Ž .Physica C 332 2000 160–165www.elsevier.nlrlocaterphysc

Dynamic studies of vortices in NbSe , from single flux lines2

to lattices

F. Pardo a,), C. Bolle a, V. Aksyuk a, E. Zeldov a, P. Gammel a, D.J. Bishop,F. de la Cruz b

a Bell Labs Lucent Technologies, 600 Mountain AÕenue, Murray Hill, NJ 07974, USAb Centro Atomico Bariloche CNEA, Bariloche, Argentina´

Abstract

We present different techniques to study the dynamics of the vortex lattice in NbSe single crystal samples. In the first2

set of experiments, we applied a field parallel to the c crystalline axis and extended the Bitter decoration technique to theŽ .study of dynamic structures by imaging the lattice during creep ‘‘decoration during motion’’ . This method exposed a new

smectic phase and an anisotropic ‘‘crystal’’ at higher fields. In the second set, we used a micro-mechanical high-Q oscillatorto study the mesoscopic flux dynamics along the crystallographic ab plane. In this case, we were able to observe singlevortex penetration, well described by a ‘1q1’-dimensional model. q 2000 Published by Elsevier Science B.V. All rightsreserved.

Keywords: Vortices; Flux dynamics; Flux penetration; Flux lattice

1. Introduction

Several techniques exist to image the spatial mag-netic structure of superconductors. Among them, theBitter decoration technique emerges as single vortexresolution — large area technique widely used tostudy static properties of vortex lattices. In the firstpart of this paper, we show an extension of thispowerful technique that allowed us to explore dy-namic properties of the lattice by decorating during

w xcreep 1 .On the other hand, the study of the temporal

behavior of individual vortices as they enter into thesample has also been hampered by the lack of suit-able experimental tools, mainly for the mesoscopicregime, where a small number of vortices are con-

) Corresponding author.

fined in a small volume. Here we used a polysiliconmicromachined mechanical resonator to resolve thedynamics of single vortices in micrometer-sized

w xsamples 2 . These experiments are described in Sec-tion 2.

2. Dynamic decoration experiments

In the magnetic decoration technique used here,Ž .the flux line lattice FLL is visualized by evaporat-

˚ing ;50 A magnetic particles onto the surface of asuperconductor held below its transition temperatureT with a magnetic field applied. The particles fol-c

low the field lines of the vortices at the surface ofthe sample and land where the vortices are located.Because each pile of magnetic particles has a finitesize, the technique is limited to fields below severalhundred oersteds. Fortunately, this range of fields

0921-4534r00r$ - see front matter q 2000 Published by Elsevier Science B.V. All rights reservedŽ .PII: S0921-4534 99 00660-7

( )F. Pardo et al.rPhysica C 332 2000 160–165 161

covers an interesting region where we can tune thevortex interaction strength relative to the pinningstrength and see a crossover from a moving Braggglass in the high field, interaction-dominated limit, toa smectic structure in the low field, disorder-dominated limit.

Our samples were high-quality, single crystals ofNbSe with typical dimensions of 0.5=0.5=0.22

mm3. Samples were cooled down to 4.2 K in amagnetic field applied in the c direction. At low

temperatures, the field was removed and the samplewas decorated after a certain period of time.

With a 1 s decoration time, the behavior of thevortex velocity defines two regimes. If the velocity isgreater than one vortex lattice constant per second,one has images of vortices in motion. For the regimeof vortex velocities less than one lattice constant persecond, one obtains quasi-static images of the slowlymoving vortices. We can work in both regimes.

ŽBecause of the critical state profile independent of

Ž . Ž .Fig. 1. Critical state during creep quasistatic, 25 G , showing topological defects clear areas . Fourier Transform in the ordered region,2 w xderived critical current profile and calculated beam profile for J s3500 Arcm 3 .c

( )F. Pardo et al.rPhysica C 332 2000 160–165162

.velocity regime , we always find a quasi-static, ho-mogeneous structure in the center of the sample andthe critical state region at the edge. The data shownhere are always from the critical state region.

2.1. Interaction-dominated regime

The large area picture of the critical state profilein the quasi-static regime shown in Fig. 1 is a clearexample of motion-induced ordering of the FLL. Thecurrent distribution calculated from the field profileshows that in the critical state region, the FLL ismuch more ordered than in the center of the sample.

ŽThe remaining topological defects few percent in.density arise mainly because of the small field

Ž .gradient. The Fourier Transform FT confirms thisas one sees six well-defined peaks although there isstill a one-dimensional modulation with two of thepeaks brighter than the other four, indicating that thepositional correlation length perpendicular to the flowdirection is still longer than that parallel to the flow.These data suggest that the increased field allows thevortex–vortex interactions to dominate over the dis-order and is the equivalent to turning down thedisorder. The data are quite similar to the predicted

w xmoving Bragg glass phase 4,5 .For the data in the high-velocity regime, we found

w xa pattern similar to that found in Refs. 7–9 , show-ing coherent motion evidenced by large flow do-mains.

2.2. Disorder-dominated regime

Ž .Because the data in Fig. 2 A are in the quasi-staticregime, the image resolves individual vortices. Thisconsists of rows of vortices aligned along the flowdirection and not an isotropic, hexagonal pattern aswould be seen for a static lattice. The FT data show

w xthe signature of a smectic phase 6 . The two sharppeaks show that the channels are well-ordered trans-verse to the flow of vortices and the broad lines ofscattering show that the vortices are liquid-like in thechannels with short-range positional correlationsalong the direction of flow.

Ž .The data in Fig. 2 B are no longer in the quasi-static regime and the image no longer resolves indi-vidual vortices as clearly, but the same smecticpattern can be seen. A careful look at this image

Ž . Ž .Fig. 2. Quasistatic decoration of the smectic structure A and BŽ .channels with different dynamics decoupling in the moving

regime at 5 G.

reveals the existence of decoupled motion betweenchannels: there are blurred and static channels.

3. High-Q micromechanical oscillator experi-ments

High-Q mechanical oscillators have previouslyw xbeen 7–9 shown to be powerful probes of con-

densed matter. However, the recent availability ofsilicon micromechanics has enormously expandedthe power of the technique by allowing high Q andsmall size. Shown in Fig. 3 is a SEM micrograph ofour micromachine. The mechanical oscillator con-

( )F. Pardo et al.rPhysica C 332 2000 160–165 163

Fig. 3. SEM image of a high-Q mechanical oscillator with a hexagonally shaped single crystal mounted on top.

sists of a plate connected via two serpentine springsto two support structures attached to the substrate.Under the plate are two electrodes on the siliconsubstrate. The outline of the electrodes is visible onthe top plate due to print through during the multipleprocessing steps. In operation, the device is oscil-lated torsionally about the long axis of the plate. Oneelectrode is used to drive the plate and the other todetect the actual movement. This torsional mode hasa resonant frequency of 45 kHz and a Q of 250,000at low temperatures. The device was built using athree-layer polysilicon process at the MCNC MUMPs

w xfoundry 10 .Shown in the inset to Fig. 3 is a blowup of the

sample used for the studies described here. It is asingle crystal with dimensions of 22=49=1.6 mm3

with a T of 7.0 K.c

A magnetic field was applied parallel to the largeface of the crystal and perpendicular to its rotation

™

axis. A sample with a magnetic moment M in a field™ ™ ™

H exerts an additional torque tsM=H on the

oscillator, shifting its resonant frequency. The smallsize of the oscillator allows us to obtain high reso-nant frequencies despite the soft spring constants,typically in the range of 0.5=10y9 N m.

Shown in Fig. 4 is the frequency and amplitudedependence for a standard ZFC–FC temperaturesweep. After applying a field of 60 Oe at 5 K, weobserve a frequency shift of roughly 20 Hz and nochange in the oscillator’s amplitude. This is a clearsignature of the Meissner state. The energy cost ofscreening a magnetic field applied parallel to theface of a thin superconductor is smaller than the costof screening the same field applied perpendicular tothe face of the sample. The resulting variation of thetorque with the tilt angle dtrdu causes a restoringforce that increases the oscillator frequency. Theresult is an increase in the oscillator frequency with

Ž .no change in the amplitude no dissipation . As weŽ .warm up the sample solid line , we do see a slight

Ž .decrease in the Meissner restoring force as l Tstarts to become comparable to the sample thickness.

( )F. Pardo et al.rPhysica C 332 2000 160–165164

Fig. 4. Temperature dependence of the oscillator resonant fre-Ž . Ž .quency top and amplitude bottom for a typical zero field

Ž .cooling–field cooling ZFC–FC experiment.

At Tf6.1 K, we see a sudden drop in theoscillator amplitude and a jump in its frequency.These changes are associated with the first flux linepenetration and uniquely define the location of thefirst penetration field H fH for our sample. Notep C1

the increase in the ‘‘noise’’ in the data that, as weshow below, is the resolution of single vortex eventsin the oscillator. As we approach T , both the fre-c

quency and the amplitude merge into the back-Ž .ground. Upon cooling the sample dashed line in the

presence of the 60 Oe field, the flux lines nucleate inthe superconductor below T , resulting in a fre-c

Žquency shift and a decrease in amplitude increase in.dissipation . Both the frequency and the amplitude

show a rich structure close to T that tends to smoothc

out at lower temperatures. This structure representsthe changes in the pinning strength of the vortexensemble as the number of flux lines changes.

Ž .Shown in Fig. 5 a is a field sweep close to Tc

after a ZFC. The frequency shift in the Meissnerstate due to the shielding currents up to H f9 OeC1

has the expected H 2 dependence. Above H , weC1

see a series of peaks in the frequency that weinterpret as the signature of the first several fluxlines entering the sample. The field scale and the sizeof the sample are consistent with this interpretation.The first flux lines that go into the sample wandersignificantly away from the field direction to takeadvantage of the point disorder. As the field in-creases, more lines enter the sample and these wan-

Ž .dering lines start to interact. Fig. 5 b shows theresponse at a lower temperature ZFC field sweep.The Meissner regime once again is quadratic, but thepenetration of single vortices above H is some-C1

what different due to the stronger effects of pinningat lower temperatures. At this temperature, as theindividual vortices enter, there are mesas betweenthe jumps. If the field is cycled back and forth afraction of an oersted, the response in the mesas isreversible, but the jumps are not. The reason for thenon-monotonic behavior with increasing field is the

Fig. 5. Different field dependencies of the resonant frequency atŽ . Ž .fixed temperatures: a individual vortex penetration, b re-

versible mesas separated by irreversible jumps, associated with aŽ .single flux line entering the sample. The lower trace is B H

extracted by counting vortices.

( )F. Pardo et al.rPhysica C 332 2000 160–165 165

mesoscopic nature of our system. As the vorticesenter the sample, sometimes it means that the entireensemble is better pinned and the frequency in-creases, but sometimes, because of interactions, it isless well pinned and the frequency decreases. The

Ž .lower trace is B H extracted from the data byŽ .counting vortices. In this case for N H flux lines in

the sample and a sample cross-section area Ss22=2 Ž .1.6 mm , we have BfN H F rS. The data are a0

discrete approximation to the continuum predictionŽ .of a linear B H near H , consistent with pointCl

w xdisorder in 1q1 dimensions 4,5 . This result is instriking contrast to the vertical slope predicted byAbrikosov’s original theory of perfectly straight vor-tices in clean samples with exponential repulsion.

Taken together, Figs. 4 and 5 provide evidence ofthe mesoscopic behavior of a small number of vor-tices in a finite-sized sample where the details of thepinning sites produce sample-specific structure in themagnetization of the superconductor.

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w x10 http:rrwww.mcnc.org.