DC susceptibility measurements

PHYSICA ELSEVIER

Physica C 245 (1995) 6-11

Critical current densities in K 3 C 6 0 / R b 3 C 60 powders determined from A C / D C susceptibility measurements M.W. Lee

a, *,

M.F. Tai b, S.C. Luo

a,

J.B. Shi c

a Physics Department, National Chung Hsing University, Taichung, Taiwan b Physics Department, National Chung Cheng University, Chiayi, Taiwan c Department of Electronic Engineering, Feng Chia University, Taichung, Taiwan Received 7 December 1994; revised manuscript received 1 February 1995

Abstract We report the magnetic Jc(T) in K3C6o and Rb3C6o powder samples for temperatures from 5 K to Tc. Jc near Tc was obtained from AC measurements whereas Jc at low temperatures was obtained from DC measurements. In the AC measurements, two X" peaks were observed on some of the samples. This is attributed to weak links in granular superconductors. The intragranular J~ is much larger than the intergranular Jc- The Jc(T) data are fitted by Jc(T)= Jc(0)(1 - T/Tc) v, with J~(0) and y as fitting parameters. In the DC measurements on Rb3C60 , Jc depends approximately linearly on temperature. Extrapolating the zero-field DC data to 0 K yields Jc(0) = 3.1 x 106 A / c m 2. This is a rather large Jc for a powdered superconductor, suggesting strong pinning in these materials. Finally, the values of y for the intergranular and intragranular components are compared with the predictions of theories.

I. Introduction AC susceptibility measurements have been widely used in the study of the magnetic properties of a superconductor. The technique is easy to perform and nondestructive to the samples. The complex susceptibility X = X '+ ix" has a slightly different meaning from that of the DC susceptibility. The real part X' corresponds to the differential quantity d M / d H . It is approximately equivalent to the zerofield-cooling susceptibility in a DC measurement; therefore it is a measure of the shielding response of a superconductor. The imaginary part X" corre-

* Corresponding author.

sponds to the energy dissipation in a material. Physical parameters such as lower and upper critical fields, To, critical current densities, irreversibility lines, etc. can be deduced from the complex X [1]. The extra information contained in X" can provide valuable information about the mechanisms that cause energy dissipation. Since the applied magnetic field is varying with time, the frequency dependence can be used to probe the dynamic behavior, e.g. vortex motion, of a type-II superconductor. Over the past several years the technique has made a great contribution to the understanding of a very important phenomenon weak links - in high-temperature superconductors [1]. In this paper we report mainly the results of AC susceptibility measurements on the fullerene super-

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M.W. Lee et al./ Physica C 245 0995) 6-11 conductors K3C6o and Rb3C60. Their critical current densities were estimated from the peak positions of X". According to critical-state models, the maximal dissipation occurs when the magnetic field just reaches the center of the sample [2]. For a long cylinder with an applied field, H a, parallel to its axis, Jc is related to H a by H a ---J~R, where R is the radius of the cylinder [2,3]. Since in general the amplitudes of the AC field are small compared to those in DC measurements, H a << H~I in most occasions, hence an AC measurement normally probes the behavior very near T¢. To extend the temperature range of Jc, we also performed DC magnetization measurements on the sample. The DC Jc was estimated from the hysteresis loops based on Bean's critical-state model. This yields Jc(T) of the intermediate temperatures. The results from the AC and DC measurements are found to agree reasonably well with each other. This implies that the results of an AC susceptibility measurement can be adequately described in terms of critical-state models. Furthermore, since the DC hysteresis technique is now a common method for characterizing Jc of a superconductor, our work demonstrates that AC susceptibility techniques can also be used reliably for the same purpose. The technique is most sensitive when used to study the behavior of J~ near T~, which is an important region for theoretical models.

7

approximately 1 p,m diameter. We attribute the difference in grain size to the conditions, especially heating temperature, of extracting the powder from the solvent. The K3C60 powder sample was prepared by a new method. 25 mg of C6o was reacted with a stoichiometric quantity of potassium hydride in a sealed Pyrex ampoule. The doping was carded out by heating the ampoule at 300°C for 5 h. For the Rb3C60 sample a pure rubidium element was used in the preparation. Doping was carded out by heating the ampoule at 200°C for 2 days then annealed at 400°C for at least 3 days. T¢ of the samples, determined from the onsets of X', were either 19.5 K (K3C60) or 30.5 K (Rb3Cr0). AC susceptibility measurements were performed on a Lakeshore 7221 susceptometer. The applied AC magnetic fields covered the range from 0.05 to 25 Oe. Eight AC field amplitudes were measured. Near the peak positions of X" data were taken in 0.2 K intervals. Since X" is very sensitive to the phase on the lock-in amplifier, the phases were carefully recorded at 5 K for each magnetic field. The AC frequency was fixed at 1000 Hz throughout the experiment. DC magnetic hysteresis loops were also measured with a Quantum Design MPMS Squid magnetometer. The loops were recorded from 0 to 1 T in 2.5 K intervals. 2.2. Critical-state models

2. Experimental 2.1. Sample preparation and measurements The C60 powder was produced by the usual method [4] in our laboratory. Pure C6o powder was extracted from carbon soot by liquid chromatography. The C6o powder was obtained by heating a concentrated solution of C6o in toluene in air. The powder was then baked in vacuum at 150°C for several hours to remove the residual solvent. X-ray diffraction and infrared absorption indicated that the powders were single phase of C60. SEM showed that the produced C60 powder had a distribution in diameter ranging from 1 to 100 Ixm. This is quite a large distribution as compared to that of the commercially available C6o powders from SES Research Inc. (Houston, TX), which are regular long rods with

Before we start the discussion on the experimental results, it is useful to give a brief review on the meaning of the imaginary susceptibility. X" corresponds to the power losses of a material due to eddy currents, hysteresis, or flux motion in an AC field. For superconductors the losses can be understood in terms of the critical-state models. For T < Tc, an AC magnetic field H a induces a shielding current on the surface of a superconductor. If H a < He1, there is no hysteresis in the M - H curve such that X" --- 0. When H a > He1, the superconductor enters the mixed state, and flux starts to penetrate into the sample. The shielding current now circulates into the interior of the sample. As a coqsequence there is hysteresis in the M - H relation. The area of the hysteresis loop is related to X" by f M d H - - xtlzoH2X" [5]. The maximal losses occur when the applied field just reaches

8

M.W. Lee et aL/Physica C 245 (1995) 6-11

2.0 O

1.5

?

a 1.0

o

~- 0.5 0.0

..-0.5 .0 ca

' o - I .5 ,,,,l

"~-2.0 ~ - o . 1 0 e i

5

l

10

=

T(K)

i

15

t

20

Fig. 1. AC susceptibility as a function of temperature for the K3C60 powder sample. The AC field amplitudes, in successive order as labeled, are 0.1, 1, 5, 10, 15, and 25 Oe.

the center of the sample (denoted by Hp). This field is related to J~ by

lip = JoR

(1)

for a long cylinder with the field along its axis. Here R is the radius of the cylinder [2]. Other sample geometries have similar relations but with different numerical factors [6,7]. In general the differences are small. Therefore a measurement of the dependence of X" on applied field can be used to calculate the J¢ of a superconductor. In our experiment the amplitude of an AC field is fixed and X" is measured as a function of temperature. In this case A, H¢a, and Jc are functions of T, but the underlying physics remains the same.

ducting fraction to be 67% (assuming a demagnetization factor of ½). Because the C60 powder had a large variation in size, the smaller powders were only about 1 p~m in diameter. This is comparable to the penetration depth A, which is in the range of 3000-4000 A [8-11]. Ramirez et al. have observed only 36% superconducting volume fraction in K 3 C 6 0 powder with 1 ixm diameter [12]. Hence we attribute the incomplete Meissner response mainly to a finitesize effect [6,13]. In Fig. 1, the low-temperature X' decreases with the amplitude of H a. The imaginary part X" is small at low temperature and increases with temperature. As H a increases, the magnitude of X" also rises. Two X" peaks were observed in low fields. The narrow peak is near To; the broader peak is at a much lower temperature. The broad peak gradually disappears when H a reaches 1 0 e . As H a increases, the peak position (denoted by Tp) shifts to a lower temperature. Assuming the powders to be cylindrical, we used Eq. (1) to calculate Jc for the peaks near To. The average diameter of the powder, estimated from SEM, is taken to be 50 Ixm. The dependence of Jc on Tp is shown in Fig. 2. J~ decreases monotonically with temperature. Since J~ for many superconductors obeys the empirical scaling relation

Jc(T) =J¢(0) 1 -

(2)

9 8 A

"H

K3Ceo

7

6

t.,}

5 O

~,.

3. Results and discussion

,

\

4 O

3 2 1

Fig. 1 shows the real and imaginary parts of the K 3 C 6 0 sample as a function of AC field amplitude. Tc of the sample, obtained from the onset of X', is 19.5 K. The transition width (10% to 50%) is 1.1 K. From the low-field X' at T = 5 K and using 1.92 g / c m 3 as mass density, we estimated the supercon-

%%

0 17.5

i

18.0

18.5

19.0

"

19.5

T(K) Fig. 2. Dependence of the critical current density on temperature for K3C6o. The solid points are from the X" peak positions of the data in Fig. 1. The dashed line represents the fit with Eq. (2).

M. W. Lee et al. / Physica C 245 (1995) 6-11

we have fitted the results with Eq. (2). Here T~ is the onset temperature and the fitting parameters are J~(0) and 7. The fit gave 7 = 2.95 and J~(0) = 2.0 × 107 A / c m 2. Two Rb3C60 samples were measured in this experiment. Here we present only the results of one of the samples with better diamagnetic signals. Fig. 3 shows the dependence of X' and X" on temperature as a function of the applied AC field amplitude. The most obvious difference is that the broad peak in X" is very pronounced. This peak also has a stronger dependence on temperature. The peak positions, based on the method discussed above, were then used to calculate their corresponding J~. The results are shown in Fig. 4. From Eq. (2), we found y = 3.3 and Jc(0) = 2.3 × 108 A / c m 2 for the peak near Tc. For the low-temperature peak we found y = 2.47 and J~(0) = 6.2 × 105 A / c m 2. For this peak we could not use the onset of X' as T~, so its value was obtained from the best fit, which gives T~ = 27.1 K. Because AC measurements can probe Jc only at high temperatures, we have carried out DC measurements of the magnetic-hysteresis loop on the sampies. This can provide the information of J~ of a broader temperature range. According to Bean's crit-

1.0

--Rb3Cs0

"~o

?

"

"

0.5

0.0 0

i

0.5

~-1.0

~

-1.5

-8

0.1 0e

,

.

24

16

32

T(K) Fig. 3. AC susceptibility as a function of temperature for the Rb3C60 sample. The AC field amplitudes, in successive order, are 0.1, 1, 5, 10, 15, and 25 Oe.

9

9 8

7 tJ

Rb3Cso

•

"

6

'.

5 4

0 v tJ

0

3 2

6

b.

1

'°?-.~

0 22

24

26

28

30

T(K) Fig. 4. Dependence of the critical current density on temperature for Rb3C6o. Solid circles are from the X" peak positions for peaks near Tc whereas the open circles are from the lower temperature peaks. The dashed lines represent fits with Eq. (2).

ical-state model AM, defined as M + - M - , is proportional to Jc, where M + and M - correspond to the magnetization of the increasing and decreasing field, respectively. For a cylindrical powder the relation is Jc = 15 AM/R, where R is the radius of the cylinder [2]. The results of Jc versus T is plotted in Fig. 5. AM was evaluated at zero applied field. By using Eq. (2), 7 was found to be 1.3. Extrapolating the data to 0 K yields Jc(0) = 3.1 × 106 A / c m 2. For a powdered superconductor without special treatment, such as irradiation to increase the number of pinning centers, this current density is considered to be high. This suggests that the pinning in the powders is rather strong. But whether the strong pinning is intrinsic to alkali-doped C60 , or extrinsic due to granularity of the powder, is not clear at this time. More systematic studies on single crystals may be able to answer this. The inset in Fig. 5 shows that the DC Jc(T) matches reasonably well with the AC Jc(T), which implies that the results of AC susceptibility measurements can be well described by the critical-state model. The double-peaks phenomenon has been widely observed in sintered high-temperature superconductors. Studies have attributed this to weak links due to their granular structures. In that case a sintered HTS material is composed of intrinsic superconducting grains separated by poor materials like insulator,

10

M.W. Lee et aL /Physica C 245 (1995) 6-11

25 6

~°~-o.o~,.°

N

20

tO ~ ~ 0 U

253(

015

o

~.J10

RbaC8° 10

15

20

25

30

T(K) Fig. 5. Critical current density, obtained from DC hysteresis-loop measurements, vs. temperature for Rb3C60. The inset shows the DC Jc (open circles), together with the AC Jc (solid circles) from Fig. 4. Jc is in a logarithmic scale.

metal, or poor superconductor. For an insulating junction the system behaves like a network of Josephson junctions, hence the system can be viewed as composed of intragranular (grain) and intergranular (junction) components. In the presence of an AC field, power losses due to each component appear in X". The peak near T~ is assigned to the intragranular component and the lower temperature peak is assigned to the intergranular component. Since the supercurrent now has to flow through the junctions, which usually have a much lower J~, the resulting macroscopic critical current can be much smaller than the intrinsic (grain) critical current. This will have a strong effect on the practical applications of the material. The two X" peaks observed in both K3C60 and Rb3C60 samples can also be attributed to weak links in the fullerene powders. Since some of the powders have sizes up to 100 Ixm, a powder can be viewed as a miniature sintered sample; therefore the two-component argument given above will result in two X" peaks. This is supported by the small coherence length, ~, in the fullerene superconductors, which is about 30 A [14,17]. Hence a small intergranular junctions will strongly affect the superconducting

state at the interface, resulting in a much smaller critical current. The situation is analogous to the case of high-temperature superconductors. The magnetic-field dependence of the intergranular peak for the K3C6o sample exhibits a quite different behavior from that of the Rb3C60 sample. For K3C60 the intergranular peak is discernible only at 0.10e; for fields above 1 0 e this peak disappears. In contrast the intergranular peak for the Rb3C60 sample persists up to the largest applied field (25 Oe) of the measurement. The difference can be understood if one considers the temperature dependence of the critical fields. Because power losses take place only when a superconductor enters the mixed state, X" starts at Hcl(T) and ends at Hc2(T). For K3C6o , the data in Fig. 1 for H a = 0 . 1 0 e shows that the intergranular X" disappears for T > 19.1 K, which gives Hc2(19.1)= 0 . 1 0 e for the junctions. Using the two-fluid relation for critical field Hc(T) =H~(0)[1-(T/Tc)2], we estimate H¢2(0) for the junctions to be = 2 0 e . This is extremely low as compared to H~2(0)= 30 T for K3C60 grains [18], indicating that the junctions are very poor superconductors. H~2(0) for Rb3C60 is more difficult to estimate due to strong overlap between the intragranular and intergranular losses. Nonetheless its magnitude is clearly much larger, indicating better intergranular junctions. Moreover some of the samples we studied did not even show the two-peak phenomenon. Therefore the weak-link effect in these materials is sample dependent and is probably related to grain size as well as the property of the junctions. From our experimental results we conclude that the weak-link effect in alkali-metal doped C6o powders is not as large as in the case of high-temperature superconductors. For the intragranular peak, the above discussion gives 7--2.95 for K3C60 and 3.33 for Rb3C60. These values are not too different from each other, but they are quite different from what is expected (7 = 1.5) from Ginzburg-Landau theory for the Jc(T) of an infinite slab near Tc [19]. The intergranular peak is due to currents flowing through junctions, which has 7 = 2.5 for the Rb3C60 sample. For Josephson junctions or proximity-effect SNS junctions the expected value of 7 is 2 [20]. This is close but not equal to our present result. As a consequence, exactly what type of junctions occurs in

M.W. Lee et al./ Physica C 245 (1995) 6-11

fullerene superconductors cannot be concluded from this work.

4. Conclusion To summarize, the critical current densities in K3C60 and Rb3C60 samples as a function o f temperature has been measured by magnetic-susceptibility techniques. The imaginary parts of the A C susceptibility exhibit characteristic features of weak links for granular superconductors. This could be a natural consequence of the small coherence length in the fullerene superconductors. The extrapolated critical current density at 0 K is rather large for a superconductor without post-treatment, which suggests strong pinning in these powdered samples. The measured Jc versus T relation does not agree with that expected from G i n z b u r g - L a n d a u theory.

Acknowledgement This work is supported by a grant, NSC83-O212M-005-020, from the National Science Council of the Republic of China.

References [1] A good review is in: Magnetic Susceptibility of Superconductors and Other Spin Systems, eds. R.A. Hein, T.L. Francavilla and D.H. Liebenberg (Plenum, New York, 1992).

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[2] C.P. Bean, Rev. Mod. Phys. 36 (1964) 31. [3] J.R. Clem, in: Ref. [1] p. 177. [4] W. Kfiitschmer, L.D. Lamb, K. Fostiropoulos and D.R. Hoffman, Nature (London) 347 (1990) 354. [5] L.D. Landau, E.M. Lifshitz and L.P. Pitaevskii, Electrodynamics of Continuous Media, 2nd Ed. (Pergamon, Oxford, 1984) p. 204. [6] J.R. Clem and V.G. Kogan, Jpn. J. Appl. Phys. 26 (1987) 1161. [7] A.M. Campbell and J.E. Evetts, Adv. Phys. 21 (1972) 199. [8] Y.J. Uemura et al., Nature (London) 352 (1991) 605. [9] R. Tycko et al., Phys. Rev. Lett. 68 (1992) 1912. [10] C. Politis, A.I. Sokolov and V. Buntar, Mod. Phys. Lett. B 6 (1992) 351. [11] A.I. Sokolov, Yu.A. Knfaev and E.B. Sonin, Physica C 212 (1993) 19. [12] A.P. Ramirev, M.J. Rosseinsky, D.W. Murphy and R.C. Haddon, Phys. Rev. Lett. 69 (1992) 1687. [13] Y. Tomioko, M. Naito, K. Kishio and K. Kitazawa, Physica C 223 (1994) 347. [14] K. Holczer et al., Phys Rev. Lett. 67 (1991) 271. [15] P.G. Spare, J.D. Thompson, R.L. Whetton, S.-M. Hwang, R.B. lOner and F. Diederich, Phys. Rev. Lett. 68 (1992) 1228. [16] C.E. Johnson, H.W. Jiang, K. Holzcer, R.B. Kaner, R.L. Whetton and F. Diederich, Phys. Rev. B 46 (1992) 5880. [17] G.S. Boebinger, T.T.M. Palstra, A. Passner, M.T. Rosseinsky, D.W. Murphy and I.I. Mazin, Phys. Rev. 46 (1992) 5876. [18] S. Foner, E.J. McNiff, Jr., D. Heiman, S.M. Huang and R.B. Kaner, Phys. Rev. B 46 (1992) 14936. [19] M. Tinkham, Introduction to Superconductivity (E Krieger, New York, 1985) p. 117. [20] P.G. de Gennes, Superconductivity of Metals and Alloys (Benjamin, New York, 1966) p. 234.