Development of Electron Holography and Its Applications to ... · In electron holography, the...
Transcript of Development of Electron Holography and Its Applications to ... · In electron holography, the...
PrintedwithpermissionofTheInstituteofPureandAppliedPhysics(IPAP)
JAPANESE JOURNAL OF APPLIED PHYSICSVol.47, No.1 (2008) pp.11-18 : Invited Review Paper
�JSAPInternationalNo.18(July2008)
Development of Electron Holography and Its Applications to Fundamental Problems in Physics
Development of Electron Holography and Its Applications to Fundamental Problems in PhysicsAkiraTonomura1,2,3,*
Wecannowutilizethewavepropertiesof
electronstoconductfundamentalexperiments
onquantummechanicsbecauseofthedevel-
opmentofbrighterelectronbeamsaswell
as theabilitydirectly to imagethequantum
worldbyutilizing thephase informationof
electrons.Inthispaper,wedescribenewpossi-
bilitiesthathavebeengeneratedbyelectron-
phasemicroscopyusingelectronmicroscopes
equippedwithcoherentyetbrightelectron
beams.
KEYWORDS:electronholography,Lorentz
microscopy, superconductor,
vortex, ferromagnet, Nb,
YBCO,Bi-2212
�. IntroductionElectronholographywasdevisedbyGabor
almostsixdecadesagoasameansofbreaking
throughtheresolutionlimitofelectronmicro-
scopes.1)He inventeda two-step imaging
method,holography, tobreak through the
resolutionlimitcausedbytheabsenceofaber-
ration-freelenssystemsinelectronmicroscopy.
Inholography,ahologramisfirstformedwith
electronsasan interferencepatternbetween
theobjectwaveanda referencewave.The
hologram is then illuminatedbya reference
opticalwavetoreconstructtheelectronwave-
frontsasopticalwavefronts.
Inelectronholography, theaberrations
in theelectron lens systemcanbeoptically
compensatedfor in its reconstructionstage.
Gabor'soriginalapproachwas in-lineholog-
raphy, where the electron wave passing
around the object is used as a reference
wave.1)Thiskindofhologramis,sotospeak,a
defocusedelectronmicrographphotographed
under coherent illumination, similar to the
FresnelfringesfirstreportedbyBoersch.2)
Although the ideaofholographywas
first demonstrated in optical experiments
by Gabor,1) the first experiment on elec-
tronholographywas carriedoutbyHaine
andMulvey,3)usingthein-linemethod.Their
reconstructedimagewas,however,disturbed
bytheFresnelfringesthatareproducedbythe
conjugate image,which isalways formed in
additiontothereconstructedimageinholog-
raphy.Hibi4)obtainedsimilar resultsusinga
pointedfilamenthedevelopedasacoherent
electronsource.
Thereconstructionofclear images, free
fromtheeffectsofconjugateimages,wasfirst
demonstratedbyLeithandUpatnieks5)using
off-axis laserholography,where the recon-
structedandconjugateimagescouldbesepa-
rated into twobeams traveling indifferent
directions. Itwas alsodemonstratedopti-
callybyDeVeliset al.6)thatimagereconstruc-
tionfreeofconjugate-imagedisturbances is
possibleeveninanin-lineholographyprovided
thathologramsareformedintheFraunhofer
diffractionareaoftheobject.
Encouragedby this experiment, Tono-
muraet al.7)demonstratedanelectronversion
ofthisFraunhoferholographyusinga100kV
electronmicroscopeequippedwithapointed
cathode, and clear-cut images were first
obtained. This in-lineholography entailed
some limitations, such as small sizes for
objectssurroundedbyclearspaces.However,
thecoherenceconditionsrequiredfortheillu-
minatingelectronbeamaremuch lessstrin-
gentthanthoseforoff-axisholography.
Off-axis electronholographywas first
carriedoutbyMöllenstedtandWahl,8)which
howeverhadtobemadeinone-dimensional
imagingtomakeupfor thepoorcoherence
of theelectronbeam.Aslit-shapedelectron
sourcewasemployed to formahologram
withmanycarrierfringes,andanimageofa
one-dimensional tungstenfilamentwasopti-
callyreconstructed.
Image formationusingelectronholog-
raphywasthusconfirmedtobefeasible.The
resolutionof the reconstructed imageswas
low (~50 Å) andnonew information was
obtainedbytheholography.Thepracticalreal-
izationofelectronholographyhadtowaitfor
thedevelopmentofacoherentfield-emission
electronsource,justasopticalholographyhad
towaitfortheinventionoflasers.
Inthispaper,weprovideanoverviewof
thepresentstatusofelectronholography,with
specialreferenceto itsrecentapplicationsto
problemsonfundamentalphysicsandalsoon
technologicalfrontiers.
�. Developments in Hologra-phy due to Advent of Coherent Beams
Wedescribe thehistoricaldevelopment
ofelectronholographyherewithadvancesin
coherentbeamtechnology,sinceabrightelec-
tronsourceusingfieldemissionswasthemost
decisivefactorinthedevelopmentofelectron
holography.
Although field emissionswere already
usedinafield-emissionmicroscopetoobserve
the tip surfacewithatomic-scale resolution
early in the20thcentury,9) itwasCreweet
al.10)whodevelopedapracticalfield-emission
gun for the scanningelectronmicroscope
(SEM)orscanningtransmissionelectronmicro-
scope(STEM),andgreatlyimprovedtheirreso-
lutions,particularly thatofSTEM, reaching
downtoatomicdimensions.11)Thisbeamis
alsosuitableasacoherentbeamforelectron
interferometery; itsbrightness isgreaterthan
thatofathermionicbeambymorethanthree
ordersofmagnitude,mainlybecauseastrong
electricfieldonthesurfaceofthecathodetip
producesnospace-chargeeffect. Inaddition,
theenergyspreadofthebeamisasnarrowas
0.3eVwhentheemissioncurrentislimitedto
10µA.Thissourcewasfirstusedonlyforscan-
ningmicroscopes,anditsaccelerationvoltage
waslimitedto30kV.
1 AdvancedResearchLaboratory,Hitachi,Ltd.,Hatoyama,Saitama350-0395,Japan2 FrontierResearchSystem,RIKEN,Wako,Saitama351-0198,Japan3 OkinawaInstituteofScienceandTechnology,Kunigami,Okinawa904-0411,Japan* E-mailaddress:[email protected](ReceivedMay28,2007;acceptedSeptember7,2007;publishedonlineJanuary18,2008) ©2008TheJapanSocietyofAppliedPhysics
JSAPInternationalNo.18(July2008)�
Westarted thedevelopmentofa field-
emissionelectronbeamatHitachi in1967
soonafterourexperimentson in-lineFraun-
hoferelectronholography.7)Fromourexperi-
encewith theholographyexperiments,we
realizedthatbrightelectronbeams,e.g.,laser
beams,wouldbeneededtoapplysuchholo-
graphictechniquestohigh-resolutionmicros-
copyforpracticaluse.Infact,theresolutionof
thereconstructedimagesusingapointedfila-
ment4)inourearlyexperiments7)didnoteven
reach thatof conventional electronmicro-
scopesduetothepoorcoherenceofelectron
beam.Ouroriginalobjectivetoovercomethe
resolutionlimitoftheelectronmicroscopesby
compensatingfortheaberrations inelectron
lenseswasbynomeansachieved.
Webegantodevelopbrighterfield-emis-
sionelectronbeams in1967andwehave
continuedtheeffortuptonow.Accelerated
electron-beamvoltageshigher than50kV
areneeded for transmissionelectronmicro-
scopes.However, thisdevelopmentwasnot
easy,sincetheelectricdischargeof thehigh
voltage in theelectronguneasilydestroyed
thetip. Inaddition,sincetheextremelysmall
electron source, typically50Å indiameter,
hadtobeimmobilizedtowithinafractionof
thesourcediameter,wehadtopreventeven
theslightestmechanicalvibrationof thetip,
theacceleratingtube,ormicroscopecolumn,
or thedeflectionof the finebeambystray
acmagnetic fields.Otherwise, the inherent
brightnessorluminosityoftheelectronbeam
woulddeteriorate.
After tenyearsofwork,wedeveloped
an80kVelectronbeam,12)whichwas two
ordersofmagnitudebrighter than thatof
the thermalbeamsused then (seeTable I).
Using thebeam,wewereable toobserve
electron interferencepatternsdirectlyona
fluorescentscreenfor thefirst time,andwe
wereabletotakeasmanyas3000 interfer-
ence fringesona film,whereas300fringes
hadbeenthemaximumuptothattime.New
informationthathadbeen inaccessiblewith
conventionalelectronmicroscopycannowbe
obtainedbyusingelectronholography.Since
the first successfuldevelopmentofabright
field-emissionelectronbeamin1979,wehave
continuedtodevelopevenbrighterelectron
beams.Thiswasmainlyachievedbyincreasing
thebeams'acceleratingvoltages.Anelectron
gunwithahigherenergy is largerandhas
thusmorespacetointroduceadditionalelec-
tron-opticalsystemstominimizetheblurring
oftheimageofthetinyelectronsourcedueto
aberrationsduringtheaccelerationprocess,e.g.,
byaddingamagneticlenstotheelectrongun.
Everytimeweincreasedbrightness,new
possibilitiesopenedupas shown inTable
I. Specific examples can be found in the
magnetic linesof force in themicroscopic
region,whichweredirectlyandquantitatively
observedinh /efluxunits13)inaninterference
micrographwithan80kVmicroscope.We
wereable tomeasure thephaseshiftswith
aprecisionassmallas1 /100ofanelectron
wavelengthwitha250kVmicroscope,14)and
carriedoutexperimentson theAharonov–
Bohm(AB)effect.Weobservedtherealtime
dynamicsofvortices inmetal15)andhigh-Tc
superconductors16)with350kV17)and1MV
microscopes.18) Ingeneral, thebrightnessof
anelectronbeamisproportionaltotheaccel-
eratingvoltage.Inreality,however,thebright-
nessoftheelectronbeamobtainedat1MVis
2×1010A / (cm2∙ster),whichismorethanone
orderofmagnitudehigherthantheexpected
value(1.2×109)estimatedfromthebrightness
at80kV.This isdue to thedecrease in the
aberrationsrealizedbyintroducingamagnetic
lenstotheacceleratingregion.Themaximum
numberofbiprism interference fringeswith
thisbeamincreasedfrom3,000to11,000.19)
Wesettledthecontroversyabouttheexis-
tenceof theABeffect (see§3.2.2) in1986
througha seriesofexperiments20–22)using
electron holography without ambiguities
aboutleakagemagneticfluxesfromsolenoids
ormagnets.
�. Applications�.� High-resolution microscopy
The resolution of the reconstructed
imageshasbeengreatlyimprovedduetothe
adventof thefield-emissionelectronbeams.
Forexample,Munch23)usedafield-emission
beamto improve the resolutionup to10Å
usingthein-lineFraunhoferholography.
Lattice imageswith2.4Åspacingwere
reconstructedby Tonomuraet al.24) using
off-axisholography,andsphericalaberrations
of the reconstructed imageswerecompen-
sated forusing the correspondingoptical
convex lens in the optical reconstruction
stage.25) Lichte26)numerically reconstructed
thelatticefringesofcarbonblackusingholo-
gramcarrier fringes (0.8Å)narrower than
latticefringes.Thereconstructed-imagereso-
lutionwasfurther improvedandtheaberra-
tionswerecorrectedbyOrchowskiet al.27)
FurtherprogresswasmadebyLichte'sgroup
andothers.
Thephase distributions of the recon-
structed imageswere successfullyused to
openupnewwaysofhitherto inaccessible
observationsonmicroscopicstatesofmate-
rials, suchas visualizing themagnetic lines
of force,13) equipotential lines,28) thickness
distributions,14)and innerpotentials.29)Many
noteworthyapplicationsarenowbeingdevel-
oped, suchas theobservationofmagnetic
domain structures in ferromagneticmate-
rials,30–32)dopantdistributions in semicon-
ductordevices,33,34) ferroelectricmaterials,35)
andvortexbehaviorsinsuperconductors.16,36)
�.� Fundamental problems with quantum mechanics
Therelativephaseofanelectronwave-
functioncannowbepreciselyanddirectly
measured,whichhasenabledeven“thought
experiments”tobecarriedoutonthefunda-
mentalsofquantummechanics.
3.2.1 Single-electron build up of interfer-ence pattern
Anelectroninterferencepatternisformed
in suchaway thata singleelectronexists
atone time in the“double slit”apparatus.
Feynmanet al.37)oncereferredtothistypeof
experimentas“impossible,absolutely impos-
sibletoexplaininanyclassicalway,andithas
TableI. Historyofdevelopmentofbrightelectronbeams.
Year ElectronmicroscopeBrightness
[A / (cm2∙ster)]Application
1968100kVFEEM
(Thermionicelectrons)1×106 Experimentalfeasibilityofelectronholography7)
1978 80FEEM 1×108 Directobservationofmagneticlinesofforce13)
1982 250FEEM 4×108 ConclusiveexperimentsofABeffect22)
1989 350FEEM 5×109 Dynamicobservationofvorticesinmetalsuperconductors15)
2000 1MVFEEM 2×1010 Observationofunusualbehaviorsofvorticesinhigh-Tcsuperconductors16)
FEEM:field-emissionelectronmicroscope
�JSAPInternationalNo.18(July2008)
accumulated elec-
t rons fo rmed the
interferencepattern
a s shown in F ig .
2(d),whichisformed
when the twoelec-
tronwavesofasingle
electronpassthrough
both s ides of the
biprismandoverlap
onthedetectorplane.
Evenasingleelec-
troncansplitintotwo
intheformofawave-
functiononbothsides
of the biprism. The
twopartial electron
waves then overlap
tointerfereontheobservationplaneandform
an interferencepatternofprobability.When
detected,however,theoverlappedwavesare
observedasasingleelectron,neveras two.
Thiscanbe interpretedas themeasurement
instantlymakingtheextendedwavefunctions
collapseintoasinglepoint.
Ourexperimentdescribed inFig.2has
oftenbeencited inphysicstextbooks,39)and
wasselectedandawardedasThe Most Beau-
tiful ExperimentsbyPhysicsWorld,40,41)which
was shared with an electron interference
experimentthatusestheactual finemultiple
slitscarriedoutbyJönssonin1961.42)
in it theheartofquantummechanics.This
experimenthasneverbeendone in just this
way, since theapparatuswouldhave tobe
madeonanimpossiblysmallscale”.
However, these thought experiments
havenowbecomefeasiblewiththeprogress
inadvancedtechnologies.38)Electronmicros-
copyallows small-scalemagnification,and
individualelectronscanbedetectedwitha
photon-countingdetector(HamamatsuPhoto-
nicsPIAS)modified tocount individualelec-
tronswithalmost100%efficiencyofdetec-
tion.Theexperimentswereactually carried
outwithafield-emissionelectronmicroscope
equippedwithbothanelectronbiprismand
atwo-dimensionalposition-sensitiveelectron-
countingsystem.AswecanobserveinFig.1,
electronsemittedfromafield-emissiontipare
senttothebiprism.The interferencepattern
is thenenlargedbymagnifying lensesand is
recordedby theelectron-counting system.
Individualelectronsaredisplayedasbright
spotsonaTVmonitor.Whenthereisasmall
numberofdetectedelectrons, theelectron
distributionappearstobequiterandomascan
beobservedinFigs.2(a)and2(b).However,
an interferencepatterngradually emerges
[Fig.2(c)]whenthenumberofbrightspots
increases,evenwhentherateofarrivingelec-
tronswas as lowas10electrons / s in the
entirefieldoftheview,meaningthatatmost,
onlyasingleelectronexistedatonetime.The
3.2.2 Aharonov–Bohm effectThe inexplicablebehaviorofelectrons is
not restricted to thedouble-slitexperiment.
Theinteractionofanelectronwavewithelec-
tromagneticfieldsalsocontradictsourrational,
classical concept. Forexample,electricand
magneticfieldsaredefinedasforcesexerted
onachargedparticle.However, theabsence
ofelectricandmagneticfieldsdoesnotneces-
sarilymeantheabsenceofvectorpotentials.
In fact,abeamofchargedparticlescanbe
physicallyaffectedintheformofphaseshifts,
evenwhenitpassesthrougharegionfreeof
magneticfieldsoutsideaninfinitelylongsole-
noidand is, therefore,notsubjectedtoany
forces.AharonovandBohm43)attributedthis
effect to vectorpotentialsexcitingeven in
thefield-freeregionoutsidethesolenoid.The
realityofvectorpotentialshasbeengreatly
disputedoverthepastcentury.44)Whenvector
potentials were extended togauge fields
particularly in the late1970s,andregarded
asa fundamentalphysicalentity in theories
unifying all fundamental forces innature,
theABeffect receivedmuchattentionas it
directly indicatedthegaugeprinciple.45)The
existenceof theABeffect thenbegantobe
questioned.46)TheABeffecthasbeencontro-
versialever since itwaspredicted.Until the
late1970s,however,discussionswerefocused
ontheoreticalinterpretationsoftheABeffect.
Theexperimentscarriedoutinthe1960swere
generallybelievedtodemonstratethattheAB
effectexisted.
BocchieriandLoinger47)claimedin1978
thattheABeffectdidnotexist.Theyasserted
that theABeffect isactuallygauge-depen-
dentandisapurelymathematicalconcoction.
According to their analysis, agauge func-
fig.1. Double-slitexperimentforelectrons.
Source
Detector
Electron biprism
fig.2. Buildupprocessofelectroninterferencepattern.Numberofelectrons:(a)8;(b)200;(c)6,000;(d)140,000. Thevideoclipcanbeseeninhttp://www.hqrd.hitachi.co.jp/global/fellow_tonomura.cfm
Invited Review Paper JAPANESE JOURNAL OF APPLIED PHYSICS
JSAPInternationalNo.18(July2008)�
tioncanbechosensothatvectorpotentials
completelyvanishoutsideaninfinitesolenoid:
consequently,thereisnoABeffect.47,48)They
alsoasserted that theSchrödingerequation
canbereplacedbyasetofnonlineardiffer-
entialequationscalledhydrodynamical equa-
tions,whichcontainonly field strengthsE
andB.ThereisthereforenoroomfortheAB
effect.
Theyalsoexpresseddoubts fromexperi-
mentalviewpointsabouttheexistenceofthe
ABeffect:48) theyclaimed that the interfer-
enceexperimentsmusthavebeenaffectedby
leakagefieldsfromsolenoidsorwhiskers.
Wecarriedoutaseriesofexperimentsto
clarify theambiguities raised in thecontro-
versy, and wehere introduce our experi-
ment,22)which isconsideredtobethemost
conclusiveone.
Weuseda toroidal ferromagnet instead
ofastraightsolenoid.Aninfinitely longsole-
noid isexperimentallyunabletobeattained,
butanequallyidealgeometrycanbeachieved
by the finite systemofa toroidalmagnetic
field.Furthermore, the toroidal ferromagnet
weusedwascoveredwithasuperconducting
niobium layer to completely confine the
magneticfieldwithinthetoroid.
Anelectronwavewas incident to the
tiny toroidal sample fabricatedbyusing the
mostadvanced lithography techniques,and
thephasedifferencebetweenthetwowaves
passing through thehole andaround the
toroidwasmeasuredintheformofaninter-
ferogram. If thephasedifference ispresent,
itshouldbegivenbye /h– timesthemagnetic
fluxenclosedbythetwowaves.
Although variousmagnetic flux values
wereused in themeasurement, thephase
difference was always either 0 orπ . The
conclusionswedrewarenowobvious.The
photographinFig.3 indicatesthatarelative
phaseshiftofπ isproducedevenwhenthe
magneticfieldsareconfinedwithinthesuper-
conductor and shielded from theelectron
wave.Thisclearlydemonstratesthatthere is
anABeffect.Anelectronwave isphysically
affectedbythevectorpotential.
Thequantizationof the relativephase
shift,inthisexperiment,either0orπ,proved
that the niobium layer surrounding the
magnet actuallybecame superconductive.
Whenasuperconductorcompletelysurrounds
amagnetic flux, the flux isquantized toan
integralmultiple of quantized flux,h /2e.
Whenanoddnumberofvorticesareenclosed
insidethesuperconductor, therelativephase
shiftbecomesπ (mod2π ).Thephaseshift is
0foranevennumberofvortices.Therefore,
theoccurrenceof fluxquantizationcanbe
usedtoconfirmthattheniobiumlayeractually
becamesuperconductive, that thesupercon-
ductorcompletelysurroundedthemagnetic
flux,andthat theMeissnereffectprevented
anyfluxfromleakingout.
�.� Imaging microscopic objects using electron phase information
TheABeffectcanalsobeusedtoobserve
themicroscopicdistributionsofelectromag-
neticfieldswithinamaterial.Morespecifically,
the thicknessdistributionwithinaspecimen
ofahomogenousmaterialcanbeobservedas
thicknesscontours inthe interferencemicro-
graphobtainedbyelectronholography.49)This
isbecausethephaseofanelectronwave in
thiscase isshiftedbythe line integralofthe
innerpotentialwithinthespecimenalongthe
electron trajectorywhen theelectronwave
passesthroughit.Althoughphaseshiftscan,
ingeneral,bedetectedfromstandardinterfer-
encepatterns“with”aprecisionofonly2π / 4,
theprecisioncanbe improvedto2π /100by
usingaphase-amplificationtechniquepecu-
liartoholography. Infact, thistechniquehas
allowedustothedetectchangesinthickness
duetomonatomicsteps14)andcarbonnano-
tubes.50)
3.3.1 Magnetic lines of forcePhaseshift isproducedbyvectorpoten-
tials.Whenthephasedistributionisdisplayed
asan interferencemicrograph, thecontour
fig.3. ConclusiveexperimentofABeffect.(a)Interferencepattern;(b)schematicofasample;(c)scanningelectronmicro-graphoftoroidalferromagnet.Electronwavespassingthroughinsideandoutsidethetoroidalmagnetarephase-shiftedbyπ bythequantizedmagneticfluxofh / (2e)thoughthewavesnevertouchthemagneticfields.
Magnetization
(a) (b)0.1µm
fig.4. Cobaltfineparticle.(a)Schematicdiagram;(b)interferencemicrograph.Onlythetriangularoutlineofthisparticlecanbeobservedbyelectronmicroscopy.However,twokindsofcontourfringesappearinitsinterferencemicrograph:narrowfringesparalleltotheedgesindicatethethicknesscontours,andcircularfringesintheinnerregionindicatein-planemagneticlinesofforce.
�JSAPInternationalNo.18(July2008)
vorticesproduced inaniobiumthin filmby
applyingamagneticfieldof100Gappliedto
thefilmandbyreversingthepolarityof the
field.Theoriginalvorticeswould like toexit
thefilm,butcannot immediatelydososince
theyarepinnedbydefects,whereastheoppo-
sitelyoriented vorticesbegin topenetrate
intothefilmfromitsedges.Wherethetwo
streamsof vorticesandantivortices collide
head-on, theheadsof thevortex–antivortex
ofvortexstreamsannihilateeachother.The
directobservationofthispairannihilationof
vorticescansimulatethatofparticlesandanti-
particles,sincevorticesareelementaryparti-
clesinsuperconductorsinthattheycannotbe
dividedanyfurther.
High-Tcsuperconductorshave longbeen
expectedtobeusedinpractice,buttheirlow
critical currentshave impeded theprocess.
Theircriticalcurrent is lowbecauseof their
high-temperatureoperationandtheir layered
structureofmaterials,bothofwhichenable
thevortices tomoveeasily.Wedevelopeda
1MVfield-emissionelectronmicroscope18) to
investigatethebehaviorofvortices inhigh-Tc
superconductors. The1MVelectronswere
required toobserve thevorticesso that the
electronscanpenetrateafilmthickerthanthe
magneticradius(penetrationdepth)ofvortices
inhigh-Tcsuperconductors.Weobservedthe
internalbehaviorof vortices insidehigh-Tc
Bi-2212(Bi2Sr2CaCu2O8+δ) thinfilmswiththis
microscope.
Columnardefectswereproducedbyirra-
diating the samplewithhigh-energyheavy
ions, which are considered tobeoptimal
pinningtrapsforvortices in layeredstructure
materials.As shown in theelectronmicro-
graph in Fig. 6(a), they are produced in
Bi-2212filmsastilted,whichcanbeobserved
as tinyblack lines.When these imagesare
defocused, theyareblurredandeventually
disappearcompletelybyspreadingout.When
theyaredefocusedeven further,however,
vorteximagesappear,sincetheyareproduced
bythephasecontrast.TheresultingLorentz
micrographofvorticesisshowninFig.6(b).
The micrograph reveals two different
kindsof images,circularandelongated.The
elongated images indicatedbythearrows in
themicrographareonlyproducedattheloca-
tionsofthecolumnardefectsandcorrespond
tovorticestrappedalongthetiltedcolumns.
Weconfirmedthevalidityof this interpreta-
tion in the simulation. The circular images
areproducedinregionswithoutdefects,and
thereforecorrespondtovorticesperpendicu-
larlypenetrating the film.Thishasenabled
us touse the vortex images to investigate
whether vorticesare trappedornotunder
variousconditions.51)
3.3.3 Unusual behaviors of vortices in high-Tc superconductors
Vorticesusually forma closelypacked
triangular lattice.52)Thisoccurseveninaniso-
tropichigh-Tcsuperconductors,aslongasthe
magnetic field isdirectedalong theanisot-
ropyc-axis.Whenthemagneticfieldissteeply
tiltedaway fromthec-axis,however,Bitter
imagesrevealthatthevorticesnolongerform
atriangularlattice.Instead,theyformarraysof
linearchainsalongthedirectionofthetilted
fieldasobservedinYBCO(YBaCu3O7.8),53)or
alternatingdomainsofchainsandtriangular
latticesas inBi-2212.54,55)While thechain
fringesindicatethemagnetic linesofforcein
themagneticfluxunitsofh /e inthecaseof
puremagneticfields.
There is an example observation of
magneticlinesofforceinsideaferromagnetic
fineparticle inFig.4.Narrowfringesparallel
totheedges indicatethethicknesscontours.
Thecircularfringesintheinnerregionindicate
magnetic linesofforce,sincethethickness is
uniformthere.
3.3.2 Vortices in superconductorsVorticesinsideasuperconductingthinfilm
canbevisualizedasblack-and-whitespotsina
defocusedimage,oraLorentzmicrograph.15)
Whenthefilm is tiltedandamagnetic field
isapplied, thusproducingvortices,electrons
passing through thevortices in the filmare
phase-shifted,ordeflected,by thevortices'
magneticfields.Thevorticescanbeobserved
bysimplydefocusingtheelectronmicroscopic
image.That is,when the intensityofelec-
tronsisobservedinanout-of-focusplane,the
phasechange is transformed intothe inten-
sitychangeandavortexappearsasapairof
brightanddarkcontrastfeatures.
We can thusobserve thedynamicsof
vorticesinrealtimeusingtheLorentzmicros-
copy.Observations include thebehaviorsof
vorticesatpinningcentersandsurfacesteps
undervarioussampletemperatureandapplied
magnetic field conditions. In fact, vortices
moveininterestingwaysasiftheywereliving
organisms.
There is an interestingexample inFig.
5,wheretwokindsofvortex images,whose
contrastsarereversed,appearinasinglefield
ofview.Theyareactuallyvorticesandanti-
fig.5. Annihilationofvorticesandantivorticesinthinfilmofniobium.(a)Beforeanni-hilation;(b)afterannihilation.Whenthemagneticfieldappliedtothefilmissuddenlyreversed,somevorticesremainatdefects,whereasothersbegintoleavethem.Antivor-ticesbegintomoveinfromtheedgesofthefilm.Wherestreamsofvorticesandanti-vorticescollidehead-on,thevortex–antivortexpairsoftheheadsofthetwostreamsannihilateeachother.
fig.6. Comparisonofcolumnar-defectimageandvorticesinBi-2212thinfilm.(a)Electronmicrograph;(b)Lorentzmicrograph.Somevorticesaretrappedatcolumnardefectsandothersareuntrapped.Theimagesofuntrappedvortexlinesperpendiculartothefilmplanearecircularspotshavingbrightanddarkregions.Vorteximageslocatedatthepositionsofcolumnardefectsareelongatedspotswithlowercontrastindicatedbythearrows,sincethesevortexlinesaretrappedatcolumnardefectstiltedat70°.
Invited Review Paper JAPANESE JOURNAL OF APPLIED PHYSICS
JSAPInternationalNo.18(July2008)�
stateinYBCOcanbeexplainedbythetilting
ofvortex lineswithin the frameworkof the
anisotropicLondon theory, thechain-lattice
state inBi-2212has longbeen anobject
ofdiscussion. Forexample,Grigorievaand
Steeds55)concludedfrombothBitterobserva-
tionsthatthechainvorticesandlatticevortices
arebothtilted,butindifferentdirections.On
theotherhand,Huse56)suggestedtwosetsof
vortices,onesetrunningparalleltothelayers
andtheothersetrunningnormaltothelayers.
However, thismodelwasnotabletoexplain
whythetwoperpendicularvorticescrosseach
othertoformstablechains,sincenointerac-
tiontakesplacebetweenthetwoperpendic-
ularmagneticfields.
In1999,Koshelev57)proposedasolution
forthechain-latticestate;Josephsonvortices
penetratebetweenthe layerplanesandthe
pancakevorticesthatperpendicularlyintersect
theJosephsonvorticesformchains;therestof
thevorticesformtriangular lattices.However,
Koshelevconsideredthesecond-orderapprox-
imation and determined that there was
energyreduction in thisvortexarrangement
byassumingthataverticalvortex linewinds
slightly inoppositedirections justaboveand
below the crossing Josephson vortex as a
resultof the interactionwith the Josephson
vortex; the circulating supercurrentof the
JosephsonvortexexertsLorentzforcesonthe
verticalvortexline.
Nodirectevidenceforsuchmechanisms,
however,was found throughexperiments
becauseof the lackofmethodsofdirectly
observing thearrangementsof vortex lines
inside superconductors.Lorentzmicroscopy
withour1MVelectronmicroscopewasused
todeterminewhetherthevortex lines inthe
chain states insidehigh-Tc superconductors
weretiltedornot.
Wefoundthatvortex lines inYBCOare
tiltedtogether inthedirectionoftheapplied
magneticfield,as isevidentfromtheLorentz
micrographs in Fig. 7, where the vortex
imagesbecamemoreelongatedandformed
linearchains togetheras thetiltingangleof
themagnetic field increased. In thecaseof
Bi-2212,ourobservationsbyLorentzmicros-
copyrevealedthatneitherchainvorticesnor
latticevorticestilted,butbothstoodperpen-
dicular to the layerplane.58) Inourpresent
experiment,wewerenotable todetect the
slightwindingsof thepancakevortex lines
Koshelevpredicted. Ifvortex linesweretilted
atananglecomparabletothatoftheapplied
magnetic field, thevortex images inFig.8
shouldhavebeenelongated.
Ourfindingthatbothchainvorticesand
latticevorticesinBi-2212standstraightalmost
perpendiculartothefilmplaneanddonottilt
isclearevidenceoftheKoshelevmechanism.
Althoughtheclearestevidenceforthismodel
wouldofcoursebegivenifJosephsonvortices
wereobservedalongchainvortices.However,
themagnetic field of a Josephson vortex
extendswidelybetweenthe layers, therefore
makingitdifficulttodetectwithourmethod.
Whenamagneticfield isappliedparallel
to the layerplane,no vertical vortices are
produced;therefore,novorteximagescanbe
observedinFig.8(a).EventhoughJosephson
vorticesparalleltothelayerplaneshouldexist,
thesevorticescannotbeobservedbyLorentz
microscopybecauseof thewidedistribution
ofthevortexmagneticfield.Whenthevertical
magnetic fieldBp increases,vertical vortices
begintoappearalongstraight lines indicated
by thewhitearrows inFig.8(b),whichare
considered tobedeterminedby Josephson
vortices. Since vorticesarearrangedalong
straight lines,wecouldfindnootherreason
for theproductionof chain vorticesother
thanassumingthatverticalvorticescrossing
Josephson vortices formchains.AboveBp
=1G,verticalvorticesalsoappearbetween
chainvortices,asshownin(c).
Thevorticesdonotformacloselypacked
triangular lattice,but theyare locatedalong
straightlines[Figs.8(b)and8(c)].Thereason
theyappearalongstraightlinesisthatperpen-
dicularvorticestendto lineupdenselyalong
theJosephsonvortices.
(a) (b) (c) (d)
2µm Tilted Vortex
B
fig.7. LorentzmicrographsofvorticesinYBCOfilmsampleattiltedmagneticfields(T=30K;Bp=3G).(a)θ=75°,(b)θ=82°,(c)θ=83°.(d)Schematicoftiltedvortexlines.Whenthetiltangleθbecomeslargerthan75°,thevorteximagesbegintoelongateand,atthesametime,formarraysoflinearchains.
fig.8. SeriesofLorentzmicrographsofvortices in field-cooledBi-2212 filmsamplewhenmagneticfieldBpperpendiculartolayerplanebeginstobeappliedandincreasesatfixedin-planemagneticfieldof50GatT=50K.(a)Bp=0;(b)Bp=0.2G;(c)Bp=1G.
Invited Review Paper JAPANESE JOURNAL OF APPLIED PHYSICS
�0JSAPInternationalNo.18(July2008)
Akira TonomuraisafellowofHitachi,Ltd.,agroupdirectorofRIKEN,andaprincipalinvestigatorofOkinawaInstituteofScienceandTechnology.HegraduatedfromtheUniversityofTokyo,DepartmentofPhysics, in1965and joinedHitachi,Ltd.Sincethen,hehasbeenengagedinexperimentalresearchesonelectronphysicsusingelectronmicroscopes.From1973hestayedforoneyearatTübingenUniversitytoresearchonelectroninter-ferometry.Heservedconcurrentlyasthedirectorofthenational“ElectronWavefrontProject”(ERATO)from1989to94.HewasawardedtheNishinaMemorialPrizein1982,theJapanAcademyPrizeandImperialPrizein1991,andtheBenjaminFranklinMedalinphysicsin1999.In2000,hewaselected
asaforeignassociateoftheNationalAcademyofSciencesintheUnitedStates.Since2005,hehasbeenalsoelectedasamemberofScienceCoun-cilofJapan.HeisnowamemberoftheJapanAcademy.Heisrecognizedforhispioneeringworkinthenewfieldofelectronholog-raphywhichwasmadepossiblebythedevelopmentof“coherent”field-emissionelectronbeams.Thismethodisusedforthedirectobservationofbothmicroscopicelectromagneticfieldsandmagneticvorticesinsupercon-ductors,andtheverificationoffundamentalphenomenainquantumme-chanicssuchasAharonov–Bohmeffectandsingle-electronbuild-upofaninterferencepattern.
of force inh /eunits and thedynamicsof
quantizedvortices in superconductors.This
measurementandobservation technique is
expectedtoplayan importantrole in future
researchanddevelopmentinnanoscienceand
relatedtechnology.
�. ConclusionsSome experiments that were once
regarded as “thought experiments” can
nowbecarriedoutbecauseofrecentdevel-
opments inadvanced technologies suchas
coherentelectronbeams,highlysensitiveelec-
trondetectors,andphotolithography.Inaddi-
tion, thewavenatureofelectronscannow
beutilized toobservemicroscopicobjects
thatwerepreviouslyunobservable.Examples
are thequantitativeobservationofboththe
microscopicdistributionofmagnetic lines
1) D.Gabor:Proc.R.Soc.London,Ser.A���(1949)454.
2) H.Boersch:Naturwissenschaften��(1940)711[inGerman].
3) M.E.HaineandT.Mulvey:J.Opt.Soc.Am.��(1952)763.
4) T.Hibi:J.ElectronMicrosc.�(1956)10.5) E.N.LeithandJ.Upatnieks:J.Opt.Soc.Am.��
(1962)1123.6) J.B.DeVelis,G.B.Parrent,andB.J.Thompson:
J.Opt.Soc.Am.��(1966)423.7) A.Tonomura,A.Fukuhara,H.Watanabe,and
T.Komoda:Jpn.J.Appl.Phys.�(1968)295.8) G.MöllenstedtandH.Wahl:Naturwissen-
schaften��(1968)340[inGerman].9) E.W.Müller:Z.Phys.�0� (1937)541[inGer-
man].10) A.V.Crewe,D.N.Eggenbeerger,D.N.Wall,
andL.N.Welter:Rev.Sci. Instrum.�� (1968)576.
11) A.V.Crewe,J.Wall,andJ.Langmore:Science���(1970)1338.
12) A.Tonomura,T.Matsuda,J.Endo,H.Todokoro,andT.Komoda:J.ElectronMicrosc.��(1979)1.
13) A.Tonomura,T.Matsuda,J.Endo,T.Arii,andK.Mihama:Phys.Rev.Lett.��(1980)1430.
14) A.Tonomura,T.Matsuda,T.Kawasaki,J.Endo,andN.Osakabe:Phys.Rev.Lett.��(1985)60.
15) K.Harada,T.Matsuda,J.Bonevich,M.Igarashi,S.Kondo,G.Pozzi,U.Kawabe,andA.Tonomura:Nature��0(1992)51.
16) A.Tonomura,H.Kasai,O.Kamimura,T.Matsuda,K.Harada,Y.Nakayama,J.Shimoyama, K.Kishio,T.Hanaguri,K.Kitazawa,M.Sasase,andS.Okayasu:Nature���(2001)620.
17) T.Kawasaki,T.Matsuda,J.Endo,andA.Tonomura:Jpn.J.Appl.Phys.��(1990)L508.
18) T.Kawasaki,T.Yoshida,T.Matsuda,N.Osakabe,A.Tonomura,I.Matsui,andK.Kitazawa:Appl.Phys.Lett.��(2000)1342.
19) T.Akashi,K.Harada,T.Matsuda,H.Kasai,A.Tonomura,T.Furutsu,N.Moriya,T.Yoshida,T.Kawasaki,K.Kitazawa,andH.Koinuma:Ap-pl.Phys.Lett.��(2002)1922.
20) A.Tonomura,T.Matsuda,R.Suzuki,A.Fukuhara,N.Osakabe,H.Umezaki,J.Endo,K.Shinagawa,
Y.Sugita,andH.Fujiwara:Phys.Rev.Lett.��(1982)1443.
21) A.Tonomura,H.Umezaki,T.Matsuda,N.Osakabe,J.Endo,andY.Sugita:Phys.Rev.Lett.��(1983)331.
22) A.Tonomura,N.Osakabe,T.Matsuda,T.Kawasaki,J.Endo,S.Yano,andH.Yamada:Phys.Rev.Lett.��(1986)792.
23) J.Munch:Optik��(1975)79.24) A.Tonomura,T.Matsuda,andJ.Endo:Jpn.J.
Appl.Phys.��(1979)9.25) A.Tonomura,T.Matsuda,andJ.Endo:Jpn.J.
Appl.Phys.��(1979)1373.26) H.Lichte:Optik�0(1985)176.27) A.Orchowski,W.D.Rau,andH.Lichte:Phys.
Rev.Lett.��(1995)399.28) S.Frabboni,G.Matteucci,andG.Pozzi:Phys.
Rev.Lett.��(1985)2196.29) M.Gajdardziska-Josifovska,M.R.McCartney,
W.J.deRuijter,D.J.Smith,J.K.Weiss,andJ.M.Zuo:Ultramicroscopy�0(1993)285.
30) R. E.Dunin-Borkowski,M.R.McCartney,B.Kardynal,M.R.Scheinfein,D.J.Smith,andS.S.P.Parkin:J.Appl.Phys.�0(2001)2899.
31) D. Shindo, Y.G. Park, and Y. Yoshizawa:J.Magn.Magn.Mater.���(2002)101.
32) Y.Zhu,V.V.Volkov,andM.DeGraef:J.Elec-tronMicrosc.�0(2001)447.
33) W.D.Rau, P. Schwander, F.H. Baumann,W.Höppner,andA.Ourmazd:Phys.Rev.Lett.��(1999)2614.
34) Z.Wang, T.Kato,N.Shibata, T.Hirayama,N.Kato,K.Sasaki,andH.Saka:Appl.Phys.Lett.��(2002)478.
35) H.Lichte,M.Reibold,K.Brand,andM.Lehmann:Ultramicroscopy��(2002)199.
36) T.Matsuda,S.Hasegawa,M.Igarashi, T.Kobayashi,M.Naito,H.Kajiyama,J.Endo,N.Osakabe,andA.Tonomura:Phys.Rev.Lett.��(1989)2519.
37) R.P.Feynman,R.B.Leighton,andM.Sands:The Feynman Lectures on Physics (Addison-Wesley,Reading,MA,1965)Vol.III,p.1.1.
38) A.Tonomura,J.Endo,T.Matsuda,T.Kawasaki,andH.Ezawa:Am.J.Phys.��(1989)117.
39) Forexample,P.A. Tipler:Physics (FreemanWorth,NewYork,1999)4thed.,p.509.
40) R.P.Crease:Phys.World��(2002)No.9,19.41) R.P.Crease:The Prism and the Pendulum: The
Ten Most Beautiful Experiments in Science(RandomHouse,NewYork,2003)p.190.
42) C. Jönsson:Z.Phys.��� (1961)454[inGer-man].
43) Y.AharonovandD.Bohm:Phys.Rev.���(1959)485.
44) C.N.Yang:inQuantum Coherence and Deco-herence,ed.K.FujikawaandY.A.Ono(Elsevier,Amsterdam,1996)p.307.
45) T.T.WuandC.N.Yang:Phys.Rev.D��(1975)3845.
46) M.PeshkinandA.Tonomura:Lecture Notes in Physics(Springer,Heidelberg,1989)Vol.340.
47) P.BocchieriandA.Loinger:NuovoCimentoA��(1978)475.
48) P.Bocchieri,A.Loinger,andG.Siragusa:NuovoCimentoA��(1979)1.
49) A.Tonomura:Electron Holography (Springer,Heidelberg,1999)2nded.
50) Q.Ru,G.Lai,K.Aoyama,J.Endo,andA.Tonomura:Ultramicroscopy��(1994)209.
51) A.Tonomura,H.Kasai,O.Kamimura,T.Matsuda,K.Harada,Y.Nakayama,J.Shimoyama, K.Kishio,T.Hanaguri,K.Kitazawa,M.Sasase,andS.Okayasu:PhysicaC���(2002)68.
52) U.EssmannandH.Träuble:Phys.Lett.A��(1967)526.
53) P.L.Gammel,D.J.Bishop,J.P.Rice,andD.M.Ginsberg:Phys.Rev.Lett.��(1992)3343.
54) C.A.Bolle,P.L.Gammel,D.G.Grier,C.A.Murray,D.J.Bishop,D.B.Mitzi,andA.Kapitulnik:Phys.Rev.Lett.��(1991)112.
55) I.V.GrigorievaandJ.W.Steeds:Phys.Rev.B��(1995)3765.
56) D.A.Huse:Phys.Rev.B��(1992)8621.57) A.E.Koshelev:Phys.Rev.Lett.��(1999)187.58) A.Tonomura,H.Kasai,O.Kamimura,T.Matsuda,
K.Harada,T.Yoshida,T.Akashi,J.Shimoyama,K.Kishio,T.Hanaguri,K.Kitazawa,T.Matsui,S.Tajima,N.Koshizuka,P.L.Gammel,D.Bishop,M.Sasase,andS.Okayasu:Phys.Rev.Lett.��(2002)237001.