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Fluxon propagation in long overlap Josephson junctions
Physica 108B (1981) 1301-1302 North-Holland Publishing Company
TD 5
FLUXON PROPAGATION IN LONG OVERLAP JOSEPHSON JUNCTIONS* S.N. Ern~, A. Ferrigno**, T.F. Finnegan
Physikalisch-Technische Bundesanstalt, Institut Berlin, AbbestraBe 2-12, D-IO00 Berlin 10, West Germany R. Vagl io I s t i t u t o di Fisica, UniversitA di Salerno, 1 84100 Salerno, I t a l y We report here the f i r s t preliminary results of an experimental and t h e o r e t i c a l study of long Josephson junction behaviour to assess the a p p l i c a b i l i t y of the recently developed fluxon propagation formalism to a real experimental s i t u a t i o n . The frequency dependence of the microwave r a d i a t i o n emitted by long, overlap junctions (including changes induced by e x t e r n a l l y - a p p l i e d magnetic f i e l d s ) has been measured and is found to be in good agreement with the numerically calculated response of the junction. I.
INTRODUCTION
A long Josephson tunnel junction (long with respect to the Josephson penetration depth~kj) I can support the resonant propagation of fluxons. This mode of propagation leads to z e r o - f i e l d steps, or dc-current s i n g u l a r i t i e s , in the s t a t i c current-voltage c h a r a c t e r i s t i c 2 and is accompanied by the emission of microwave r a d i a t i o n at the junction edges3, 4 . The frequency of this emitted r a d i a t i o n may be tuned via an external magnetic f i e l d and hence may be useful in applications of these superconducting devices as microwave o s c i l l a t o r s 5. In this paper, we preseDt the preliminary results of an e x p e r i me n t a l -th e o r e ti c a l i n v e s t i g a t i o n of long overlap tunnel junctions to assess the q u a n t i t a t i v e l i m i t s w i t h i n which the fluxon mathematical formalism° can be used to predict the response of a real physical system. 2.
The c a l c u l a t i o n parameters were chosen to correspond to one of the junctions we have measured. The model junction chosen therefore had a length 1 = 1 3 . 3 ~ j an e f f e c t i v e energy gap parameterA = 1.3 mV, and McCumber parameter Bc = 165"/I" . This large value of Bc required s i g n i f i c a n t refinement in the numerical calculation methods to assure that the required computation time was manageable. The surface impedance losses were approximated via a resistance in p a r a l l e l to the junction s t r i p l i n e inductance corresponding to a c i r c u i t Q of about 50. The voltage of the z e r o - f i e l d steps could 9.0
9.2
,
, /....
94v(GHz)96
,
/ Ro
** Guest s c i e n t i s t supported by the "Deutscher Akademischer Austauschdienst".
0378-4363/81/0000-0000/$02.50
i
(theory) =0.12m~
t~
~3C
,? •t
* Work supported in part by a grant from the Federal Department of Commerce (Germany) and by the "Progetto F i n a l i z z a t o S u p e r c o n d u t t i v i t a " .
© North-HollandPublishingCompany
~e •
o.,5
THEORETICALMODELING
Theoretical analyses of the long overlap Josephson junction have been recently reported4, 6, and we f o l l o w here closely the mathematical f o r malism previously described including the d e f i n i t i o n s of a l l relevant parameters. In the present numerical computations, surface impedance losses and a nonlinear q u a s i p a r t i c l e resistance have been included as improvements to the e a r l i e r calculations.
1~0
~8
; i Rolmeas)=O.l'mg
O~E
j
No = 1 RN= 0,05 ~
0 37'
;8
39' VlpV) LO
~I
'2
Figure I: Experimental (open c i r c l e s ) and computed ( s o l i d c i r c l e s ) voltage/frequency dependence ( 0 = eV/h) of the f i r s t z e r o - f i e l d step of a Nb-Nb oxide-Pb tunnel junction with a measured I o = 21.8 mA at T =4.2 K. (The open t r i a n g l e indicates the maximum measured current f o r this step.) The arrows indicate the bias points at which the indicated dynamic resistances have been determinded.
1301
1302
be computed (within about 0.1%) both as a function of bias current I and applied magnetic f i e l d H. which in our model is formally proport i o n a l ~o the current I F through one of the e l E trodes. 3.
EXPERIMENTALCONSIDERATIONS
Both the dc c h a r a c t e r i s t i c and coherent microwave r a d i a t i o n emitted by Nb-Nb oxide-Pb tunnel junctions with current densities of about 100 A/cm2 were measured. The detailed method of junction f a b r i c a t i o n has been described elsewhere/ . One end of the overlap junction was weakly-coupled to a 50.FLmicrostrip l i n e (formed on the junction substrate), which in turn was coupled to a conventional X-band superheterodyne receiver. With this geometry, the coherent power observed was between 10-15 and 10-13 W. Experimental results are presented fo r ajurrction having an area 0.48 mm x 0.07 mm and a normal state resistance R = O . 0 5 /L . In t h e o r e t i • .N c a l l y modellng thls j u n c t i o n , the e l e c t r o magnetic c i r c u i t parameters reported in Ref. 7 were use to determine the j u n c t i o n ' s inductance and capacitance. 4.
RESULTSAND CONCLUSIONS
For this p a r t i c u l a r j un c ti o n , both the experimentally-measured and corresponding t h e o r e t i c a l l y computed lowest order z e r o - f i e l d steps (No = I) are shown in Fig. I. The shape (slope) and maximum current amplitude of the steps are in very good agreement; however, t h e i r voltage amplitudes d i f f e r by about 9 %. The l a t t e r difference may be a t t r i b u t e d to uncertainties in the junction inductance, capacitance, and other parameters such as ~ j and Bc. ( I t should be emphasized that in e f f e c t no adjustable parameters have been used in the t h e o r e t i c a l calculations reported here. With a multi-parameter optimization for a p a r t i c u l a r junction within the l i m i t s of the known junction parameters, the agreement between theory and experiment can be improved, but then !
i
1
I
0.~5
the r e s u l t obtained would not be a p a r t i c u l a r l y c r i t i c a l test of the a p r i o r i theory.) In Fig. 2, the calculated and measured magneticf i e l d tuning of the microwave frequency for the respective points indicated by the arrows in Fig. I are shown. Within the computational u n c e r t a i n t i e s , the theory and experiment are in good overall agreement both q u a l i t a t i v e l y and q u a n t i t a t i v e l y . The maximum computed frequency increase is greater than that observed, but may be due at least in part to noise in the real junction which has not been included in the calculations. Work is in progress to extend and f ur t her r e f i n e these preliminary results which have important p o t e n t ia l applications to a whole class of low temperature physical systems that can be understood and analyzed w i t h i n the framework of elementary e x c i t a t i o n s known as solitons 8. 5.
[ii
Fulton, T.A. and Dynes, R.C.: Single Vortex Propagation in Josephson Tunnel junctions. Solid State Comm. 12 (1973) 51-81.
i2]
Chen, J.T., Finnegan, T.F. and Langenberg, D.N.: Anomalous dc Current S i n g u l a r i t i e s in Josephson Tunnel Junctions. Physica 55 (1971) 413 - 420.
L3J
Parmentier, R.D.: Fluxons in Long Josephson Junctions, in Lonngren, K. and Scott, A. (eds.), Solitons in Action (Academic Press, New York, 1978), 173 - 199 .
[4]
Ern~, S.N. and Parmentier, R.D.: Microwave o s c i l l a t o r s based on the resonant propagation of fluxons in long Josephson junctions. J. Appl. Phys. 51 (1980) 5025 - 5029.
[5]
Finnegan, T.F., Toots, J . , and Wilson, J.: Frequency-Pulling and Coherent-Locking in Thin-Film Josephson O s c i l l a t o r s , in Krusius, M. and Vuorio, M. (eds.) Low Temperature Physics - LT 14 (North Holland, Amsterdam, 1975) 184 - 187.
[6]
ErnG, S.N. and Parmentier, R.D.: Microwave Radiation From Long Josephson Junctions. IEEE Trans. Magn. MAG-IZ (1981) 804 - 806.
[7]
Lacquaniti, V., Marullo, G., and Vaglio,R.: A.C. Properties of Nb-Nbx 0v- Pb Josephson Tunnel Junctions f o r 2e/h ~easurements. IEEE Trans. Magn. MAG-15 (1979) 593 - 594.
[81
Maki, K.: Solitons in Low Temperature Physics. J. de Physique 39 (1978) C6 - 1450 - C 6 - 1455.
I
(bl
LIJ
0.30 K.U
0
uZ
0.15
S
o
0
0 0 0
REFERENCES
0
¢Y
0
1.5 3.0 Iv/Io
I
I
I
0
1.5
3.0
_ _
H.
Figure 2: Magnetic-field-dependent frequency tuning of the No = I step shown in preceding f igu re: (a) computed via d i g i t a l simulation and (b) experimentally measured via emitted microwave r a d i a t i o n .
TD 5
FLUXON PROPAGATION IN LONG OVERLAP JOSEPHSON JUNCTIONS* S.N. Ern~, A. Ferrigno**, T.F. Finnegan
Physikalisch-Technische Bundesanstalt, Institut Berlin, AbbestraBe 2-12, D-IO00 Berlin 10, West Germany R. Vagl io I s t i t u t o di Fisica, UniversitA di Salerno, 1 84100 Salerno, I t a l y We report here the f i r s t preliminary results of an experimental and t h e o r e t i c a l study of long Josephson junction behaviour to assess the a p p l i c a b i l i t y of the recently developed fluxon propagation formalism to a real experimental s i t u a t i o n . The frequency dependence of the microwave r a d i a t i o n emitted by long, overlap junctions (including changes induced by e x t e r n a l l y - a p p l i e d magnetic f i e l d s ) has been measured and is found to be in good agreement with the numerically calculated response of the junction. I.
INTRODUCTION
A long Josephson tunnel junction (long with respect to the Josephson penetration depth~kj) I can support the resonant propagation of fluxons. This mode of propagation leads to z e r o - f i e l d steps, or dc-current s i n g u l a r i t i e s , in the s t a t i c current-voltage c h a r a c t e r i s t i c 2 and is accompanied by the emission of microwave r a d i a t i o n at the junction edges3, 4 . The frequency of this emitted r a d i a t i o n may be tuned via an external magnetic f i e l d and hence may be useful in applications of these superconducting devices as microwave o s c i l l a t o r s 5. In this paper, we preseDt the preliminary results of an e x p e r i me n t a l -th e o r e ti c a l i n v e s t i g a t i o n of long overlap tunnel junctions to assess the q u a n t i t a t i v e l i m i t s w i t h i n which the fluxon mathematical formalism° can be used to predict the response of a real physical system. 2.
The c a l c u l a t i o n parameters were chosen to correspond to one of the junctions we have measured. The model junction chosen therefore had a length 1 = 1 3 . 3 ~ j an e f f e c t i v e energy gap parameterA = 1.3 mV, and McCumber parameter Bc = 165"/I" . This large value of Bc required s i g n i f i c a n t refinement in the numerical calculation methods to assure that the required computation time was manageable. The surface impedance losses were approximated via a resistance in p a r a l l e l to the junction s t r i p l i n e inductance corresponding to a c i r c u i t Q of about 50. The voltage of the z e r o - f i e l d steps could 9.0
9.2
,
, /....
94v(GHz)96
,
/ Ro
** Guest s c i e n t i s t supported by the "Deutscher Akademischer Austauschdienst".
0378-4363/81/0000-0000/$02.50
i
(theory) =0.12m~
t~
~3C
,? •t
* Work supported in part by a grant from the Federal Department of Commerce (Germany) and by the "Progetto F i n a l i z z a t o S u p e r c o n d u t t i v i t a " .
© North-HollandPublishingCompany
~e •
o.,5
THEORETICALMODELING
Theoretical analyses of the long overlap Josephson junction have been recently reported4, 6, and we f o l l o w here closely the mathematical f o r malism previously described including the d e f i n i t i o n s of a l l relevant parameters. In the present numerical computations, surface impedance losses and a nonlinear q u a s i p a r t i c l e resistance have been included as improvements to the e a r l i e r calculations.
1~0
~8
; i Rolmeas)=O.l'mg
O~E
j
No = 1 RN= 0,05 ~
0 37'
;8
39' VlpV) LO
~I
'2
Figure I: Experimental (open c i r c l e s ) and computed ( s o l i d c i r c l e s ) voltage/frequency dependence ( 0 = eV/h) of the f i r s t z e r o - f i e l d step of a Nb-Nb oxide-Pb tunnel junction with a measured I o = 21.8 mA at T =4.2 K. (The open t r i a n g l e indicates the maximum measured current f o r this step.) The arrows indicate the bias points at which the indicated dynamic resistances have been determinded.
1301
1302
be computed (within about 0.1%) both as a function of bias current I and applied magnetic f i e l d H. which in our model is formally proport i o n a l ~o the current I F through one of the e l E trodes. 3.
EXPERIMENTALCONSIDERATIONS
Both the dc c h a r a c t e r i s t i c and coherent microwave r a d i a t i o n emitted by Nb-Nb oxide-Pb tunnel junctions with current densities of about 100 A/cm2 were measured. The detailed method of junction f a b r i c a t i o n has been described elsewhere/ . One end of the overlap junction was weakly-coupled to a 50.FLmicrostrip l i n e (formed on the junction substrate), which in turn was coupled to a conventional X-band superheterodyne receiver. With this geometry, the coherent power observed was between 10-15 and 10-13 W. Experimental results are presented fo r ajurrction having an area 0.48 mm x 0.07 mm and a normal state resistance R = O . 0 5 /L . In t h e o r e t i • .N c a l l y modellng thls j u n c t i o n , the e l e c t r o magnetic c i r c u i t parameters reported in Ref. 7 were use to determine the j u n c t i o n ' s inductance and capacitance. 4.
RESULTSAND CONCLUSIONS
For this p a r t i c u l a r j un c ti o n , both the experimentally-measured and corresponding t h e o r e t i c a l l y computed lowest order z e r o - f i e l d steps (No = I) are shown in Fig. I. The shape (slope) and maximum current amplitude of the steps are in very good agreement; however, t h e i r voltage amplitudes d i f f e r by about 9 %. The l a t t e r difference may be a t t r i b u t e d to uncertainties in the junction inductance, capacitance, and other parameters such as ~ j and Bc. ( I t should be emphasized that in e f f e c t no adjustable parameters have been used in the t h e o r e t i c a l calculations reported here. With a multi-parameter optimization for a p a r t i c u l a r junction within the l i m i t s of the known junction parameters, the agreement between theory and experiment can be improved, but then !
i
1
I
0.~5
the r e s u l t obtained would not be a p a r t i c u l a r l y c r i t i c a l test of the a p r i o r i theory.) In Fig. 2, the calculated and measured magneticf i e l d tuning of the microwave frequency for the respective points indicated by the arrows in Fig. I are shown. Within the computational u n c e r t a i n t i e s , the theory and experiment are in good overall agreement both q u a l i t a t i v e l y and q u a n t i t a t i v e l y . The maximum computed frequency increase is greater than that observed, but may be due at least in part to noise in the real junction which has not been included in the calculations. Work is in progress to extend and f ur t her r e f i n e these preliminary results which have important p o t e n t ia l applications to a whole class of low temperature physical systems that can be understood and analyzed w i t h i n the framework of elementary e x c i t a t i o n s known as solitons 8. 5.
[ii
Fulton, T.A. and Dynes, R.C.: Single Vortex Propagation in Josephson Tunnel junctions. Solid State Comm. 12 (1973) 51-81.
i2]
Chen, J.T., Finnegan, T.F. and Langenberg, D.N.: Anomalous dc Current S i n g u l a r i t i e s in Josephson Tunnel Junctions. Physica 55 (1971) 413 - 420.
L3J
Parmentier, R.D.: Fluxons in Long Josephson Junctions, in Lonngren, K. and Scott, A. (eds.), Solitons in Action (Academic Press, New York, 1978), 173 - 199 .
[4]
Ern~, S.N. and Parmentier, R.D.: Microwave o s c i l l a t o r s based on the resonant propagation of fluxons in long Josephson junctions. J. Appl. Phys. 51 (1980) 5025 - 5029.
[5]
Finnegan, T.F., Toots, J . , and Wilson, J.: Frequency-Pulling and Coherent-Locking in Thin-Film Josephson O s c i l l a t o r s , in Krusius, M. and Vuorio, M. (eds.) Low Temperature Physics - LT 14 (North Holland, Amsterdam, 1975) 184 - 187.
[6]
ErnG, S.N. and Parmentier, R.D.: Microwave Radiation From Long Josephson Junctions. IEEE Trans. Magn. MAG-IZ (1981) 804 - 806.
[7]
Lacquaniti, V., Marullo, G., and Vaglio,R.: A.C. Properties of Nb-Nbx 0v- Pb Josephson Tunnel Junctions f o r 2e/h ~easurements. IEEE Trans. Magn. MAG-15 (1979) 593 - 594.
[81
Maki, K.: Solitons in Low Temperature Physics. J. de Physique 39 (1978) C6 - 1450 - C 6 - 1455.
I
(bl
LIJ
0.30 K.U
0
uZ
0.15
S
o
0
0 0 0
REFERENCES
0
¢Y
0
1.5 3.0 Iv/Io
I
I
I
0
1.5
3.0
_ _
H.
Figure 2: Magnetic-field-dependent frequency tuning of the No = I step shown in preceding f igu re: (a) computed via d i g i t a l simulation and (b) experimentally measured via emitted microwave r a d i a t i o n .