We present magnetization measurements of mesoscopic superconducting niobium
loops containing a ferromagnetic (PdNi) pi-junction. The loops are prepared on
top of the active area of a micro Hall-sensor based on high mobility
GaAs/AlGaAs heterostructures. We observe asymmetric switching of the loop
between different magnetization states when reversing the sweep direction of
the magnetic field. This provides evidence for a spontaneous current induced by
the intrinsic phase shift of the pi-junction. In addition, the presence of the
spontaneous current near zero applied field is directly revealed by an increase
of the magnetic moment with decreasing temperature, which results in half
integer flux quantization in the loop at low temperatures.Comment: 4 pages, 4 figure

A. Barone

A. Bauer

A. I. Buzdin

C. Strunk

F. W. Grover

I. O. Kulik

J. Bentner

L. N. Bulaevskii

M. Aprili

M. L. Della Rocca

M. Reinwald

W. Wegscheider

English

arXiv

We present magnetization measurements of mesoscopic superconducting niobium loops containing a ferromagnetic (PdNi) pi junction. The loops are prepared on top of the active area of a micro-Hall sensor based on high mobility GaAs/AlGaAs heterostructures. We observe asymmetric switching of the loop between different magnetization states when reversing the sweep direction of the magnetic field. This provides evidence for a spontaneous current induced by the intrinsic phase shift of the pi junction. In addition, the presence of the spontaneous current near zero applied field is directly revealed by an increase of the magnetic moment with decreasing temperature, which results in half integer flux quantization in the loop at low temperatures

Bauer, Andreas

Bentner, Johannes

Aprili, M.

Della Rocca, M. L.

Reinwald, Matthias

Wegscheider, Werner

Strunk, Christoph

University of Regensburg Publication Server

Spontaneous Supercurrent Induced by Ferromagnetic π Junctions

Bauer, A.

Bentner, J.

Della Rocca, L.

P H Y S I C A L R E V I E W L E T T E R S week ending28 MAY 2004VOLUME 92, NUMBER 21Spontaneous Supercurrent Induced by Ferromagnetic  JunctionsA. Bauer,1 J. Bentner,1 M. Aprili,2 M. L. Della Rocca,2 M. Reinwald,1 W. Wegscheider,1 and C. Strunk1,*1Institut fu¨r Experimentelle und Angewandte Physik, Universita¨t Regensburg, 93040 Regensburg, Germany2CSNSM-CNRS, Universite´ Paris-Sud, 91405 Orsay Cedex, France†(Received 4 December 2003; published 26 May 2004)217001-1We present magnetization measurements of mesoscopic superconducting niobium loops containing aferromagnetic (PdNi)  junction. The loops are prepared on top of the active area of a micro-Hall sensorbased on high mobility GaAs=AlGaAs heterostructures. We observe asymmetric switching of the loopbetween different magnetization states when reversing the sweep direction of the magnetic field. Thisprovides evidence for a spontaneous current induced by the intrinsic phase shift of the  junction. Inaddition, the presence of the spontaneous current near zero applied field is directly revealed by anincrease of the magnetic moment with decreasing temperature, which results in half integer fluxquantization in the loop at low temperatures.DOI: 10.1103/PhysRevLett.92.217001 PACS numbers: 74.50.+r, 85.25.CpS FMd /F FξRe{F(d/)}FFξ0a"0"0 loopcbπΦ0/2Sπ loop d" "π "0" FMSFreeEnergyLI /S Φ0 LI /S Φ0γ= -1γ = -2.5γ = -5= 1γ= 2.5γ= 5γFIG. 1. The origin and signature of  junctions with ferro-magnetic weak links. (a) Inside the ferromagnet (FM) the realpart of the Cooper pair wave function F exhibits spatialoscillations with wavelength F. The dot marks the value ofdF=F used in our  junctions. (b) In zero external magneticfield, a spontaneous flux   0=2 is required to maintain thecondition of fluxoid quantization if a  junction is inserted intoa superconducting loop. (c),(d) Sketches of the free energy of arent and a corresponding magnetic flux of half a fluxquantum 0 in the ground state [see Fig. 1(b)]. The loop (c) and a 0 loop (d) as a function of the magnetic flux fordifferent values of   1=0LIC as described in the text.As first predicted by Josephson [1], Cooper pairs can betransferred coherently between two weakly coupledsuperconducting electrodes at zero bias voltage. The re-sulting supercurrent through such a weak link is drivenby the phase difference ’ of the superconducting wavefunction across the junction. In conventional tunnelcoupled Josephson junctions the current-phase relation,which connects the supercurrent IS flowing through ajunction and the phase difference of the superconductingwave function or pair amplitude, is given by IS’ IC sin’ [2]. The critical current IC is the maximumsupercurrent the junction is able to sustain. The sinusoidalshape of the current-phase relation is expected to bemodified if the weak link is realized by a ballistic pointcontact (ScS) or a diffusive normal metal bridge (SNS)[3,4] rather than by a tunneling barrier.If the weak link consists of a thin ferromagnetic layer(SFS), the result can be a Josephson junction with a built-in phase difference of . This has been predicted byBuzdin et al. [5], who calculated that the pair amplitudeF inside a ferromagnet in contact with a superconductorshould oscillate as a function of position [see Fig. 1(a)].The origin of the oscillation is the exchange splitting ofthe conduction bands in the ferromagnet, in which theCooper pairs acquire a nonzero total momentum. Theoscillation period F is determined by the exchange field.Thus, by choosing appropriate values of the exchangefield and the thickness dF of the ferromagnetic layer,the ratio F1=F2 of the pair amplitude on both sides ofthe junction can become negative and with it the currentthrough the junction [5]. Such junctions are called junctions, because the difference in sign between F1 andF2 corresponds to a phase difference of  across thejunction and hence IS’  IC sin’ . It was pointedout by Bulaevskii et al. [6] that a superconducting ringwith an inserted  junction exhibits a spontaneous cur-0031-9007=04=92(21)=217001(4)$22.50 spontaneous supercurrent has to flow even in the absenceof external flux in order to maintain the uniqueness of thewave function along the loop provided that the criticalcurrent is sufficiently large. This is illustrated in Fig. 1(c),where we have plotted the free energy of the  loop in theabsence of an applied field [6] as a function of the nor-malized flux through the loop LIS=0 for different values2004 The American Physical Society 217001-1FIG. 2 (color). Shadow mask and sample layout. The samplesare niobium (Nb) loops with a planar ferromagnetic palladium-nickel (Pd0:82Ni0:18) Josephson junction. (a) The polyethersul-fone (PES)/germanium shadow mask. (b) Scanning electronmicrograph of the sample after lift-off. The loop is placed ontop of the flux-sensitive area of the micro-Hall cross made of aGaAs=AlGaAs heterostructure. (c) The relative shifts of thethree metal films on the substrate are achieved by adjustingdifferent tilt angles before each evaporation. (d) Cross sectionof the planar Josephson junction.P H Y S I C A L R E V I E W L E T T E R S week ending28 MAY 2004VOLUME 92, NUMBER 21of   1=0LICT; dF=F, where L is the loopinductance. Here we assume a sinusoidal IS’ for sim-plicity [3]. For   1 a phase transition occurs in theloop to a ground state with two degenerate minima cor-responding to half a flux quantum. In Fig. 1(d) we haveplotted the free energy for a 0 loop for comparison.The first experimental indication for the oscillatorycharacter of the induced superconductivity in thin ferro-magnetic films was the observation of a nonmonotonicsuppression of TC with increasing film thickness of theferromagnet in SF multilayers (see, e.g., [7]). An impor-tant step towards  coupling in magnetic Josephsonjunctions was the introduction of diluted ferromagnets(e.g., CuxNi1x [8] or PdxNi1x [9]), which allow largerlayer thicknesses for  junctions than concentrated fer-romagnets. Recently several experiments have revealedmore direct evidence of  coupling in planar ferromag-netic Josephson junctions [8–10] and in nonequilibriumsuperconductor/normal-metal junctions [11–13]. In addi-tion, the first phase sensitive measurements on suitablyoriented grain boundary junctions with high-temperaturesuperconductors [14] as well as 0- dc SQUIDs [15] andnetworks of  junctions [16] were performed to obtain adirect signature of the  shift of the phase of the super-conducting wave function.The latter experiments concentrated on the high-temperature regime, where the induced supercurrentsare negligible. In this Letter we focus on the low-temperature regime where the  junction manifests itselfby spontaneous supercurrents, resulting in half integerflux quantization. The spontaneous current induces anasymmetry in the switching fields between differentflux states of the loop and it can also be observed directlyin the temperature dependent magnetization in the ab-sence of an external magnetic flux.In order to obtain clean S=F interfaces the differentmetal layers are evaporated in a single vacuum run usinga high-temperature stable shadow mask [17,18] madeof polyethersulfone (PES) and germanium (Ge) [seeFig. 2(a)]. The samples are niobium square loops withan average linewidth of 700 nm and a layer thickness of80 nm. The effective side length d  7:4 m of the loop requires a magnetic field of B0  37:5 T to obtainone flux quantum in the loop; the average inner diameterof the loop leads to an estimated self-inductance of L 23 pH [19]. The niobium ring is interrupted by a planarferromagnetic Josephson junction made of a palladium-nickel alloy (Pd0:82Ni0:18) [9,10] [see Figs. 2(c) and 2(d)for details on the geometry]. For this nickel concentrationthe PdNi is a weak ferromagnet with a moderate ex-change field [20]. The character (0 or ) of the junctionis determined by the ferromagnetic layer thickness; in ourcase a ferromagnetic layer thickness dF of 7.5 nm resultsin a  junction (F  2:4 nm) [10]. For comparison,niobium loops containing a conventional weak tunnelingbarrier instead of the magnetic interlayer are preparedon the same GaAs chip. The 0 loop has a slightly217001-2smaller effective size of d  7:1 m corresponding toB0  40:8 T.The local magnetic flux of the loop is measured by amicro-Hall sensor in the ballistic limit. Here the Hallvoltage VH is related to the magnetic flux  via  ne=AVH=I, where   0:035 is the geometric fillingfactor of the loop within the flux sensor, n is the electrondensity of the sensor, e the electron charge, I the currentthrough the sensor, and A the active area of the sensor[21]. The sensors are made of a modulation dopedGaAs=AlGaAs heterostructure containing a two dimen-sional electron gas 190 nm below the surface. At 4.2 K theheterostructure has a mobility of 750 000 cm=Vs and anelectron density of 2:66	 1011 cm2.The magnetic response of a superconducting loop witha conventional Josephson junction is expected to showflux quantization, provided that the width of the super-conducting strip is larger than the magnetic penetrationdepth and that the LIC product of the loop is larger than0=2 [22]. Figure 3 shows the Hall voltage VH gen-erated by the magnetic flux of the circulating current inthe loops at 2 K when sweeping the external magneticfield. The contribution of the applied magnetic field hasbeen subtracted. The sample is magnetically shielded by acryoperm can, reducing the residual magnetic field toabout 4 T. Reversing the sweep direction results in astrongly hysteretic magnetization curve (not shown for217001-2bδV( nV)Hπ0B ( T)applied µdown sweep up sweepδV(nV)HB ( T)applied µπ0down sweep up sweepadown sweep up sweepπ0B ( T)applied µdδV(nV)Hc0ΦappliedΦπ0Φ0-Φ00Φ00− Φ0−Φ 00B =19,2 Tcool µB =1,72 Tcool µB =-1,72 Tcool µΦFIG. 3 (color). Signature of the  state in the switching behavior during magnetic field sweeps. (a),(b) Magnetization tracesVH  IS for a  and a 0 loop. All data are taken at 2 K using a measurement current of 20 A. The critical currents are 65 A forthe 0 junction and 27 A for the  junction. By choosing cooling fields slightly below and above zero applied flux and performingsweeps of the magnetic fields in both field directions, an asymmetric switching behavior of the  loop is observed, while the 0 loopshows symmetric jumps with respect to the cooling field. (c) Relation between the total magnetic flux , applied flux applied (linearbackground), and the flux LIS generated by the supercurrent in the loop. The applied relation of a  loop (red) is shifted by 0=2with respect to that of a conventional 0 loop. During the field sweep, only the sections with positive slope can be traced, which leadsto a hysteretic switching behavior for LIC > 0=2. The three vertical lines in each curve indicate the applied flux during fieldcooling below the critical temperature for the three sets of measurements discussed. (d) Reversal of the symmetry properties of the and the 0 loop when choosing a cooling field equal to half a flux quantum.P H Y S I C A L R E V I E W L E T T E R S week ending28 MAY 2004VOLUME 92, NUMBER 21clarity) and trapped magnetic flux in the loop. To avoidflux trapping, every field sweep plotted in Fig. 3 wasperformed after field cooling down from 10 K, which ishigher than the critical temperature of bulk niobium.Each curve contains two measurements in positive andnegative sweep directions, respectively. Figures 3(a) and3(b) correspond to cooling fields Bcool  =1:7 T,slightly above and below zero magnetic field. The mag-netization traces of the 0 loop (black) show diamagneticscreening until the critical current is reached and one fluxquantum enters the loop as indicated by a sudden jump ofVH. The further rise of Bapplied is again screened untilmore flux quanta enter and a 0-periodic sawtooth pat-tern emerges. At low temperatures, the jump height cor-responds to 0 and is used for the determination of thefilling factor  for each sample. The magnetic response ofthe  loop looks qualitatively similar but is stronglyasymmetric with respect to the applied flux. The originof the switching behavior is further illustrated inFig. 3(c), where the black trace shows the multivaluedrelation between  and applied for a hystereticJosephson-junction loop with LIC > 0=2 [22]. Weagain assume a sinusoidal current-phase relation for sim-plicity [3]. The left trace (red) in Fig. 3(c) sketches the-shifted applied relation expected for a  loop. It is217001-3seen that the branch near   0 has a negative slope andthe corresponding states are unstable. As a consequencethe loop should generate a spontaneous current, whoseorientation depends on the sign of the small initialcooling field. The essential signature of the -shiftedapplied relation is a pronounced asymmetry of theswitching fields, which are defined by the vertical slopesof the red curve in Fig. 3(c). This asymmetry results fromthe orientation of the spontaneous current selected by thecooling field and is clearly seen in the magnetizationcurves of the  loops in Figs. 3(a) and 3(b) (red). Onthe other hand, when applying a cooldown field of Bcoolclose to half a flux quantum [see Fig. 3(d)], the situationreverses when compared to Bcool  0. Now the 0 loopshows asymmetric and the  loop shows symmetricswitching. This can be understood again from Fig. 3(c):At applied  0=2 the state of the  loop is uniquelydefined, whereas for the 0 loop two states compete, whichare energetically degenerate.Besides the signature of the spontaneous current in themagnetization curves one would like to directly see itsemergence when cooling down below TC. Figure 4 showsthe temperature dependence of the magnetic flux detectedin the loops. The raw data of the temperature sweepscontained a large contribution from the temperature217001-3π0T (K)ΦΦ(0)ΦΦ(0)V(nV)HV(nV)Hπ0ab0.250-0.25-0.500.250-0.25-0.500 2 4 6 8 100 2 4 6 8 100012.6-12.6-25.19.5-9.5-18.9Φapplied=0Φapplied 0= /2ΦFIG. 4. Temperature dependence of the spontaneous current.The measurements show the temperature dependent magneticflux produced by a  and a 0 loop when cooling (a) in zero fieldand (b) in a magnetic field equal to half a flux quantum in theloop. Below T  5 K the  loop develops a spontaneouscurrent when cooling down in zero field, while the magneticflux through the 0 loop remains zero. When applying a fieldequal to half a flux quantum 0 the roles of the  and the 0loops are exchanged. At low temperatures the spontaneous fluxof both loops saturates close to 0=2, as expected. To avoidheating of the sensor at the lowest temperatures, the measure-ment current has been reduced to 7 A.P H Y S I C A L R E V I E W L E T T E R S week ending28 MAY 2004VOLUME 92, NUMBER 21dependent longitudinal resistance of the Hall probe whichis nearly independent of the magnetic field [23]. By sub-traction of two temperature sweeps at slightly differentcooling fields with opposite spontaneous current, the Hallsignal has been extracted. The first pair of measurementsis taken around applied  0. In order to satisfy the con-dition of fluxoid quantization the  loop is forced togenerate a spontaneous circulating current IS. At lowtemperatures the total flux total  LIS approaches0=2. Indeed, the loop shows a small but clearly visibleHall signal as the temperature of the junction is reducedin zero applied field, which results from the magnetic fluxgenerated by the spontaneous current. This can be takenas direct evidence for the half integer flux quantizationinduced by the  junction. As expected, the 0 loop showsno significant variation of the Hall voltage. Finally, theroles of the  and 0 loops can be exchanged by applyingan external flux applied  0=2 during the cooldown. Inthis case, the Hall voltage of the loop is constant and nospontaneous current arises, as the fluxoid quantizationcondition is initially compatible with the applied fieldequivalent to 0=2. On the other hand, the 0 loop devel-217001-4ops a supercurrent with LIS  0=2 to provide integerflux quantization.In summary, we have demonstrated experimentally thepresence of spontaneous magnetic moments in supercon-ducting loops containing a ferromagnetic junction. Thisis the most direct evidence for the existence of inhomo-geneous superconductivity in the magnetic layers andcan be compared with the direct detection of half fluxquanta in tricrystalline yttrium barium copper oxideloops, which are a hallmark of the d-wave symmetry ofthe order parameter in high-TC superconductors [14]. The loops can be viewed as a macroscopic analog of a spin1=2 with two degenerate states at zero magnetic field.We thank J. Eroms and J. Stahl for technical supportand S. Lok for helpful discussions. This work was sup-ported by the Deutsche Forschungsgemeinschaft. Thework of M. A. and M. L. D. R. has been supported by theESF through the ‘‘-shift’’ program.*Electronic address: christoph.strunk@physik.uni-regensburg.de†Also at LPQ-ESPCI, 75005 Paris, France.[1] B. D. Josephson, Phys. Lett. 1, 251 (1962).[2] B. D. Josephson, Rev. Mod. Phys. 36, 216 (1964).[3] I. O. Kulik and A. Omelyanchuk, Sov. J. Low Temp. Phys.4, 142 (1978) [Fiz. Nizk. Temp. 4, 296 (1978)].[4] T. T. Heikkila¨, J. Sa¨rkka¨, and F. K. Wilhelm, Phys. Rev. B66, 184513 (2002).[5] A. I. Buzdin, L. N. Bulaevskii, and S.V. Panyukov, JETPLett. 35, 178 (1982) [Pis’ma Zh. Eksp. Teor. Fiz. 35, 147(1982)].[6] L. N. Bulaevskii, V.V. Kuzii, and A. A. Sobyanin, JETPLett. 25, 290 (1977) [Pis’ma Zh. Eksp. Teor. Fiz. 25, 314(1977)].[7] C. L. Chien and D. H. Reich, J. Magn. Magn. Mater. 200,83 (1999).[8] V.V. Ryazanov et al., Phys. Rev. Lett. 86, 2427 (2001).[9] T. Kontos et al., Phys. Rev. Lett. 86, 304 (2001).[10] T. Kontos et al., Phys. Rev. Lett. 89, 137007 (2002).[11] J. J. A. Baselmans et al., Nature (London) 397, 43 (1999).[12] J. A. Baselmans, B. J. van Wees, and T. M. Klapwijk,Phys. Rev. B 65, 224513 (2002).[13] J. J. A. Baselmans et al., Phys. Rev. Lett. 89, 207002(2002).[14] J. R. Kirtley et al., Nature (London) 373, 225 (1995).[15] W. Guichard et al., Phys. Rev. Lett. 90, 167001 (2003).[16] V.V. Ryazanov et al., Phys. Rev. B 65, 020501 (2002).[17] T. Hoss et al., Physica (Amsterdam) 14E, 341 (2002).[18] P. Dubos et al., J. Vac. Sci. Technol. B 18, 122 (2000).[19] F.W. Grover, Inductance Calculations: Working Formulasand Tables (Dover Publications, New York, 1962).[20] The Curie temperature measured by the anomalous Halleffect in a bare thin film is 200 K; the value of theexchange energy is estimated to be of the order of 52 meV.[21] A. K. Geim et al., Appl. Phys. Lett. 71, 2379 (1997).[22] A. Barone and G. Paterno, Physics and Applications ofthe Josephson Effect (Wiley, New York, 1982).[23] M. A. Paalanen et al., Phys. Rev. B 29, 6003 (1984).217001-4

Crossref

Spontaneous Supercurrent Induced by Ferromagnetic
                    
                      π

We present magnetization measurements of mesoscopic superconducting niobium loops containing a ferromagnetic (PdNi) π junction. The loops are prepared on top of the active area of a micro-Hall sensor based on high mobility GaAs/AlGaAs heterostructures. We observe asymmetric switching of the loop between different magnetization states when reversing the sweep direction of the magnetic field. This provides evidence for a spontaneous current induced by the intrinsic phase shift of the π junction. In addition, the presence of the spontaneous current near zero applied field is directly revealed by an increase of the magnetic moment with decreasing temperature, which results in half integer flux quantization in the loop at low temperatures