Quantum Transport in the Charge-Density-Wave State of the Quasi Two-Dimensional Bronzes (${\bf PO_2}$) 4(${\bf WO_3}$)$_{\bf 2m}({\bf m}={\bf 4, 6})$

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Quantum Transport in the Charge-Density-Wave State of the Quasi Two-Dimensional Bronzes (PO_2)

4(WO_3)_2m(m = 4, 6)

C. Le Touze, G. Bonfait, C. Schlenker, J. Dumas, M. Almeida, M. Greenblatt, Z. Teweldemedhin

To cite this version:

C. Le Touze, G. Bonfait, C. Schlenker, J. Dumas, M. Almeida, et al.. Quantum Transport in the Charge-Density-Wave State of the Quasi Two-Dimensional Bronzes (PO_2) 4(WO_3)_2m(m = 4, 6).

Journal de Physique I, EDP Sciences, 1995, 5 (4), pp.437-442. �10.1051/jp1:1995100�. �jpa-00247068�

Classification

Physics Abstracts

71A5L 72.15E 72.15G

Short Communication

Quantum lYansport'in the Charge.Density.Wave State of the

Quasi Two-Dimensional Bronzes (P02)4(W03)~m(m

=

4, 6)

C. Le Touze

(~),

G. Bonfait

(~),

C. Schlenker

(~),

J. Dumas

(~),

^{M. Almeida}

(~),

M. Greenblatt (~) and Z-S- Teweldemedhin

(~)

(~) Laboratoire d'Etudes des Propriétés Electroniques des Solides (*) CNRS, BP 166, 38042 Grenoble Cedex 9, France

(~) Departameuto de Quimica, ICEN, INETI, P-2686 Sacavem Codex, Portugal

(~) Department of Chemistry, Rutgers, The State University of New Jersey, Piscataway, N-J- o8855-0939, U.S.A.

(Received

6 February 1995, accepted 17 February1995)

Abstract, Magnetotransport bas been studied _on trie _quasi two-dimensional monophos- phate tungsten bronzes

(P02)4(W03)2m

for _{m =} 4 and 6, between 0.3 and 300 K in fields _up to 18 T. These compounds show several charge density _wave transitions. Large magnetoresistance

is found in trie charge-density-wave state for magnetic fields applied perpendicular to trie layers.

At low temperatures, Shubnikov-de Haas oscillations

are attributed to trie existence of small

carrier pockets left by trie charge density _{wave gap} opening. Trie _size of these pockets is of trie

order of _a few % of trie two-dimensional high temperature ^Brillouin zone and smaller _m the

case m = 6 than in _{m =} 4. This

is due to _{a more} pronounced low-dimensional character and therefore to _a better Fermi surface nesting in trie compound _m

= 6 than _{m m =} 4.

1, Introduction

It is _now well-known that

quasi-twc-dimensional (2D)

metals often show electronic instabilities.

These instabilities _con lead either to _a

charge-density-wave (CDW)

state as in some

layered

transition metal

dichalcogenides

and in _some transition metal bronzes and oxides

il,

_{2], or} to

superconductivity

_as in trie

copper-based high

Tc oxides. Trie

mechanisms,

which control which type ^of

instability

takes

place,

_are not well understood at the moment. In this context, ^{it is}

interesting

to

study

_{a new}

family

of

quasi

2D

metals,

the

monophosphate

tungsten bronzes, of

general

formula

(P02)4(W03)2m.

These materials have been

synthesized

and their

crystal

structure studied _more than ten years ago [3]. ^{Their lattice is} orthorhombic and built with

perovskite Re03-type

infinite

layers

(*) Associated to Université Joseph Fourier, Grenoble, France.

@ Les Editions de Physique 1995

438 JOURNAL DE PHYSIQUE I N°4

of W06 octahedra

parallel

to the

(a,

_b)

plane, separated by

P04 tetrahedra Since the Sd 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

^when m increases. This eifect _may lead to increased electron-electron interaction due _to weaker

screening

^eifects.

Band _structure calculations

using

_a

tight binding

extended Hückel method in _a 2D approx-

imation have been

performed

for the

compounds

_m

= 4 and 6.

They

lead _to three bands

crossing

the Fermi level. Trie three

corresponding

sheets of the Fermi surface

(FS)

have also been calculated [8].

Nesting properties

_{appear on} trie

resulting

^{FS obtained from} trie _super- position ^{of these sheets. This behaviour bas been related} to _a sc-called hidden

nesting

[9], or

hidden

one-dimensionality,

due to the _presence of infinite chains of

W06

octahedra

along

the

a and

(a

+ b) axes. The FS _can then be described _as

being

due, in _a first

approximation,

to

the

superposition

of three

quasi

ID FS.

The

physical properties

of the members m = 4 and _m

= 6 have _now been well studied [4, Si.

Two anomalies in the electrical

resistivity, indicating

the existence of two electronic instabilities, have been found for _m

= 4.

X-ray

diffuse scattenng studies have demonstrated that

they correspond

to incommensurate CDW [2,6]. ^{In the} m = 6 case, a third

instability

has been found _at low temperature

(Tp3

" 30

K), by

both structural and Hall eifect studies [7,

iii.

Large magnetoresistance

^found at low temperatures in fields

perpendicular

to the

layers

in both

compounds

has been attributed to the _existence of small electron and hole

pockets

_on

the Fermi surface of the CDW state [7]. ^In this context, one may expect quantum transport to appear in the

low-temperature

CDW state. This could

give

information _on the Fermi surface

in the CDW state. If this _were the _case, the comparison of the results for _m

= 4 and 6 would be

interesting.

We therefore have

performed

resistivity measurements down to o.3 K in fields up to 18 T for both compounds.

2.

Experiment

Single crystals

used in these studies have been _grown

by

solid state reaction [4] or

by

chemical vapor transport

technique

_[Si. The

crystals

_{are in} the

shape

of

platelets parallel

to the

la,

_b)

conducting plane,

of

typical

_size 1x1.5 x 0.i mm~. Silver contacts _were

deposited

_on the

crystal

surface

by evaporation.

The current _was

always parallel

to the

la, b)-plane.

The

resistivity

has been measured between o.3 and 300 K in _a commercial

~He

_{cryostat in}

a

magnetic

field _{up to} 18 T

perpendicular

to the

la,

b)

plane, provided by

_a

superconducting

coil.

Figure

la shows the resistance _{as a} function of temperature for _a

crystal

_m

= 4 in _a field of o T and 14 T. One notes _a

giant magnetoresistance

in the low temperature ^CDW state.

Both Peierls transitions at Tpi _# 80 K and Tp2 _" 52 K do not _seem to be

displaced by

the

magnetic

field. However _a minimum appears in thc

resistivity

around io K under 14 T. The

magnetoresistivity

is

plotted

_{as a} function of

magnetic

^field at o.3 K in

Figure

16. One _can

see small oscillations above 12 T. These oscillations _are better _seen if _one subtracts the _non-

oscillating background. Figure

2a shows the denvative of the

oscillatory

_{part as a} function of

1/B

in the range il-16 T. The oscillations _are

periodic

with _a

period

^of 1.65 _x lo~~

T~~

If _one

assumes that these oscillations _are of the Shubnikov-De Haas type, the field

Bn corresponding

to a maximum of the

resistivity

is related _to the _area of _an extremal orbit _on the Fermi surface

through: Bj~

=

(2e là)

_(7r

IA f)(n

+ ~t), ^where ~t is _a constant of the order of

unity. Figure

2b shows

Bj~

_{as a} function of the

integer

_n. The observed oscillations

correspond

to rather

large

008

~ ^{Bm 14 T m~4}

m-4

~ Il ~

E 0.04 +

à

~

~ ^{" ~}

ÉIÎ

Bm 0 T

~ ~~

T»0.3 K

o o

o 50 ioo 130 o 4 3 12 16

a)

T(K)

b)

_(T)

Fig. I. P4W8032

(m

₌

4) (a)

Electrical resistivity _{as a} function of temperature for _a magnetic field of o and 14 T. Trie current is parallel to trie

(a,

_b) plane and trie field to trie c-axis.

(b)

Magne~

toresistance

Ap/p

_{as a} function of field at T

= 0.3 K

«

X _o12

~ 3

/

83 m-4 ,'

]

$ ^~~~ A=000>6T-' ,"

o ~

Î

À fl

w / ~

~

~

~ '

£ Tm0.3 K

, /

$ -013

~ 006 0 07 0 03 0Ù9 0 16 32 48 64

~) ^{l la (T'l b ~}

Fig. 2. P4W8032

(m

= 4)

(a)

Derivative of trie oscillatory part of trie magnetoresistivity _vs.

l/B.

T = 0.3 K

(b)

Inverse positions of trie maxima

,

1/Bn

_vs. trie integer _n.

values of _n, in trie _{range 35 to} 60.

Results obtained _{on a}

crystal

with _{m =} 6 _are shown in

Figure

3 and 4. As shown previ-

ously

[7,

iii,

the

resistivity

is _one order of

magnitude higher

in the _{case m}

= 6 than _m

= 4

(Fig. 3a).

At the _same time, the magnetoresistance _is lower. One should

point

out that trie low temperature transition at 30 K is not seen, either _in trie

resistivity

_{or in} trie magnetore-

sistivity

_curve.

Figure

3b shows

Ap/p

_{as a} function of B. Trie

magnetoresistance

seems to be

approximately

linear _m B and strong oscillations _appear above 8 T. Trie

oscillatory

part

2

1.2

Ê _{Bm 14 T} ^~~~

mm6

~

°'~

II

à

~ l

_

j

~' ~"

^0.4

^ÉÀÎ

B- 0 T

~ ~

~ Tm0.3 K

0 0

0 50 Io0 150 200 250 0 4 3 12 16

~) ^T(K)

~)

^(T)

Fig. 3. P4W12044

(m

= 6)

(a)

Resistivity _{as a} fuuction of temperature ^for _a magnetic field of 0 and 14 T

(b)

Magnetoresistivity _us. B, T

= 0.3 K.

440 JOURNAL DE PHYSIQUE I N°4

0.2 0 12

1

₀ ^~"~

~

~"~

~ II

à

_~ ^°°~

II

à

o Î

1

~~

Tm0.3 K

)

_-0.i

T_o 3

~

0 2

006 008 0 012 0 4 8 12

~~ _l la (T-' )

~)

~( K)

Fig. 4. P4W12044

(m

= 6) (a) Oscillatory part of trie magnetoresistivity _vs.

IIE.

T

= 0.3 K

(b)

Amplitude of trie peak _{n =} 8 _vs. temperature.

of

Ap/p

is shown in

Figure

4a _{as a} function of

i/B

in trie range 7-16 T.

While,

_{on average,}

the

amplitude

is

decreasing

us.

i/B,

it is dear that the

analysis

requires several

periods.

A Fourier

analysis

leads to the

periods Ai

_# 9 _x

io~~

T~~ _and

A2

_" 7 _x io~~

T~~,

much

larger

than in the _m

= 4 _case. The _curve of

Bj~

~s. n

gives

values of _n in the 5 to io range. The

amplitude

of the most intense

peak,

found to be _n

= 8, is

plotted

_{as a} function of temperature

m

Figure

4b. It follows _a law of the type

xl

sinhx, _as

expected

from the Shubnikov-de Haas

theory

_[14].

3. Discussion

All these results _are consistent with _an

imperfect nesting

^{of the Fermi} surface _m the normal metallic

phase.

^{Successive CDW} instabilities

destroy large

parts ^{of the Fermi surface.}

However,

m the lowest temperature state, _some carrier

pockets

_are still present. ^{The Peierls} instabilities

are therefore _m all _cases metal-metal transitions.

The

large positive magnetoresistance

^found in the CDW state has to be attributed to the presence of both electron and hole

pockets

and therefore _{to a}

nearly compensated

metal.

However, ^the

complexity

of the Fermi

surface,

with several types ^of

pockets,

_{prevents us} from

making simple predictions

for the temperature behaviour of the magnetoresistance at low temperature. It should be noted that the apparent increase of the

resistivity

at 14 T in the

case m = 6

(Fig. 3a)

is due _to the fact that this field

corresponds

to a maximum of _an oscillation A similar eifect _{may occur m} the

compound

_m

= 4

(see Fig. la).

The field

dependence

of _p, which does net show _a B~ behaviour in both

compounds

indicates that the compensation _is not

perfect.

This is consistent with Hall eifect measurements which show _a n-type ^behaviour [7].

The carrier

trajectories

_{are in any case}

expected

to be dosed for this geometry

(B II c).

This _is corroborated

by

the observation of quantum transport ^{in both}

compounds.

The

high

field oscillations found in the _m

= 4

compound

have _a low

amplitude,

but

Figure

2a shows that the

frequency

in i

/B

is rather well-defined. One may then evaluate the _size of the

corresponding trajectory through

the usual formula: A ₌

27re/hAf.

This calculation leads

to _an area

Ai

of 6 _x 10~~

À~~

_{and to}

a F S _area of

roughly

^{5.4% of} the two-dimensional Brillouin _{zone in} the

high-temperature

state. The existence of the Shubnikov de Haas oscil- lations therefore corroborate that the CDW _gap

openings

^leave _verjr small

pockets

_on the F S.

In the _case of the

compound

_m

= 6, the situation is _more

complicated

since the oscillations

cannot

obviously

be descnbed

by

_a

smgle frequency,

_as shown _m

Figure

4a. One _{may per-}

form _a Fourier transform of the

oscillatory

part of the

magnetoresistance,

which leads to two well-defined

penods: ^Ai

_# 9 _x lo~~

T~~,

A2

" 7 _x lo~~ T~~ _A

possible

explanation ^for this

result could lie in the existence of several

pockets. However,

the existence of two well-defined

periods

could also be due _{to a}

warping

of the

cylinder corresponding

to the relevant sheet of the F S. This _warping would be related _to the transverse

coupling

^{between trie}

layers

and to trie deviation from

perfect twc-dimensionality.

In this

model,

trie two

periods

_are attributed to two extremal _areas of trie undulated

cylinder.

Trie average value of 8 _x lo~~ T~l _corre-

sponds

to _an orbit _area of1.2 _x lo~~

À~~,

therefore of

roughly

1.1% of the

high-temperature

twc-dimensional Brillouin _zone. The size of the carrier

pocket

is thus much smaller in trie

m = 6 than in trie m = 4

compound.

This may mdicate _a better F S

nesting

in trie first

case. One should _note that this _is consistent with _{a more}

pronounced

2D character for _m

= 6

and the

experimentally

observed

higher

Peierls transition temperature. ^{We have} shown indeed

recently

that when _m increases _up to 12, both trie Peierls transition temperature and trie _room temperature

resistivity

increase [12].

In trie _case of _m

= 6, _one can evaluate trie

cyclotron

_mass from trie temperature

dependence

of trie

amplitude

of trie oscillations. Trie thermal factor is

expected

_to be

xl

sinhx with

x =

27r~km"T/àeBn (T

is the

temperature)

for the n~~ oscillation. From the

experimental

value of _x

= oAl T obtained for the oscillation _at B

= 15.9 T

(n

₌

8),

the effective

cyclotron

mass is found to be o.45 times the free electron _mass. A similar result is obtained from the temperature

dependence

of the

amplitude

of the oscillation _at B

= loA T. This indicates that the carriers _are rather

light.

The

large

value of the index _n of the oscillations

(n

= 35 to

60)

for _m

= 4 indicates that trie field

corresponding

to the quantum limit is

high,

in the _range of several hundreds of T. It is smaller for _{m =} 6

(of

trie order of loo

T),

which is related to the smaller size of the

pocket

in the last _case

4. Conclusion

The results of quantum transport ⁱⁿ the

monophosphate

tungsten ^bronzes corroborate that there _are small electron and hale

pockets

in the CDW state of these

compounds.

Trie _size of these

pockets

_can be evaluated _{to a} few % of trie _area of trie two-dimensional Brillouin _zone.

Trie carriers _are found to be

comparatively light,

with _an effective _mass smaller than that of the froc electron. Further work will involve _more extensive studies in order to obtain trie

effective _{mass, as} well _as the

Dingle

temperature in both

compounds.

Acknowledgments

The authors wish to thank J-P-

Pouget

for very

helpful

discussions. This work _was

partially supported by

JNICT,

Portugal,

under contract

STRRDA/C/CEN/431/92

and

by

a JNICT- CNRS agreement

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