Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://www.cplire.ru/html/lab234/pubs/2007_18.pdf Äàòà èçìåíåíèÿ: Fri Jan 25 15:10:02 2008 Äàòà èíäåêñèðîâàíèÿ: Tue Oct 2 08:24:04 2012 Êîäèðîâêà: Ïîèñêîâûå ñëîâà: m 5

JOURNAL OF APPLIED PHYSICS 102, 093911 2007

Planar Josephson tunnel junctions in a transverse magnetic field
R. Monacoa
Istituto di Cibernetica del C.N.R., 80078, Pozzuoli, Italy and Unita' INFM-Dipartimento di Fisica, Universita' di Salerno, 84081 Baronissi, Italy

M. Aaroeb and J. Mygind
Department of Physics, B309, Technical University of Denmark, DK-2800 Lyngby, Denmark

V. P. Kosheletsc
Institute of Radio Engineering and Electronics, Russian Academy of Science, Mokhovaya 11, Bldg 7, 125009, Moscow, Russia

Received 27 August 2007; accepted 26 September 2007; published online 13 November 2007 Traditionally, since the discovery of the Josephson effect in 1962, the magnetic diffraction pattern of planar Josephson tunnel junctions has been recorded with the field applied in the plane of the junction. Here we discuss the static junction properties in a transverse magnetic field where demagnetization effects imposed by the tunnel barrier and electrodes geometry are important. Measurements of the junction critical current versus magnetic field in planar Nb-based high-quality junctions with different geometry, size, and critical current density show that it is advantageous to use a transverse magnetic field rather than an in-plane field. The conditions under which this occurs are discussed. © 2007 American Institute of Physics. DOI: 10.1063/1.2809310
I. INTRODUCTION

It is well known that a magnetic field H modulates the critical current Ic of a Josephson tunnel junction JTJ .1 Indeed the occurrence of such diffraction phenomena Ic H is one of the most striking behaviors of JTJs.2 In the case of a planar JTJ, it was Josephson himself3 who pointed out that the gradient of the Josephson phase , which is the difference between the complex wave function phases in the electrodes, can be expressed as = 2d
e 0 0

H

n,

1

where n is a unit vector normal to the insulating barrier separating the two superconducting electrodes, 0 is the vacuum permeability, and 0 = h /2e is the magnetic flux quantum. If the two superconducting films have thicknesses d1,2, London penetration depths L1,2, and t j is the barrier thickness, then the effective magnetic penetration de is given by4 de = t j +
L1

important to point out that nearly all work was done with the external magnetic field applied in the barrier plane. In fact, since Eq. 1 states that is insensitive to transverse fields, this is the most obvious choice of the magnetic field orientation. For the earlier reasons, a magnetic field parallel to the barrier of planar JTJs is applied in the practical applications of the Josephson magnetic diffraction phenomena such as, for example, the suppression of the direct current Josephson effect in superconductor­insulator­superconductor mixers for photon detection6 and in specially shaped JTJs for particle detection,7 the magnetic biasing of a flux flow oscillator,8 and the tuning of resonant fluxon oscillators.9
II. TRANSVERSE MAGNETIC FIELD

tanh

d 2

1 L1

+

L2

tanh

d 2

2 L2

,

which, in the case of thick superconducting films di Li , + L2. reduces to de L1 Since Rowell5 in 1963 made the first experimental verification of Eq. 1 , a large number of theoretical and experimental papers have been devoted to the study of magnetic diffraction patterns, in various Josephson junctions. Nowadays the Ic H curves for planar JTJs having the most common geometrical and electrical parameters are fully understood see, for example, Chaps.4 and 5 of Ref. 1 . It is
a b c

Electronic mail: roberto@sa.infn.it Electronic mail: aaroe@fysik.dtu.dk Electronic mail: valery@hitech.cplire.ru

In 1975 Rosenstein and Chen10 first reported on the effect of a transverse magnetic field on the critical current of a JTJ with overlap geometry. Among other things, they showed that the value of the junction critical field Hc at which the magnetic diffraction pattern first goes to zero, changes with the inclination of the field with respect to the barrier plane, the minimum being obtained when the field is transverse. This was the first experimental observation that transverse fields could be more efficient that parallel ones in modulating the Josephson current. Soon after, Hebard and Fulton11 correctly interpreted the findings of Ref. 10 in terms of stationary screening currents which develop when a superconductor is subjected to an external magnetic field. To better understand the mechanism through which also a transverse field is able to modulate the critical current of a planar JTJ, let us consider first a single isolated superconducting film immersed in a uniform static magnetic field H perpendicular to its surface. This system has received a continuous interest over the years and here we only recall the main features. For a deep treatment of this topic we remand to Ref. 12, and
© 2007 American Institute of Physics

0021-8979/2007/102 9 /093911/4/$23.00

102, 093911-1

Downloaded 15 Nov 2007 to 129.125.20.91. Redistribution subject to AIP license or copyright, see http://jap.aip.org/jap/copyright.jsp


093911-2

Monaco et al.

J. Appl. Phys. 102, 093911 2007

references therein. We assume that the film thickness d is larger than its London penetration depth L and that the field everywhere is much smaller than the critical field which would force the film into the intermediate or normal state, i.e., that the film is in the flux-free Meissner regime. At the top and bottom film surfaces, the flux lines are excluded from the interior of the film where H = 0. In fact, due to the screening currents Js = H , they bend as they approach the film surface, flow along the film surfaces, concentrate at the film edges, and bent backward. Due to continuity, Hn, the component of H normal to the surface, may be taken to be zero, while its tangential component Ht decays exponentially inside the film on the scale of L. The knowledge of the distribution of the magnetic field lines around the film requires a self-consistent solution of a magnetostatic problem combining the London equation H 2 + L 2H =0 in the superconducting film and the fourth Maxwell equation H =0 in the empty space around the film with boundary conditions appropriate to the film surface geometry. This problem can be solved analytically only for simple axially symmetric cases such as, for example, that of an ellipsoid of revolution with the axis of revolution parallel to the applied field H .13 If the film width w is much less than its length, but much greater than its thickness d, then we can approximate the film as a elliptical oblate cylinder of infinite length whose cross section has axes w and d; with the applied magnetic field H directed along the minor axis, then Ht, the component of H tangent to the surface, only depends on the angle with respect to the minor axis: Ht / H =1/ cos2 + d / w 2 sin2 , whose maximum value w / d 1 occurs at the cylinder edges =± /2 .14 If the film width w is comparable to its length, the film can be approximated by a disk whose diameter w is much greater than its thickness d, with the external field applied parallel to its axis. In this case, for symmetry reasons, on the disk top and bottom surfaces the magnetic field lines are radial and Ht only depends on the distance r from the disk center; it is null at the center of the disk and increases as we move outward.15 The surface or sheet current density js, defined as the screening current density Js integrated over the specimen thickness, equals in magnitude Ht and is everywhere orthogonal to H. Numerical simulations carried out for a Nb disk having L = 90 nm show that the shape of Ht r only depends on the disk aspect ratio w / d, as far as d L. We found that at the disk border Ht is several times larger than the applied field H , as shown in Fig. 1 for three values of the disk aspect ratio w / d = 10, 100, and 1000, with d =1 m. Both film approximations lead one to conclude that a thin superconducting film of any geometry in a transverse field produce a magnetic field: i whose orientation on the film end surfaces is parallel to surfaces themselves; ii whose direction near the borders of the film end surfaces is perpendicular to the borders themselves; and iii whose strength is proportional to the transverse applied field intensity and exceeds its value near the borders of a film with a large aspect ratio w / d. Now, we can consider the situation in which two superconducting films partially overlap to form a planar JTJ. If the tunnel barrier is very transparent, then the screening currents

FIG. 1. Computed normalized magnetic induction field Ht / H at the border of a Nb superconducting disk in a perpendicular field H . The disk thickness is d =1 m and diameters w = 10, 100, and 1000 m. 2r / w is the normalized disk radius.

cross the barrier and the two films act as one single fused film. In the opposite case the screening currents in the two films are independent on each other and no cross talk is allowed. In the intermediate situations, a fraction of the screening currents in one film crosses the barrier and circulates in the other film and vice versa. It is clear that, for a given transverse field and a given junction and electrodes geometry, the transition from the fused to the independent films regime can be controlled via the barrier transparency, i.e., in our case by the Josephson current density Jc. The determination of the magnetic field distribution in a system made by two superconducting film forming a planar JTJ is a very complex task, since it also involves the Josephson equations. The analysis becomes even more difficult when the JTJ is biased the distribution of the bias current peaks near the film edges and the junction dimensions exceed the Josephson penetration depth J = /2e 0deJc. However, following Ref. 14, we can argue that in the independent films regime, the intensity of the in-plane magnetic field felt by a planar JTJ placed at the borders of two superconducting films can exceed by several times the value of the applied transverse field. In fact, the screening currents flowing within a depth L,b in the top surface of the bottom film and those flowing within a depth L,t in the bottom surface of the top film have opposite directions. Consequently, the associated magnetic fields add in the barrier plane and a more efficient modulation of the JTJ critical current is achieved.

III. EXPERIMENTS

In order to prove the advantages to use a transverse field rather than an in-plane one, we have measured the transverse magnetic diffraction patterns Ic H of planar high quality JTJs having different geometries, sizes, and critical current densities. The samples were placed on the axis of a superconducting coil surrounded by a Pb shield and a cryoperm can in order to attenuate the earth magnetic field. The magnetic field produced by the coil was calculated through COMSOL MultiPhysics numerical simulations.

Downloaded 15 Nov 2007 to 129.125.20.91. Redistribution subject to AIP license or copyright, see http://jap.aip.org/jap/copyright.jsp


093911-3

Monaco et al.

J. Appl. Phys. 102, 093911 2007 TABLE I. Relevant parameters for two overlap-type Josephson tunnel junctions whose transverse magnetic diffraction patterns are shown in Fig. 2. Sample Jc A/cm2 60 410 de nm 180 240 L/
J

Hc A/m 3.2 13

F Hc = Hc + H A/m

FP c

Nb / Alox / Nb Nb / AlN / NbN

10 25

36 + 58 = 94 36 + 131 = 167

one-dimensional junction in presence of an in-plane external field applied perpendicular to the long junction dimension L can be expressed as the sum of two terms
FIG. 2. Magnetic diffraction patterns measured in a transverse field H two overlap-type junctions L W =500 4 m2. The closed circles refer a Nb / Alox / Nb JTJ having Jc =60 A/cm2, de = 180 nm, and J 50 The open circles refer to a Nb / AlN / NbN with Jc =400 A/cm2, = 240 nm, and J 20 m. The dotted lines show the procedure used determine the junction critical field Hc . of to m. de to

Hc = HF + HFP = c c =
0 0d e

0 0d e

L =

+2 JJ
0 0d e

c

1 1 + L

J

L

+

2

0J c 0d e

.

2

A. Overlap-type junctions

Figure 2 compares the diffraction patterns measured in a transverse field of two overlap-type junctions having the same geometry and dimensions, but different critical current density Jc. The junctions have been fabricated with the trilayer technique in which the junction is realized in the window opened in a SiO2 insulating layer. The thicknesses of the base, top, and wiring layer are 200, 100, and 400 nm, respectively. Details of the fabrication process can be found in Ref. 16. The junction length is L = 500 m, while the width is equal to 4 m. The base and top electrode widths are 540 and 506 m, respectively. The so called "idle region," i.e., the overlapping of the wiring layer onto the base electrode is about 3 m all around the barrier. In Fig. 2 the junction critical currents have been normalized to their maximum values in order to make the comparison easier. The closed circles refer to a Nb / Alox / Nb-Nb tunnel junction having a critical current density Jc =60 A/cm2, while the open circles refer to a Nb / AlN / NbN-Nb sample with Jc =400 A/cm2. As expected, considering that the field lines associated to the screening current are perpendicular to the electrodes edges, the shape of these Ic versus H curves looks very like that of the expected for long one-dimensional overlap-type junctions when a uniform external field H is applied in the barrier plane in the direction perpendicular to the junction length. In fact, according to the analysis of Refs. 17 and 18, for small field values Meissner regime the critical current Ic decreases linearly with the applied field Ic H = Ic 0 1- H / Hc , where Hc is the critical field at which Ic would vanish if flux quanta did not start to enter the junction barrier. The skewness seen in the experimental Ic-H curves being larger for the sample having the larger Jc is due to the self-field produced by the bias current I flowing in a close-by superconducting strip in the chip circuitry. The skewness does not prevent us from measuring the junction critical fields Hc determined by linearly extrapolating the branches starting at maximum critical current to I =0 dotted lines in Fig. 1 ; in fact, when I = 0, the bias current self-field effects vanish. The critical field Hc for a long

The first term HF in Eq. 2 dominates in low Jc samples for c which L j and corresponds to the critical field of a pointlike junction which exhibits the well known Fraunhofer diffraction pattern. The second term HFP Jc / de becomes c dominant in the high Jc regime when L j. It was first introduced by Ferrell and Prange19 in order to describe the self-field limiting effects in long inline-type junctions. Table I reports the values of Jc and de used to predict the critical field Hc from to Eq. 2 . The last two columns allow the comparison between Hc and Hc. We observe that for both samples Hc Hc and the ratio Hc / Hc changes from about 30 to about 13 when we move from the low to the high Jc junction. The data in Table I unambiguously indicate that a transverse field can be more effective than an in-plane one and, remembering that the two samples have the same geometrical details, the effect of a transverse field weakens as the junction transparency increases.
B. Annular junctions

Further, we have measured the static properties of several Nb / Alox / Nb-Nb annular JTJs having the same critical current density Jc =60 A/cm2 J =50 m , the same width R =4 m, but different radius R ranging from 80 to 500 m. The fabrication details are the same as those for the overlap-type JTJs discussed previously. The diffraction patterns in transverse magnetic field will be reported elsewhere20; here we focus our interest on the values of the critical fields. The analogous of Eq. 2 for a one-dimensional annular junction having radius R in an in-plane field is21 Hc = HB + H c
MM c

= 2.404

0

2

0d e

R

+ RJc .

3

Again we have a contribution HB, independent on the c Josephson current density Jc, typical of small and intermediate radius annular JTJs immersed in a uniform in-plane magnetic field which results in a periodic radial field Hr cos felt by the junction.22,23 In such case, the Ic versus H curve follows a Bessel, rather than a Fraunhofer, behavior 2.404 is the argument corresponding to the first minimum of the zero-order Bessel function . The second term HMM = RJc c

Downloaded 15 Nov 2007 to 129.125.20.91. Redistribution subject to AIP license or copyright, see http://jap.aip.org/jap/copyright.jsp


093911-4

Monaco et al.

J. Appl. Phys. 102, 093911 2007

TABLE II. Relevant parameters of the Nb / Alox / Nb annular Josephson tunnel junctions used in the experiments. R mm 0.08 0.25 0.32 0.50 R/
J

Hc A/m 2.7 1.5 1.3 1.2

B Hc = Hc + H A/m

MM c

1.6 5 6.4 10

18 6+ 4+ 3+

+ 48 = 66 150 = 156 192 = 196 300 = 303

cated close to the borders of superconducting films with a large aspect ratio. This is due to screening or Meissner currents induced by the transverse field that circulate mainly on the film surface borders which in turn behave as intrinsic control lines. We suggest that a transverse magnetic field can be usefully exploited in those applications where the Josephson critical current and the Fiske resonances need to be suppressed.
A. Barone and G. PaternÐ, Physics and Applications of the Josephson Effect Wiley, New York, 1982 . 2 P. W. Anderson and J. M. Rowell, Phys. Rev. Lett. 10, 2130 1963 . 3 B. D. Josephson, Adv. Phys. 14, 419 1965 . 4 M. Weihnacht, Phys. Status Solidi 32, K169 1969 . 5 J. M. Rowell, Phys. Rev. Lett. 11, 200 1963 . 6 V. P. Koshelets, S. V. Shitov, L. V. Filippenko, A. M. Baryshev, H. Golstein, T. de Graauw, W. Luinge, H. Schaeffer, and H. van de Stadt, Appl. Phys. Lett. 68, 1273 1996 . 7 E. P. Houwman, J. G. Gijsbertsen, J. Flokstra, and H. Rogalla, Physica C 183, 339 1991 . 8 T. Nagatsuma, K. Enpuku, F. Irie, and K. Yoshida, J. Appl. Phys. 54, 3302 1983 . 9 N. Martucciello, J. Mygind, V. P. Koshelets, A. V. Shchukin, L. V. Filippenko, and R. Monaco, Phys. Rev. B 57, 5444 1998 . 10 I. Rosenstein and J. T. Chen, Phys. Rev. Lett. 35, 303 1975 . 11 A. F. Hebard and T. A. Fulton, Phys. Rev. Lett. 35, 1310 1975 . 12 E. H. Brandt and J. R. Clem, Phys. Rev. B 69, 184509 2004 . 13 A. C. Rose-Innes and E. H. Rhoderick, Introduction to Superconductivity Pergamon, Oxford, 1969 , Par. 8.7. 14 S. L. Miller, K. R. Biagi, J. R. Clem, and D. K. Finnemore, Phys. Rev. 31, 2684 1985 . 15 M. Kobayashi and Y. Sugiyama, IEEE Trans. Magn. 26, 297 1990 . 16 P. N. Dmitriev, I. L. Lapitskaya, L. V. Filippenko, A. B. Ermakov, S. V. Shitov, G. V. Prokopenko, S. A. Kovtonyuk, and V. P. Koshelets, IEEE Trans. Appl. Supercond. 13, 107 2003 . 17 C. S. Owen and D. J. Scalapino, Phys. Rev. 164, 538 1967 . 18 A. Barone, W. J. Johnson, and R. Vaglio, J. Appl. Phys. 46, 3628 1975 . 19 R. A. Ferrell and R. E. Prange, Phys. Rev. Lett. 10, 479 1963 . 20 R. Monaco, J. Mygind, M. Aaroe, and V. P. Koshelets, "Annular Josephson tunnel junctions in a transverse magnetic field," unpublished . 21 N. Martucciello and R. Monaco, Phys. Rev. B 54, 9050 1996 . 22 N. GrÜnbech-Jensen, P. S. Lomdahl, and M. R. Samuelsen, Phys. Lett. A 154, 14 1991 . 23 N. Martucciello and R. Monaco, Phys. Rev. B 53, 3471 1996 . 24 A. Davidson, B. Dueholm, B. Kryger, and N. F. Pedersen, Phys. Rev. Lett. 55, 2059 1985 .
1

in Eq. 3 was numerically found by Martucciello and Monaco;21 considering that HMM / HB = R / J 2 / 2.404, it bec c comes dominant when R Rm = 2.404 J.9,23 For the given de and Jc, Eq. 3 has a minimum when R = Rm and linearly increase with R when R Rm. The last two columns of the Table II report, respectively, the transverse critical field Hc measured for four annular junctions having different radii and the expected parallel critical field Hc according to Eq. 3 with Jc =60 A/cm2 and de = 180 nm. For all samples we observe once again that Hc Hc and that the ratio Hc / Hc changes from about 25 to about 250 when we increase the ring diameter, i.e., the top and bottom film widths, confirming that the effect of a transverse field strengthens as the electrode widths increases. In particular, for the three largest rings, having the so called Lyngby geometry,24 i.e., the base and top electrode widths match the ring diameter, this ratio is proportional to R. The smallest ring R / J 1.6 has the base electrode width equal to 540 m that is considerably larger than the ring diameter 160 m.
IV. CONCLUDING REMARKS

We have measured the pattern of planar JTJs having barrier transparencies. Our that a magnetic field is more tion critical current Ic when than parallel to the junction

transverse magnetic diffraction different geometries, sizes, and measurements clearly indicate effective to modulate the juncapplied perpendicularly rather plane provided the JTJ is fabri-

Downloaded 15 Nov 2007 to 129.125.20.91. Redistribution subject to AIP license or copyright, see http://jap.aip.org/jap/copyright.jsp