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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


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


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.


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°.



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.


�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

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