Conduction anisotropy, Hall effect and magnetoresistance of (TMTSF)ReO at high temperatures

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15 Νοε 2013 (πριν από 3 χρόνια και 4 μήνες)

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Conduction anisotropy, Hall effect and magnetoresistance of
(TMTSF)
2
ReO
4

at high temperatures



B.Korin
-
Hamzi
ć

a*
, E.Tafra
b
, M.Basletić

b
, A.Hamzić

b
, G.Untereiner
c
, M.Dressel

c

a
Institute of Physics, HR
-
10001 Zagreb, Croatia

b
Department of Physics, F
aculty of Science, HR
-
10002 Zagreb, Croatia

c

Physikalisches Institut, Universität Stuttgart, D
-
70550 Stuttgart, Germany


Received ; accepted



Abstract


We present the high temperature results for conductivity, Hall effect and magnetores
istance (i
n the least
-
conducting direction) for
(TMTSF)
2
ReO
4,
at ambient pressure and above anion
-
ordering metal
-
insulator transition (T
AO
≈ 180 K). The pronounced conductivity
anisotropy, a small and smoothly temperature dependent Hall effect and a small, positive and temperature dependent magnetores
istance are
analyzed within the Fermi
-
liquid and non
-
Fermi liquid models.


Keywords:
transpor
t measurements, conductivity, magnetotransport, organic superconductors



Interacting electrons in 1D form a non
-
Fermi liquid
(FL) state, usually called Luttinger liquid (LL) [1] which
exhibit temperature (and energy)
power
-
law behaviour with
intera
ction dependent exponents.
There is a long standing
controversy whether the transport properties of Bechgaard
salts (TMTSF)
2
X at high temperatures should be
understood in terms of the usual FL or LL theory [2,3]. The
crossover from LL to a usual FL behavio
r is expected as the
temperature is lowered [3,4]. The high temperature Hall
effect results of X=PF
6
, obtained by two groups, were
interpreted differently, using the FL theory [5] and LL
concept [6]. The aim of our work was to contribute to this
still open

question by measuring the transport properties of
X=ReO
4
, a compound that is expected to be more
anisotropic than X=PF
6

[2].


(TMTSF)
2
ReO
4

is metallic down to T
AO
≈ 180 K.
Fig. 1a
shows the temperature dependence of the resistivity
measured along the three crystal directions and normalized
to their respective room temperature values (ρ
RT
). The
pronounced differences are evident: ρ
a
(T)

~ T
1.84
(240K < T
< 300K); ρ
b
(T
) ~ T
0.25

(for T > 257 K, where a minimum
occurs, and ρ
b

increases

at lower T); ρ
c
~ T

0.4

(190K < T <
300K). We point out that this is for the first time that this
kind of behaviour for ρ
b
(T) is found in one member of the
Bechgaard salts family.


All

the data presented in Fig.1a are measured at ambient
pressure and considered as the constant
-
pressure data. Due


*Corresponding author. E
-
mail:
bhamzic@ifs.hr

to the pronounced
thermal expansion of the (TMTSF)
2
X,
the conversion to the constant
-
volume

ρ
(V)
(T) data has to be
done in order to compare the experimental results with the
theoretical models [3]. Using the same procedure as for
X=PF
6

[6,7] we have obtained (cf. Fig.1b) ρ
(V)
a

~ T
+0.46

and
ρ
(V)
b
~ T
-
0.66
(200K < T < 300K). The dashed line presen
ts
the expected LL power
-
law for ρ


[4]. Namely, in a system
of weakly coupled Luttinger chains, the transverse and
T
(K)
180
200
220
240
260
280
300
320

/

RT
0.8
0.6
0.4


/

RT
1.2
0.9
0.6
a
b'
c*

(th.)~
T
- 0.38

b'
~
T

0.256

b'
(V)
~
T

- 0.66

a
(V)
~
T
0.46

a
~
T
1.84

c*
~
T

- 0.4
a
b'
b
a

Fig.1a.
ρ
a
, ρ
b’

and ρ
c*

resistivity
vs.

temperature for three crystal
directions, normalized to their room temperature v
alues (ρ
RT
).

Fig.1b. ρ
a
(T) and ρ
b’
(T) corrected for thermal expansion.

longitudinal resistivity are given as ρ


~ T
1
-


and ρ
||
~
(g
1/4
)
2
T
16Kρ
-
3

(α = 1/4(K
ρ
+1/K
ρ
)
-

1/2 is the Fermi surface
exponent, g
1/4

is the

coupling constant, K
ρ

is the LL
exponent [4]). The comparison with our ρ
(V)
a

data yields K
ρ

= 0.22, in a reasonable agreement with the value for X=PF
6

[6,8]. On the other hand, by using K
ρ

= 0.22, we obtain ρ

~
T
-
0.38

(dashed line in Fig.1b), while ρ
b
~T
-
0.66
. In spite of the
crudeness of our analysis, the 1.7 times higher exponent
value cannot be consistent with the model predictions.


However, ρ
(V)
a

can also be satisfactory compared with
the FL theoretical model with the electron relaxation time τ

that varies over the Fermi surface [9]. In this approach it is
proposed that a quasi
-
1D conductor behaves like an
insulator (dρ
a
/dT < 0), when its effective dimensionality
equals one, and like a metal (dρ
a
/dT > 0), when its effective
dimensionality is gre
ater than one. In this sense, our results
suggests that X=ReO
4

is a 2D anisotropic metal at high
temperatures. Unfortunately, the lack of a comprehensive
transport theory (with anisotropic τ) for ρ
b

and ρ
c

prevent us
to reach the final conclusion concernin
g the FL approach.


Fig. 2 shows the temperature dependence of R
H

above
T
AO
, and normalized to R
H0
= 3.5

10
-
3
cm
3
C
-
1

value, derived
in a band model. The Hall coefficient is positive (hole
-
like)
and slightly temperature dependent.


R
H
of the weak
ly coupled 1D Luttinger chains does not
depend on temperature and it is given by a simple formulae
R
H

= R
H0
[4]. The slight temperature dependence and about


20% scattered results can not exclude a possible LL
interpretation. However, the controversy with

the LL model
arises because of the number of carriers (
n
) participating in
the
dc

transport. Based on the optical conductivity results
for (TMTSF)
2
X salts (considered as a strong evidence for
the LL behavior) it was proposed that only 1% of
n

participate
in
dc

transport [8]. This should give a factor of
100 higher R
H

value than we have obtained experimentally.


In the framework of the FL
description with anisotropic
τ, R
H

may depend on temperature [9]: it is strongly
temperature dependent at low temperatures, while at high
temperatures T ≥ t
b
(≈ 300 K) it saturates at the R
H0
value.
The dotted line in Fig.2 shows the theoretically predicte
d
R
H
(T) ~ T
0.7

behavior obtained for a chosen set of
parameters [7,9]. The temperature dependence of R
H
, as
well as the experimental values (albeit somehow higher)
satisfactory follow the predicted behavior. We can therefore
conclude that the FL descriptio
n with anisotropic τ [9]
remains valid for
ρ
(V)
a

and

Hall effect.


The temperature dependence of the transverse
magnetoresistance (MR) for T >180 K and for the particular
geometry (
j
||
c*
,
B
||
b'
) is

shown in Fig.3 as (Δρ
c*
/ ρ
c*
)
1/2

vs.
T. It was predi
cted [10], in the simple FL model based on
the band theory for isotropic τ, that MR is the largest for
j
||
c*

and
B
||
b'
, because Δρ
c*

c*
=(ω
c*
τ)
2


c*
is the
cyclotron frequency associated with the electron motion
along the
c*
axis; ω
c*
τ ~ v
a
τ, v
a

is the Fe
rmi velocity along
the chains). Indeed, the MR in the usual geometry (
j
||
a
,
B
||
c*
) was not detectable in the high temperature region. As
there are neither theoretical models with the anisotropic τ
nor the LL description for our geometry, we have compared
o
ur MR with this model and the published results for
X=PF
6

and X=ClO
4

[10]. Surprisingly, in spite of different
ρ
b
(T) and ρ
c
(T) behaviour of three different salts, it turns
out that in the whole temperature region MR follows the
same law (Δρ
c*
/ ρ
c*
)
1/2

~T
-
1.5

(or, using the assumptions of
the above model τ ~T
-
1.5
). This suggests that the scattering
mechanism which governs the transport along the
c*

axis
remains unchanged over the entire temperature range.
The
MR data did not give any evidence of different
regimes in
the normal state of Bechgaard salts that could be related to
the
1D


2D dimensionality crossover from the LL
behaviour to a FL one. The inter
-
chain transport, although
diffusive (since dρ
b
(V)
/dT < 0) at high temperatures, assures
a strong enoug
h coupling between the chains and the FL
description should be appropriate for the transport
properties of Bechgaard salts at high temperatures.


[1]

F.D.M.Haldane, J.Phys.C 14 (1981) 2585

[2]

T.Ishiguro et al., Organic superconductors, Springer, Berl
in,1998

[3]

D.Jérome, Organic conductors, Dekker, NY, p.405, 1994

[4]

A.Lopatin

et al., Phys.Rev.B 63 (2001) 075109

[5]

G.Mihály et al., Phys.Rev.Lett. 84 (2000) 2670

[6]

J.Moser, et al., Phys.
Rev.Lett. 84 (2000) 2674

[7]

E.Tafra et al., to be published (2002)

[8]

A.Schwartz

et al.,
Phys.Rev.B 58 (1998) 1261

[9]

A.T.Zheleznyak and V.M.Yakovenko, Eur.Phys.J.B 11 (1999) 385

[10]

J.R.Coop
er and B.Korin
-
Hamzi
ć,

Organic conductors, Dekker, NY,




p.359, 1994.

T
(K)
160
180
200
220
240
260
280
300
R
H
/
R
H0
0
1
2
3


Fig.2. R
H

vs.

T, no
rmalized to R
H0

(derived in a band model). Dashed line:
a guide to the eye; dotted line: theoretically predicted R
H
(T) behavior [9].

T
(K)
180
200
220
240
260
280
300


c*
/

c*
)
1/2
0.01
0.1
B
(T)
0
2
4
6
8


/

0
(%)
0.00
0.04
T
= 187 K
~ T
-1.5

j
||
c*
B
||
b'
B
= 9T


Fig.3. The transverse magnetoresistance for
j
||
c*
,
B
||
b'
and B = 9 T,
presented as (Δρ
c*

c*
)
1/2

vs.

temperature. Inset: magnetoresistance
vs.

magnetic field at
T
= 187 K.