us. m} for 4 < _m < 14. Trie

reciprocal

_carrier

density

evaluated from trie chemical formula

(2/m

conduction electron _on trie average per W

atom)

is also

plotted

us. m for

comparison.

One notes _a

steep

increase of

p(300 K)

with _m for _even

m

compounds.

Trie increase _is weaker for odd _m members. Trie

larger

_room

temperature resistivity

for

large

m members of trie _serres is

striking:

it coula be related to

slightly

different

crystal

structures

since most odd _m

compounds

show monoclinic distortions

[39].

^{Whether this induces}

stronger

electron-phonon coupling

is not clear at trie _moment. One should also note that the

difference

in

resistivity

between odd and _{even m seems} to vanish for

large'm,

thus when _one

approaches

W03.

In order to account for these results, _one has also to consider the existence of

intergrowths

in the

large

m

compounds (see

^for

^example

^Ref.

[39] ).

^These

intergrowths

_may ^{induce inhomo-}

geneities

and disorder which coula increase the electrical

resistivity.

^{However this should not be} the _case for the low _m

compounds:

for

example

the factor of1o between the _room

temperature

resistivity

of the _m

= 4 and 6

compounds

has been found in

crystals

from different

origins

and is _very

reproducible.

This cannot be attributed to

intergrowth problems

since these

phases

do

not suffer from such defects. Some intrinsic mechanism must then be involved.

The

large

_increase ^of

p(300 K)

_us. m for _{even m}

compounds

cannot either be attributed to the

change

_in the carrier concentration which in _a first

approximation

should induce a

much weaker

increase,

as shown in

Figure

16. Two mechanisms _can be invoked to account for these

properties,

either _{an increase} of the

electron-phonon coupling

_or of the electron-electron

interactions. An increase of the

resistivity

^has been observed at low

temperatures

on most

compounds

for _m > 7. This may

suggest

that the second mechanism is _more

likely

to be dominant.

,

6. Conclusion

The

monophosphate tungsten

bronzes

(P02)4(W03)2m Provide

_a mortel

system

^for

quasi-two

dimensional conductors where the Peierls

temperatures

and the electrical

resistivity

can be vaned _{as a} function of the _m

parameter.

^This

parameter

is correlated with the thickness of the

conducting layers

_as well _as with the average carrier concentration

density.

The small _m

compounds (m

=

4, 6)

show conventional CDW

properties,

with metallic _or semi-metallic behaviour _over the whole

temperature

_range and _a decrease of carrier _concen- trations below the Peierls

temperatures.

^{In the low}

temperature

CDW states,

they

exhibit

giant positive magnetoresistance

attributed to the coexistence of

high mobilitiy

^{electron and}

hole

pockets

left

by

the CDW gap

openings. Quantum transport

allows _an evaluation of the size of these

pockets

which _are found to be of the order of

1%

of the two-dimensional

high

temperature

Brillouin zone. The _m

= 5

compound

also shows

instabilities,

with _a behaviour different from what is found in the 4 and 6

compounds.

This coula be due to the different

crystallographic

structure since the _m

= 5 member _can be viewed _{as an}

intergrowth

^of the

m = 4 and 6 ones. Also CDW fluctuations may be

important

^{in this}

compound

above the

instability temperatures.

For _m > 7, different

type

^of

transport properties

as well _as

higher

order harmonics of the CDW satellites found

by X.ray

diffuse

scattering

studies show that the instabilities _are not

conventional Peierls transitions. For _m

=

8,

the

transport properties

are determined

by

the absence of

long

_range CDW

ordering

and may be attributed in the low

temperature regime

to weak localisation related to

quantum

interference effects induced

by

the short CDW correlation

length.

Systematic

studies of these bronzes for 4 < _m < 14 show that the Peierls _or

instability temperatures

are increasing with _m.

High

transition

temperatures,

above _room

temperature

and _up to soc

K,

are found for _{m >} 8. The _increase of

TP

with _m may be attributed to _an

increase of the low-dimensional character. This _may be due to _a decrease of the transverse

coupling

with

increasing

m.

taking place

if the conduction electrons _are located towards the

center of the

W06 layers.

The Fermi

cylinder

would then be less

warped

for

larger

_m, this

favounng

the onset of CDW instabilities at

higher temperatures.

Finally

the _room temperature

resistivity p(300 K)

is found to increase with _m,

rapidly

for

even m

compounds.

The odd _m members show

higher

values of

p(300 K).

This _can be due _to

a different

crystal

structure _since most odd _m

compounds

^show a monoclinic distortion. The