Hysteresis studies in Clarke solder-blob junctions

Journal of Low Temperature Physics, Vol 33, Nos. 5/6, 1978

Hysteresis Studies in Clarke Soider-Blob Junctions

Madhu Prasad, V. S. Tomar, N. S. Natarajan, Hari Kishan, and M. S. R. Chari

Nat iona l Phys ical Laboratory, N e w Delhi, India

(Received June 9, 1978)

A study of hysteresis in Clarke solder-blob functions has been carried out in the temperature range 4.2-1.2K. The temperature dependence of the critical current, the variation of the constant-temperature critical current with sequential sweep cycles, and the effects of an external field are studied. All the experimental results are explained as due to a net trapping of magnetic flux in the junction loop whenever a hysteretic curve is traced. The origin of the flux can be traced to the inductance of the superconducting loop and the electrical or geometrical asymmetry.

1. I N T R O D U C T I O N

Quantum interference phenomena 1-4 of the supercurrents in a pair of Josephson junctions have been widely studied, yielding valuable informa- tion on flux trapping, 5 self-field effects, 6'7 vortex motion, 8'9 and other related aspects. 1~ Josephson junctions may be divided into two broad categories, nonhysteretic and hysteretic, depending on whether or not their current voltage ( I - V ) characteristics exhibit identical switching between the zero- voltage and finite-voltage state.

In the present work hysteresis in Clarke solder-blob junctions has been studied in the temperature range 4.2-1.2 K. The junctions, which are nonhysteretic at 4.2 K, tend to become hysteretic at lower temperatures. It has been noticed that whenever a junction becomes hysteretic, the critical current shows a roughly periodic variation with sequential sweep cycles at constant bath temperature. Since the junction is magnetically shielded and the temperature is kept constant, this variation is attributed to a net trapping of flux within the superconducting loop connecting the two weak links. A full analysis of the experimental results on the magnitude of hysteresis has shown that the inductance of the superconducting loop and electrical or geometrical asymmetry lead to a net trapping of flux.

521

0022-2291/78/1200-0521505.00/0 �9 1978 Plenum Publishing Corporation

522 Madhu Prasad et al.

Section 2 deals with the experimental details. Section 2.1 describes the fabrication technique for the junction and precautions taken to ensure that we are dealing only with double Josephson junctions and not multiple junctions. Section 2.2 describes the three different aspects of the junction behavior studied. Section 3 presents the unanalyzed experimental data as obtained from the study. An analysis of the data is given in Section 4 in terms of trapping of a net flux in the course of making a measurement. Section 5 shows that the inductance and electrical or geometrical asymmetry is responsible for flux generation and its trapping within the loop. In conclusion, it is shown that very act of taking a measurement with a hysteretic double junction leaves a residual magnetic field, which in turn modulates the value of the current.

2. E X P E R I M E N T

2.1. Junction Fabrication

A Clarke junction essentially consists of a superconducting wire covered with a dielectric medium. At points along the wire where it is desired to establish a "weak link" the thickness of the dielectric medium is reduced and the assembly is embedded in a second superconducting material (Fig. 1). In the present series of experiments niobium was the superconducting wire, NbxOy the dielectric, and a 60/40 composition of commercial Pb-Sn solder the second superconductor. It was found that when Nb was oxidized by exposure to air or by baking in an oven at 80~

r H H . ' ~ ~ /Ia I

NIOBIUM W I R E - - V ~ - - P b - S n SOLDER

V- JUNCTION VOLTAGE

Ix= MODULATING CURRENT

I = B I A S CURRENT Fig. 1. Schematic diagram of a solder-blob junption.

Hysteresis Studies in Clarke Solder-Blob Junctions 523

scratched at two points with a sharp knife, and embedded in a blob of solder at the first at tempt, Clarke junctions with good hysteretic characteristics at low temperatures were formed. On the other hand, if the solder blob did not adhere at the first at tempt, the junction characteristics were erratic. When a very thick oxide was formed by heating the niobium to red hot temperature (600~ in atmosphere, Clarke junctions that showed no hysteretic characteristics even at the lowest temperatures were formed.

2.2. M e a s u r e m e n t s

Since we are dealing with a situation where the hysteretic Clarke junction retains a flux memory of every reading, the sequence and method of taking the observations is of utmost importance. Three aspects of the junction behavior were studied: (a) temperature dependence of the critical current; (b) variation of the critical current with sequential sweep cycles, keeping the temperature constant; (c) magnetic field modulation of the critical current.

15

t IE Io

n., 5 J E3, 0

,, B = C

t2 v2

Fig. 2. A typical hysteretic junction.

0'.5 ~.'o VOLTAGE ( V ) mV ~-

current-voltage characteristic of a


1 2

<C I 0 E

1 I 1 i

I 2 3 4

T " K ~

E ?

b

o)~,,,

I I I I

0 I 2 3 4

T ~

Fig. 3. Temperature dependence of the critical current of hysteretic junctions. (a) SLUG I; (b, c) SLUG II; (d) SLUG IIl.


l T

M

\ \

\ \ \

1 I 1 1 ~

Z 3 4

T "K

<I E

8 -

6 -

4 -

2 -

0 ~

I I r

i 2 3

T*K --

Fig. 3. Continued.

",Q..


The I - V curves were recorded on an X - Y recorder. A typical cur rent - voltage characteristic of a hysteretic junction is shown in Fig. 2. As can be seen, there is a switching from the superconducting state to the finite-voltage state at a current I1, and on the return path, upon reduction of the current, the system is restored to the supercurrent-carrying state at a different current value I2. The quadrilateral A B C D represents the amount of hysteresis for the junction.

To study the tempera ture dependence, the I - V curve of the junction was recorded and the tempera ture of the helium bath varied by reducing the pressure in the cryostat. After allowing a sufficient interval of time to establish thermal equilibrium, the next I - V curve was recorded. This was continued at intervals of roughly 0.05 K down to the lowest tempera ture ( - 1.2 K).

For the study of the variation in critical current with sequential sweeps, the temperature was held at a constant value and current-vol tage curves were recorded after specific intervals of time. Later, when it was found that the time interval was of no consequence, this interval was standardized to a period of 1 min to allow any minor thermal instabilities introduced in the system due to the passage of the current to stabilize. These sets of sequential sweeps were recorded at various temperatures.

Since it should be possible to simulate the effect of the t rapped flux in a nonhysteretic junction by means of a modulation flux, i.e., by applying an external flux, a modulation current was passed when the junction was nonhysteretic. The direction of the applied flux could be reversed by reversing the direction of the modulation current. The periodicity in the critical current with modulation current gives the modulation current corresponding to a flux quantum. The same procedure of taking the modulation characteristics with forward and reverse modulation currents was repeated when the junction was hysteretic to record the effects when the applied flux is partially suppressing the t rapped flux and when the applied flux is adding to the t rapped flux.

3. RESULTS

(a) A study of the tempera ture dependence of the critical current in hysteretic junctions showed that the critical current varied between two limiting profiles (Fig. 3). As can be seen from Fig. 3, the two profiles tend to diverge at lower temperatures. This is a significant point, which will be invoked later in discussion.

(b) Figure 4 shows a reproduction of I - V curves recorded with sequential sweeps at one temperature. The variation of critical current with sequential sweeps for various temperatures is shown in Fig. 5. As can be seen


Y T.4~

VOLTAGE

Fig. 4. Recordings of the I - V curves with sequential sweep cycles (denoted by the numbers) at the same temperature for a hysteric junction.

from the unanalyzed data, there is some sort of periodicity in the variation. It will be shown in the analysis that when this variation is plotted against the magnitude of hysteresis, periods become well-resolved.

(c) As mentioned in the previous section, modulation in the nonhysteretic junction is taken to be a measure of the flux quantum. Such a graph recorded near the boiling point of helium is shown in Fig. 6. Figure 7 shows the effect of modulation current on hysteretic junctions at various temperatures.

4. ANALYSIS OF T H E RESULTS

The variation of the critical current due to external noise signals can be ruled out because, while a nonhysteretic junction does not show any change in critical current junction with sequential sweeps, a hysteretic junction investigated at the same time and place and in the same assembly shows a periodic variation with sequential sweeps (Fig. 8).

Figure 3d shows the temperature-dependent profiles for a SLUG that is nonhysteretic in the beginning but becomes hysteretic at lower temperatures. The critical current rises steadily with a decrease in temperature as long a~ the SLUG is nonhysteretic. However, with the onset of hysteresis,


11,5

10.5

I1.0

I 10.6

10.2 E

T = 3.60*K

T = 3.87"K

9 . 8

9 . 4

I

0 I0 20 30 40 50

a N (NUMBER OF SWEEP CYCLE)

I 5

E

~ - 7

T = 2 . 9 3 " K

o ° o o ° ~ @ o o ° 0 0 o 0 o o

T = 4 . 0 * K

t T ~ l r

I0 20 30 40 50

N(NUMBER OF SWEEP CYCLE)

Fig. 5. Sequential sweep dependence of the critical current at different temperatures: (a) SLUG I; (b) SLUG II.

the critical current fluctuates in a periodic manner with temperature , leading to the appearance of two specific envelopes. Ambegaokar and Baratoff 12 have computed the variation of the critical current with tempera ture for tunnel junctions. The simple unresolved data for a typical S L U G (Fig. 9) that is hysteretic seem to indicate that the shape of both the upper and lower envelopes is linear and at variance with the theoretical predictions of


8 I T = 4 16~

H- 8 6

i0 20 30

IH ( MODUL AT ION CURRENT ) m A . . . . .

E

T , 4 . 1 8 e K

I I I I 5 aO 15 20 _

0 Q

0 o 0

[H ( MOOULATION CURRENT ) mA

Fig. 6. Modulation characteristics in the absence of hysteresis: (a) SLUG I; (b) SLUG II.

Ambegaokar and Baratoff. This is because when successive observations are being taken at different temperatures, the critical current is influenced by two distinct mechanisms: the first is due to the reduction in temperature, and the second is due to the flux that is trapped due to consecutive measurements. When a number of critical current measurements are taken at each temperature for the same sample and the maximal and minimal points corresponding to n~o and (n + 1/2)d~0 are plotted against temperature, it is seen that both the upper and lower envelopes take on a shape which is in conformity with the law of Ambegaokar and Baratoff (Fig. 10).

The variation of the critical current with sequential sweep cycles has already been shown in Fig. 4. It can be noticed that for different sweeps the area of the hysteretic loop A B C D is not constant, but increases and decreases with sequential readings. Since our hypothesis is that the hysteresis is representative of a certain quantum of trapped flux, the sequential I - V graphs have been analyzed by plotting the critical current

5 3 0 M a d h u Prasad et al.

readings against the sum total of hysteresis introduced in the junction up to that point. The measure of the hysteresis has been taken as ~ ( I 1 - I 2 ) , i.e., ~, AB, as well as ~ ( V 1 - V2), i.e., ~.(BC-AD). [We will henceforth refer to the calculation of the t rapped flux against the parameters ~ ( I1 -12 ) and ~ ( V 1 - I,'2) as Dr , and qbr V, respectively.] When the sequential measurements are analyzed against these parameters the periods become well- resolved, as can be seen in Fig. 11. Since with a decrease in tempera ture there is an increase in hysteresis, the flux difference between two consecutive curves becomes greater and greater. Thus, while at the highest tempera ture a period may be defined by as many as up to four points, at an intermediate tempera ture it is defined by about two points, and at a still lower temperature, consecutive points even skip a period. This periodicity in 11 against ~.(I1-/ '2) or T.(V1- 1/'2) is again representative of a flux quantum.

iO 5

I1.~ ~ 0 I I - ' l l l

i0.5

l iO 4

r E ii 0

-

10.6

I02

9.7 - e o o

9.3 ~

r �9 3 36~

I H I

I., t

T �9 3 60"K

[ . I

I . t

T �9 3.8?~1C

~ t

! 0 IO 20 $0 40

a ,~J4 ( MODULATION CURRENT ) mA ,-

Fig. 7. Modulation characteristics in the presence of hysteresis: (a) SLUG 1; Co) SLUG II. The forward and the reverse direction of the modulation current is denoted by the two directions of the arrow.


8

I0 B

i 6 B ~6

4

T : 2 93~

INI

T : 4 0 " )

N

3

0 S I0 15 20

b I , (~OOUt.ATtON CURn(NT } mA

Iwt

2~

Fig. 7. Continued.

Coming now to the modulation part of the experiment, the periods generated in the critical current by passing the modulation current when the junction is nonhysteretic provide us with a measure of the flux quantum in terms of current, i.e., it denotes how many modulation current units are equal to a flux quantum. When this external applied flux qbA, whose magnitude is known, is superimposed on the flux trapped in the hysteretic junction, the variation of the critical current with sequential sweep cycles is increased or decreased depending upon whether it is adding to or subtrac- ting from the trapped flux. Since from the plot of 11 against ~ (I1 -12) and ~ , ( V 1 - V2) the flux quantum can be deduced, a plot of 11 against ( ~ r +dPA) should give a periodic behavior with a period alP0. ((I)7- denotes dPT, or qbr,,.) As can be seen from Fig. 12, this is indeed the case. The depth of modulation increases with a decrease in temperature and the total variation in the critical current remains the same as the variation in the critical current with sequential readings. One interesting point is that in the direction when the two fluxes are additive, there are fewer points in a period than in the direction when the two fluxes are opposing each other. This again seems to

532 Madhu Prasad et ah

T = 1.24"K

HYSTERETIC

18

<%

E 14

0.9 ~ - o ~ ,, ,, o

0.7 l 0 tO

NONHYSTERETIC

I 2O

N (NUMBER OF SWEEP CYCLE) =

Fig. 8. Sequential sweep dependence of the critical current of a hysteretic and a nonhysteretic SLUG loaded in the same dewar.

prove that it is the t rapped flux that introduces the variations in the critical current.

5. O R I G I N OF T H E T R A P P E D F L U X

We can now infer that there is a flux trapped in the presence of hysteresis in the system. In this section it is shown that a large inductance can lead to the trapping of flux within the loop. Halse and Salleh 13 have showed that for a double junction with an asymmetry paramete r N, a loop of inductance L, and a critical current ratio a of the two individual contact currents, a current I introduces a flux K I in the loop, where K is given by

1 - a L K + N

l + a 2

Here K represents the effective inductance. For a unidirectional current, the self-generated flux is proportional t o / , which can get trapped, as suggested

Hysteres i s Studies in C larke S o l d e r - B l o b Junct ions 5 3 3

E

2 o

18

f6

14

12

to

x \ \ \

\x\ *~. \,

\\\1 \ \ \ \ \ -

\ "q \

% %

%

I I I II It-

0 ! It 3 " r ~

Fig. 9. Temperature dependence of the critical current for SLUG IV.

by Jaoul. 5 When a current I1 is established, a circulating current proportional to KI1 is set up in the superconducting loop, which is referred to as the excluded flux. Similarly, on the return trace, when the current /2 is reached, the excluded flux would be KI2 . The difference K ( I 1 - I2) is the flux trapped and this in turn will be effective as a residual flux for the next cycle. Thus

~ T l = K (I1 -- I2)

or Crz is proport ional to I1 --Iz. The analysis of the experimental data in terms of the paramete r

(V1 - V2) runs closely parallel to that in terms of the hysteresis parameter ( I t - / 2 ) . The flux trapped qbT~ in traversing the hysteresis curve is readily

534 Madhu Prasad et ai.

t E

t O

15

10

o',,~

\ \ \ \

\ \ \ \

\ \ \ \

\ \ \ \ \ \

\ \

f 'i I t , . I 2 3 4 5

"11" oK ~--

Fig. 10. Profiles constructed for the variation of the critical current with temperature for SLUG IV from sequential sweep measurements. The profiles are in agreement with those predicted by Ambegaokar and Baratoff.

explained as being traceable to the inductance of the loop formed between the two weak links and is proport ional to I1 - 12, while a separate source of qbr,, is not readily traceable. From the experimental data Va and V2 are not linearly dependent 14 on I t and/2 . However , plots of ~ (V1 - V2) vs. ~ (It - I2) are linear (Fig. 13) and this explains the close parallelism between our analyses with respect to ~', ( I x - / 2 ) and ~ ( V 1 - V2).

6. C O N C L U S I O N S

(a) In a junction that is hysteretic the measurement of the critical current introduces a certain amount of t rapped flux. This flux is cumulative in nature and hence leads to a periodic variation of the critical current with sequential sweeps.


I io 4

? ,~

, , , , , , , , , o o z 0 4 o ' ~ o ' e ~o ~'z ~ ~. ' 6 ' a 2 0 2 2 2 4 z'.~

(V I I V~) m V ~

l ' ~ ' V ', ~' , q V~ v ~; ; "/ '~' '/ ; v j Y" v. T Y v ~ v

6

C 5

i r , T , ,

o ,o 20 3o 40 50 ,so 70 ao g,o

( I , - I z) mA

9

I T �9 2 93"x

d

,2 i l l 2 4 } o ~ i 4 Z 4 a ~ 4 ~,0

( V, - V~, )mY- -

Fig. 11. Analyzed plots of the critical current against the parameters ~ ( I1 - / 2 ) and ~.. (V1 - V2) from the data of Fig. 5. The solid lines represent the expected periodic behavior. (a, b) SLUG I; (c, d) SLUG If.

536 Madhu Prasad et al .

r ,:::t

E H

t E

9 .7

9 .5

9 .7

9.5

9 . 3

0

T = 3 . 8 7 OK

a

.. | =,.

5

(~T~- ~B~) / ~o-_

I I 5 I0

( (I:)TI4" ~A, )/~o

[ P

15

I 9 ,7

,,r E 9.5 ..z

9 .3

i

5

~ (~Tv- 4'At)/+o--

T - 3.BT'K

b

9.7

t 9 .5 ,<

E

9.3 ! !

0 5 iO 15

Fig. 12. Analyzed plots of the critical current against ( O T + O A ) , where Or represents OTV, and OAt and OAt denote the two directions of applied flux. (a-f) SLUG I; (g-i) SLUG II.


l I1.0 - ~

< 10,6- E

10.2 i '7 0 5 IO

T �9 3 . 6 0 " K

_10.$

10.2 I I ! I ' I I 0 5 IO 15 20 25

. 0

t

I02

. 0

T ~ 106

,-7 I02

T �9 3.BO "K

d

o 5 Io

0 5 I0 15 20 ZS

Fig. 12. Continued.

538 Madhu Prasad et aL

T �9 5 . 3 6 ~

<[ I II

e I 0 l I �9

0 5 I n 15

(~T,- @, l ) / i o " t l

!.,, IO I I I l i 1

0 $ I0 15 20

(4>.r, + 4%)/@o "

2 5

T �9 $ .36 "K

tO 0 5 10 15

i i

E II

IO 0 $ IO 15 2 0 2~

Fig. 12. Continued.

Hysteresis Studies in Clarke $older-Blob Junctions 539

1 E

T �9 4 ()*K

; ' : . o ." : 5 IC ~5 20

(*,; *,, )/*o - -

E

4 p ;

0 2 4 6 8 IU

< ~,,- +o,1/+o

T �9 4 ='K

t

0 2 ~ 4 6 8 IO 12

t 0 ~o ~ ~

E

4 i ~ i i

0 5 I0 15 2 0

Fig. 12. Continued.

$40 Madhu Praatd et ai.

I E

T E

T = 2 93~

i ,

0 5 tO 15

0 5 I0 15 2Q

Fig. 12. Continued.

(b)'The temperature dependence of the critical current when seen without the effect of the trapped flux follows the law of Ambegaokar and Baratoff.

(c) The net flux trapping could be due to the inductance of the superconducting loop and the electrical or geometrical asymmetry.

ACKNOWLEDGMENT

The authors wish to thank Dr. A. R. Verma, Director, National Physical Laboratory, New Delhi, for encouragement and for permission to publish this work.


I000 T - 3.87"k

800 �9 �9149 . .o �9

600

200

a

I I I J -

0 S 10 15 20

~ ( I o - - [ i ) m A

Fig. 13. A plot of ~ (V1 - V2) against ~' ( l ] - 12) for data at the highest temperatures. Similar curves are obtained for data taken at lower temperatures. (a) SLUG I; (b) SLUG II.

>-

I

~ - 4 0 0

542 Madhu Prasad et ai.

> E

>~ I

>-

2 4

12

T 14 "k

�9 b

IO 20 30 40 50

= E { I , - 12)mA :-

Fig. 13. Continued.

R E F E R E N C E S

1. R.C. Jaklevic, J. Lambe, J. E. Mercereau, and A. H. Silver, Phys. Rev. 140A, 1628 (1965); J. Lambe, A. H. Silver, J. E. Mercereau, and R. C. Jaklevic, Phys. Left. 11, 16 (1964).

2. J. Clarke, Phil. Mag. 13, 115 (1966). 3. A. Th. A. M. de Waele and R. de Bruyn Ouboter, Physica 41, 225 (1969). 4. T. A. Fulton, L. N. Dunkleberger, and R. C. Dynes, Phys. Rev. B 6, 855 (1972). 5. O. Jaoul, Reo. Phys. Appl. 5, 885 (1970). 6. T. A. Fulton and J. Clarke, J. Appl. Phys. 40, 4470 (1969). 7. M. R. Halse and K. M. Salleh, J. Phys. C 5, 1643 (1972). 8. R. de Bruyn Ouboter, M. H. Omar, A. J. P. T. Arnold, T. Guinau, and K. W. Taconis,

Physica 32, 1448 (1966); M. H. Omar, W. H. Kraan, A. Th. A. M. de Waele, and R. de Bruyn Ouboter, Physica 34, 525 (1967).

9. V. S. Tomar, N. S. Natarajan, M. Prasad, M. S. R. Chari, and H. Kishan, in Low Temperature Physics LT 14 (Proc. 14th Int. Conf. Low Temp. Phys., Otaniemi, Helsinki, Finland, 1975), Vol. 4, p. 202.

10. V. S. Tomar, M. Prasad, N. S. Natarajan, H. Kishan, and M. S. R. Chari, Nucl. Phys. Solid State Phys. (India) 18C (1975).

11. T. A. Fulton and L, N. Dunkleberger, 3". Appl. Phys. 45, 2283 (1974).


12. V. Ambegaokar and A. Baratolt, Phys. Rev. Lett. 10, 486 (1963); Erratum 11, 104 (1963). 13. M. R. Halse and K. M. Salleh, J. Low Temp. Phys. 11,201 (1973). 14. Madhu Prasad, Ph.D. thesis, Delhi University (1977).

Documents

Hysteresis studies in Clarke solder-blob junctions