(TMTSF)2ClO4 in the extreme quantum limit

SvntheticMetals, 27 (1988) B41 B48

1341

(TMTSF)2CIO 4 IN THE EXTREME QUANTUM LIMIT

R.V.

Chamberlin, (I) M.J. Naughton, (2) X. Yan, (2) L.Y. Chiang, (3)

S.-Y.

Hsu, (2,3) and P.M. Chaikin (2,3,4)

(1)Department of Physics, Arizona State University, Tempe, AZ 85287

(U.S.A

(2)Department of Physics, Philadelphia,

PA 19104

University of Pennsylvania, (U.S.A.)

(3)Exxon Research and Englneering Co., Annandale,

NJ 08801

(U.S.A.)

(4)Department of Physics, Princeton,

NJ 08540

Princeton University,

(U.S.A.)

ABSTRACT Magnetotransport

and m a g n e t i z a t i o n measurements on (TMTSF)2CIO 4

in fields up to 31 T reveal an e x t r a o r d i n a r i l y stable semimetallic state, with a constant filling factor

(~),

from 8 to 27 T.

The

relative Hall value and energy gap of this state suggest that it is related to the ~=i/3 fractional quantum Hall effect. there

At 27 T

is a new transition to a compensated semiconducting phase.

After a brief properties

review of the "low-field" behavior,

we discuss the

of these novel high-field phases.

INTRODUCTION The B e c h g a a r d family I of charge-transfer where x=ClO4,

salts

[(TMTSF)2X;

PF 6, ReO 4, etc.] are highly anisotropic

organic

conductors which exhibit a rich variety of ground states characteristic

of quasi 2-dimensional electronic

systems.

interest has been in the field-induced s p i n - d e n s i t y - w a v e transitions resistance

in these materials. 2 (Pxx), Hall

measurements "low-field" stable

(SDW)

We have made 3 longitudinal

resistance

(Pxy), and m a g n e t i z a t i o n

on (TMTSF)2CIO 4 in fields up to 31T. SDW transition,

Recent

After

the final

(TMTSF)2CIO 4 remains in a remarkably

state from 8 T to 27 T, where there is a new t r a n s i t i o n to

a v e r y - h i g h field behavior

(VHF) phase.

Here we here we will

focus on the

in these high-field phases.

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B42

BACKGROUND

The (TMTSF)2CIO 4 crystal consists of rectangular TMTSF molecules

stacked along the a axis.

The s t o i c h i o m e t r y and

structure of the crystal yield a conduction electron density of ~1021/cm 3 with an approximate bandwidth ratio of 100:10:<1 a:b*:c* directions.

The purity of a particular

in the

(TMTSF)2CIO 4

sample depends on how rapidly it is cooled through a structural phase transition near 24K;

high quality,

slow cooled,

samples may

have mean-free paths in excess of 10~m.

For magnetic

H>2-3T applied normal

electron motion in the c*

to the a-b* plane,

fields

d i r e c t i o n becomes negligible and (TMTSF)2CIO 4 becomes quasi-2D. M a g n e t o t r a n s p o r t measurements a series of steps and plateaus

in fields up to 20T (Fig. i) show

in Pxy, somewhat

q u a n t u m Hall effect, 4 but several from the usual QHE. not integral

Briefly,

the values of the Pxy plateaus are

fractions of h/e 2 (25.8...kQ/layer),

sharply during the first few plateaus, in l/H,

reminiscent of the

features 5,6 d i s t i n g u i s h this Pxx increases

the steps are not p e r i o d i c

the fields at which the steps occur

(as well as the

numbers and types of steps) are sample purity and temperature dependent,

and there is distinct hysteresis between the up- and

d o w n - f i e l d sweeps.

M a g n e t i z a t i o n 7 and specific heat 8 m e a s u r e m e n t s

show that the Hall steps are in fact due to a cascade of t h e r m o d y n a m i c phase transitions. Several theories 9-13 have been developed which give good, least qualitative, 2.4

"~-

i

~

i

u n d e r s t a n d i n g of these transitions. E

1

l

r

at

The Fermi

1--24

1.6

16

t

c~x 0 . 0

-0.11~

0

t

I

4

I tJ

1

I

13

l

1:'

I

J

1

16

~('r) Fig. i. Hall (dashed) and longitudinal (solid) resistivities for (TMTSF)2CIO 4 at 0.7 K. A brief shoulder at 7.5 T coincides with a sharp reduction in PxxThe ratio of Pxy from this shoulder to the high-field plateau is 1:(2.96±0.05).

B43 surface consists of two warped planes about ka-±K/2a. (TMTSF)2CIO 4 is highly anisotropic,

the b* bandwidth

Although in pure

samples at low fields is sufficient to suppress the usual instabilities,

and the system is an open-orbit metal.

applied parallel

ID

For H

to c*, net electron motion is along the a axis

with o s c i l l a t o r y motion in the b* direction. the b* oscillations decrease, (Hth=4.5T at 0.7K) s p i n - d e n s i t y wave.

With increasing H,

until at the threshold field

the system becomes unstable

to formation of a

The theories consider the field d e p e n d e n c e

of

the particular nesting vector which gives the maximum c o n d e n s a t i o n energy.

Transitions occur when a new distortion becomes

and the system d i s c o n t i n u o u s l y transitions,

readjusts the SDW.

favorable

Between

minor adjustments maintain the lowest total energy.

A l t h o u g h E F is pinned

in a gap,

impurities and the u n d e r l y i n g open-

orbit 3D nature of this system lead to nonlocalized gap states. Thus,

neither Laughlin criterion 14 of a mobility gap nor a field

recurrent energy is met.

Nevertheless,

the adjustments which

m a i n t a i n the lowest energy provide ostensibly constant Landau filling

(~) at nonquantized values of Pxy"

Incomplete nesting of the self-consistent SDW potential pockets of electrons and holes, carriers.

In moderate

fields,

leaves

but greatly reduces the number

of

a typical sample of (TMTSF)2CIO 4 may

contain more than 105 layers of high-mobility,

quasi

2-D electrons,

with a carrier density of about 1011/cm 2. EXTREME QUANTUM LIMIT The existing theories all predict that E F should go to the single

remaining large gap at a final transition

(usually taken to

be the one near 8 T), above which the system should become insulating.

Figure 2 shows that, at 0.7 K,

semimetallic

from 8 to 27 T.

Furthermore,

(TMTSF)2CIO 4 remains the fact that

Pxy is

constant shows that the carrier density is changed in such a way as to m a i n t a i n a fixed Landau filling over this entire Insight into the origin of this unpredicted, stable

range.

extraordinarily

state comes from the relative values of Pxy-

A recent

theory 15 has shown that impurity scattering and magnetic b r e a k d o w n will

reduce the magnitude of Pxy, but since these effects are

s u b s t a n t i a l l y constant, remain quantized.

the ratio between successive plateaus will

Thus one expects

ratios of 1/3:1/2:1

steps p r e c e d i n g the final transition. temperatures, these

ratios.

Indeed,

for the 3

at very low

Ribault 16 has found that the plateaus do scale with Furthermore he finds that the ratio of the 8 T step

B44

is 1:2.9.

We have

measured numerous

2

samples and find that the magnitude of the high-field plateau may

7

range from 6 to 18 kQ/layer,

whereas

the

ratio of the 8 T Hall step is i n v a r i a b l y 1:(2.96±0.05).

The

combination of constant Pxy with this u n i v e r s a l

| i

li ,

" I ~ c LI!

F

step size strongly suggests

that the

carriers are in a

:i-

fractional q u a n t u m Hall effect 17 state with

0

8

16

24

32

9=i/3.

H(T)

It should be

emphasized,

Fig. 2. Hall (dashed) and longitudinal (solid) resistivities at 0.7 K in fields up to 31 T. The high-field plateau persists out to 27.1±0.1 T where a sharp decrease in Pxy and dramatic increase in Pxx (note logarithmic scale) define the VHF transition.

not expected,

I

I

I

I

I

I

I

I

(TMTSF)2CIO 4 has neither nor fixed EF; it has the freedom to

adjust a SDW d i s t o r t i o n

I

to m a i n t a i n

"L"

the lowest

total energy.

:~ 10

Further evidence

for

a fractionally quantized

I

[] "~ .N ~4

FQHE is

since

a fixed carrier d e n s i t y additional

100

however,

that the "usual"

state comes from the

1

energy gap for resistive excitations. 25 T

A semilog

plot of Pxx vs.

~'~.

ckO.1

inverse

temperature at 25 T I

0

i

}

j

i

i

I

0.5 ]/TEMP. (K - 1 )

i

(crosses in Fig.

I

1.0

Fig. 3. Semilog plot of longitudinal resistance as a function of inverse temperature. The best fits to the data (solid lines) give activation energies of 6.0±0.5 K at 25 T and 4±1 K at 29 T.

3)

shows an a c t i v a t i o n energy of 6.0±0.5 K, which is about an order of magnitude

less than

the cyclotron energy.

B45

A l t h o u g h 6 K corresponds to a p a i r - c r e a t i o n energy of about twice that found for the 1/3 FQHE state in the h i g h e s t - p u r i t y s e m i c o n d u c t i n g devices, 18 quantitative

comparison may be

m e a n i n g l e s s because of the vastly different systems. do show,

however,

that the resistive excitations

i m m e d i a t e l y preceeding with ~ i )

the 8 T transition

Figs.

1 and 2

in the state

(presumably a s s o c i a t e d

have a significantly higher barrier;

suggesting that the

s t a b i l i t y of the 8 to 27 T state cannot be explained by a singlee l e c t r o n energy gap. Independent

support for the fixed Landau filling and extreme

stability of the state from 8 to 27 T comes from the m a g n e t i z a t i o n measurements,

Fig.

a paramagnetic paramagnetic

4.

jump,

The "low-field"

transitions are signalled by

followed by a diamagnetic

recovery.

The

steps at higher fields can be ascribed to de H a a s - v a n

A l p h e n oscillations

from quantized edge states, 19 and are not

a s s o c i a t e d with any phase transitions. 20 oscillations

Removing these

reveals that the intrinsic m a g n e t i z a t i o n d e c r e a s e s

linearly from 8 until 18 T, where it saturates to a negative value. A linear diamagnetic filling,

term is most

readily related to a fixed Landau

for which the net energy increases as H 2, p r o d u c i n g a

m a g n e t i z a t i o n which decreases linearly with field. 21

Even though

the net orbital magnetic energy in (TMTSF)2CIO 4 (dashed curve

in

3) becomes positive above ~22 T, 22 the ~=i/3 state persists

Fig. until

27 T.

Several transition 40

Finally

(TMTSF)2CIO 4 must find a new ground state.

features distinguish

the very high-field

(VHF)

from the cascade of low-field transitions.

I

I

I

1

I

80

I

/i/

20

First,

40

.~

o v

-20

-40

"\\

I

8

I

/i

~

I

16

1

,

1

24

I

-40 I

3~ 8o

Fig. 4. M a g n e t i z a t i o n of (TMTSF)2CIO 4 at 0.7 K (points). Fourier filtered data (solid) showing the intrinsic h i g h - f i e l d behavior. The magnetic energy (EM=;M'dH, dashed) becomes positive above ~22 T

B46 Pxxincreases dramatically, 30 T at 0.7K. 28 T.

Second,

Third,

nearly 3 orders of magnitude

Pxy decreases sharply,

from 25 to

to 0±5 k~/layer above

the VHF transition has a negative

field slope;

the

field at which it occurs decreases with increasing temperature. Finally there is no conspicuous paramagnetic anomaly a s s o c i a t e d with the VHF transition.

Recently

(TMTSF)2CIO 4 has been found to

be reentrant, 23 implying that the VHF behavior

is independent of

all the field-induced SDW phases.

Nevertheless,

a c t i v a t e d behavior

3) with an energy gap of 4±1 K.

Hence,

metallic

(pluses in Fig.

at 29 T,

Pxx shows

(TMTSF)2CIO 4 can be made s e m i c o n d u c t i n g without

crossing any obvious transition lines. A possible m e c h a n i s m for the VHF state might be strong I-D localization due to the enhanced anisotropy of the electrons these

fields.

in

An alternative explanation could be a subtle onset

of some type of c h a r g e - d e n s i t y wave. 24

Very recent m e a s u r e m e n t s 25

have shown a threshold electric field for depinning the carriers the VHF state.

in

Wigner 26 localization in very-high fields is

p r e d i c t e d to be weakly first order, 27 with saturated diamagnetism, 28 and is expected to become e n e r g e t i c a l l y

favorable

to a Laughlin liquid at a phase boundary with a negative slope; 29 consistent with what is observed. are necessary, localization

however,

field

Additional measurements

before the precise nature of the electron

in the VHF state can be established.

Existing theories

for the behavior of (TMTSF)2CIO 4 have not

considered the direct Coulomb interactions between electrons. M a n y - b o d y interactions are essential Laughlin

liquid,

mechanisms.

for the formation of the

and for the majority of electron l o c a l i z a t i o n

Their neglect may explain why the ~=i/3 state

from 8

to 27 T and the VHF state above 27 T were unpredicted. CONCLUSIONS High field m a g n e t o t r a n s p o r t and m a g n e t i z a t i o n m e a s u r e m e n t s (TMTSF)2CIO 4 reveal an e x t r a o r d i n a r i l y stable semimetallic with constant Landau filling,

from 8 to 27 T.

on

state,

The ratio of the

Hall

steps preceeding this state and its relatively small energy

gap,

strongly suggest that it is related to the ~=i/3 fractional

q u a n t u m Hall effect. independent

The m a g n e t i z a t i o n measurements provide

support for the stability of this phase,

and also

indicate why the system must eventually find another ground state. At 27 T there is a new transition to a novel with a relatively small Hall

resistivity,

semiconducting

and a saturated

state,

B47

diamagnetism.

The behavior of this v e r y - h i g h - f i e l d phase

indicative of strongly localized electrons, without

is

yet it can be a c c e s s e d

crossing any obvious phase boundaries.

These m e a s u r e m e n t s

show that the high-field behavior of (TMTSF)2CIO 4 remains an interesting experimental and theoretical

challenge.

ACKNOWLEDGEMENTS This

research was supported by an ASU Research

(R.V.C.) (M.J.N.

and National

Incentive Grant

Science Foundation Grant No. DMR8514825

and P.M.C.).

We would like to acknowledge

the assistance

of the staff at the National Magnet Laboratory,

e s p e c i a l l y B.L.

Brandt,

c o n v e r s a t i o n s with

J.S.

Brooks,

M. Ya Azbel,

M.J.

and L.G. Rubin,

Burns,

and useful

P.K. Lam, and J.E. Northrup.

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