An ac biased superconducting flux transformer

(' ) University of Nice Sophi Antipolis, UA CNRS 190, Prc lrose. 06108 Nice Cedex, Frnce Lbortorium voor ste Stof-Fysic en Mgnetisme, Ktholieke Universiteit Leuven, B 3001 () Belgium Heveriee, The coupled motion of the vortex lttices of two electriclly insulted, superimposed, Abstrct. thin films (primry nd secondry) in perpendiculr mgnetic field, is predicted superconducting two superconducting electrodes forming the device. The effect of n exteml electromgnetic the rdition, of frequency v, on Josephson junction is chrcterized by current steps in the v, superconducting films in perpendiculr mgnetic field. Figure I shows the superimposed, of the two superconducting films seprted by configurtion dielectric lyer D. The pplied J. Phys. III Frnc-e 4 (1994) 2281-2287 NOEMBER 1994, PAGE 2281 clssifiction Physic-s Absn.cts 74.50 74.60 74.75 An c bised superconducting flux trnsformer A. Gilbert ('), Ivn K. Schuller (2),.. Moshchlkov (3) nd Y. Bruynserede j3) () University of Cliforni Sn Diego, L Joll, CA 92093-0319, U-S-A- (Received 3 Februiy J994, ccepted 5 Ap.il J994) Rksumd. On prdvoit un comportement de type Josephson pour le mouvement coupld de deux r6seux de vortex dns deux films minces superpos6s (le primire et le secondire), isolds et plongds dns un chmp mgndtique perpendicuiire. Lorsqu'un cournt trverse dlectriquement film primire, l diffdrence entre [es tensions moyennes ux bornes du primire et du secondire le dues u mouvement des vortex en rdgime de «flux flow» ob6it h une Eqution identique h celle du modble d'un lien fible Josephson. Si un cournt lterntif est superposd u cournt continu, des mrches de type Shpiro sont prddites dns l crctdristique cournt-tension. Contrirement h l'effet Josephson clssique, l position en tension de ces mrches ddpend du chmp mgndtique ppliqud. to exhibit Josephson-like behvior. For dc pplied current flowing in the primry film, the difference between the time-verged primry nd secondry flux flow voltges obeys the voltge of resistively shunted junction model. If n c current is superimposed on the dc equtions Shpiro-type steps re predicted in the current-voltge chrcteristic. In contrst to the currenj, Josephson effect, the voltge positions of these steps cn be tuned by the pplied conventionl mgnetic field. The sensitivity to rf or microwves of conventionl Josephson coupled junction is relted to the phse coherence provided by the wek overlp of the superconducting wve function of chrcteristics, I(). The voltges,,, t which the nth step occurs, re current-voltge proportionl to the pplied frequency,,,n(h2e) v while the rtio directly 484 MHz is constnt. A different type of wek coupling cn be obtined between two electriclly isolted,

vortices of flux fio li2 e 2.07 x flux trnsformer» [1-5], there exists mgnetic- couplifig dc vortices confined to the two superconducting films. When dc current of sufficient between degree of coupling between the vortex lttices in the two superconducting films. For low bis the mgnetic coupling is strong nd both lyers show the sme dc voltges current, to the coupled motion of vortices in the two lyers (Fig. 2). For very high bis corresponding of the vortex rry in the S lyer. This regime is chrcterized by finite dc voltge motion in the P lyer nd very low voltge in the S lyer (Fig. 2c). Therefore, by tuning the generted bis current in the P lyer it is possible to induce continuous cross-over from fully dc to completely decoupled independent motion of vortices of the two lyers (Fig. 2bj. coupled in this pper, we predict tht new Josephson-like effect occurs when n dditionnl c 2282 JOURNAL DE PHYSIQUE III N 11 B I. Configurtion of the d-c- flux trnsformer P is the primry film ; D the dielectric lyer nd S Fig. secondry film. the mgnetic field, perpendiculr to the films, cretes vortex rrys in both films. Quntized 10' Tm form tringulr lttice in ech film. In this configurtion of the so clled «to unpin the vonices is pssed through one of the films (primry P), the vortex mgnitude is set in motion, inducing dc voltge long its length. If the mgnetic coupling with the lttice secondry (Sj vortex lttice is strong enough, this will be drgged long by the superimposed of the (Pi vortex lttice nd dc voltge ppers cross the (S) film. By mesuring the motion dc voltge in (S) versus the pplied dc bis current through (P), it is possible to determine the current, the fst motion of the vortex rry in the P lyer becomes independent of the slow The coupled motion of vortices implies the existence of certin phse coherence for the prmeter describing the condenste in the two lyers. This coherence is lost superconducting the motion of the vortices in the two lyers becomes decoupled (t high dc bis current). when In ll the previous studies on the dc flux trnsformer only the dc current in the P or S films hs been considered. current is superimposed t intermedite dc bis currents. We show tht this type of mgnetic leds to phse coherence nd obeys equtions nlogous to the Josephson effect. If n coupling wve is pplied, Shpiro steps pper t voltges which opens up new electromgnetic

'' i' * ' ' ) ( (l (hi (cl lp j (hi (cl (l N ii AN Ac BIASED SUPERCONDUCTING FLUX TRANSFORMER 2283,,,, - o P (l 16) Ill idc j p s P 0 j 2. Schemtics of the motion of the vortices lttices in the primry P nd in the secondry S Fig. film. ) coupled motion of vortices in the two lyers with low bis current superconducting in P. b) Wekly coupled regime. c) Decoupled motion of vortices with high bis current in P. The J current-mesured voltges re lso shown. corresponding

for rf detection devices. These voltges,, re proportionl to the pplied possibility but in contrst to the conventionl c Josephson effect, the constnt of frequency, v, (nd therefore the voltge positions,,) cn be tuned by the pplied proportionlity mgnetic field. perpendiculr flux lttices, the viscous drg force proportionl to the vortex rry speed individul nd periodic coupling force between the two rrys. The coupling force experienced by dxdt the generl cse of current flowing in the primry (lj nd in the secondry In the differentil equtions describing the coupled motion of the primry nd secondry (lj, s shown in the figure I. L nd L re respectively the width nd the length of the films. For.v the film criticl currents nd flux flow resistnces re ssumed to be the sme I-e- simplicity, l 1, l nd R R, L,,(dvdt BR (I, (l for simplicity sinusoidl coupling force [?]. This force is due to periodic ssuming of the two flux lttices in the S nd P superconducting lyers. lo is relted to the mtching field dependent penetrtion depths [5-6]. mgnetic defining phse difference By where l b L B (2 r dfildt I,j L. Bd(,r >.,)dt (4) (L2 However, the proportionlity coefficient between nd d4dt (reltion (6)) is different from tht of Josephson junction. Thus, the coupled motion of the vortex lttices is nlogous to the behviour of Josephson junction. For Josephson junction, when two superconductors re 2284 JOURNAL DE PHYSIQUE III N The models [2-4] describing the motion of the primry nd secondry vortices tke into ccount the Lorentz force due to the pplied current I in the P lyer, the pinning force for the P is equl nd opposite to tht felt by S. vortices re [4] L (durdt ) BR ilr l j lo sin [(2 ri)(,v -.r,)] (I j l + lo sin [(2 ri )(.v -,r, )] (2),R [2 fio((3)"b)]" is the spcing beetween vortices which re locted t x nd R. (nd,) re the mesured voltges cross the length The first term on the right hnd side describes the flux flow regime when current L,. (or I,) is driven in the P (or S) film. The second term describes the mgnetic coupling by l mximum mgnetic coupling force F by the reltion [4] F nd is function of fil, insultor thickness, the superconducting film thicknesses nd their temperture nd the (2 grl)(.i >.,) (3) nd voltge difference nd subtrcting (2) from (1) R +210sin 4 l-i, 1 (5) with r [2 B fio (3 )"]" dfildt (6) (5) is formlly identicl to the equtions of the Resistively Shunted Junction Model Eqution of Josephson wek link without cpcitnce [7] (RSJM) R + l sin 4 1 (7) 2 lo is the mximum Josephson current nd I the current flowing in the wek link. wekly coupled, the phses of their order prmeters re correlted. For superconducting

N ii AN Ac BIASED SUPERCONDUCTING FLUX TRANSFORMER 2285 the motion of the vortices of the two films re correlted. Since the phse trnsformer, corresponds to tht of Josephson junction nd the reltion (2rl)(>.->.) L,, B (2 7r ) d4dt is similr to the Josephson eqution c Josephson effects should be present. n the dc effect, the current-time verged voltge I() chrcteristics of Josephson For with l Therefore, the voltges nd, re identicl nd given by :, lo, the vortex rrys in the P nd S lyers re wekly coupled. A pnil decoupling 2 the two vortex lttices occurs nd one lttice begins to slip reltive to the other with the of difference (2 «l )(i -,r,j. The voltges nd, re different nd finite voltge phse is induced. squre of the voltge difference is indeed proportionl to the squre of the driven current in Josephson-type effect. Inserting the totl current in eqution (7) we obtin : o i fi l + l, sin 2 rut (10) 6 f fl 2 6 8 10 0 [orb units) I (h2 e) d4dt, both dc nd junction in the RSJ model cn be obtined by solving eqution (5). The solution is [7] 0 for ll nd R(l -1$)' for ll (8) 2 lo for the d-c- trnsformer [4]. For1 2 lo, the two superimposed vortex lttices re strongly coupled nd locked together. < (R2 )[l +1, 2 l] (9) This is nlogous to the phse locked coupling of Josephson wek link in the non dissiptive stte. For1 In order to verify eqution (8) we nlysed the experimentl results obtined t T 1.4 K by Ekin et l. [3] on n AlSiOAl flux trnsformer. As shown in figure j3), the (P) t different pplied mgnetic fields. The pplied mgnetic fields re B 4 5.9 nd 7.9 Guss nd the corresponding decoupling currents 2 lo re respectively 1.8 1.3 nd ma. For the c effect, n c current l superimposed on the dc current l gives rise to novel R + l sin 4 s96 796 io 3. Squre of the mesured voltge difference i', iei,iii,v the squre of the intensity of Fig. primry dc current dopted from AlSIOAl flux trnformer dt [3]. the

nvj In this cse, nd in nlogy with Josephson junction, Shpiro steps [8] should pper on where n is n integer nd j, the first step, is given by eqution (6). v i (L B ) ' (3 )" IL, ] ' [B 2 4 o] " with L in meters nd B in Tesl. Note tht the rtio vj is proportionl to B " nd cn 0.658 MHzL. The first Shpiro step will be observed t i 10 L for n c regime of type II superconducting films with periodiclly modulted thickness of the order of 2286 JOURNAL DE PHYSIQUE III N 11 the I() chrcteristics shown figure 4. These steps correspond to the verge voltges v j 4. Shpiro steps of the c bis flux trnsformer for two vlues of the pplied mgnetic field Fig. B,). (B The equivlent frequency to voltge rtio is given by 20.8 Lj ' B " MHz. ' (I1) therefore be tuned by the pplied mgnetic field. Figure 4 shows schemticlly how the voltge positions of the steps re moving for two vlues of B. For B 10 T nd L 10 m, the rtio v current with frequency of 6.58 MHz. For n AlSiOAl flux trnsformer [3], the mximum voltge of the wek coupled regime is 5.9 x estimted to be of the order of 0.2 m for B 10 Tesl. In order to observe severl in the I() chrcteristic, the frequency of the c current should be of the order of steps MHz. As in the cse of the Josephson effect, n estimte of the step width is very difficult. 10 We should point out tht n c quntum interference effect ws observed in the flux flow micron [9]. Severl steps in the I( chrcteristics of Al films pper t well-defined when the vortex motion is induced by superimposed dc nd 10 MHz rf currents in voltges, field of few Guss. These steps pper s result of the vortex lttice mtching to mgnetic the periodic pinning structure produced by the thickness modultion. In the flux trnsformer, the vortex rry in the secondry film plys the role of the periodic pinning structure. The

N ii AN Ac BIASED SUPERCONDUCTING FLUX TRANSFORMER 2287 In summry, we hve shown tht the equtions describing the motion of the vonices in flux trnsformer re equivlent to the equtions of Josephson wek link (the superconducting Shunted Junction model). A direct nlogy exists between the coupling of the Resistively supported by the office of Nvl Reserch t UCSD nd the Belgin High Temperture Work Incentive nd Concerted Action Progrms (t KUL). Superconductivity Giever I., Fix pinning nd flux flow resistivity in mgneticlly coupled superconducting films, ii Rev. Lent. 16 (1966) 460. Phys. cldis P. E., Prks R. D. nd Dniels J. M., Phse incoherence in the dc superconducting [2] Phys. Rev Lett. 21(1968) 1521. trnsformer, Ekin J. W.. Serin B, nd clem J. R., Mgneting coupling in superposed type II superconducting [3] Phys. Rev. B 9 (1974) 912. films, clem J. R., Theory of mgneticlly coupled type II superconducting films, Phys. Rev B 9 (1974) [4] 898. [5] Sherril M. D. nd Lindstrom W. A., Superconducting dc trnsformer coupling, Phys. Rei. B 11 j1975) l125. Ekin J. W. nd clem J. R.. Mgneting coupling force of the superconducting dc trnsformer, Phys. [6] B 12 j1975) 1753. Rev. Mrtinoli P.. Dldini O., Leemnn c, nd Stocker E., c quntum interference in superconducting [9j with periodiclly modulted thicknes, Solid Stte Commiin 17 (1975) 205. films dvntge of the flux trnsformer is however tht it offers the possibility to tune the importnt vj by the mgnetic field which chnges the pinning structure. rtio of the order prmeter in Josephson junction nd the mgnetic coupling of vortices in phse superconducting trnsformer. A new type of c Josephson-type effect is predicted nd the dc of the Shpiro steps is dependent on the mgnetic field pplied perpendiculr to the position This flux trnsformer cn be used s n rf detector or clibrted detector for smll films. fields. A prcticl dvntge might be tht the flux trnsformer is esier to fbricte mgnetic conventionl Josephson junction. thn Acknowledgements. References Brone A. nd Ptemo G., Physics nd Applictions of the Josephson Effect (John Wiley, New [7] 1982). York, Wldrm J. R., Pipprd A. B. nd clrke J.. Theory of the current-voltge chrcteristics of SNS [8] nd other superconducting wek [inks. Philos. Tins Roy. Sc Lnd. A 26811 970) junctions 265.

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