Frontier 1

Direct Observation of
Vortices in Superconductors
by Using a Field-Emission Electron Microscope
Akira TONOMURA
Advanced Research Laboratory, Hitachi, Ltd.
Hatoyama, Saitama 350-0395, Japan
CREST, Japan Science and Technology Corporation
Kawaguchi, Saitama 332-0012, Japan

Abstract
A dissipation-free current can be obtained in a superconductor only when the tiny magnetic vortices,which penetrate a superconductor
when a magnetic field is applied, are pinned down against the current-induced force. These vortices in superconductors have become dynamicallyobservable by Lorentz microscopy using a 300-kV field-emission transmission electron microscope. As material defects can be observed while thevortices are being observed, the vortex pinning phenomena critical to the practical applications of superconductors can now be microscopicallyand dynamically observed.

1. Introduction
Vortices are closely related not only to thefundamentals of superconductors but also totheir practical applications of superconductors.
When we want to use a type II superconductor, for example, as a dissipation-free conductor of a large electric current, we need to keep
vortices from moving due to the Lorentz force
exerted on them by the current. Otherwise, thevoltage difference induced by the movementof magnetic flux eventually breaks down su-

perconductivity due to the dissipation. To increase the critical current at which vortices begin to move, we need to fix them in place. The
mechanism of the vortex pinning, however, is
not well understood because it is both microscopic and complicated. The efforts to develop
practical superconducting materials with large
critical currents have, therefore, largely beenprocesses of trial and error.
The direct observation of the vortex be-

SourceLens
A

B

Magnetic field

Prism

Fig. 1. Phase shift of electron beams enclosing magnetic flux
A relative phase shift between two electron beams starting from a source point, passing through points A and B in amagnetic field, and combining at an observation point is proportional to the magnetic flux enclosed by the two beampaths.

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JSAP International No.2 (July 2000)

havior at pinning centers was a dream of electron microscopists for almost 40 years.1-3), andwas finally realized4) by utilizing the phase information provided by a bright field-emission
electron beam.5-7)

2. Observation Principle
The principle behind the observation ofvortices is based on the use of the phase information of an electron wave transmitted
through magnetic fields of vortices.8) The phaseshift of electron waves due to electromagnetic
fields can be derived using the Schrödinger
equation. When the effect of electromagnetic
fields on electron waves is weak, the relative
phase shift ∆S between two beams startingfrom the same point, passing through points A
and B in electromagnetic fields (A, V), and combining at another point is calculated as follows.
S = (1/ h) o (mv - eA)ds = (1/ h) o ( 2meV - etA)ds....(1)Here t is the unit tangent vector of theelectron trajectory and the integration is carried out along a closed loop connecting thetwo electron trajectories. This equation showsthat the phase shift in an electron beam is determined by electromagnetic potentials (A, V)
rather than electromagnetic fields (E, B).
Aharonov and Bohm asserted that an electron beam can be affected physically (phaseshifted) by potentials even when it passes
through field-free regions on both sides of an
infinitely long solenoid and is therefore subjected
to no forces.9) This Aharonov-Bohm effect was
confirmed by using toroidal ferromagnets.10)

Magnetization

0.1 m

(a)

(b)

Fig. 2. Cobalt fine particle.
(a) Schematic diagram(b) Interference micrograph
Only the triangular outline of this particle is observed by electron microscopy. Two kinds of contour fringes appear in its interference micrograph8) : narrow fringes parallel to the edges
indicate the thickness contours, and circular fringes in the inner region indicate in-plane magnetic lines of force.

This principle has been used to observe
the microscopic distributions of electromagnetic
fields. To be more specific, the thickness distribution of a specimen uniform in material canin principle be observed because the phase ofan electron wave is shifted by the inner potential of the specimen when the wave passes
through it. For thickness changes in the atomic
range, though, the phase shift calculated from
Eq. (1) is smaller than 2π. More precise measurements of the electron phase became feasible with the development of a “coherent”
field-emission electron beam and electron holography.8) In fact, thickness changes due tomonatomic steps11) and carbon nanotubes12)
have actually been detected as phase shifts of
the order of 1/100 of 2π.
In the case of pure magnetic fields, thephase shift ∆S due to vector potentials can also
be calculated from the magnetic flux Φ passing through the closed loop connecting the two
trajectories:
S = - e o Ads = - ehh

BdS = - eh ....(2)When the phase distribution due to magnetic fields is displayed as an interference micrograph obtained through the electron holography process,8) it can be interpreted in the following straightforward way.
1. Contour fringes in the interference micrograph indicate magnetic lines of force, since

there is no relative phase shift (∆S) between
two beams passing through two points
along a magnetic line (see Fig. 1).
2. Contour fringes show magnetic flux in unitsof h/e, since the phase difference between
two beams enclosing a magnetic flux of h/e
is 2π.
Magnetic lines of force inside a ferromagnetic fine particle are shown in Fig. 2. Narrow
fringes parallel to the edges indicate thickness
contours. The circular fringes in the inner region indicate magnetic lines of force, since thethickness is uniform there.
Interference microscopy is not the only
technique that can be used to visualize thephase distribution. For example, a phase object can be observed in an out-of-focus image
because the phase change is transformed into
an intensity change when the image isdefocused. A vortex in a superconductor, whichacts as a pure weak phase object to an illuminating electron beam, has been visualized as a
black-and-white spot in a defocused image,or Lorentz micrograph.4)

3. Observation of Vortices inSuperconductors
Vortices can be detected by using thephase shift of an electron wave which inter-acts with the magnetic fields of the vortices.

3.1 Observation of magnetic lines
of force of vortices leaking fromthe superconductor surface
A thin-film sample was prepared by evaporating lead onto a tungsten wire from one direction. A magnetic field perpendicular to thefilm was applied, and the sample was cooled
to 4.5 K. Magnetic fields partially penetrating
the film were observed in an electron-holographic interference micrograph by using anelectron beam incident parallel to the film surface.
Interference micrographs13) for film thicknesses of 0.2 µm and 1 µm are shown in Fig.
3. The lower black region in each micrographis the shadow of the lead thin film, and thecontour fringes above it correspond to the magnetic lines of force in flux units of h/2e, since
the micrographs are phase-amplified by a factor of two. One fringe indicates the magnetic
line of force of a single vortex. It can be seenfrom these two micrographs that the mannerof magnetic field penetration varies for different thicknesses.
When the film is 0.2-µm-thick (Fig. 3(a)),
isolated vortices can be seen. A magnetic line
is produced from a region as narrow as 0.15µm and fans out into the free space on the left
side of the micrograph. A magnetic line form-

JSAP International No.2 (July 2000)

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ing an arc is also seen on the right. It is a magnetic line connecting an antiparallel pair of vortices. This vortex and antivortex pair was presumably created by thermal excitation due tothe Kosterlitz-Thouless transition and is thought
to be frozen to be pinned.
Magnetic lines of force penetrate a thicker
film not as individual vortices but as bundles ofvortices. No vortex pairs are seen in Fig. 3(b).
This can be interpreted as follows: when astrong magnetic field is applied to a thick filmof lead, which is a type I superconductor, thefilm is divided into normal and superconducting domains (intermediate state). Magnetic lines
of force can pass through normal regions. Sincea normal region is surrounded by a superconducting region, the total flux is quantized to
an integral multiple of h/2e. An extremely thinfilm, however, looks as if it were a type II superconductor.

(a)

2 m

(b)

2 m

Fig. 3. Interference micrographs of magnetic lines of force leaking outside from vortices in a thin film of lead (phase
amplification: A × 2).
(a) Film thickness = 0.2µm(b) Film thickness = 1.0µm
One contour fringe corresponds to the magnetic flux of one vortex, or h/2e. Individual vortices penetrate the film thinnerthan 0.5µm (mixed state), but bundles of vortices penetrate the thicker film (intermediate state).

3.2 Observation of vortices insidesuperconductors
Vortices inside a superconductor can beobserved when an electron beam passes
through a thin-film sample.14) The experimental arrangement for observing vortices in a superconductor is shown in Fig. 4. When a superconducting thin film is tilted and a magnetic

field is applied horizontally, electrons passing
through vortices in the film are phase-shifted,
or deflected, by the magnetic fields of the vortices. Consequently, when the phase distribution is observed as an interference micrograph,projected magnetic lines of force can be ob-served.15) However, by using this method it is
not easy to observe dynamics of vortices. Thiscan be done more easily by using Lorentz microscopy, in which vortices can be observed bysimply defocusing the electron microscopic
image. That is, when the intensity of electrons
is observed in a out-of-focus plane, a vortex
appears as a pair of bright and dark contrast
features ( Fig. 4).

A. Vortex depinning at different
defects

Electron Wave

Vortices

Defocused image

Fig. 4. Principle behind vortex observation.
An incident electron wave is phase-shifted, or deflected, by the magnetic fields of vortices. In the defocused
image, a vortex appears as a spot consisting of black-and-white contrast (Lorentz microscopy).

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JSAP International No.2 (July 2000)

Lorentz microscopy can reveal when andhow vortices are depinned when a driving force
is applied and increased. An example is shownin Fig. 5. Lines of point defects (black dots in
Fig. 5) in a thin film of Nb were produced byirradiating it with a focused Ga-ion beam andchanging the irradiation dose from line to line.
The dependence of the pinning force on theion doses producing the defects was investigated by observing behavior of the vortices
when the driving force was increased by changing the applied magnetic field.
When a magnetic field of 100 G was applied, vortices were produced so close together
that the vortices pinned at the defects could
not be distinguished from unpinned vortices.
When the magnetic field was decreased, only
unpinned vortices began to leave the film but
weakly pinned vortices also began to move:vortices hopped from one defect to anotheralong a defect line as if they were jumping over
stepping stones.

Frontier 1

Direct Observation of
Vortices in Superconductors
by Using a Field-Emission Electron Microscope

It can be seen from the Lorentz micrograph that all the unpinned vortices left thefilm during this experiment and that vortices
pinned at defects produced by the ion irradiation with the dose of 1000 times larger thanthe unit dose did not move at all. No vortices
remained trapped at defects produced by irradiation with less than 10 times the unit dose.
For the defects produced by irradiation with
20- and 70 times doses, some of the pinned
vortices were trapped at the defects depending on the ion dose.
If the critical current is to be increased, all
the vortices have to be pinned. When there aremany defects, vortices are pinned by them. Toomany defects lead to the destruction of the superconductivity, but there are other factors influencing the vortex pinning effect. The interaction between vortices, for example, plays animportant role in increasing critical current, especially when the magnetic field is strong.

1 m

Fig. 5. Vortices trapped at lines of defects.
The numbers below the micrograph indicate the Ga-ion doses in units of 10-10 C. Vortices are trapped more strongly at
defects produced by irradiation with larger doses.

B. Effect of vortex-vortex interaction on vortex pinning
When a weak magnetic field (< 7 G) wasapplied to a thin film of Nb containing widely
spaced defects with fairly strong pinning forces(ion dose of 70 times the unit dose), vortices
pinned at the defects did not begin to moveeasily, while unpinned vortices far from defects
began to move freely. Vortices passing near thedefects at which other vortices were pinned,
however, were deflected by the magnetic repulsive force between the pinned vortices andthe moving ones. Even unpinned vortices ingeneral did not move smoothly but hopped
from one point to another due to the existence of weak pinning centers inherent in Nb
samples, making the chance of vortices to collide with the vortices trapped at the defects at
a high speed. In that case, an additional vortex
sometimes entered a defect. However, twotrapped vortices were unstable since the defect radius (150 Å) was smaller than that of avortex (300 Å) and consequently in a few seconds one escaped from the defect. On rare occasions, vortices were even bounced from thevortex trapped at a defect.
Very interesting phenomena were foundto occur when vortices were densely packed.
Vortices in general repel each other because of
their magnetic fields. When they are squeezed
by an external magnetic field, however, theytend to form a closely packed lattice. In a material containing strong pinning centers (e.g.
defects), vortices cannot form a single lattice
but instead form domains of lattices ( Fig. 6).

1 m

Fig. 6. Vortex configuration near artificial point defects.
Red spots indicate point defects produced by irradiation with a focused Ga-ion beam, and green spots indicate vortices.
Vortices cannot form a single lattice since they are strongly trapped at the defects. When you look at this micrograph at
a grazing angle, you can see domain boundaries of vortex lattices.

JSAP International No.2 (July 2000)

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second, forming a new domain structure. Whenthe increasing force reached another criticalvalue, they flowed again along new domainboundaries. This process was repeated, resulting in intermittent vortex rivers here and there.
This was the first direct observation of vortices
flowing in the form of plastic flows.17), which
was confirmed by numerical simulations madeby Nori and his colleagues.18, 19)

C. Peculiar vortex pinning in anarray of pinning centers

1 mFig. 7. Video frame during river flow.
When a driving force is exerted on vortices that form domains of lattices due to the existence of point defects, thevortices begin to flow in rivers along the domain boundaries. The images of vortices in the rivers are blurred because
those vortices moved while this frame was being shot.

When a force was exerted on such a configuration of vortices and then increased, thevortices flowed intermittently along the domainboundaries.16) Each defect strongly pinned not
only a single vortex but also a domain of vortices. When the force reached a critical value,
the weakest regions of the vortex configura-(a)tion near the domain boundaries collapsed andvortices in those regions flowed in rivers.
A video frame of such a vortex river isshown in Fig. 7. The images of vortex inside
the river are blurred because those vortices
moved during the exposure time (1/30 sec) for
one frame. This flow stopped in less than a

The vortex pinning behaved completely
differently when the pinning centers weredensely arranged. This change in behavior occurred especially for a regular array of artificial
point defects produced in a Nb thin film, where
vortices formed regular and rigid configurationsat specific values of magnetic fields. The net
pinning force increased at these specific magnetic fields, which is known as the peak effector the matching effect of the critical current,
found by macroscopic measurements.
Lorentz micrographs showing the configurations of vortices relative to defect positions
are shown in Fig. 8. At the matching magnetic
field H1 (Fig. 8(b)), all the defects are occupied
by vortices and the lattice formed is a rigid
square one. The peak effect of the critical current observed macroscopically can be explained
microscopically: when vortices form a stable(b)

Fig. 8. Lorentz micrographs of vortices.
(a) H = 4H1 (H1: matching magnetic field)(b) H = H1(c) H = 1/4H1
Purple vortices form a regular and rigid lattice at these specific magnetic fields. If one of these vortices is thermally depinned from its red
site by any chance, it cannot find a stable vacant site to hop to, thus producing a strong pinning effect.

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JSAP International No.2 (July 2000)(c)

Frontier 1

Direct Observation of
Vortices in Superconductors
by Using a Field-Emission Electron Microscopeand regular lattice without vacancies, even if avortex is depinned from one pinning site dueto thermal excitation, it can find no vacant site
to move to. As a result, a stronger force is required to move the vortices.
Regular lattices were formed not only at
H = H1 (matching magnetic field, see Fig. 8(b))
but also at H = mH1/n (n and m; integers) as in
the case of H = 4H1 (Fig. 8(a)). In this vortex
configuration, defect positions forming asquare lattice were first occupied by vortices.
Then two vortices aligned in the vertical direction were inserted at every interstitial site, andfinally an additional vortex was inserted in the
middle of two adjacent defects located vertically. Figure 8(c) shows the case at H = 1/4H1.
Vortices occupy every fourth site in the horizontal direction, thus forming a centered (4 ×2) rectangle lattice. The reason the pinning force
as a whole becomes stronger at the specificvalues of magnetic fields comes from the factthat vortices form rigid and regular lattices.
When “excess” or “deficient” vortices
were produced at magnetic fields different fromthe specific ones, such vortices could hop under a weaker force (see Fig. 9), just like “electrons” and “holes” that flow in a semiconductor. On the other hand, when a stronger force
was applied to vortices forming a regular lattice, we observed a quite different flow of vortices such as a simultaneous movement of vortices along a lattice line.

just before the annihilation of such a pair andthe other just after. When this pair annihilated
each other, the next vortex and antivortex approached by hopping and annihilated eachother. The results of macroscopic measurements, such as magnetization measurementsof this state, provided no evidence of this phenomenon because the total magnetic flux inthis field of view is zero as long as the sample
contains equal numbers of vortices andantivortices. The annihilation process was revealed only when the vortices and antivortices
were individually observed in real time.
Antivortices have a dramatic effect onvortex pinning in the case where strong pinning centers exist locally. In fact, when the magnetic field applied to a film was decreased, only
the unpinned vortices left the film. Then,
antivortices were produced from the film edges
even though the magnetic field was not applied in the opposite direction. The produced
antivortices approached the trapped vortices atthe pinning centers, collided head-on with themand disappeared. The cause of the antivortices
is as follows: the magnetic lines of a trapped
vortex produced from the top surface of thefilm went the long way beyond the film edge
and returned to the original vortex from theback surface. Therefore, the direction of themagnetic field was opposite at the film edge,

thus producing antivortices at the edge.
The mutual annihilation of a trapped vortex and an incoming antivortex is equivalent to
the depinning of the trapped vortex. Therefore
when such an event occurs, the effective vortex depinning can take place easily.

E. Unconventional vortex movements in high-Tc superconductors
The critical current of high-Tc superconductors is, in general, very low because boththe high temperature and the layered structureof the materials make it easy for vortices in themto move. When the vortex movement at thedepinning threshold was investigated by gradually increasing the magnetic field applied tovortices in a high-Tc Bi2Sr2CaCu2O8+δ(Bi-2212)
superconductor, it was found that vortices
moved in quite different manners dependingon the applied magnetic field and the sample
temperature.21) In particular, the vortex movement above 25 K was quite different from that
below this temperature.
Below 25 K all the vortices migrated slowly
at almost the same speed (Fig. 11(a)). Their
speed was 1.5 µm/s at 20 K, and decreased
rapidly when the temperature was lowered.
Above 25 K, however, vortices moved in different forms of plastic flow depending on thestrength of the magnetic field. When it was

D. Effect of antivortices on vortex
pinning
We found unexpectedly during our observation experiments of vortices that
antivortices were often produced and had agreat influence on vortex pinning through theprocesses of creation and annihilation ofantivortices.20) This happened in commonplace
processes, such as magnetization measurements. When the magnetic field applied to a
Nb thin film was suddenly switched off, 90%of the vortices left the film instantly, 10% arepinned at weak pinning centers for a while,and then gradually left the film by hopping.
When the magnetic field was then applied in the opposite direction and gradually
increased, the speed of the vortices increased.
Before they left the film, however, antivortices
appeared at the edges of the film and moved
towards the inner region of the film. Where
streams of vortices and antivortices collided
head-on, the antiparallel pairs at the heads ofthe two streams annihilated each other.
Figure 10 shows two video frames, one

1 m

Fig. 9. Hopping interstitial vortex.
When the applied magnetic field is different from the specific values, “excess” or “deficient”
vortices are produced and can easily hop from one site to another just like the “electrons” or“holes” in a semiconductor when a driving force is applied to them.

JSAP International No.2 (July 2000)

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(a)

(b)

Fig. 10. Annihilation of vortices and antivortices in a thin film of niobium.
(a) Before annihilation(b) After annihilation
When the magnetic field applied to the film is suddenly reversed, some vortices remain at weakly
pinning defects while others begin to leave them. Antivortices begin to move in from the edges ofthe film. Where streams of vortices and antivortices collide head-on, the vortex-antivortex pairs of
the heads of the two streams annihilate each other.

less than 1 G, the extremely sparse vortices
trapped at preferential points suddenly hopped,
one by one, from one point to another (Fig.
11(b)). The hopping was so frequent and sudden that the vortex image on video looked as
if it were blinking on and off.
When the magnetic field was increased,
the slow migration movement evident below
25 K remained the same but the individual hopping movement above 25 K changed. The
forms of movement depended on how closely
the vortices were packed, and such forms asfilamentary flow, river flow, and lattice-domain
flow were observed as the magnetic field increased.
This temperature-dependent change inthe kinds of vortex movement seen in high-Tc
superconductors can be interpreted as a resultof vortices being pinned at extremely tiny defects, perhaps oxygen defects. The coherence
length (the radius of the normal core of thevortex) is as small as 10Å in Bi-2212, whereas
in niobium it is 300 Å. Therefore, below 25 K
vortices are trapped by oxygen defects, which
act as densely distributed pinning centers. Sincea single vortex line penetrating a film 2000 Å
thick may be collectively pinned by more than
100 oxygen defects, it would appear to movesmoothly in the direction of the applied force.

2 m(a)Fig. 11. Movement of vortices in a thin film of Bi-2212(a) Migration movement below 25 K(b) Hopping movement above 25 K
At temperatures below 25 K a single vortex line is collectively pinned by a great number of oxygen defects and migrates
slowly, assisted by thermal activation, when a driving force is applied. Above 25 K the oxygen defects no longer have apinning effect strong enough to withstand the increased thermal vibration of the vortices, and the pinning effect atlarger defects, which predominates at higher temperatures, results in hopping movement.

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JSAP International No.2 (July 2000)(b)

Frontier 1

Direct Observation of
Vortices in Superconductors
by Using a Field-Emission Electron MicroscopeThis is because the thermally activated vortex
line would begin to be depinned from these
defects one by one on one side of the line andto become pinned at new defects on the otherside. This would result in a migration that resembles the movement of an object through aviscous fluid.
Increased thermal vibration, however,causes the vortices to be easily depinned fromsmall defects, and above 25 K the pinning effect of the oxygen defects practically vanishes.
The pinning at other larger and sparser defects,
which below 25 K is hidden by the strong pinning at oxygen defects, predominates above
25 K because the pinning at larger defects isless influenced by thermal vibration.
Since these larger defects are distributed
more sparsely, vortices depinned from one defect hop to another. When vortices become
more abundant and form a closely packed lattice, it becomes difficult for them to move individually. The specific forms of movement are
determined by the competition between random pinning forces and vortex-vortex forces.

4. Conclusion
Vortices in superconducting thin films
were directly observed by monitoring the phaseof an electron beam passing through them. This
became possible after a bright electron beamand phase-imaging techniques were developed.
The microscopic mechanism of vortex pinning
was investigated by using these techniques toobserve vortices depinned from material defects
by applying an increasing force. A 1000 kV
field-emission transmission electron microscope22) has just been developed (Fig.12) andwill be used to explore many interesting features of vortices in high-Tc superconductors. Applications of this new microscope are not limited to superconductivity. A bright electron
beam having an extremely short wavelength
will bring to the nanoscopic region in scienceand technology new possibilities, especially inhigh-precision measurements and in fundamental experiments in quantum mechanics, justas other bright sources such as synchrotron
radiation sources and neutron sources now do.

Fig. 12. 1000-kV field-emission transmission electron microscope.

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