Macroscopic nature of transport properties in high-Tc superconductors

Physica B 164 (1990) 139-149 North-Holland

MACROSCOPIC NATURE OF TRANSPORT PROPERTIES IN HIGH-T, SUPERCONDUCTORS Yoshio MUTO, Norio KOBAYASHI High Field Laboratory for Superconducting Japan

and Kazuo WATANABE Materials, Institute for Materials Research,

Tohoku

University, Sendai 980,

The behavior of electrical resistance in magnetic fields is described for high quality CVD superconducting oxide films exhibiting very high critical currents at liquid nitrogen temperature, even in high magnetic fields up to 27 T. Results are discussed on the basis of the recent idea of flux creep. The most promising material for application seems to be the Y(RE)-Ba-Cu oxide system

1. Introduction Since the discovery of high temperature superconductivity of La-Ba-Cu oxide [l] with T, below liquid-nitrogen temperature and that of Y-Ba-Cu oxide [2] with T, above liquid-nitrogen temperature, numerous studies have been performed toward the basic understanding and also application of the cuprate high temperature superconductors. It was mid-November 1986 when we became aware of the great work by Bednorz and Muller [l], just after we had succeeded in generating 31.1 T [3] using our hybrid magnet, HM-1. We immediately began to prepare the La-Ba-Cu oxides and confirmed that the crystal structure of the superconducting phase is the so-called 2-l-4 system, belonging to the perovskite structure. This indicated that the new oxide superconductor had two-dimensional character or a strong anisotropy. Since we believed that a high-T, material should also exhibit a high upper critical field Hc2, we measured the electrical resistance in high magnetic fields up to 21 T until the beginning of 1987 [4, 51. As shown in fig. 1, it was pointed out that (1) the onset of the resistance drop is shifted toward a lower temperature with increasing field, as shown by arrows, exhibiting the characteristic of a superconducting transition, and (2) the resistive transition is very wide, exhibiting a twostep drop which is clearly seen in low magnetic fields near 2T. About the latter, we suggested

6-

2 E4[L 2-

0

t

I__&_ .c.0” 000

10

0

I

2o

I

T(K)

(

3o

I

I

.

40

Fig. 1. Resistive transition of La,,78Bao,ZZCu,.2504-1 in vatious magnetic fields. The onsets of superconductivity are shown by arrows.

the existence of two superconducting phases due to inhomogeneity in the sample itself. At that time we expected that after obtaining a homogeneous sample, we could have a resistive transition with a narrow width. This sample had T, = 33.5 K and the slope of Hc2 at T,, dH,,ldT, defined by the onset of resistance drop was 1.8 T/K and Hc2 at 0 K, H&O), was estimated to be 43 T which was quite high compared with conventional superconductors. However, dH,,ldT at T, determined by the mid-point of the resistive transition was not linear but had a positive curvature in the temperature dependence. Furthermore, in a follow-up study on La-Sr-Cu oxide, we showed the possibility of Hc2(0) to be

0921-4526/90/$03.50 0 1990 - Elsevier Science Publishers B.V. (North-Holland)

140

Y. Muto et al. I Transport properties in high-T, superconductors

more than 70 T (61 as obtained by the mid-point definition, which was the world record at that time. We also noticed an unusual low value of the G-L coherence length c(O) of 18 A, as estimated from the Hc2(0). Following on the discovery of Y-Ba-Cu oxide system by Wu et al. [2], Syono et al. (7, 81 succeeded in preparing the l-2-3 compound and independently confirmed its crystal structure. Hiraga et al. [93 succeeded in a direct observation of the atomic arrangement of the, high-T, superconductor YBa,Cu,O,_, by high resolution electron microscopy. Furthermore, Muto et al. [lo] measured the temperature dependence of the resistivity in various magnetic fields up to 23.4 T. The data showed that HJO) determined at mid-point and end-point (i.e. p = 0) was 96 T and 61 T, respectively. Therefore, the Y-Ba-Cu oxide became very hopeful as a new high field superconducting material if a high critical current could be achieved. Using this Hc2 value, 4&(O) was estimated to be 15 8, which was also too short. Then Noto et al. [ll] began to study the current-carrying properties of the Y based system, but the critical current density J, was disappointingly low. It is very important to note that Miiller et al. [12] had already found that an oxide superconductor in a magnetic field might be in a superconductive glass state, immediately after their confirmation [13] of the diamagnetism relating to superconductivity. At the beginning of 1988, we studied the

newly discovered Bi-Sr-Ca-Cu oxides [14] and Tl-Ba-Ca-Cu oxides [ 151. These investigations were done since the characterization of new high-T, superconductors would not be complete without an accurate determination of the critical fields. The critical-field studies on the ceramic samples mentioned above are summarized [16] in table 1. The results on the Y-Ba-Cu oxide ceramics agree well with other studies. The dH,,l dT at T, for Bi- and Tl-based oxides are rather small compared with those of Y or rare-earth based l-2-3 oxides. H,,(O) amounts to several hundred oersteds and HJO) is 100-150 T, where the WHH-Maki theory is applied for the extension to 0 IS. The G-L parameter K is found to be about 100, where oxide superconductors are in the dirty limit of type II superconductivity. The thermodynamic critical field H,(O) is estimated to be 0.6-1.0 T. It should be emphasized that the coherence length c(O) is of the order of 15 A which is quite short and almost of the same order of magnitude as the lattice constant. The penetration depth h(0) is about 1500 8, which is of the same order of magnitude as that estimated from the temperature dependence of A by means of the BCS theory or the London phenomelogical theory. Therefore, the superconducting properties of the oxide superconductors are not so very different from the BCS prediction. However, it should be kept in mind that these oxides have a very short coherence length, comparable to their lattice constant, and also should exhibit

Table 1 Superconducting parameters. T,

dH;,ldT

dH,,ldT

(1O-4 T/K)

(T/K)

H,,(O) ( 10-4T)

H,,(O)

(K)

DY Ho

92 91 90 89

4.7 6.4 6.1

2.4 2.3 3.0 2.3

330 450 450 -

150 140 190 140

110 90 10s

Bib TIC

105 114

4.1 4.5

1.5 1.3

420 500

110 100

85 80

RE”

Y Gd

’ REBa,Cu,O,. b Bi,,,Pb, ,Sr,Ca,Cu,O,. ’ Tl,Ba,Ca,Cu,O,.

K

(T)

K(O) (T)

5(O)

A(O)

(4

(4

0.71 0.82 0.91 _

15 15 13 15

1600 1400 1400 -

0.66 0.65

17 18

1500 1400

141

Y. Muto et al. I Transport properties in high-T, superconductors

large anisotropy due to the two-dimensional-like crystal structures.

2. Critical current density In 1988, Yamane et al. [17] succeeded in obtaining a Y-Ba-Cu oxide film of very good quality prepared by chemical vapor deposition, which had very high criticial current densities [16, 181 at liquid nitrogen temperature, even in the high magnetic fields up to 27 T generated by our HM-1 [3]. The transport critical current densities measured at 77.3 K were 41, 19 and 6.5 x lo4 A/cm* at 2, 10 and 27 T, respectively. The critical field defined by zero resistivity was estimated to be 35 T at 77.3 K. The E&*(O) amounts to 180 T. The critical current density should be at least beyond 1 X lo4 A/cm* for practical purposes. Therefore, this film has become a good candidate material for future superconducting magnets. Here we describe the progress of our recent study of such films [19]. The CVD films were epitaxially grown on SrTiO, (10 0) single crystal substrates at a deposition temperature as low as 850°C where p-diketonate chelates of Y, Ba and Cu were used as source materials. A film with a strong c-axis orientation can be prepared when the source gas of Cu is first introduced for 3 min before the introduction of the mixture source gases of Y, Ba and Cu. It is emphasized that films were cooled in 1 atm of oxygen from a deposition temperature to room temperature for 60 min; this is called in-situ oxygen treatment. Typical examples of J, values [20] obtained at 77.3 K are shown in fig. 2 as a function of the magnetic field, where J, values were defined in a 2 pV/cm criterion [21]. Three films with c-axis orientation, G-63, G-66 and G-81 show good J, characteristics. In particular, the film G-81 exhibits an excellent J, characteristic in magnetic fields up to 27 T. On the other hand, a film G-83 with a-axis orientation has a poor, low J, characteristic. Therefore J, exhibits large anisotropy, reflecting its crystal structure. Characteristics of these films are summarized in table 2. The X-ray diffraction patterns of these four

0

10

5

15

30

20

35

B (Tt5 Fig. 2. Transport critical current densities at 77.3 K defined in a 2 pV/cm criterion. The values of J, at OT were 8.4 X lo’, 1.8 X 104 and 5.6 X lo5 A/cm’, and at 27T were 3.3 X and 3.1 x (not shown), 1.5 x 10’ A/cm*, lo2 A/cm* lo4 A/cm* for G-63, G-66, and G-81, respectively.

films are shown in fig. 3. While the film G-81 does not show any trace of u-axis orientation, two films G-63 and G-66 with preferred orientations of the c-axis include a small amount of grains along the u-axis, as seen in the top two patterns. This is clearly understandable when compared with the line (200) of the film G-83. Table 2 Characteristics

of CVD Y,Ba,Cu,O,_,

films.

Sample

Dimensions of a narrow bridge w(mm) X /(mm) X t( pm)

T, (K) (zero resistance)

G-63 G-66 G-81 G-83 G-86 H-64B I-6A I-11A

0.30 0.32 0.34 0.44 0.39 0.31 0.49 0.48

90.5 91.5 92.0 86.0 90.2 90.5 91.5 91.0

x x x x x x x x

1.0 1.0 1.0 1.0 1.0 1.9 1.1 1.0

x x x x x x x x

0.8 0.6 0.9 2.2 1.4 0.8 2.0 1.6

Y. Muto et al. I Transport properties in high-T, superconductors

142

Intensity

Intensity

Intensity

Intensity

(arb. unit)

----_-____

Fig. 3. X-ray diffraction patterns indicate strong c-axis orientation (G-63, G-66, and G-81) and strong a-axis orientation (G-83). A small amount of grains with a-axis orientation perpendicular to the substrate was mixed with c-axis oriented grains except

Fig. 4. Scanning electron micrographs for CVD films. The tilm ti-63 has CuO projections. The film G-83 (a-axis orientation) has many grain boundaries.

precipitates.

Both

films G-66 and G-81 indicate

Y. Muto et al. I Transport properties in high-T, superconductors

Fig. 5. Electron observed.

probe microanalysis

for CVD films. CuO precipitates

(G-63) and Cu-rich precipitates

143

(G-66, G-81) are

Y. Muto et al. I Transport properties in high-T, superconductors

144

Figure 4 shows scanning electron micrographs (SEM) of these four films. The three films with c-axis orientation indicate the existence of precipitates or projections. Some of them may be CuO precipitates or any Cu-rich Y-Ba-Cu oxide compound. Figure 5 shows the electron probe microanalysis (EPMA) for three films with c-axis orientation. The copper content of these precipitates is higher than that of the matrix, especially when it is considered that the precipitates for G-63 correspond to CuO. Furthermore, twin boundaries in the film plane were observed by an electron microscope. Because both current and field directions are perpendicular to the c-axis, the flux lines move across the twin boundary. Therefore, twins cannot be pinning centers in the present case. Some other origin such as CuO

precipitates or any defects among c-planes should be considered. In fig. 6, J, values as a function of magnetic field are shown for the Y-based film G-81 at 77.3 K, together with J, values measured at 4.2 K on several conventional advanced superconductors such as Nb,Ge, PbMo,S, (Chevrel phase compound), Nb,(AlGe), Nb,Al and NbN. Among the conventional superconductors, Nb,(AIGe) prepared by an electron beam irradiation process exhibits the highest J, characteristic near 30 T at 4.2 K which is the same order of magnitude as the Y-based oxide films. Therefore it is concluded that the Y-Ba-Cu oxide is a very promising material for future superconducting magnets operating at liquid nitrogen temperatures.

3. Broad resistive transition -l

7 15

YBc0

( cvD-film

)

, , ,

20

25

B

30

CT)

Fig. 6. This figure compares J, of the CVD-YBCO film at 77.3 K with that of several conventional advanced superconductors at 4.2 K. Nb,(AI, Ge) prepared by an electron beam irradiation process exhibits the highest values of J, near 30 T at 4.2 K among the conventional superconductors. However, J, of the CVD-YBCO film at 77.3 K exceeds that of Nb,(AI, Ge) at 4.2 K in high magnetic fields.

Since we can obtain good quality films of the Y-based system, we return to the broad resistive transition phenomena in magnetic fields [22, 231, mainly using these oxide films. The electric resistance was measured by the usual four probe method using a DC current of 50 PA in the c-plane. Magnetic fields were applied perpendicular or parallel to the c-axis. Figure 7 shows the electrical sheet resistance of the film H&B as a function of temperature in various fields up to 25 T for both field directions. The resistive transition at zero field is sharp with a width of 2-3 K, while those in magnetic fields are quite broad even when the magnetic field is perpendicular to the c-axis. For fields parallel to the c-axis, the width of the resistive transition is very broad. In fig. 7(b), it should be noticed that each resistive transition has a knee near about 6 fi at high fields above 13 T. This means that the temperature dependence of resistance changes near this point. Quite similar behavior was obtained for a Bi,(Sr, Ca),Cu,O, CVD film [22] and a single crystal of Tl-Ba-Ca-Cu oxide [24] where the broadening is quite large when the field is parallel to the c-axis. Thus, it is concluded that such broad resistive transitions are probably not due to an inhomogeneity but an intrinsic property of cuprate superconductors.

Y. Muto et al. I Transport properties in high-l;

25

H-64B

(Blc-axis)

15 z $10

25 H-6LB

(But-axis)

15 z (LolO

5

0

50 T(K)

Fig. 7. Resistive transition of a YBa,Cu,O, film in various magnetic fields perpendicular (a) and parallel (b) to the c-axis.

4. Fluxcreep As shown in table 1, the G-L parameters of these oxide superconductors are very high. Therefore it is apparent that these cuprates belong to type II superconductors. In a type II superconductor, magnetic flux begins to penetrate into the superconductor when the field exceeds H,, but superconductivity is not destroyed until the field exceeds Hc2. Between H,, and Hc2, the magnetic flux exists in the form of isolated filaments along the field direction, where each filament carries a quantum of flux. These filaments are called flux lines and are arranged in a triangular array. This triangular lattice is often called vortex lattice. It would seem clear that a current set up in a

superconductors

145

superconducting wire will not be dissipated but will continue to flow forever. However, as first described by Anderson [25], a type II superconductor placed in a field above H,, has a nonzero resistivity and then the current does not flow forever. A current flowing in such a superconductor exerts the Lorentz force on the flux lines. If the vortex lattice is not pinned, then it will move under the Lorentz force, drawing energy from the current source. This causes a superconductor to show a finite resistivity. However, in real superconducting materials, there are many defects and impurities. Therefore, the motion of flux lines is obstructed by these defects or impurities. The pinning energy is so large in a conventional superconductor that the motion of flux lines is actually dominated by thermally activated hopping of the lines over the barriers presented by the pinning centers. This type of motion is called flux creep. On the other hand, when the Lorentz force is stronger than the pinning potential, the phenomenon called flux flow will appear. For currents weaker than the critical current in conventional superconductors, the resistivity due to flux creep is sufficiently small so that a variety of applications such as generation of a strong magnetic field becomes possible. Though the current in conventional superconductors may not be forever, its decay constant turns out to be longer than the lifetime of the universe. As for the oxide superconductors, Miiller et al. [12] pointed out that a metastability of the zero-field-cooled susceptibility and then timelogarithmic relaxation of the remanent magnetization occur. Their observation indicates the existence of a superconducting glass state related to random weakly linked superconducting grains. Yeshurun and Malozemoff [26] reported an observation of strong, anisotropic magnetic relaxation of the field-cooled and zero-field-cooled magnetization along the principal axes of a YBa-Cu oxide single crystal and interpreted it with a thermally activated flux-creep model. They emphasized that the flux creep in these superconductors was unusually large at temperature and field values at which the vortex lattice was well formed. Tinkham [27] used the idea of this giant

146

Y. Muto et al. I Transport properties in high-T, superconductors

flux creep and tried to explain the broad resistive transition in magnetic fields. His theory on the temperature and magnetic field dependences of resistivity, which drops from the normal state value to a value too small to be measured, agrees well with the data on a Y-Ba-Cu oxide single crystal measured by Iye [28]. Careful measurements of resistivity in the mixed phase by Palstra et al. [29, 301 also demonstrated the thermally activated nature of the creep process. It should be remembered that this creep model is based on the existence of Lorentz force. Here we have to add an important point. Figure 8 is the electrical sheet resistance in the magnetic field of 11 T as a function of T-’ for Bi,(Sr, Ca),Cu,O, [22] where the current is perpendicular or parallel to the magnetic field. The results are almost in agreement with each other for both directions, so it seems that the Lorentz force does not work in the mixed state. Furthermore, recently Kitazawa et al. [31] and Iye et al. [32] have reported similar results on a La-Sr-Cu oxide single crystal and Er-Ba-Cu oxide and Bi-Sr-Ca-Cu oxide films, respectively. However, unfortunately we do not yet have the experimental results for Y-Ba-Cu oxide. The

problem whether the Lorentz will be discussed again later.

force does work

5. Activation energy The low resistance portion of the electrical sheet resistance is plotted as a function of T-’ in various magnetic fields in fig. 9 for the magnetic field parallel to the c-axis. It is seen that the resistance depends exponentially on T-’ over a wide resistance range, showing a thermally activated behavior. as follows: p = p,, exp(-

U,,Ik,T)

.

The activation energy U, is estimated from the linear part. Figure 10 shows the magnetic field dependence of U, for many Y-Ba-Cu oxide films studied. On the whole, the U, values for the magnetic field perpendicular to the c-axis are much larger than those for the field parallel to the c-axis. It seems

I

I

I

I

/

I

H-64B(B~c-axis) 10 7

B(T)

0 10 A 30 ‘% 50

l=

10-l: 2: QF

lo-*:

10-3

t

I

I

I

1.0 1.1 1.2 1.3 lh

Fig. 8. Log R, versus T-’ plot of the resistance of a Bi,(Sr, Ca),Cu,O, film for transverse (0) and longitudinal (0) currents with respect to the magnetic field.

I I “1 1.5 1.6 1.7 1.6 1.9

T-'(10-k')

Fig. 9. Log YBa,Cu,O,_,

R, versus T-’ plot of the resistance of a film for magnetic fields parallel to the c-axis.

147

Y. Muto et al. I Transport properties in high-T, superconductors

be expressed as G63

BLC 0

BNC .

M(t) = M(O){1 - (k,TIE,)

’ I ‘so*”

103’*.,,’

5

1

10 B CT)

’

3 ‘*,**-’ 50

1 100

Fig. 10. Magnetic field dependence of the activation U, of several YBa,Cu,O,_, film samples.

energy

that U, is proportional to B - ’ for the field parallel to the c-axis and to B - “* for the field perpendicular to the c-axis in higher fields. However, the U, values for both directions tend to saturate toward lower fields. Magnetization measurements on the Y-Ba-Cu oxide film G-86 were done using a commercial SQUID magnetometer (Quantum Design). The activation energy V,, estimated from the electrical resistance of this film is included in fig. 10. The logarithmic time decay of magnetization, as noticed by Miiller et al. [12] and Yeshurun and Malozenoff [26] at a field of 0.1 T parallel to the c-axis is shown in fig. 11. The magnetization can I

1

““‘111

“““‘I

In t} ,

where E, is an activation energy obtained from the magnetization. In fig. 12, the U,, values obtained from the electrical resistance for Y- and Bi-based films and a Tl-based oxide single crystal are shown as a function of magnetic field. The E, values for G-86 at 0.1 T are also included, showing smaller values than the U, ones. Each activated behavior of U, and E, seems to originate from different pinning processes or different mechanisms. However, it should be discussed after the temperature and field dependences of the activation energies have been investigated in detail. In fig. 12, the activation energy U, is the largest for Y-Ba-Cu oxide film among other superconducting oxides, However, the flux creep rate even in the Y-Ba-Cu oxide is much larger than in conventional superconductors. The giant flux creep in oxide superconductors is both due to their high critical temperatures and to the very small coherence length. The higher T, means that the thermal energy for flux lines to hop over the energy barriers is larger. A short coherence length means very small energy barriers.

‘05c

‘“1

l,O-

lo3t(sec) Fig. 11. Decay of the normalized magnetization YBa,Cu,O,_, film with the field (0.1 T) parallel c-axis.

of

a to the

Fig. 12. Activation energies U, and I?,, for YBa,Cu,O, a TlBa,CaCu,O, single crystal and a Bi,(Sr, Ca),Cu,O, The E,, values estimated from the magnetic relaxation T are represented by large circles.

films, film. at 0.1

148

Y. Muto et al. / Transport properties in high-T, superconductors

The fact that the values of activation energy U,, depend roughly on the materials suggests that the true mechanism of U, is microscopically based on the electronic structure of the oxide itself. However, the variation of U, in the same superconducting oxide might be due to the different behavior of individual pinning centers. We have previously described the Lorentz force which forms the basis of the flux creep theory. As can be seen in fig. 8, it seems that our data on the Bi-Sr-Ca-Cu oxide give almost the same results for both field directions with respect to the current. If so, we are afraid that the basis of the theory may be denied, because the Lorentz force is the only mechanism we know. However, according to Matsushita [33], even when the current and the field are parallel, the Lorentz force still exists because the flux lines may be disturbed by pinning centers and then may no longer be straight. Moreover, according to recent magnetic decoration experiments by Gammel et al. [34, 351, the Abrikosov lattice was well formed at 4.2 K in fields up to 500 Oe, but there was no evidence of the lattice at 77 K even in fields smaller than Hc2. This opens up the possibility that above a certain temperature the flux lattice may melt at a field strength smaller than Hcz. This might happen in two-dimensional superconductors, because owing to the very short coherence length the superconducting Cu0 planes are only weakly coupled. In such a situation we do not know what happens with the relationship between the Lorentz force and the flux lines or melted flux lattice. Further studies are necessary to solve this flux creep problem.

the new oxide superconductors, the many experiments on superconducting ceramics and single crystals done during the last 3 years have shown some puzzling features. The problem is whether or not the behavior of the cuprate superconductors in the presence of a magnetic field is very much different from that expected on the basis of the common understanding of the conventional superconductors in a magnetic field. Whatever the expectation for future application of high-T, superconductors may be, our interest is sure to remain high, both in the search for new materials toward room temperatures superconductivity and in the study of the underlying macroscopic and microscopic mechanisms.

Acknowledgments

We would like to thank Profs. T. Hirai, Y. Syono, M. Tachiki, T. Matsushita, K. Noto, T. Fukase, H. Fujimori, M. Kikuchi, K. Hiraga, M. Suzuki and K. Hamasaki, Drs. H. Yamane, K. Togano, H. Iwasaki, T. Kajitani, H. Morita and D. Shindo, Messrs. H. Kurosawa, H. Kawabe, H. Masumoto, S. Nakajima, E. Aoyagi and K. Oh-ishi and Miss A. Tokiwa for their help and discussions. This work was partly supported by Grant-in-Aid for Scientific Research on Priority Area “Mechanism of Superconductivity” from the Ministry of Education, Science and Culture.

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