Acoustic surface wave study of perpendicular field superconducting proximity effect in Cu-Pb-Cu sandwiches

Volume 35A, number 4

ACOUSTIC

PHYSICS LETT ERS

SURFACE

SUPERCONDUCTING

14 June 1971

WAVE STUDY OF PERPENDICULAR

PROXIMITY

EFFECT

IN Cu-Pb-Cu

FIELD

SANDWICHES

M.C.JAIN and D.R.TILLEY Department of Physics, University of Essex, Coichester, Essex, UK Received 5 May 1971 4nnlo ilar critical field versus temperature of various Cu—Pb-Cu sandwiches. We A study wasthe made of pe~-~ determined critical field trom acoustic surface wave attenuation. The experimental points were compared with ~ theoretical expression given previously, using one disposable parameter, and found to be in satisfactory agreement.

0

2

It has been pointed out recently [1] that the

superconducting proximity effect has been studied in zero magnetic field and in a field parallel to the interface between the films, but not so far m perpendicular field. Ref. [1] included measurements of the perpendicular critical fields of rolled Nb foils, which have a microstructure of alternating high and low ic regions. There were in qualitative agreement with the theory given in ref. [1]. We present here critical field measurement of Cu-Pb-Cu film systems, which permit a more quantitative cornparison with theory. We prepared specimens on a quartz substrate in a conventional evaporator which included a Meissner trap and a crystal thickness monitor. The pressure during evaporation was less than 3 x 10-6 torr and there was an interval of only a few seconds between evaporation of successive films. We checked the thicknesses, optically, and measured the conductivities of the films on monitor strips evaporated at the same time. We measured the critical fields by attentuation of surface ultrasonic waves; the experimental details were the same as in ref. [2]. An advantage of this technique [3] is that the attentuation depends on the behaviour of the composite specimen as a whole. For magnetic fields less than about 200 gauss we used a calibrated, air cored Helmholtz pair; for higher fields we used an iron cored electromagnet. We aligned the magnetic field relative to the specimen with the aid of the sharp minimum m attenuation at par-

I

6 I

I

Specim.n n~1

\.

-

~

“

N

—

2

‘

Theoretical Curves

-

-

S

*

-

2

I

0

2 T ~K (Spec~.ns1 & 3)

6

Fig. 1. Perpendicular critical fields compared with theory, for three specimens. Note displaced horizontal axis for specimen 2. tan{~(a -e)~d ~ 1 1

=

+~)2

~2

tanh{(a +E)1d }.

y(a 1

allel orientation. In the Werthamer approximation [4-6] and in the dirty limit, the critical perpendicular field of a symmetric Cu-Pb-Cu sandwich is given by

T °K(Spec 2)

I

.~

2

2

Here a1 and a2 are related to the temperature dependent coherence lengths in Pb and Cu respectively by a = ~ 2. d1 and d2 are the thicknesses 217

Volume 35A, number 4

PHYSICS LETTERS

14 June 1971

Table 1 Specimen

dpb (A)

dCu

No

1 2

3500 2500

1150 1100

4.6 4.2

1.7 0.53

6.1 6.1

0.45

500

0.7

4:Th

3

2500

1150

5.9

5.3

jO

(1.31

524

(A)

~Pb ‘< 1 ~l~cm

of the Pb film and of either Cu film. The critical field He 1 of the sandwich is proportional to the eigenvalue e, Hc1 = ~ e/2r, where q~0is the fux quantum. Eq. (1) is the generalisation to finite Cu thicknesses of the equation for He1 given in ref. [1]. In the dirty limit, ~ is equal to ~Pb/aCu, the ratio of the conductivities. To get a significant attenuation, we used relatively clean films; we therefore adjusted y for each specimen so that the solution of eq. (1) for e = 0 gave the measured critical temperature. The variation with temperature of a~, or ECu, depends on the mean free path 1. We used for ~Cu an interpolation formula which has the correct behaviour in both clean anfl dirty limits (liv F/2rkBT and (liv F l/6ITkBT)T respectively) The parameter a1 is proportional to the perpendicular critical field Hc2 (Pb) of the lead film taken in isolation (scaling factor 217/po), and for its temperature variation we used the empirical form given by Cody and Miller = tem2)/(1 +at~)where t is [7]: the a1(t) reduced a1(0)(1 -t T/TC (Pb), and a is a parameter of perature, order unity which for a given thickness d can be obtained from fig. 9 of ref. [7]. We took a = 0.9 for all three of our specimens. Our results for three specimens are presented in table 1 and fig. 1. The agreement between theory and experiment is satisfactory. Apart from parameters characterizing the specimens, table 1 gives the values of y and a 1 (0) used to draw the theoretical curves. We note that ‘ increases with ~Pb/aCu. The values of a 1(0) are converted to He2 (Pb) at 4.2 K, that is the critical field the lead film would have

218

aCu x 106 l~1cm1

Hc~(Pb) (gauss)

‘ic

°K

taken in isolation. These critical fields are around 10% higher than those of Cody and Miller [7] for lead films of the same thickness. This is consistent with the fact thatour vacuum during evaporation is not quite as good as that of ref. [7] and in fact our previous critical field values [21were also a little higher than those of ref. [71. Further attenuation experiments on proximity effect in parallel and perpendicular fields are under way. Martinoli has informed us that the theoretical derivation of ref. [1~ has been given independently in his paper in the Proceedings of the Stanford Conference (to be published). His paper also ineludes resistive measurements of the perpendicular critical field of binary films. We are grateful to Dr. L. Mackinnon for his help and encouragement throughout this work. We should like to thank Mrs. S. Sussmann for help with computing. References

[1] D. R. Tilley and R. Ward, Solid State Communications 8 (1970) 1983. [2] M. C.Jain and L, Mackinnon, Phys. Letters 32A [3] H. Krlltzig, Phys. Letters 33A (1970) 343. [4] G. Deutscher and P. G. De Gennes, Superconductivity, Ch17 ed. R. D, Parks (Marcel Dekker, New York, 1966) [5] N. P. R. Hurault, Werthamer, Phys. Rev.20132 (1963) 2440. [61J. Phys. Letters (1966) 587. [7] GD. Cody and R. E. Miller, Phys. Rev. 173 (1968) 481.