Article / Letter to editorLeids Instituut Onderzoek Natuurkund

Aarts, J.

Indenbom, M.V.

Kes, P.H.

Marchevsky, M.

English

Leiden University Scholary Publications

VOLUME 78, NUMBER 3 P H Y S I C A L R E V I E W L E T T E R S 20 JANUARY 1997itzerlandObservation of the Correlated Vortex Flow in NbSe2 with Magnetic Decoration.M. Marchevsky, J. Aarts, and P. H. KesKamerlingh Onnes Laboratory, Leiden University, 2300 RA Leiden, The NetherlandsM. V. IndenbomInstitut de Génie Atomique, Département de Physique, Ecole Polytechnique Fédérale de Lausanne CH-1015 Lausanne, Sw(Received 29 July 1996)In weakly pinning type-II superconductors the vortex lattice can flow coherently under the action of aLorentz force. This type of collective vortex motion in a random potential is manifested by channelingof the vortex flow along preferred paths which are stable in time. We present direct experimentalobservations of such vortex flow “channels” obtained with magnetic decoration experiments on NbSe2single crystals. [S0031-9007(96)02197-7]PACS numbers: 74.60.Geooecllmenssfrgznitscatblelesthegextndepleslyotanionofu-reseda-termcat-r-ted-toedu-out--itym-rseRecently, both theoretical and experimental interest hbeen turning to the behavior of the vortex lattice (VLin type-II superconductors moving under the actionLorentz forces from an applied current. Especially, seeral studies were made of the depinning process andonset of the lattice motion [1–4]. A novel contribution tthe subject was made by the authors of Ref. [5]. Thshowed that if pinning in the superconductor is weaand the driving force is strong enough an initially defetive vortex configuration recrystallizes into a coherentmoving perfect vortex lattice above certain critical flowvelocity yp. The lattice is oriented with one of its prin-cipal directions along the direction of motion, as was ealier suggested by the experiments of Fiory [6]. Recenthowever, a somewhat new approach to the problem wproposed in Ref. [7]. One major new conclusion frothat work is that static disorder remains in the movinsystem, which suggests the formation of a moving vortglass rather than perfect lattice ind . 2. Most interest-ing from an experimental point of view was a predictioof the existence of static, elastically coupled “channelfor vortex flow in a weakly disordered system, in contrato motion along random paths. These channels formany velocityy . 0 of the vortex configuration. A directexperimental observation of the flux-flow pattern at thlevel of the individual vortices could provide a proof fothis new theory.In this Letter we report direct high-resolution imaginof vortex-flow patterns using magnetic decoration. Thdecoration technique is a well-known method to visualiflux distributions at the surface of the superconductisample, and it has been extensively used for the imagof static vortex patterns in both conventional and high-Tcsuperconductors. A decoration pattern normally resufrom a snapshot of the magnetic field distribution at thsample surface averaged over the duration time ofdecorationtd. This timetd is given by the experimentalconditions and normally is of the order of 0.1–1 s. It itherefore, clear that in only some specific cases motion cbe probed with the decoration technique. For instan0031-9007y97y78(3)y531(4)$10.00as)fv-theyk-yr-y,asgx”toreeegngltsehe,ane,one can try to decorate the flowing flux pattern. This possible only if the pattern remains essentially stawithin the decoration timetd. If vortices move alongone line, time averaging of the attraction of the particover the deposition time leads to a decorated track ofvortex flow channel. However, turbulence or just wigglinwith an amplitude comparable to the distance to a nchannel is destructive for obtaining images of that type awill result in an approximately random distribution of thmagnetic particles at the sample surface. Several examof “decoration in motion” have been reported previous[8–10], but trajectories of the individual vortices have nbeen resolved in those experiments. Here we makeextension to the described method, improving its resolutto the intervortex spacing, and observe a novel typeordered vortex motion.One can also imagine that if the moving vortex configration is stopped it may still preserve the essential featuof the previous, moving configuration. It can be arguthat at temperatures far belowTc the stiffness of the VL,given by its shear modulusc66 and tilt modulusc44, is al-ready sufficiently large to prevent long-wavelength relaxtions, reorientations of the large vortex grains, etc. afthe driving current has been switched off. This problehas been recently studied with small angle neutron stering (SANS) [11] and decoration [12] experiments peformed on NbSe2. It was seen that the well-ordered staof the moving VL was preserved after the VL was sudenly stopped.In the following we apply the decoration methodstudy the dynamics of the vortex configuration formby the flux penetration in a zero-field cooled (ZFC) sperconducting platelet. Our experiments were carriedon single crystals of NbSe2, which is a layered superconductor with Tc ­ 7.1 K. Pinning is weak in this material; transport measurements of the critical current densgive Jc . 5 3 103 Aycm2 in an applied field of 50Oe at 4.2 K. The ratioJcyJ0 is then ,1024, whereJ0 is the depairing current density at the same teperature. Crystals were platelets with typical transve© 1997 The American Physical Society 531VOLUME 78, NUMBER 3 P H Y S I C A L R E V I E W L E T T E R S 20 JANUARY 1997phoehaymaaohrttruOonhnooolrlnalwsheeslddgeticilartedinbythe-exernionain-eshanu--ld,nedat).s)leasizes,1 mm and thickness, 50 mm. It is known thatin weak pinning materials in platelet geometry vortepenetration is governed by the edge barrier effect [13,1When an external magnetic field is applied to suchsample, penetration of the magnetic flux into the saminterior begins at the penetration fieldHp ­ Hc1 3pdyW ; hereHc1 is the lower critical field,W the samplehalf-width, andd its thickness [14]. In the absence opinning vortices accumulate in the sample center. Hoever, in real samples, edge defects and shape irregularlocally lower Hp which significantly changes the penetration picture. Vortices first enter at weak spots on tsample edge and form a flux droplet which grows twards the center of the sample when the external fiis increased. Droplet growth is stopped by the pinninDroplets are characterized by a specific shape and adegree of order in the VL close to the droplet front,we showed in a previously reported decoration studyplatelets of NbSe2 [15]. Therefore droplets are relativelwell-defined objects for studying motion-related phenoena. Although not on the scale of single vortices, this calso be demonstrated with a magneto-optical techniqFigure 1(a) shows flux penetrating into a NbSe2 platelet,visualized by measuring the Faraday rotation of polized light, transmitted through a garnet indicator filmThe temperature was 4.5 K, and a magnetic field wasplied to ZFC samples with a linear sweep from zero65 Oe. Within the experimental resolution of the meth(several microns) a gradual growth (without “jumps”) othe flux droplets with external field was observed. For tsample in Fig. 1(a) one can estimate that the sweepof 1 Oeys leads to a velocity of the penetrating frontypof about50 mmys. It is important that such experimencan be done without application of the external currentthe sample, and, therefore, problems with sample headue to dissipation in the current contacts can be avoideDecoration experiments were done as follows. Fisamples were cooled to 1.5 K in a very low applieexternal field of about 1 Oe. Then at that low temperatthe applied field was linearly increased up to about 80with a rate of 1 Oeys. At a value of approximately50 Oe the decoration filament was heated up for ab1 s. In our setup a piece of Ni wire is evaporated ait has to be heated above its melting temperature wittungsten filament. The behavior of the filament resistaduring decoration suggests that it takes,200 300 ms tomelt the wire, and, therefore, ferromagnetic materialonly evaporated during the rest of the decoration timEarlier experiments [9] suggested that the time windof particles deposition is nearly the same as the evaption time.The low-magnification image in Fig. 1(b) showsdecoration pattern of a penetrated flux “cloud” in onethe samples studied. The edge of the sample is bethe bottom of the image. The shape of the flux pattewas found to be much more complicated and irregu532x4].alefw-ities-e-ldg.ighson-anue.r-.p-todfeatestoingd.stdreeutdaceise.wra-afownsarFIG. 1. (a) Magneto-optical images taken on NbSe2 singlecrystal atT , 4.5 K during an increase of the external fieldfrom zero to 65 Oe. Sample size is about 1 mm. The exterfield is indicated in the images (in Oe), the gray scale shoa range of approximately 55 Oe, white corresponding to thighest field. Two flux droplets penetrate from opposite edgof the crystal atHa ø 32 Oe. They grow gradually withincrease of the field. (b) Result of decoration with a fiesweep 1 Oeys (different sample). The filament was switcheon for about 1 s when external field reached 50 Oe. The imashows a penetrating cloud of magnetic flux.than in either the magneto-optical or in our previous stadecoration experiments. In the latter case, under simconditions, mostly oval-shaped droplets of the penetraflux were seen. One reason for the inhomogenietiesthe flow could be that heating of the sample causedthe decoration procedure induces viscosity changes inmoving vortex “fluid.” In our experiments the temperature goes up to 3.0 K during decoration. As to the vortstructure inside the cloud, one can see that the pattis substantially smeared, presumably due to the motof the vortices during the decoration time. Except forfew small regions, no sharp regular dot pattern is seenside the cloud. It is thus evident that most of the vorticmoved. Some regions, however, are less smeared tothers, again indicating a rather inhomogeneous distribtion of vortex velocities in the penetrating droplet. In contrast, the field-cooled vortices of the 1 G remanent fiewhich are observed beyond the penetrated front, remaiimmobile and are well resolved. Another image, takenthe front of the penetrated region, is shown in Fig. 2(aOne can clearly see two line patterns (denoted by arrowintersecting in the middle of the image under an angof ,30±. Neighboring lines are nearly parallel, withVOLUME 78, NUMBER 3 P H Y S I C A L R E V I E W L E T T E R S 20 JANUARY 1997adoaanrgwth)eagaooyslling.nrtlsheenhend.n.rnedof.ewell-defined distance between them of about0.9 mm. Ifthat is taken as a vortex lattice parameter, we obtaininduction of 29.5 G, which is a typical value for the fielinside the droplets observed earlier with our decoratiexperiments [15]. It is suggestive to think, therefore, ththe trajectories of individual vortices have been resolveIn view of the previous discussion one can claim ththe vortex flow was laminar in those regions; vorticewere moving along well-defined, essentially straight chanels. We observed similar line patterns in several othsamples. Above the two “coherent” regions at the vetop of the image in Fig. 2(a), neither static nor movinvortices have been resolved. Presumably, that is duethe turbulence created by the intersection of the two floing lattices.Another interesting observation was made close tosample edge, far away from the large cloud [Fig. 2(bHere vortices just started to penetrate the sample, aFIG. 2. (a) Two line patterns (denoted by arrows) are seclose to the penetrating front. Channels of vortex flow (linetraces) intersect in the middle of the image under an anof ,30±. Neighboring channels are nearly parallel, withwell-defined distance between them of about0.9 mm. (b)Image taken close to the sample edge (which is slightly belthe bottom of the image). The very beginning of penetratimanifests itself in finger-like channels starting out of the vortebelt along the sample edge.nntd.ts-eryto-e].ndnrlewnxone can see a peculiar fingering of the flux front. Ever“finger” represents a trajectory along which the vorticemove one by one to the sample interior. They are weseparated and regular; the distance between neighborfingers roughly corresponds to an induction of 25–30 GA similar type of the moving vortex trajectories at thepenetrating front in weak-pinning materials has beerecently found with numerical simulations [16]. It isespecially interesting that these regular channels stadirectly out of the vortex “belt” close to the sampleedge, which is known to be a region of high topologicadisorder and of strong vortex density gradients [15]. Thiphenomenon can be also interpreted as a formation of telastic channels proposed in Ref. [7].Regions with channel patterns, as in Fig. 2, werobserved in all the samples decorated in this way. IFig. 3 we use one of these to make some estimates of tcorrelations in the channel flow pattern. This decoratioimage was obtained close to the front of a penetrateflux region. The size of the region of the correlatedflow was rather large in this case (,30 mm in diameter).We used part of the pattern outlined with a box toproduce the 2D autocorrelation function of the patternThe original gray-scale image was used in this calculatioThe autocorrelation function is defined asGsdx, dyd ­ZIsx 1 dx, y 1 dyd Isx, yd dx dy ,where Isx, yd is the image brightness.Gsdx, dyd givesthe probability to find a similar degree of brightness if onemoves a distanced ­ sdx, dyd from a specific point. Thesame type of analysis was first performed in Ref. [17] fostatic decoration images on YBCO. Our result is shown ithe inset of Fig. 3. One sees a line pattern superimposon the hexagonal structure. The decay of the intensityFIG. 3. Decoration image of part of a penetrating flux frontA line pattern of vortex flow in the direction perpendicular tothe front is seen. Inset: the 2D autocorrelation function of thcentral part (outlined) of the decoration image. A flow linepattern with a hexagonal trend superimposed is seen.533VOLUME 78, NUMBER 3 P H Y S I C A L R E V I E W L E T T E R S 20 JANUARY 1997innglatletatileisreiioeleeethhtihexeliieoinsthen.ticseitsineeeteeninle,onntresrlyticnsesgisv.-,the line pattern reveals a correlation length of the flowVL in the direction perpendicular to the flow directioof about 8–10 lattice parameters. The correlation lenalong the direction of the channels yields a siminumber. We think, however, that the latter is significanaffected by the field gradient in the flow direction. Thpresence of the hexagonal pattern related to a slattice suggests that at least during some portion ofdecoration time (parts of) the lattice remained immobInterestingly, a slight (,7.5%) “compression” of the staticlattice in the direction of the surrounding vortex flowseen. This might be related to compressional effectsthe flow upon the static lattice parts and needs a sepainvestigation. In Fig. 4 a reconstruction of the channpattern made by Fourier filtering the original imageshown. The figure shows that there are several regof disordered flow embedded in the line pattern. Thorigin could be a gradient of the induction in the sampwhich is seen as a changing in density of the flow linfrom the left bottom to right top corner of the imagAlso, one can see three single-row dislocations inflow pattern (marked with squares). Surprisingly, tflow lines around them are not much distorted suggesthat the dislocations did not move significantly during tdecoration time. Similar static defect structures have bfound recently in numerical simulations of moving vortelattices [3].Finally, we want to suggest some parallels betwethe results of the decorations in motion and our earFIG. 4. “Reconstruction” of the channels made by Fourfiltering the original image. Parallel flow lines and regionsdisordered flow are seen. Extra rows in the flow pattern endby dislocations are denoted by solid squares.534gthrytiche.ofatelsnsir,s.eengeennerrfgresults on droplet formation [15]. First, a relation iseen between the well-ordered vortex lattice close todroplet front and the observed correlated vortex motioThe regular oval shape of the droplets in our stadecorations suggests laminar vortex flow at least cloto the droplet front. When the external field reachesfinal value the vortex lattice channels freeze resultingthe highly ordered VL grains. The orientation of thstatic VL remains unchanged from the direction of thflow channels, e.g., preferentially normal to the droplfront. Furthermore, an equivalence is suggested betwstatic dislocations in the flow pattern and similar defectshe decoration patterns of the droplets (See, for exampFig. 3 of [15]).In conclusion, we performed decoration experimentsmoving vortex lattices. We visualized regions of coherevortex flow in the sample and observed periodic structuof single-vortex flow channels. Channels are neaparallel and well separated. We also observed stadefects in the flowing lattice and estimated correlatioin the flow pattern.We acknowledge stimulating discussions with P. LDoussal, F. Nori, D. Feinberg, and V. Vinokur. Thiwork is part of the research program of the “Stichtinvoor Fundamental Onderzoek der Materie,” whichfinancially supported by “NWO.”[1] S. Bhattacharya and M. J. Higgins, Phys. Rev. Lett.70,2617 (1993).[2] K. Harada et al., Nature (London)360, 51 (1992); A.Tonomura, Jpn. J. Appl. Phys.36, 2951 (1995).[3] D. W. Braunet al., Phys. Rev. Lett.76, 831 (1996).[4] R. Wördenweber, P. H. Kes, and C. C. Tsuei, Phys. ReB 33, 3172 (1986).[5] A. E. Koshelev and V. M. Vinokur, Phys. Rev. Lett.76,3408 (1996).[6] A. T. Fiory, Phys. Rev. Lett.27, 501 (1971).[7] T. Giamarchi and P. Le Doussal, Phys. Rev. Lett.76, 3408(1996).[8] H. Träuble and U. Essmann, Phys. Status Solidi25, 395(1968).[9] N. V. Sarma and A. Wilcockson, Philos. Mag.20, 539(1969).[10] L. Ya. Vinnikov, A. O. Golubok, V. A. Marchenko, andG. I. Salnikov, Metallofizika5, 103 (1983) (in Russian).[11] U. Yaronet al., Phys. Rev. Lett.73, 2748 (1994).[12] A. Duarteet al., Phys. Rev. B53, 11 336 (1996).[13] M. V. Indenbomet al., in Critical Currents in Surpercon-ductors,edited by H. W. Weber (World Scientific, Singapore, 1994).[14] E. Zeldovet al., Phys. Rev. Lett.73, 1428 (1994).[15] M. Marchevsky, L. A. Gurevich, P. H. Kes, and J. AartsPhys. Rev. Lett.75, 2400 (1995).[16] C. Reichhardtet al., Phys. Rev. B53, R8898 (1996).[17] P. L. Gammelet al., Phys. Rev. Lett.59, 2592 (1987).

Observation of correlated vortex flow in NbSe2 with magnetic decoration

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Observation of correlated vortex flow in NbSe2 with magnetic decoration

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