Effect of weak links in n-type superconducting ceramics

Applied Svprrconduclivity Printed in Great Britain.

EFFECT

Vol.1, Nos l-9. pp. 925 - 933. 1993 All rights reserved

OF WEAK

LINKS

Copyright

IN n-TYPE

0964-1807/93 $6.00 + 0.00 @ 1993 Pergamon Press Ltd

SUPERCONDUCTING

CERAMICS

T. Grenet

Laboratoire

and M. Cyrot

Louis NCel, CNRS, BP 166,38042

ABSTRACT:

Grenoble Cedex 9, France

Unusual forms of resistive superconducting

transition

have been observed in some n-type cuprate ceramics. Their shape are strongly magnetic field dependent.

In some cases, the transition shows

a double peak behavior : the resistivity presenting reaching

zero. This behavior

two maxima before

and its change with magnetic

been explained by an interplay between the superconducting of the grains and the Josephson temperature

field has transition

of the intergranular region.

We present a model based on a self consistent medium approach which describes the various behaviors one can observe in these ceramics. Superconductivity interest

has been

superconductors studied2

in granular systems has always attracted a lot of attentionl. further

enhanced

since

the discovery

of high

This

temperature

because of the intrinsic granular structures of the ceramics. We have

the

superconducting

properties

of the

electron-doped

compounds

Ln2_xMxCu04_y (Ln = Pr, Nd, Sm, Eu ; M = Ce and Th). The granular structure of the sample influences

strongly the superconducting

behavior.

resistive transition have been observed, sometimes In this paper

,after reviewing

the different

Some unusual forms of the

causing a “double peak” transition.

behaviors

we have observed

in these

ceramics, we develop a model to interpret it. The sample is described as a colIection of superconducting concentration

grains with a distribution

of Tc due to the strong dependence

of oxygen and Ce or Th. The intergrain

ability to permit

a Josephson

described

via a distribution

materials

is the resistivity

current

between

of Josephson

region is described through the

the superconducting

temperature.

of Tc on

grains. This is

The third characteristic

of the grains and of the intergrain

of the

regions. We develop a

theory based on a self consistent medium. The different behaviors that we observed are due to the interplay temperatures.

between

the Josephson

The behavior under a magnetic

change of the Josephson temperature

with field. 925

and the superconducting field is mainly explained

critical

by the rapid

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The behavior of the r~istivity versus tempcratur~ strongly depends on the sample. Moreover for a given sample it strongly changes with magnetic field. The different behaviors are so anomalous that they seen unreasonable at first sight.

T (K)

3.0

,

,

,

,

[

,

,

,

,

,

,

-

2.5 b- 1 kOe 2.0-

d- 30 kOe e- 59.6 kOe

1.5-

.50

’ 0

lo

’ ’ 10

’ ’ 15

kg ’ 20

’

I 25

’

30

00

1: resistivity versus temperate fields for a Nd-Ce-Cu-0

’

T (KI

T (K) XI

cc> &me

’ 5

curves measured at different magnetic

sample (a), a Pr-Th-Cu-0

sample (b), a

Sm-Ce-Cu-0 sample (c) and a Eu-Ce-Cu-0 sample.(d). Some are well behaved in the sense that the resistivity in zero field strongly decrease at Tc and under magnetic field Tc (H) justdecreases (fig. la). In figure lb, we show one sample which is reasonably well behaved under zero field but in intermediate field has a

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knee below Tc. In figure lc, we observe that below Tc the resistivity decreases to a minimum, then increases before decreasing to zero with temperature. This maximum of resistivity increases with magnetic field. In figure ld, after the minimum below Tc the resistivity increases up to the lowest temperatures used in our experiment. We also note in this case that the resistivity just below Tcg is larger in very low field than in high field. Figure 2 shows the behavior of a sample of Sm&eo.1$u03,97 which presents this so strange double peak behavior. Below the critical temperatu~ of the grains there are two maxima in the resistivity versus temperature.

1.8 r

1RfRf30K)

Tonset

1.2

0.60

0.0

f;,irrure2: resistivity versus temperature curves measured under different fields for a Sm-Ce-Cu-0 sample We first give the qualitative explanation for the following three unusual behaviors a) b)

increase of resistivity below Tcg minimum of resistivity at Tmin and further increase of resistivity below Ttin

behavior at very low temperature c> increase to the lowest temperature used.

:

either decrease to zero resistivity or,

For behavior “a” suppose that we have a range of grain critical temperatures in between Tcmax and Tcmin which is likely to occur as Tc is strongly dependent on all concentrations3. Some grains below Tc map become superconducting. In between two superconducting grains conduction is due to tunnelling and the intergrain resistivity increases with decreasing temperature. This can cancel the decrease of resistivity due to the transition of the superconducting grains. The distribution of Tc is peaked near a temperature Tonset and below this temperature a large number of grains become superconducting and the resistivity strongly decreases.

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For behavior “b”. When most grains are superconducting at Tmin the resistivity is due to the intergrain region. The behavior of the tunnel junctions makes the resistivity increase when decreasing the temperature, producing the observed minimum. For behavior “c”. If the tunnel junctions have low enough resistivity a Josephson Current can occur and the resistivity if the junctions will decrease to zero giving a zero resistivity to the macroscopic sample. IF the tunnel junctions have large resistivity no Josephson current can occur and the resistivity always increases with decreasing temperature. This qualitative explanation relies on conventional superconductivitfl.

It requires

first that the intergrain resistivity is of the order of the grain resistivity. This requirement was not fulfilled with usual conventional superconductors(l). Secondly it requires that the temperature below which Josephson current occurs is lower than the critical temperature of the grains. In order to build the model, we have use an effective medium approach due to Landaue# for the calculation of the resistivity. In this approach the medium is described using two kind of grains A and B defined by their different conductivity OA and bg. The medium has an effective conductivity on obtained by assuming that on the average, the polarizability created by a grain A or B in this effective medium is zero. This model has been refined by Yoshida(6) and applied to grains which have a core and a shell made of different materials. In the following we will use this particular refinement. We have to describe the following situations -

:

two normal grains with a resistive junction

- two superconducting grains linked by a Josephson current - two superconducting grains linked by a resistive junction when the temperature is larger than the Josephson temperature - one normal grain and one superconducting grain with a resistive junction. Thus we introduce the following type of cells made of a core and a shell

:

a)

a normal core surrounded by a normal shell

b)

a superconducting core surrounded by a superconducting shell

c>

a superconducting core surrounded by a normal shell.

The cores represent the grains which can be either normal or superconducting depending on the temperature and the magnetic field.

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TABLE I cell

Reasons

Ratio x;

Normalcore

T > Tc (0) or H > Hc2 (T)

1 -cs Cs2 Cj

i=3

Superconducting shell

H
Superconducting core

H < Hc2 (T)

fT Cs2 (1-Cj)

i=4

Tunnel junction

and superconducting neighbor andT>Tj fT (1-Cs) cs

i=S

HTj

(l-fT) Cs2 (l-cj)

i=6

or H c Hc2 (T)

(1-f$ cs (l-C@

i=7

Normal shell Superconducting core

i=l i=2

or H < Hc2 (T) and normal neighbor Superconducting core Weak link

and normal neighbor

The shell represents the intergrain region. A normal shell can be either a tunnel junction or a weak link. A superconducting shell is a junction with a Josephson current. In table 1, we describe the different types of cells, the reason of their appearance and the probability of appearance. Cs is the probability that a grain is superconducting, Cj is the probability that the junction i.e. the shell is superconducting which happens for T < Tj where Tj is the Josephson temperature of the junction. fT is the ratio of tunnel functions. Thus l-fT is the ratio of weak links. We have seven types of cells. The main approximation in the model is that we have excluded correlations between the shells of neighbo~g

cores. The self consis#nt equation reads

igl = = Xi Si

0

where Si is the normalized conductive

of the cell i. To calculate it we assume that

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all the cells have the same size

- the normal core has resistivity Oid - the junction has resistivity Gin which does not change when the grains become superconducting

for weak links or which becomes activated in the case of tunnel

junctions. In order to describe the inhomogeneity

of the system, we consider a distribution

function for the critical temperature of the grains, a distribution function of the normal resistance of the junctions, the latter will permit to calculate the critical current and the Josephson temperature of the junction. When we apply a magnetic field, in order to calculate the ratio of the superconducting grains as a function of T and H we introduce two experimental parameters dHc2 Cab) dHc;! 6) T=Tc,and the London penetration depth XL. In order T=Tcand dT dT to describe the effect of the field on a junction, we introduce a third distribution junction which gives the distribution of size of the junctions and, assume that the critical current, hence the Josephson temperature follows

where @ is the flux into the junction. All these data permit to calculate the seven normalized conductivities.

In order to

decrease the number of parameters, we take for the distribution of resistance and size of the junctions

:

D(L)

=k

ifL<&

=o

ifL>&,

and D(R)

=&ifRR,,

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TABLE II Lax = 0.5 pm R,=Rco+500A 0,x = 103 (Qm)-l

(3,o = 1.2 105 (Qm)-1 dBc+) = - 0,2T/K dT

dBq(a,b) = dT

- 5

fT = 0.70

T/K

Table II gives in the first column the parameters used in our calculation which are either given in the literature or measured independently. The second column gives the values of the parameters that we have adjusted to fit the experimental curves. On figure 3 we show two sets of curves in order to show the effect of fT the number of tunnel junctions. 7.0

I

1

50 kOe

I

1

I

,30-,

I

H=

I

I

I

I

I

1OkOe

6.0 5.0 4.0 3.0 2.0 1.0

H-O

q.

0.0 0

5

20

10

25

T(I(;S

(a>

I

0.0

0

4 *Vf2

l6

2o

0.9

Figura: calculated resistivity curves using the parameters values listed in Table II and: fT = 0.5 (a) and fT = 0.3 (b). The temperature dependance of the normal state resistivity is omitted.

The height of the maximum is strongly increasing with this number. This permits us to evaluate the ratio of tunnel junctions compared to weak link by fitting this maximum. The position of this maximum with field permits to determine the average value of the size of the junctions. The distance between T,., and Tonset gives indication on the range

932

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of T, in our materials. Thus by analyzing the shape of the curves of resistivity versus temperature one can extract a lot of informations on the granularity of the system. In figure 4 we give a particular fitting of a Sm Ce Cu 0 sample.

1

0

mre

5

10

15 T (K)

4: compared experimental

20

25

30

(with experimental

points) and

calculated resistivity curves in the case of a Sm-Ce-Cu-0 sample.

In conclusion, we have shown that the curves resistivity versus temperature as a function of magnetic field can present a lot of unconventional behavior. By fitting this behavior with a simple mean field theory one can extract impo~~t ~owledge

on the

granularity of the system, for instance the range of critical temperature. Note that the highest critical temperatures of the grains correspond to the temperature below which the resistivity deviates from the normal state behavior (restored under high enough magnetic fields) and that the transition of these grains to the superconducting state causes an increase instead of a decrease of the global sample’s resistance. We can also extract the size of the junction, the ratio of tunnel versus weak links and the Josephson temperature of the junctions. By measuring the resistivity after treatments, one can also follow the evolution of the junctions’ characteristics.

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REFERENCES

1. Y. Shapira and G. Deutscher,

Phys. Rev. B 27,4463

(1983).

2. A. Gerber, J. Beille, T. Grenet and M. Cyrot, Europhys.

Lett. 12,5,441

(1990).

A. Gerber, T. Gerber, M. Cyrot and J. Beille, Phys. Rev. Lett. 65,320l

(1990).

3. J.T. Market-t et al, Physica C 158, 178 (1989).

4. See for instance,

M. Cyrot and D. Pavuna, Introduction

high Tc superconductors.

5. R. Landauer,

World Scientitic 1992.

J. Appl. Phys. 23, 779 (1952).

6. K. Yosida, J. Phys. C : Solid State Phys. 15, L 87 (1982). Phil Mag 53,55 (1986).

to superconductivity

and