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Critical exponent of the electrical conductivity in the paracoherence region of a thin film of YBa2Cu3O7−x

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Critical exponent of the electrical conductivity in the paracoherence region of a thin film of YBa2Cu3OT_x

MANMEET K MARHAS, K BALAKR/SHlqAN, V GANESAN,

R SRINIVASAN, D KAIqJILAL*, G K MEHTA*, G K MURAIJ13HAR**, G M O H A N RAO**, S E N T H I L N A T H A N * * and S M O H A N * *

Inter University Consortium for DAE Facilities, University Campus, Khandwa Road, Indore 452 001, India

*Nuclear Science Centre, Post Box 10502, Anma Asaf All Marg, New Delhi 110067, India

**Instrumentation and Services Unit, Indian Institute of Science, Bangalore 560012, India Abstract. Critical exponent of the electrical conductivity in the paracoherenee region ('y) of the high temperature superconductor YBa2Cu3OT_ x (YBCO) has been estimated for high quality thin film on ZrO 2 substrate prepared by high pressure oxygen sputtering. High energy ion irradiation was carried out using 100MeV t607+ ions at liquid nitrogen temperature to see the effects of disorder on the value of the exponent. The critical exponent ('D changes from a value of about 2 to 1.62 upon irradiation. Studies were also carded out on this film to see the effect of ageing and annealing.

Keywords. High temperature superconductors; resistivity; critical exponents; paracohet~mce;

heavy ion irradiation.

1. I n t r o d u c t i o n

Excess conductivity studies in the paracoherence region o f high temperature superconductors (HTSC) is a subject o f interest for the past few years. Superconducting transition is a second order phase transition characterized by an order parameter which is zero above the transition temperature Too and grows to a finite value below T~o. Large number of studies were performed to study the effect of fluctuations o f this order parameter as a tool to understand the nature of the phase transition near /'co. Fluctuation induced excess conductivity above the mean field temperature (T,,) in the so called paraconductivity region has been well studied by m a n y authors (Frietas et al 1987; Ausloos and Laurent 1988; H a g e n et al 1988; Veira et al 1988; Srinivasan e t al 1989). H o w e v e r there are only a few studies in the paracoherence region of the high temperature superconductors.

In granular high temperature superconductors in a region of a few degrees above the temperature of zero resistivity it has been noted that the ~onductivity varies as (T-T+~) -~ (Rosenblatt et al 1990; Krishnan et al 1992; Pureur et al 1990; Soret and A m m o r 1991). Rosenblatt et al (1988) explained this behaviour as a phase transition arising from the onset o f phase coherence between the different grains, in accordance with the theory of Deutseher et a l (1974). H o w e v e r Rosenblatt et al (1990) found a value of 2.7 for 7 in sintered pellet while the other investigators have found a value close to 1-3. Rosenblatt and his eoworkers (Lebeau et a l 1988) have shown that the tunneling Hamiltonian for these granular superconductors can be put in one to one correspondence with the Hamiltonian for a 3D XY ferromagnet.

The critical exponent in the conductivity will then match with the critical exponent 585

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for the susceptibility of the 3D XY ferromagnet. This susceptibility exponent has been calculated to be 1.316 from renormalization group theory calculation (Le Guillou and Z, inn-Justin 1977). It was also shown by several workers that the disorder in the strength of the exchange interaction does not change the critical exponent. If the y in the conductivity of the granular superconductor is to be identified with the corresponding exponent in the susceptibility of the 3D XY ferromagnet, one would expect that the conductivity exponent also to be independent of disorder.

We performed experiments on a superconducting thin film of YBa2CU3OT_ ~ of about 3000 ~ with heavy ion irradiation to see if the conductivity exponent remains unchanged or it changes with irradiation and subsequent annealing. The results are reported.

2. Experimental

High quality thin film of YBCO was prepared using high pressure oxygen sputtering facilities available at the Indian Institute of Science, Bangalore. C axis oriented film of YBCO was grown on (100) plane of the ZrO 2 as the substrate. Orientation was confirmed from powder X-ray diffraction pattern carried out using Rigaku D/MAX X-ray diffractometer. Figure 1 shows the X-ray diffractogram of the film before irradiation. Precise four-probe electrical resistance measurements were carried out using a fully automated electrical resistance measurements system comprising of a closed cycle refrigerator, a Schlumberger nanovoltmeter, an Advantest constant current source and a DRC-93C Lakeshore temperature controller. Temperature was controlled to an accuracy of 10 mK using a calibrated platinum resistance thermometer.

2 X Theta

Figure I. X-ray diffractogram for uninadiated film of YBCO.

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Conducting silver paint was used to make ohmic contacts and extreme care was taken for the temperature stability and to correct the effects o f thermal emfs.

The sample was irradiated by 100MeV oxygen ion beam [=60*v] from the 16 MV tandem Pelletron Accelerator (Kanjilal et al 1993) at the Nuclear Science Centre, New Delhi. It was mounted on a liquid nitrogen cooled cold finger of the scattering chamber in the materials science beamline. The chamber was evacuated to a pressure o f 1.6 × 10 -7 m bar. The temperature of the top surface o f YBazCu3OT_ ~ film was about 95 K. The irradiation to a fluence level of 10:3 particles/cm 2 was carried out using a beam having a flux of about 10:: particles/cm2/sec and keeping the sample in a secondary electron suppressor geometry. The total number o f particles falling on the sample was estimated by a combination of current integrator and pulse counter. After irradiation the cold finger got warmed up naturally to room temperature. After 10 h the chamber was vented to atmospheric pressure using dry nitrogen gas.

Resistance measurements were carried out before and after irradiation as well as after 60 days of irradiation to see the effects of ageing. The film was then annealed

¢E+007 . . . : . . .

O3 E 3E+007

c- O

2E+007 O E

(3 0O

00 1 E+O07

FY

oE+o 9.b6

x s~

x x

x q,

x

x

X ~ * + +

x s +

x x x x x

4 - , I - 4 .

÷ 4-

J[2)

x x

, . (1)

*4- b)

ii

+ + 4 - + 4-

+

Unirrodioted thin film

)

Irrodioted thin film

~ , (3) Irrodioted thin film offer 2 months

t I ! I s J t I I I I I I I I I t I I t t t t t t i i | i

--100.00 150.00 200.00

Temperature(K)

Figure 2. Variation of resi~ance &q a function of temperature for unirradiated sample (1), irradiated sample (2) and irradiated sample after 2 months (3) in the temperature range 80 K to 200 K.

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in flowing oxygen at 500"C and once again the measurements were done to see the effect of annealing.

3. Results

Thickness o f the film used was approximately 3000 .~. TRIM calculations for the electronic energy loss as well as the range of oxygen ions in both Y~Ba2Cu3OT_ x and ZrO 2 substrate were made. For a thick sample of Y~Ba2Cu3OT_ x the range is 48 ~m. Since the range is more than the thickness of the film used, all the oxygen ions passed through the film and there was no implantation of oxygen ions. One can expect a uniform damage to the sample. The electronic stopping power for 1 0 0 M e V oxygen ion beam in YBa2Cu3OT_ ~ is 145.7 eV/A and nuclear stopping power is 0.0828 eV/A. These are nearly constant over the depth o f the film. However the oxygen ions would have been stopped in ZrO 2 substrate in which the range was 300 I~m.

The results of the electrical resistance measurements as a function of temperature is shown in figure 2. It is apparent that electrical resistance of the sample at room

(2) Irradiated thin film / /

(3) Irradiated thin fiJ~m t" /

~ 1 . 5 E + 0 0 7

. . . - . . . after 2 months = . . ~ f ~ ,)

~ 1.0E+007

i ,/ i; !

i ~ 5.0E+006

f,

. . . , . . .

JJ,,

. . . , . . .

O.OE+O(~.~(~ ' 8 2 . 0 0 84.00 ~6.oo 88.(X) 90.00 92.00

TemperGture (K)

Figure 3. Variation of resistance as a function of temperature near the superconducting transition temperature for unirradiated sample (1), irradiated sample (2) and irradiated sample after 2 months (3).

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temperature increased after irradiation. Also the slope (dR/dT) was more for the irradiated sample than for the unirradiated sample. Such a behaviour has been observed in samples in which oxygen content is decreased or other defects are induced. Figure 3 shows the resistance vs temperature in a very narrow region near the transition temperature. It is clear from this figure that the zero resistance transition temperature of the irradiated sample is slightly less than that of the unirradiated sample.

Data points were taken at every 50 mK interval. Then a plot of log(R) was made against log(T-/'co) using an approximate value of

Too

by judging at which temperature resistance went to zero in figure 3, the exact values of y and

Tco

were determined by the following procedure. The plot of lqg(R) vs log(T-Too

)

shows a linear region in the temperature range of ~I"K above

Tco.

From this plot the slope T of the linear region is estimated. This is a linear plot whose intercept should give

T~o.

This

T~o

was slightly different from the

T~o

which was used in the plot of log(R) vs log(T-T~o). This value of

T~o

was again used to get a fresh value of T. This procedure was repeated twice and we found that the value of

T~o

and y converged very rapidly. Figures 4-6 show the plots of log(R) vs log(T-T~o). The value of

4.00

~'~3.50

J 3.00 0

2 . 5 0

f .

/

Unirradioted thin film

¢ . 5 0 . . . . . . , , , j , , , , . . . . . , . , . . . . . . , , T c o = 8 5 . 1 1 8 , r = 1 . 9 8 6 ± 0 . 0 5

2. o_%. 86 . . . - 6 % . . . . - 6':;6. . . 6'~6' ' . . . . . 6 % . . . . 6 .40

Log (T-Tco)

Figure 4. Plot of log(R) vs log(T-Tco) for unirradialed sample.

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4 . 5 0

4 . 0 0

$

I

./z

ii

. . - - . . 3 . 5 0

n,,-

C~

0 - J 3 . 0 0

2 . 5 0

I r r a d i a t e d thin f i l m

I I I I I I ! I I I I ! !' I I ! I I I | I ! ! 1 I

T c o = 8 4 . g s g , r = 1.62::1:..06

2"0-00.70 ... -

6'6b.

... - O'3b. ... - (3'i0. ... 0''".10 " ' ' '6'30' ' .

Log(T-Tco)

Figure 5. Plot of log(R) vs Iog(T-Tco) for irradiated sample.

conductivity exponent (y) changes from its original value of 1.99 :t: 0-05 to a value o f 1-62 ± 0.06 upon irradiation. A value of - 2 or more for critical exponent has been found by other workers for good quality thin films showing a sharp transition (Nedellec et al 1989; Krishnan 1993).

The film was kept stored in a desiccator for about another two months and once again the whole experiment was repeated to find whether any change is there in the value o f V due to ageing. Curve 3 in figure 3 shows a variation o f resistance as a function o f temperature, it is obvious that Too for this sample has come down to a value o f - 8 2 K. An accurate analysis of resistance data gives a value of 81.88 K. The exponent ¥. changes from 1.99 ± 0.05 before irradiation to 1.62 ± 0.06 after irradiation and to 2-39±0-089 after ageing. A look at the resistance curve shows that the resistance of the aged film at room temperature is lower than the resistance of the unirradiated film and the temperature coefficient dR/dT of the aged film is almost the same as the dR/dT for the unirradiated film. This indicates that the defects created by the heavy ion irradiation have atleast been partially annealed by ageing.

We tried to anneal the sample at 500"C in flowing oxygen to see whether the superconducting properties are recovered. But the sample deteriorated and lost the

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t r r o d i o t e d thin f i l m , o f f e r 2 m o n t h s

| I I I I I I | i I I | f | I I I I , I I ' I I I I ! I |

T c o = 8 1 . 8 8 , r = 2 . 3 9 ~ . 0 9 6 . 7 0

l

6 . 2 0 *

d

4 . 7 0

'¢ 2-00 4 6 . . . . - ' 6 ' 5 6 " . . . . . 6 ' 6 6 . . . - . 0 . 2 0 " . . . 0 . 4 0 ' . . . 0 . 6 0

Log(T-Tco)

~ . . ~ _ j 5 . 7 0 0 " ~ 0 ___J

5 . 2 0

Figure 6. Plot of log(R) vs log(T-Tco) for irradiated ~mple after two months.

superconducting properties. The resistance at room temperature had increased by a factor of 8382 at room temperature and also the temperature variation was semiconductor- like and such a plot is shown in figure 7. In fact a plot of log(R) vs T -v4 (figure 8) in the temperature range between 300 K to 80 K showed a linear behaviour with a break at about 1 5 0 K . Such a linear b e h a v i o u r is attributed to v a r i a b l e r a n g e h o p p i o g . H o w e v e r we are u n a b l e to e x p l a i n as to why there is a b r e a k at 150 K.

4. Discussion

When the energy o f the incident projectile is beyond a certain value it has been observed that the electronic loss can also produce defects and atomic displacements which cause a change in the electrical properties of the material. We used oxygen ions in the hope that these ions will produce such displacements preferentially at the oxygen sites in the superconductor especially at the grain boundaries. The increase in electrical resistance and slope dRIdT certainly arises due to such defects.

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However it was surprising that T~ value did not come down substantially on ir/adiation. The observed effect of ageing on the resistance and dR/dT is to be expected. However the substantial reduction in T~o indicates that the strength of the weak links has been reduced probably because the oxygen displaced at the grain boundary has slowly diffused out. However the annealing procedure we followed resulted in further increase in deterioration of weak links and also possibly of the grains.

What was surprising is the large change in the value of critical exponent ¥ from 1-99 + 0.05 to 1.62 + 0.06 upon irradiation to 2.39 + 0.09 on ageing. If the analogy of the tunneling Hamiitonian with 3D XY Ferromagnet Hamiltonian is fully valid then such a large variation in the value of critical exponent would not be expected in the light of some renormalization group calculations and the experimental work o f Kaul (1988). Heisenberg model (Lubensky 1975; Grinstein and Luther 1976;

Khmelnitzki 1976; Jug 1983; Weinrib and Halperin 1983) including both bond and site disorder showed that the critical exponents remain unchanged by short range disorder as long as the specific heat critical exponent oc is negative. On the other hand, unconventional renormalization treatment predicts that the value of the critical exponent will depend on frozen disorder even when the specific heat exponent is less than zero. However this matter requires further detailed study.

6 E + 0 0 6 . . . f . . . i . . . , . . .

5 E + 0 0 6 or)

E

c - 4 - E + 0 0 6

©

( b 3 E + 0 0 6 (...) c - O

co 2 E + 0 0 6 or) (].)

r r

1 E + O 0 6

U

Ip

*

$

**

Figure 7. Plot o f R vs T for the sample after annealing in flowing oxygen at 500"C for 30 rain, after 70 days.

°~"*"~'' " - ~ " ~ . ~ o ... 5 o . o o ~ o o . o o ~ 5 o . o o ' ... ' ... ' .... ~;b'6'86 . ... 2 s o . o o ~ 6 ' . 8 6 ' ' .... S~'6.oo

Temperature (K)

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6.70

f Y 6.20 ___] 0

5.70

5 2 ~ I l l l l t l l l l l l l l l l l l l l l I t t l l l i i l l i l t l l l i l l l l t l i l l l l l l l l t l l t l l l l l l l

" .22 0.24 0.26 0.28 0.30 0.32 0.34-

T^(-0.25)

Figure 8. Plot of R vs T~-I/4) for the semiconducting sample of YBCO film after annealing.

Acknowledgement

The authors of IUC-DAEF are thankful to Prof. S Lal for his constant encouragement right from the beginning of this work.

References

Ausloos M and Lanrent Ch 1988 Phys. Rev. B37 611

Deutscher G, Imry Y and Gunther L 1974 Phys. Rev. B10 4598 Freitas P P, Tsuei C C and Plaskett T S 1987 Phys. Rev. B36 83B Grinstein G and Luther A i976 Phys. Rev. BI3 1329

Hagen S J, Wang Z Z and Ong N P 1988 Phys. Rev. B38 7137 Jug G 1983 Phys. Rev. B27 609

Kanjilal D, Chopra S, Narayanan M M, lyer S I, Jha V, Joshi R and Datta S K 1993 Nucl. Instr.

Met& A 3 ~ 97

Kanl S N 1988 Phys. Rev. B3g 9178

Khmelnitzki D E 1976 Soy. Phys. JETP 41 98!

Krishnan H, Sankanmarayamm V and Srinivasan R 1992 Physica C194 163

Krishnan H, 1993 Paraconductivity and paracoherence studies on some high temperature superconductors, Ph.D. Thesis, Indian Institute of Technology, Madras

Lebeau C, Raboutou A, Pcytal P and Rosenblatt J 1988 Physica B152 100

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Le Guillou J C and Zinn-Justin J 1977 Phys. Rev. Left. 39 95 Lubensky T C 1975 Phys. Rev. BI1 3573

NedeUee P, Lesueur J, Traverse A, Bemas H, Dumoulin L and Laibowitz R B 1989 J. Less Common Metals 151 443

Pureur P, Schaf J, Gusmao M A and Kunzler J V 1990 Progress in high temperature superconductivity (ed.) R Nieholsky (Singapore: World Scientific) 25 236

Rosenblatt J, Peyral P, Raboutou A and Lebeau C 1988 Physica B152 95 Rosenblatt J, Raboutou A, Peyral P and Lebean C 1990 Rev. Phys. Appl. 25 73 Sovet J C and Ammor L 1991 Physica C177 45

Srinivasan R, Krishnan H, Sankaranarayanan V, Gopalakrishnan I K, Sastry P V P S S, Yakhmi J V and lyer R M 1989 Physica C159 797

Veira J A, Maza J and Vidal Felix 1988 Phys. Lett. A131 310 Weinrib A and Halperin B 1 1983 Phys. Rev. B27 413

References

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