Magnetic imaging by spin-polarized scanning tunneling spectroscopy applied to ultrathin Fe/W (110) films

Spin-Polarized

Scanning Tunneling Spectroscopy

Applied to

Ultrathin Fe/W(110) Films

Dissertation

zur Erlangung des Doktorgrades

des Fachbereichs Physik

der Universität Hamburg

vorgelegt von

Oswald Pietzsch

aus Hamburg

Hamburg

Prof.Dr. RolandWiesendanger

Prof.Dr. RobertL.Johnson

Prof. Dr. MichaelFarle

Gutachter derDisputation:

Prof.Dr. RolandWiesendanger

Prof.Dr. HansPeter Oepen

Datumder Disputation:

14.5.2001

Vorsitzender desPromotionsausschusses:

Inhaltsangabe

Die Erforschung immer kleinerer magnetischer Strukturen bis hinab zur

atomaren Skala ist aktuell von groÿem wissenschaftlichen Interesse.

Zu-gleich ist dieser Forschungszweig von höchster technologischer Bedeutung

für die Entwicklung magnetischer Datenspeicher extremer Dichte sowie für

dieErschlieÿung desneuen GebietsderMagneto-Elektronik. Dieinder

vor-liegendenArbeitvorgestelltemagnetischsensitiveMikroskopie-Methode der

spin-polarisiertenRastertunnelspektroskopieisteinneues,äuÿerst

leistungs-fähigesForschungswerkzeug, dessenroutinemäÿiger Einsatzhier zumersten

Malzusammenhängend dargestellt wird. In seinemräumlichen

Auflösungs-vermögenübertritdasVerfahrendiebislangeingesetztenMethoden

höchst-auflösendermagnetischerMikroskopie umzweiGröÿenordnungen.

Nach einer im Kapitel 1 gegebenen allgemeinen Einführung werden die

theoretischenGrundlagenderspin-polarisiertenRastertunnelmikroskopieim

Kapitel 2 dargestellt. Es folgt in Kapitel 3 eine eingehende Beschreibung

des instrumentellen Aufbaus des speziell für magnetische Untersuchungen

konzipierten Rastertunnelmikroskops. An dicken (50 Monolagen) und

dün-nen (7 Monolagen) Gd-Filmen, epitaktisch gewachsen auf W(110), werden

ersteUntersuchungenzurmagnetischenSensitivitätdesMikroskops

durchge-führtundwichtigeErkenntnissehinsichtlichderAnisotropieferromagnetisch

beschichteter Tunnelspitzen gewonnen; dies wird in Kapitel 4 beschrieben.

ZurEinführungindieUntersuchungdesSystemsnano-skaligerEisenstreifen

auf einem gestuftenW(110) Substrat wird in Kapitel 5 ein Überblick über

bereits publizierteErgebnisse gegeben,auf dieimWeiterenaufgebautwird.

Das System von Eisenstreifen wird dann im Kapitel 6 als Modell genutzt,

an dem praxisnah der magnetische Kontrastmechanismus des Mikroskops

erläutert wird. Mit einem auf höchste laterale Auösung optimierten

Ver-fahren wird das magnetische Domänensystem der Eisenstreifen sodann im

Detail untersucht, das durch ein kompliziertes Wechselspiel

widerstreiten-der Anisotropien auf der Nanometer-Skala bestimmt ist. Es wird sowohl

die in der Filmebene liegende Magnetisierung von Fe-Streifen einer Dicke

von lediglich einer atomaren Lage beobachtet, als auch die senkrecht zur

Filmebene stehende Magnetisierung von Streifen, die zwei atomare Lagen

dick sind. Diese Ergebnisse sind im Kapitel 7 dargestellt. Das Kapitel 8

ist Beobachtungen gewidmet, die am System der Eisenstreifen in variablen

magnetischen Feldern erzielt wurden. Es konnte eine vollständige

Hyste-resekurve bestimmt werden; dieder Hysterese zugrunde liegendenProzesse

werden im Detail beobachtet. Damit wird zugleich die wichtige Tatsache

demonstriert,dassspin-polarisierteRastertunnelmikroskopieauchinstarken

Abstract

Theexplorationofmagneticstructuresataneversmallerultimatelyatomic

 scale is currently a topic of great scientic interest. It is also of highest

technological relevance in engineering extreme density magnetic data

stor-age devices and developing the new eld of magneto-electronics. In this

presentworkspinpolarizedscanningtunnelingspectroscopy(SP-STS)is

in-troduced asanew, extremelyversatileinvestigation tool. For therst time,

itsapplication onaroutinebasisiscomprehensivelydemonstrated.

Regard-ingspatialresolution, thismethod surpassesother highresolution magnetic

microscopytechniques bytwo orders of magnitude.

After a general introduction given in Chapter 1 the theoretical

founda-tionsofSP-STMwillbepresentedinChapter2. Theinstrumentalsetupofa

scanningtunnelingmicroscope,customdesignedforthepurposeofmagnetic

investigations, is described in Chapter 3. First results in the study of the

microscope's magnetic sensitivity were obtained on thick (50 monolayers)

andthin(7 monolayers) Gdlms grown epitaxiallyonW(110). These

mea-surements also provided important insights into the magnetic anisotropies

oftunnelingtips coatedbyferromagneticthinlms and willbe discussedin

Chapter 4. As an introduction to the investigation of the system of

nano-scale ironwires grownon astepped W(110)substrate anoverviewof

previ-ously published results will be given inChapter 5. Arrays of Fe nanowires

willthenbeusedinChapter6asamodeltodiscussthepracticalapplication

andthemagneticcontrastmechanismofthemicroscope. Optimizedfor

high-estspatialresolution,themethodwillthenbeappliedtoa detailedstudy of

themagnetic domain structure of the Fe stripeswhich are characterized at

the nanometer scale by a complicated interplay of competing anisotropies.

In Chapter 7 observations of stripes of single atomic layer thickness and

stripesoftwo layersthicknessaredescribed,themagnetization beinginthe

lmplane forthe former,and perpendicularto thelm planefor thelatter.

Chapter 8 is dedicated to observations made on the array of Fe stripes in

variable external magnetic elds. A complete hysteresis loop is presented,

acquiredat the nano-scale. Also, detailsof theremagnetization processlike

domainwallmotion,domain creationandannihilation, areobserved. These

resultshighlight theimportantfactthatSP-STS canroutinelybeappliedin

1 Introduction 2

2 Theory of SP-STM 9

2.1 TheTunnel Eect . . . 9

2.2 TheTunneling Process intheSTM . . . 11

2.3 ScanningTunneling Spectroscopy . . . 16

2.4 SpinPolarized ScanningTunneling . . . 19

2.4.1 SpinPolarized Constant Current Imaging . . . 20

2.4.2 SpinPolarized ScanningTunneling Spectroscopy . . . 22

3 Instrumental Setup 25 3.1 The Cryo STM . . . 25

3.1.1 Chamber system . . . 25

3.1.2 MagnetCryostat System. . . 26

3.2 STM Design. . . 28

3.2.1 Approach Mechanism . . . 30

3.2.2 SampleRotation . . . 31

3.2.3 TipExchange Mechanism . . . 33

3.2.4 ElectricalConnections . . . 34 3.3 Performance . . . 34 3.3.1 MicroPositioning. . . 34 3.3.2 AtomicResolution . . . 35 4 Results on Gd(0001)/W(110) 37 4.1 Thick Films . . . 37 4.2 Ultrathin Films . . . 40

4.2.1 Conclusionsand Open Questions . . . 45

5 Fe/W(110) Films: Previous Results 46 5.1 Morphology . . . 46

6 Spin Polarized Imaging 50

6.1 UncoatedTips . . . 50

6.2 MagneticallyCoated Tips . . . 51

6.2.1 SpinResolved Spectraof 1.5MLFe/W(110) . . . 52

6.2.2 TheImpact ofBiasVoltage on theContrasts . . . 54

6.2.3 Accelerated DataAcquisition . . . 57

6.3 TipIssues . . . 58

6.3.1 TipMagnetic Anisotropy . . . 58

6.3.2 Tip-Sample Interaction. . . 59

7 The Domain Structure of Fe Nanowires 61 7.1 Overview . . . 61

7.2 Magnetization inMono-andDouble Layers Fe . . . 63

7.2.1 DomainWalls . . . 68

8 Field Dependent Measurements 72 8.1 TheDevelopment of theDomains . . . 72

8.1.1 Hysteresisat theNano-Scale . . . 76

8.1.2 Mechanismsof Magnetization Reversal . . . 77

8.1.3 ResidualDomains . . . 78

8.2 TipswithIn-Plane Anisotropy . . . 80

8.3 Non-Magnetic Tips . . . 85

8.3.1 DomainProperties . . . 89

8.3.2 Outlook . . . 91

9 Summary 92

Introduction

Thequestforanunderstandingofmagnetismatanatomiclengthscaleisone

ofthecurrentfrontiersincondensedmatterandmaterialsscience. Thanksto

greatadvancesinultrahighvacuum(UHV) technology andmolecular beam

epitaxy(MBE) techniquesduringthe pastdecadeithasbecomepossibleto

study magnetism underthe conditionof reduced dimensionality,such asin

ultrathin lms of magnetic material, in nanowires, clusters, or even single

adatomsonasurface. Magneticmaterialsoftwo,one,orzerodimensions

ex-hibita largenumberof surprisingproperties. Theseareof greatinterestfor

fundamental research. Although considerable experimental and theoretical

progresshasbeenachievedinthelast fewyearsthesubjectmatterismainly

still inthe eldof basic research. Inrecent years themain driving force in

thiseld, however, camefrom appliedphysicsand technology. The demand

for ever higher data storage and processing capacity intensied the

world-wide requestfor nano-techniquesthatpromise to be ableto tailormagnetic

materialsexhibitingwelldenedproperties. Thediscoveryofthegiant

mag-netoresistance eect (GMR) [13] adecade ago hasinitiated a vast amount

of research activities, and it also had an enormous impact on technology

relatedto magnetic data storage. It is a unique situation that, despite the

factthatmanyriddlesstill haveto besolved, thetechnologicalapplications

alreadyhavereachedthemassmarket,theperhapsmostprominentexample

beingIBM's hard diskreadhead which isbasedon theGMReect.

Currently, the data storage industry reports an increase in areal data

densityof60 percent annually. While, for futuresystems,thespin

informa-tionofasingleatomisconceivedthe ultimate physical unitto magnetically

store a bit of information, the next serious obstacle to soon be approached

technologically is the superparamagnetic limit. Decreasing bit sizes lead to

signalenergiesbecomingsosmallastobecomparablewiththeambient

ther-mal energy, resulting in a decay of the stored magnetic signal. The lower

limitforthemagneticgrainsize(whichisequivalenttoaswitchingunit)has

recentlybeenestimatedto 600nm 3

In general,GMRdevices relyonmultilayerstacksof magnetic and

non-magnetic metallic ultrathin lms of nanometer thickness, i. e. on vertical

magnetic nanostructures. The study of laterally structured nanomagnetic

systemsof only one or zero dimensionswas hamperedin thepastbya lack

of an adequate magnetic imaging technique being able to provide a

resolu-tion thatcould holdpacewiththe reductioninsize of theentities thatcan

beproducedinacontrolledfashion(foranoverviewontherelevanceofsuch

structuressee, e. g.,[5]).

InthisworkIwillpresentspinpolarizedscanningtunnelingspectroscopy

(SP-STS)asanew, extremelyversatileimagingtoolfor thestudyofsurface

and thin lmmagnetism. The newmethod combines the well known

capa-bility of a scanning tunneling microscope (STM) to achieve highest spatial

resolution witha sensitivityfor thespin of the tunneling electrons. In this

waySP-STSallows tocorrelate structural,electronic, andmagnetic

proper-ties ofa sampleat an unprecedented spatialresolution.

ToputSP-STS inperspective,ashortreviewofother magneticimaging

methodscurrently inuseisgiveninthe following. The mostwidelyapplied

experimental method in the study ofultrathin ferromagnetic lms is based

on the magneto-optical Kerr eect (MOKE). A beam of polarized light is

directedontothemagneticsample,andtherotationofthepolarizationinthe

reectedlightrevealsthemagneticproperties. Themethodiseasytoemploy,

providesa resonable surfacesensitvity (atapenetration depthof 20 nm)

and is robust in an applied external magnetic eld. The spatial resolution

of MOKE microscopy, however, is ultimately limited to about 300 nm by

the wave length of the probing light. It is clear that the received signal is

an average over the respective surface fraction. MOKE hasbeen employed

in scanning near-eld optical microscopy (SNOM) in order to circumvent

this limitation. A lateral resolution of approx. 50 nm has been obtained

so far [6]. MOKE is the method of choice to measure spatially averaged

hysteresiscurvesof thinlms.

Scanning electron microscopy with polarization analysis(SEMPA)is an

ultra-high resolution magnetic imaging technique. A nely focused beam

of electrons is scanned across the surface, and the spin polarization of the

secondaryelectronsemittedfromthesampleisanalysed. Thelateral

resolu-tion limit dependsonly on the beamwidth; the signal intensities, however,

get extremely small eventually. This method allows to measure all three

magnetization components simultaneously. The surface sensitivity is very

high(1 nm probingdepth), and thelateral resolution is about 20 nmup

to-date[7,8]. Itisaseveredrawbackofthistechnique thatmeasurementsin

strongappliedmagneticeldsare,exceptforveryspecialcases,notpossible.

InLorentzmicroscopyatransmissionelectronmicroscope(TEM)isused

to measure the deection of an electron beam due to the magnetic

leading to a cancellation of the signalin certaingeometries. Several modes

ofapplication areused, e.g. the defocused or Fresnel mode, or the

dieren-tialphasecontrast (DCP)mode,thelatterreachingaresolutionbetterthan

10 nm [9]. A review of the various modes of operation is given in [10] and

referencestherein.

Using photons for probing and also for signal detection has the great

advantage thatlarge external magnetic eldscan be applied to thesample.

ThishasbeendemonstratedatX-raywavelengthsbymagnetictransmission

X-ray microscopy (MTXM) [11]. Themethod relies on theX-raymagnetic

circular dichroism (XMCD) as a contrast mechanism and is unique in that

it provides chemical sensitivity. Absorption rates at element-specic core

levels exhibit adependenceon the projection of themagnetizationonto the

photonpropagation directioninferromagneticsamples. A lateralresolution

of25 nmhasbeen reportedrecently [12].

A new versatile technique for magnetic domain observation has been

developed by a combination of X-ray magnetic linear dichroism (XMLD)

spectroscopyand photoelectron emissionmicroscopy(PEEM) [13]. The

ex-cited secondary electrons give rise to the signal in the PEEM and provide

a spatial resolution of  20 nm. The sampling depth of XMLD-PEEM is

about 2 nm. Recently, ithasbeen shown [14] bya combined application of

thelinearandcirculardichroismeectandanX-raysourcetunableinenergy

thatmeasurementsonbothsidesofaninterfaceconsistingofultrathinlayers

of antiferromagnets and ferromagnets can be carried out opening the door

for abetter understandingof theexchange bias eect whichis ofhigh

tech-nologicalrelevancefor tailoringthe characteristicsofmagnetic propertiesin

magneto-electronic devices.

In magnetic force microscopy (MFM) the external magnetic stray eld

ofthe sampleisprobedbyamagnetictipxed toa exiblecantilever. Two

modesofoperation areinuse. Either themagneticdipolar forceexertedon

thetipbythe samplestrayeldismeasuredviathecantilever deection,or

the force gradient is measured by oscillating the cantilever at its resonance

frequencyanddetecting theshift infrequency dueto thestrayeld

interac-tion. The lateralresolution achieved sofar isabout 2050 nm[15,16]. This

method has reached a considerable degree of industrial applications since,

ifmoderate resolution is sucient, itcan be applied at ambient conditions.

For ahigher resolution ultra-high vacuum(UHV) isrequired.

Pierce [17] expecteda scanningtunneling microscopeto betheultimate

microscopicalmagneticinvestigationtoolifthetipitselfisa source of

spin-polarizedelectrons. Scanningtunnelingmicroscopy(STM)anditsderivative

scanningforcemicroscopy(SFM)aretheonlytechniquesavailableproviding

real space images of surfaces at theultimate, atomic resolution. After rst

reports on spin-polarized vacuum tunnelingbyWiesendanger et al. [1820]

STM (SP-STM) studies are still extremely rare up to-date. This is owed

partlyto certaintechnical diculties(e.g.one needsareliablein situtip

ex-change mechanism inorder to compare measurements taken with normal

tipsto thosetaken withspinpolarizedtips),butthemainproblemisto

un-ambigiouslydiscriminatemagneticallycausedcontrastsfromthosecausedby

otherfeaturesoftheelectronicdensityof statesneartheFermilevel. Apart

fromtheinstrumentalproblemsjustmentioned thequestionofassigningthe

observed contrasts inSP-STM imagesto magneticproperties ofa sampleis

ofa morefundamentalnature. Ingeneral, onlya smallmodication of

con-ventional STM images due to spin polarization was anticipated. Applying

theargumentthatthetunnelingcurrent isdominatedbythedelocalizedbut

only weakly polarized s;p electrons, Himpsel et al. [5] expected an

appre-ciable spin-polarized contribution only at rather short tunneling distances,

i.e.at hightunnelingcurrentswhere localized3d statesofhighpolarization

gain weight. However, the authors already pointed to d-like surface states

identied byStroscio et al. [21] at Fe andCr surfaces using an STMinthe

spectroscopic mode of operation. Indeed, when Bode et al. [22] succeeded

in resolving the magnetic domain structure of thin Gd lms they operated

their SP-STM in the spectroscopic mode, and it was the well-known

spin-split surface state of Gd that gave rise to the magnetic signal. As will be

described theoreticallyinChapter2and furtherillustrated byexperimental

results in Chapters 4-8, SP-STS can directly address such highly polarized

features by selectively evaluating their density of states at a properly

cho-senenergy. Making use ofthe spin valve eectone can measurelocallythe

dierential conductance dI=dU which will be dierent for a parallel or an

antiparallel congurationof the magnetization of tipand sample. By

map-ping the dI=dU signal as a function of the lateral tip position an image of

themagnetic domain structure of the sample can be obtained. In this way

domainimaginghasbecomepossibleatanunprecedentedspatialresolution.

Moreover,sincethetopographyofthesamplecan beimagedinconventional

constantcurrent imagingmodesimultaneouslytothedI=dU mapthe

struc-tural,electronicand magneticproperties ofthesample canbecorrelated at

highprecision. An exampleis displayed in Fig 1.1. There isone important

conclusion thatcan be drawnat rstsight froma comparison ofa constant

current image and a simultaneously recorded dI=dU map: while an eect

of spin polarization is hardlymeasurable in many cases in thetopographic

image, the magneticcontrast is most obvious inthe dI=dU map. This

con-clusionwillbesupportedbynumerousexamplespresentedlaterinthiswork.

In recent years, threedierent experimental concepts have been applied

to achieve spin-polarized vacuum tunneling. (i) Ferromagnetic thin lm

probe tips have been used in the early experiments by Wiesendanger et

(dier-20 nm

Figure1.1: STMimagesof1.5MLFeonasteppedW(110)singlecrystal. (a)T

o-pographicimageacquiredin constantcurrentmode,(b)simultaneouslymeasured

dI=dUmap. Thecontrastsin(b)revealthemagneticdomainstructureofthe

sam-plewhichisinvisiblein(a). Tunnelingparameters: I =300nA,U = 300mV.

gurationsof tip and sampleexploiting the spin valve eect. (ii) GaAshas

been used as sample or as tip material because of its optical polarization

properties. Alvaradoetal. [23]injected spinpolarizedelectrons fromabulk

ferromagnetic tipand measured the circular polarization of the

recombina-tion luminescence. Jansen et al. [24,25] applied GaAs tips as a source of

spinpolarizedelectronsbyopticallypumpingwithcircularly polarizedlight.

(iii)Usinganamorphousmagnetictipmaterial oflowcoercivityin

conjunc-tionwitha smallcoil wound around thetip Wulfhekelet al. [26,27]rapidly

switched the tipmagnetization byapplying ahighfrequency a.c. current to

the coil and measured the dierential magnetic conductance dI=dm

t using

alock-intechnique.

The experimental results reported in this work were achieved following

Bode's approach. While in one of the early spin-resolved experiments tips

made from bulk ferromagnetic material have been used [20], here

conven-tionalnon-magnetictungstentipscarryinganultrathinlmofferromagnetic

materialareappliedmainlyfortheadvantageofamuchlower strayeld

ex-erted by the highly reduced quantity of magnetic material at the tip. In

orderto use such tipsit ismandatory to have facilities available to prepare

tips in situ, i.e. to clean them in UHV from oxide layers, to grow

epitax-ial lms on them in a controlled fashion, and to insert a tip into the STM

withoutbreakingthevacuum. Theserequirementsarefarfrombeingtrivial

tofulll, and therearebut asmall number ofexperimentalsetups available

wordwideifanythatallowforsuch anarrangement. InChapter3Iwill

describe indetail how theseproblems have been resolved.

Thestartingpointfortheexperimentalpartofthisworkwillbein

Chap-ter 4 a presentation of some early results obtained on Gd lms grown on

W(110)intworanges ofthickness. Filmsof 50 monolayers (ML)Gdserved

asa rst test systemfor thegeneral magnetic sensitivityof the new

micro-scope. Next, results from a lm of only 7 ML Gdwill be described. It has

dicularto the sample plane. Although this study remained incomplete due

to certainexperimentalproblems theresults turned out later to be of great

value in a rather unexpected way. It provided the freedom of choice with

regard to themagnetic anisotropy ofthetip, and thisis themain reasonto

presentthe datahere.

The main focus throughout this work will be on the magnetic domain

structure ofthe system of1.5 MLFe grown ona stepped W(110) substrate

whichwillbecoveredinChapters5-8. Thissystem,foranumberofreasons,

provides an excellent model to demonstrate the power of SP-STS. First of

all,acomprehensivecorpsofliteratureisavailable,themajorityofthe

publi-cationsbeingconnectedto theworkofUlrichGradmannandHans-Joachim

Elmers. Thanksto the longterm workof theirgroups thegeneral magnetic

structureofultrathin Felms onW(110)iswell known. A shortreviewwill

be given inChapter 5. It isan important prerequisite for a new method in

order to establish its validity that it is able to reproduce earlier conrmed

results. Albeit,asIwillshowinChapters6-8,thereismuchmoretodiscover

inasystemascomplexasthisone. Asasecondreason,thetypicalmagnetic

domain widths of the Fe lms are below the resolution limit of established

domain imaging techniques but are in a range which is particularly suited

for STMimaging.

The magnetic characteristics of 1.5 ML Fe/W(110) are determined by

an in-plane magnetization for areas covered by just a single atomic layer

of iron whereas areas covered by two atomic layers are magnetized

out-of-plane. Whengrownonavicinal W(110)substrateat elevatedtemperatures,

the iron lm forms a sytem of stripes extending along the tungsten step

edges. From the available literature it is known that the magnetization in

adjacent doublelayer (DL)stripespointsalternatingly upand down dueto

dipolar coupling. It was the main goal of the current study to resolve this

out-of-plane magneticstructure of the DL stripes,and iteventually showed

upasa strongbright-and-dark contrast (cf.Fig1.1(b)). WhileinChapter6

emphasis will be put on the details of the imaging process, Chapter 7 is

dedicatedto a discussionofthe magnetic domain structure ofthe sample.

As an ultimate proof of the magnetic origin of theobserved contrasts I

willpresent imageswhichwereacquiredfromasampleexposedto avariable

externalmagneticeld. Nexttoitsunrivaledspatialresolutionitisa

partic-ularstrengthofthe SP-STStechnique thatitcanbeapplied instrong

mag-netic elds. In Chapter8this featurewill bedemonstrated alonga detailed

study ofthe magnetization reversalin ultrathinmagnetic nanowires. Based

oninformationacquiredatthenano-scale,acompletehysteresisloopcanbe

extracted from SP-STM images. Moreover, the processes behind hysteretic

behavior, i.e. domain wall movement, domain creationand annihilationare

observed indetail.

ex-more closely a previous discovery we repeatedly ran into more unexpected

eects of either the sample or, of equal importance, of the ferromagnetic

tunneling tips. Experimenting with dierent coating materials for the tips

had a dramatic inuence on the obtained magnetic images. A variation of

the magnetic tip anisotropy allowed to observe either domains or domain

walls, and in certain cases of both simultaneously. Surprisingly, even bare

non-magnetictungstentipscanbeusedtoobservemagneticallycaused

phe-nomena. Examples willbepresentedinChapter8.

Can atomic resolution be achieved in spin polarized scanning tunneling

experiments? Yes,itcan. Surprisingly,itistheconventionalconstantcurrent

imagingmodeinconjuntionwithaferromagneticallycoatedtipthathas

pro-videdtherstatomicallyresolvedimagesofanantiferromagneticallyordered

MnmonolayeronW(110),verifyingatenyearsoldtheoreticalpredictionby

Blügelet al. [28]on the existenceof two-dimensional antiferromagnetism in

monolayer lms. In this systemthe magnetic orientation changes from one

atomto itsnext nearestneighbor, andatomic resolutionis aprerequisitein

ordertogainmagneticinformationatallsincethemagneticmomentscancel

atanylargerscale. Itwasmygreatpleasuretotakepartinthisexperiment,

"discovering the grail of magnetic imaging", asStefan Heinze coined it. It

has been described in detail in Ref. [29] and more comprehensively in the

recently published Ph.D. thesis of Heinze [30] whom the brilliant theory is

owed that guided the experiment. On the experimental side, the ground

hadbeen preparedbyanearliercareful studyofthegrowthofultrathin Mn

lms on W(110) by Matthias Bode and co-workers [31]. Once the

prepa-ration of magnetic thin lm tips had been mastered on a routine basis the

actual experiment was performed ina rather straightforward manner. It is

a rare condition that both theoretical and experimental expertise combine

insuch afruitfulwayinone group aswasthecasehere. For areviewofthe

experiment Irefer thereader to theliteraturecited.

Many ofthe results thatwill be presentedinthis workdeservea deeper

theoreticalanalysis. Thistaskought to be tackled fromtwo sides: (i)

Clas-sicalmicromagnetictheory,basedon acontinuumapproach,can beapplied

inorderto describetheoreticallytheexperimentally observeddomain

struc-tures; (ii) ab-initio calculations based on the full-potential linearized

aug-mentedplanewave(FLAPW)methodhaverecentlybeenappliedwithgreat

successto ahost ofmagnetic systems[32]. Thisapproach isvery promising

inthatitaddressesdirectlythespinresolvedelectronicstructureofasample

Theory of Spin Polarized

Scanning Tunneling

Spectroscopy

2.1 The Tunnel Eect

Aconvenientstartingpointforthetheoryofscanningtunnelingspectroscopy

istheeectoftunnelinginonedimensionlikeitisintroducedinvirtuallyall

basic quantum mechanics textbooks. The eect to be described is a result

ofthewave-particle dualism whichis unknownto classical physics.

IfaparticleoftotalenergyE impingesuponapotentialbarrierofheight

V

0

andnitewidthsitwill,accordingtothelawsofclassicalphysics,onlybe

abletopassthebarrierifE isgreaterthanV

0

,otherwiseitwillbereected.

If the particle is of microscopic dimensions as, e.g., an electron, it must be

describedintermsofquantumphysics,andtheresultiscompletelydierent.

Even for the case E < V

0

there is a certainprobability to nd theparticle

behind the barrier, and this phenomenon is known as tunneling. The most

simple situation is a single particle, let's say an electron of kinetic energy

E, incident from the left upon a one-dimensional potential barrier. The

I

II

III

0

s

V(z)

z

E

0

s

y y

*

a)

b)

potential can bewritten asfollows V(z)= 8 > < > : 0 z<0 V 0 0<z<s 0 z>s (2.1)

Theelectronisdescribedbyitswavefunction (z)whichisasolutionofthe

time-independent Schrödinger equation

 h 2 2m d 2 dz 2 +V(z) ! (z)=E (z): (2.2)

Herem is theelectron mass, and h isPlanck'sconstant divided by2. We

candistinguishthreeregions(cf. Fig.2.1): regionIleftofthebarrier,z<0,

region II the barrier itself, 0 < z < s, and region III right of the barrier,

z>s. Inthe regionsI and IIIV(z) =0,and theelectron wave function is

thatofa freeparticle,of thegeneral form

(z)=Ae ikz +Be ikz z<0 (z)=Ce ikz +De ikz z>s k= p 2mE  h : (2.3)

A;B;C ;andDarearbitraryconstants. Insidethebarrier,thatis0<z<s,

V(z)=V

0

,and the ansatz is

(z)=Fe ik 0 z +Ge ik 0 z 0<z<s k 0 = p 2m(E V0)  h : (2.4)

Thetotal energy isnegative inthisregion since E<V

0

,thus k 0

iscomplex,

andtheexponents become real:

 2 = k 02 = 2m(V 0 E)  h 2 ; (2.5)

therefore the exponentials are real functions describing waves which decay

exponentiallywithin thebarrier.

In region I the general solution of the Schrödinger equation is a linear

combination of a wave traveling to the right and a wave reected at z =0

traveling to the left which combineto a standing wave. At z =0 thewave

function penetrates into the classically forbidden barrier region II where it

is exponentially damped but remains nite at z = s. In region III the

transmittedwave travels to the right, and since no reection occurs we can

determine a rst constant, D = 0. The overall wave function, in terms of

its probability density 

, is depicted schematically in Fig. 2.1(b). The

(z)andalsoitsrstderivative d

dz

(z) arerequiredtobecontinuousfor

allz,andbymatching thepartialsolutions found for therespective regions

at the points z = 0 and z = s (wave matching method) we can obtain a

set of four equations that allows to determine the values for theremaining

constants B;C ;E;F in terms of A. This last constant can be chosen to

normalize the wave function. Now we can gain an exact expression for the

transmissioncoecient,whichistheratioofthetransmittedandtheincident

probabilityuxj T and j 0 ,respectively: T = j T j 0 = 1 1+(k 2 + 2 ) 2 =4k 2  2 sinh 2 (s) (2.6)

Inthe limit of s1 this formulareduces to

T 16 k 2  2 (k 2 + 2 ) 2 exp( 2s) (2.7)

When this last expression is a good approximation, T is extremely small.

Themost important result, however,is theexponential dependenceof T on

the width sof the potential barrier. It is this relationship that isexploited

in the scanning tunneling microscope. It is the key to the extremely high

resolution whichallowsfor astudy ofconducting samplesurfaceson ascale

where individualatoms can beresolved.

2.2 The Tunneling Process in the STM

Inan STM measurement a ne metallic tip isapproached asclose asa few

Å (1Å= 10 10

m) to the surface of a conducting sample. The tip is then

scannedlinebylineacrossthesurfacebymeansofappropriatepiezo-electric

elements, and, with a small bias voltage applied, a tunneling current I(U)

can be measured which will, according to Eq. (2.7), vary exponentially as

a function of the distance between tip and sample. This is an example

of metalvacuummetal tunneling. The tunneling barrier between the two

electrodes inthis case isthevacuumgap.

Insidethe metallicelectrodestheelectrons maybe describedinthe

free-electron-gas model. All electronic statesare occupied up to the Fermilevel

(for simplicity, we assume a temperature of 0 K resulting in a sharp edge

in the Fermi function, separating occupied and unoccupied states). The

height V

0

of the insulating vacuum barrier is given bythe work function 

of the metallic electrode, i.e.the energy required to extract an electronout

ofthesurfaceinto thevacuum. isamaterial parameter, andforsimplicity

we assume that tipand sample are made fromthe same metal thus having

thesame workfunction. Thewidthofthebarrierisgivenbythetipsample

Tip

Sample

+

-z=0

z s

=

eU

bias

f

s

E

F

E

Vac

f

_t

Figure 2.2: Schematics of thetunneling process in theSTM.The barrierheight

is given by thework function of the electrodes, the barrier width correspondsto

thetipsampledistance. AnappliedbiasvoltageU

bias

shiftstheFermilevelsoftip

andsamplerelativetoeachother. Electronscan tunnelfromthenegativelybiased

sample to the tip. A change of bias polarity reverses thecurrent direction. The

sketchindicatesthedecayofasamplewavefunction inthebarrierregion.

to the tip, and the net tunneling current is zero. If we apply a small bias

voltage U

bias

between tipand sample theFermi levelsof theelectrodeswill

shiftaccordingly withrespectto each other (cf.Fig. 2.2). Now a tunneling

current can ow. Throughout this work we will use the convention that

the tip potential always is held grounded. Thus, for positive sample bias

electronswilltunnelfromoccupiedstatesofthetipintounoccupiedstatesof

the sample, and for negative sample bias theelectrons come from occupied

sample states and go to unoccupied tip states. Thus the direction of the

current dependson the polarity ofthe applied bias voltage U

bias .

Ifwe considerthe limitof smallbiasvoltage,i.e. eU

bias

,theenergy

of the tunneling electrons is approximately equal to the Fermi energy E

F .

Insidethe barrierthe wave function of anelectron decays:

(z)= (0)exp( z); = q

2m=h 2

; (2.8)

withtheso-calleddecayconstant. Wecandeterminetheprobabilitydensity

wofndinganelectronatthetippositionsbytakingthesquareofthewave

function: w=j (s)j 2 =j (0)j 2 exp( 2s); (2.9)

For a typical metal we may assume   4 eV. This results in a decay

constant 1 Å 1

increasedby1Å.Thesenumbers illustratethe enormous verticalresolution

thatcanbeachievedbytheSTM.Thisfeatureallowstodetectchangesinthe

tip-sample distanceofthe order of 0:01Å or less. Further, we canconclude

fromEq. (2.8) the important factthatthetunneling current will be carried

almostexclusivelybytheoutermostatomatthetipapexwhilecontributions

from atoms of the next atomic layer within the tip crystallite can in most

cases be neglected. Therefore, the tunneling process in an STM is highly

localized in the sense that it occurs between one atom at the tip and the

samplespot rightbelowit. Thus,whenscannedacrossasamplesurface,the

tipprobeslocalpropertiesofthesamplewithalateralandverticalresolution

thatallows,ingeneral, to resolve individualatoms.

Until now, we have considered tunneling only in the picture of a

one-dimensionalmodel. Thismodelwassucienttointroduce somebasic

mech-anismsthatallowanunderstandingofthe tunnelingprocessingeneral. But

already the term "local", introduced inthe last paragraph, requiresan

ex-planation that can not be given based on this simple model. Furthermore,

wedidnotdiscussthe propertiesoftheprobingtipatall. Itwasintroduced

justasaconductingelectrodebeinglocatedadistancesawayfromthe

sam-ple surface. In most cases, our major concern will be the properties of the

sample, and only insecond place we want to know thetip. In an STM

ex-periment,the ideal of anon-intrusive measurement would be a point probe

withan arbitrarilylocalized wave function [33]. A realistic tip, however, is

made from a certain material having its atoms at the apex arranged in a

particular way, i.e. it has a certain geometry in space and a more or less

extendedwave functionwhich willbedierentfrom thatofa freeatombut

alsofrom thatofa solid. Inother words, the tiphasanelectronic structure

thathasto beaccounted forina 3-dimensional approach.

In1961,twentyyearsbeforetheinventionoftheSTMbyBinnig,Rohrer

and co-workers [34], in his investigation of the tunneling process between

two planar electrodes separated by an oxide layer, Bardeen [35] developed

anexpression forthe tunnelingcurrent,basedupontime-dependent

pertur-bation theory, that has since been used as a fundament to many fruitful

approaches towards a theoryof the tunneling process in the STM. Here, it

is presented inthe formulation of Terso and Hamann [33,36], adoptedfor

a systemof tip and sample separated by a vacuum barrier, and the limits

of small bias voltage and low temperature are assumed. In this model the

tunnelingcurrent isgiven by

I = 2  h e 2 U X  jM  j 2 Æ(E  E F )Æ(E  E F ); (2.10)

withethe electroncharge, and theindices and  refer to thetipand the

d

R

r

0

Figure 2.3: Modeltip asintroducedby

Tersoand Hamann [33]. Thetip shape

isarbitrarybutsphericalatitslowerend.

R is the radius of curvature, the center

of curvature at ~r

0

. Distance of nearest

approachto the sample surface(shaded)

isd.

problemisthe calculationofthe tunnelingmatrix elementM



of the

tran-sition between states

of the sample before tunneling and



of the tip

after tunneling, and E

 (E

) is the energy of state

 (

) in theabsence

oftunneling. According toBardeen, thematrix element isgiven by

M  =  h 2 2m Z d ~ S(   ~ r   ~ r   ): (2.11)

Theintegrationhastobecarriedoutoverasurfacewhichislocatedentirely

withinthebarrier. Inordertocalculatethematrixelementtheenergylevels

andwave functionsofboth tipand sampleneed tobeknown. Thisrequires

a knowledge of their respective atomic structure. While, in general, this

information will be (or can be made) available for the surface, it is almost

impossible to know the details of the microscopic atomic structure of the

tipsince a tip is prepared in a relatively uncontrolled and nonreproducible

manner. 1

However,somesimplifyingassumptionshavebeenintroducedthat

allowedtosuccessfullyinterpretSTMimagesqualitativelyinawiderangeof

applications. Terso and Hamann proposed a model tip of arbitraryshape

butwithalowerend beingaspherical potential well witharadiusof

curva-tureR , thecenter of curvature located at a position~r

0

, thespherical tipa

distanced above the samplesurface, cf.Fig.2.3. 2

In the Terso-Hamann model, the simplest possible wave function for

this tip is assumed, a spherical s-wave function while wave functions with

an angular dependence (l 6=0) areneglected. Nowthe matrix element can

1

Oneway to obtaininformation onthetip's atomicstructureiseld ion microscopy

(FIM).However,aspontaneousrearrangementofthetipapexatomsisnotunusualduring

scanning, showing up as achange inimaging quality, leaving the experimentatoragain

withatipofunknownatomicstructure.

2

Werecallthatthetunnelingcurrentiscarriedalmostexclusivelybytheonetipatom

closest to the sample surface. This might intuitively suggest a spherical tip apex. In

theTerso-Hamannmodelthis caseis consideredthe limitofsmallestpossible radiusof

be evaluated andthus thetunneling current which isthenproportional to I /Un t exp(2R ) X  j  (~r 0 )j 2 Æ(E  E F ); (2.12)

whereU isthe appliedvoltage,n

t

istheconstantdensityofstatesofthetip

at theFermilevel. The quantity

n s (~r 0 ;E F )= X  j  (~r 0 )j 2 Æ(E  E F ): (2.13)

is the local density of states (LDOS) of the surface at the Fermi level E

F ,

evaluatedat thecenterofcurvature~r

0

ofthe eectivetip. Thesamplewave

functionsdecayexponentiallyinto the vacuum(the zdirection isnormalto

thesurface): j  (~r 0 )j 2 /exp( 2s); (2.14)

andthetipsampledistanceisdened bys=d+R . Furthermore,boththe

verticalandthelateralresolutionoftheSTMcanbeshowntobedetermined

bya characteristic length L=[(d+R )=] 1=2

[33,36,37].

The Terso-Hamann modelleads to some remarkable results. Themost

important is thatthe tunnelingcurrent is determined bysample properties

alonewhiletheroleofthetipisreducedsimplytothatofaprobe. Themost

widelyapplied mode of STMoperation makesdirect useof this remarkable

feature. In the constant current mode a feedback loop regulates the

tip-sample distance z = z

0

+
z as to keep the tunneling current at a chosen

set-point valuewhile the tip isscanned across the samplesurface. The

val-ues of the corrugation
z(x;y) can be plotted as a function of the lateral

tip position (x;y). Constant-current STM images now can be interpreted

as contour maps of constant sample LDOS, and to a rst approximation

these constant LDOS contours followthe topographyof thesamplesurface.

In this way the details of the surface geometry like step edges, islands,

de-fects, surface reconstructions etc. can be made visible. After its invention

the STM was most widely applied in the study of structural properties of

surfaces. This new microscopy technique allowed to addressquestions that

werepreviouslynot accessiblebyothersurface sensitive methods whichrely

onthe reectionof electromagneticor matterwaves atperiodicstructures.

However,thesimpleinterpretationoftheconstantcurrentdataasa

topo-graphicimageofthesamplehastobeusedwithsomecare. Thisisespecially

true when the level of atomic resolution isbeing approached. At this level

the TersoHaman model is still able to reproduce the lattice periodicity

ofclose-packed metalsurfaces butfailsto reproduce theexperimentally

ob-servedcorrugationamplitudesifrealistictipradiiandtunnelingdistancesare

assumed. Thisdeciency of the TersoHamann model iswell understood;

cor-d

z

2 symmetry. Chen's model also nicely tsanother observation frequently

made inatomic resolution experiments: during a scan at low tunneling

re-sistance often a sudden drastic enhancement of the observed contrast can

be noticed which, using Chen's picture, can be understood intuitively as a

switching froman s-orbitalto a d-orbitalat thetip.

But also at a length scale greater than the surface lattice constant the

topographicinterpretationofconstantcurrentimagesrequiressomecaution.

DuetothelocalcharacteroftheprobetheSTMissensitivetolocalvariations

intheelectronicstructureofthesamplethatmayarisee.g.fromthepresence

ofadsorbates,alloying,or,inthecaseof ultrathinlms, fromdierent local

coverages. Not in all cases these variations can be interpreted simply as a

variation in height of the sample as is suggested by the constant current

images. Dierent chemical species at a surface will exhibit dierent work

functions. Certain adsorbates on top of a surface may even appear not

as protrusions but as depressions giving rise to anticorrugation. This can

oftenbe observed for oxygen adatomson metal surfaces. Any alteration of

the localelectronic structure will more or less modify the constant current

image. Whatappearsasafurthercomplication atrstsight,however, turns

out as an opportunity to gain access to highly valuable information about

the surface under study. It is the local electronic structure rather than the

mere topography that is addressed by the scanning tunneling spectroscopy

modeofSTMoperation,and aswewillseelater, thismode playsakeyrole

inthe processof magneticimaging.

2.3 Scanning Tunneling Spectroscopy

Eq.(2.12) was derivedinthe limit of small biasvoltage It canbe written

I(~r 0 ;U)/eU s (~r 0 ;E F ): (2.15)

Inthe rangeofafewmillivolts thetunnelingcurrent islinearlyproportional

to the applied voltage U. For higher voltages, this is no longer true. The

Ohmicbehaviorisreplacedbya moreor lesscomplicated non-linear

depen-dence I = I(U). This is the result of the particularities in the electronic

structure of the sample surface, the details of which can be studied locally

by scanning tunneling spectroscopy. As will be shown next, curves of the

dierential conductance dI=dU versus U reveal theLDOS structure within

theprobedenergy range E

F eU.

In general, the eect of a nite bias voltage will be a distortion of the

wave functionsofboth tipand sample, and also theenergy eigenvalues will

be modied, which is dicult to account for. Therefore, the undistorted

zero-voltage wave functionsand eigenvalues are usually taken asa rst

amountofjeUj,andanystructureintheLDOSwillbeincludedintheshift.

In this approximation the result of Terso and Hamann is modied to the

energy integral I / Z eU 0 n t (eU ")n s (")T(";eU)d"; (2.16) where n t and n s

arethe densities of states of tip and sample, respectively,

and all energies are taken with respect to E

F

. Here, the energy and bias

voltage dependence of the transmission coecient T enters to account for

thefactthatthedecaylength dependsonthese parameters. T isgiven by

T(";eU)=exp ( 2s  2m  h 2   t + s 2 + eU 2 "   1=2 ) : (2.17)

Since, however, the increase of T with increasing biasis smooth and

mono-tonic itappears asa backgroundon which the LDOS structureinformation

issuperimposed [18].

If we assume n

t

= const: we yield from dierentiating Eq. 2.16 with

respect to U: dI dU (U)/n t (0)n s (eU)T(eU)+ Z eU 0 n t (eU")n s (") dT(";eU) dU d": (2.18)

Thesecondterm describesthebackgroundvariationdue tothebiasvoltage

dependence of the transmission coecient, and the bias voltage dependent

LDOS structure can be attributed to the rst term. The dierential

con-ductance dI=dU(U) is the central quantity we are interested in when we

perform an STS experiment. The details of the LDOS can be probed at

highspatialresolution byvaryingthebiasvoltage. By choosing axedtip

sample separation and ramping thevoltage between, e.g., +1 V and 1 V

and measuring the dI=dU(U)signal asa functionof biasvoltage we obtain

a spectrum ofthe LDOSinthe energy interval. An example isdisplayed in

Fig.2.4, revealing thecharacteristics intheelectronic structureof ultrathin

Fe lms at threedierent coverages on a W(110)substrate.

There is, however, another eect related to the transmission coecient

thathastobetakenintoaccountwhichdependsonthepolarityoftheapplied

biasvoltage. Thiseect isillustrated inFig.2.5. When farawayfrom each

other, the Fermi levels of tip and sample are independent. When brought

into tunnelingcontactthey will acquirean equilibrium,i.e. theFermilevels

of tip and sample will eventually be equal. A bias voltage shiftsthe Fermi

levels with respect to each other. At positive sample bias, tunneling will

occurfromoccupiedtipstatesintoemptysamplestates(Fig.2.5a),whileat

negative samplebias the uxis fromoccupied samplestatesinto emptytip

Figure 2.4: Tunneling spectra

takenatsamplelocations

exhibit-ing three dierent coverages of

Fe/W(110) revealing maxima in

the dierential conductance at

energiescharacteristicforthe

re-spectivecoverageregimes[40].

current, since these electrons "feel" a lower tunneling barrier height than

electrons from states lyinglower in energy. This is indicated inFig. 2.5by

arrowsofdierentsize. Thiseectintroducesanasymmetryinthe

measure-ment process when the polarity of the bias is changed: If, for example, we

areinterested in two features of the sample LDOS,one beingenergetically

locatedat,say,+800mV(unoccupied samplestates)andtheotherat 800

mV(occupied samplestates)withrespectto thesampleFermilevel, wecan

easily probe thefeature having positive binding energy,since the tunneling

process into the region of interest (RoI) is most eective at this bias. In

order to probe the other feature we have to switch the bias polarity. Our

region of interestnowlies inan energetic range where tunneling is least

ef-cient; instead, the spectralcharacteristics will be increasinglymoulded by

contributions whicharedueto emptytip states,andtheassumptionof atip

withan contourless electronic structure becomes increasingly questionable.

Butstillthecondition holdsthatthetip electronicstructurewill stay

unal-teredduring a measurement while the sampleLDOS featureswill varyasa

functionoflateralposition(x;y),thusallowinginmostcasestoseparatetip

eectsinthespectraasaconstantbackground againstthespatialvariations

ofsampleLDOS properties.

Ingeneral,thereareanumberofexperimentalproceduresthatcanbe

ap-pliedfor aspectroscopicmeasurement. Theprocedure usedthroughoutthis

workisthefollowing: Simultaneously totherecordingof aconstantcurrent

image a measurement of the local conductance I(U) and thelocal

dieren-tial conductance dI=dU is carriedout. At every pixelthe value
z(x;y) is

measured, providing the data base for the constant current topography of

RoI

RoI

a)

b)

E

F

E

vac

Figure 2.5: Schematicsof thepolarityeect of thetransmissioncoecient. The

regionof interest(RoI) isindicated byashadedrectangle. a)Atpositivesample

bias,unoccupiedstatesofthesampleareeectivelyprobed. b)Atnegativesample

bias,occupiedsamplestatestakepartintunneling. Theregionofinterest,however,

is now in adisadvantageousenergetic range. Instead, unoccupied tip statesgain

weight(afterHamers[41]).

tunneling resistance U=I). Typical stabilization values used during the

ex-perimentsareU =1 VandI =300pA.Thefeedbackloopisthen switched

o,and the voltageis ramped from, e.g. +1 Vto 1 Vwhile thetunneling

current I =I(U) ismeasured. Fromthis curve the dierential conductance

dI=dU can, in principle, be obtained by numerical dierentiation. Since

around U =0V the current becomes extremely small, the signal-to-noise

ratio will be unsatisfactory. Thisproblem canbe circumventedbyapplying

alock-intechnique: whilerampingthe d.c.voltagea smalla.c. signal(30

mV,f

mod

1:8kHz)isadded,andthein-phasecurrentmodulations,i.e.the

dI=dU signal, are detected by a lock-inamplier. Signal variations due to

noiseareeectivelylteredsincetheydonotfollowtheconstantmodulation

frequencyandphase. ThedI=dU versusU curvethenprovidesaspectrumof

theLDOS.Sincethismeasurementiscarriedoutateverypixelthecomplete

setofdataprovidesastackofspectroscopiclayersdI=dU(U;x;y). The

spa-tial distribution ofa spectroscopicfeature of interest, for example asurface

state peak characteristic for acertaincoverage ofa depositedthinlm,can

be plottedasamapofthedierential conductance attheenergeticposition

ofthis particular feature. Thismapcan be compared to thesimultaneously

acquired topography, and structural and electronic properties can thus be

correlated.

2.4 Spin Polarized Scanning Tunneling

ferro-with majority spin (") and the other with minority spin (#). 3

Due to the

magneticexchangesplittingE

ex

theminorityspinbandislledlessthanthe

majority spin band. This imbalance, giving rise to the magnetic moment,

showsup asaspin splitdensityof statesat theFermilevel. If theSTMtip

canbe madesensitive tothe spinof the tunnelingelectrons it shouldbean

ideal toolfor the investigationof magnetismat ultimate spatial resolution.

One way to obtain a spin sensitive tip is to coat a regular tip with a thin

lmof a ferromagneticmaterial, e.g. Fe or Gd. Inthis casethetip exhibits

a spin split band structure itself, and the interplay of the band structures

shouldaectthe tunnelingprobabilitiesofelectronsasafunctionofthespin

orientation.

2.4.1 Spin Polarized Constant Current Imaging

Inhisrecenttheoreticaltreatmentofspinpolarizedscanningtunneling

Hein-ze [30] generalized the Terso-Hamann model to the case of spin polarized

tunneling. The DOS for both spin directions of the tip is assumed to be

constant but of unequal value: n " t =const., n # t = const.,but n " t 6=n # t . This allowstodenen t =n # t +n " t andm t =n # t n " t

forthetip. Similarquantities

canbedenedforthesample,butagaintheydependonthetippositionand

thebiasvoltage:

~ n s (~r 0 ;U)=n~ " s (~r 0 ;U)+n~ # s (~r 0 ;U) (2.19) and ~ m s (~r 0 ;U)=n~ " s (~r 0 ;U) n~ # s (~r 0 ;U); (2.20) where n~ s (~r 0

;U) is calledthe integrated local density of statesof thesample,

and m~

s (~r

0

;U) its integrated local spin density of states. In terms of these

quantities thetunnelingcurrent canbe expressedasfollows:

I(~r 0 ;U;(~r 0 ))/ n t ~ n s (~r 0 ;U) | {z }

non spinpol arized +m t ~ m s (~r 0 ;U)cos(~r 0 ) | {z } spinpol arized : (2.21)

Therighthandsidenowcontainsthesumoftwoterms,acontributionwhich

is not spin polarized, I

0

, and a contribution which depends on the relative

spin orientation of tip and sample, I

P

, and, in order to obtain a magnetic

contrast, it is desired to maximize I

P

over I

0

. Since, in general, tip and

samplewillnot sharethe samemagnetization axis,thecosineoftheangle 

between themagnetizationdirectionsoftipandsampleenters. Whereasthe

magnetization direction ofthe tip ~

M

t

can be assumedx inmost cases the

samplemagnetization ~ M s (~r 0

;U) may change as a function of position, and

accordinglytheanglebetween them isafunction of thelateraltipposition,

3

Theargument isnotrestrictedtoferromagnetsbutholdsfor anymagneticmaterial

=(x;y). Thisallows toinvestigate themagneticdomain structureofthe

sampleviathe variationofthespindependentpartofthetunnelingcurrent.

It isobvious thatthe spinpolarized contribution ismaximal for a collinear

conguration ~ M t k ~ M s

, i.e.  = 0 for theparallel case ("") or  = for the

antiparallel case ("#), while it vanishes for ~ M t ? ~ M s , i.e.  = =2. For a

collinear oraperpendicularcongurationthetotal tunnelingcurrent canbe

conveniently given intermsof thecontributing spin channels:

I(~r 0 ;0) = I "" (~r 0 )+I ## (~r 0 )=I p (~r 0 ) (2.22) I(~r 0 ;) = I "# (~r 0 )+I #" (~r 0 )=I ap (~r 0 ) (2.23) I(~r 0 ;=2) = 1=2[I "" (~r 0 )+I ## (~r 0 )+I #" (~r 0 )+I "# (~r 0 )] = 1=2[I p (~r 0 )+I ap (~r 0 )]: (2.24)

The decomposition of the density of states into a spin averaged and a spin

polarizedpart,Eq.(2.21),allowstodenethepolarizationoftipandsample

intermsof thesequantities:

P t = m t =n t (2.25) ~ P s (~r 0 ;U) = m~ s (~r 0 ;U)=~n s (~r 0 ;U); (2.26)

and the polarization of the entire tunneling junction consisting of sample,

vacuum gap, and tip, is given by the product of the polarizations of both

electrodes: P ts =P t
~ P s (z;~r k ;U): (2.27)

Note that the sample polarization depends also on z since the decay rates

for s,p and d electronsmaydier.

Inconstantcurrentimaging,twoeectshavetobeconsidredthatleadto

a degradation of magnetic contrasts. First of all, the non-polarized part of

the tunneling current I

0

increases monotoneously withincreasing bias

volt-agewhilethepolarizedpartI

P

maystayconstant;thustheconstantcurrent

imagewill inmost casesbedominatedbyI

0

[42]. Second,thesample

polar-ization ~

P

s

isan energy integrated quantity evaluated in theenergy interval

selected by the chosen bias voltage. As a consequence, the polarization ~

P

s

may be degraded by an inclusion of states exhibiting a polarization of

op-posite sign. This eect is schematically illustrated in Fig. 2.6(a-d) along a

ctitious spinsplitdensityof states. (b) and(c)represent n~

s

and m~

s as

de-nedinEqs. (2.19)and(2.20),respectively,and(d)symbolizestheresulting

polarization ~

P

s

whichrepeatedlychangessigninthe intervalE

F

eU. This

may even lead to a complete cancellation of the spin polarized part of the

tunneling current, thus preventing the extractionof any magnetic

informa-tion from the sample. Dueto the described problems theconstant current

n

n

n +n

n -n

Polarization [%]

E

ex

a)

E

b)

c)

d)

E

F

100

-100

n(E)

eU

Figure 2.6: (a) Schematic illustration of the spin split density of states at the

Fermilevel. MajorityandminorityspinstatesareshiftedbyanamonutE

ex . (b) Total DOS n " +n #

. (c) Dierenceof majorityand minorityDOS, n "

n #

. (d)

PolarizationP(U)asafunction ofbias.

by numerous examples throughout the remainder of this work, a method

derived fromaspectroscopic approach ismore appropriate forthis task.

However, constant current magnetic imaging has recently been applied

withgreat successto magnetic imagingat theultimate,atomiclength scale

by resolvingfor the rst time the 2-dimensional nearest-neighbor

antiferro-magnetic order of a single monatomic layer of Mn grown on W(110) [30].

Such asystemofchemically identicalbut magneticallyinequvalent atoms is

particularly challenging since the total magnetization is zero and the

mag-neticinformation can befound exclusively at theatomiclength scale. Thus

atomic resolution and magnetic sensitivityis required simultaneously. The

contrast mechanism in this case relies on the fact that the 2-dimensional

translational symmetry of the magnetic superstructure is lower than that

of the chemical surface unit cell which leads to a strong enhancement of

the spin polarized contribution to the tunneling current [30,42]. Constant

currentimaginghasagreatpotentialinthestudyofperiodicmagnetic

struc-turesat theultimate length scale.

2.4.2 Spin Polarized Scanning Tunneling Spectroscopy

For high contrast studies of magnetic domain structures it is necessary to

know the energetic ranges of high polarization within the density of states

structure. This knowledge can be obtained by applying the spectroscopic

modeofthe STM.DierentiatingEq. (2.21) yieldsthespinpolarized

dier-ential conductance, dI(U) dU /n t n s (~r 0 ;E F +eU)+m t m s (~r 0 ;E F +eU)cos(~r 0 ): (2.28)

E Tip

E

E

ex

Sample

n

n

E

F

eU

E

E

n

n

E

F

eU

D

U

mod

a

b

Figure 2.7: Probingthespin split densityof states. (a)Constant current

mea-surement. Allstatesintheinterval[E

F ;E

F

+eU]contributetothesignal,indicated

bythe gray-shadedarea. Polarizationeects maybedegraded oreven cancelled.

(b)Spectroscopicmeasurement. ThedI/dU-signal isacquiredat E=eU as

indi-catedbythenarrowgray-shadedarea. Theenergyresolutionisdeterminedbythe

amplitudeofthea.c. modulationvoltage
U

mod

ofthelock-inamplier.

quantities n~

s

and m~

s

whichare central to the constant current mode, while

in the latter the dierential conductance is directly proportional to n

s and m s at an energy E F

+eU. Inconstant current imaging thenon-spin

polar-ized contribution I

0

increases with U while the spin polarized contribution

I

P

maystayconstant. Ontheotherhand,inadI=dU measurementthe

volt-age canbeadjusted asto maximizethe spin polarized contribution m

s over

thespin averaged contribution n

s

. The energetical positions of such ranges

of highpolarizationcan be extracted fromspectral curves measuredon

op-positely magnetized sample locations. Thus, the spectroscopic approach is

particularly suited to image the magnetic domain structure of a sample by

selectively probingfeaturesoftheLDOS exhibitingahighspinpolarization.

AschematicillustrationofthetwomodesofSP-STMapplicationisgivenin

Fig.2.7.

MakinguseofEqs.(2.25)and(2.26)wecanrewriteEq.(2.28)asfollows:

dI(U) dU /n t (U)n s (~r 0 ;E F +eU)[1+cos(~r 0 )P t (E F +eU)P s (~r 0 ;E F +eU)]: (2.29) The tilde of P s

has been dropped since this quantity is no longer energy

integrated. We have reintroduced the bias dependence of the tip related

quantities n

t

(U) and P

t

(U) to account for the fact that in a spectroscopic

measurementthelimitofsmallbiasvoltagewill,inmostcases,notbegiven.

Recallingthe discussionofthe polarityeecton thetransmissioncoecient

onp.17wecanexpectthatanystructureofthetipDOSwillbeparticularly

noticeableinthenegativesamplebiasrange. ForaferromagnetictipitsDOS

structuremayinclude highlypolarizedfeaturesthatshowupat certainbias

voltages. Sincethecontrastrequiredtostudythemagneticdomainstructure

ofasampledependsonthetotalpolarizationofthetunnelingjunctionwhich

An extrapolation of a value for the sample polarization is, however, not

Instrumental Setup

We have endeavored in designing an STM which is extremely stable and

which meetsthreeoperational conditions: ultra-high vacuum, low

tempera-tures, and highmagnetic elds [43]. For the purposeof our special interest

ininvestigationsinsurfacemagnetismwehavesuppliedtheinstrumentwith

some unique features, like sample rotation, easy tip exchange mechanism,

and an arrangement for MOKE measurements. In this chapter I will

de-scribe the instrument indetail.

3.1 The Cryo STM

3.1.1 Chamber system

The new cryomagnet-STM chamber is added to a four-chamber UHV

sys-tem[44]consistingofacentraldistributionchamber,apreparationchamber

equipped with resistive and electron beam heating and a sputter gun, an

MBE chamber with ve evaporators and a home built STM especially

de-signedfor timeresolved growthstudiesdescribed elsewhere[49],ananalysis

chamber containing facilities for standard surface characterization as, e.g.

lowenergy electron diraction(LEED),Augerelectronspectroscopy(AES)

andspin-resolvedphotoelectronspectroscopy(SP-PES),and,withinan

addi-tionalsatellitechamber,acommercialvariable-temperatureSTM[45]which

canbeoperated ina temperature rangeof 30K<T <1000K. Aloadlock

allowsforfastintroduction ofsamplesandtipswithoutventingthechamber

system. To prevent from acoustical and low frequency building vibrations

the whole system is installed in an acoustically shielded laboratory with a

foundation being completely separated from the rest of the building. The

UHV chamber system is supported by a table with additional pneumatic

3.1.2 Magnet Cryostat System

Magnet

The magnet cryostat system(Fig. 3.1) is a modied Spectromag 4

He bath

cryostatwithaLN

2

radiationshield[46]. The2.5Tsuperconductingmagnet

isasplitcoil typewitha62 mmbore. Homogeneityoftheeldina10mm

diametersphericalvolumeatthesamplelocationisspeciedto1partin10 2

.

Themaximumsweep rate accountsto 2.5Tperminute. The central region

of the magnet (cf. Fig. 3.2) has two cutaways of 80 Æ

and 90 Æ

, respectively,

and a minimum height of 42 mm thus providing two access openings to

the microscope. Samples and tips are being exchanged through the 80 Æ

window whereas the 90 Æ

window is usedto carryout magneto-optical Kerr

eect (MOKE) measurements, and to allow for metal or molecular beam

evaporation onto the sample surface. To obtain proper UHV conditions

the magnet is designed to safely endure bakeoutat 120 Æ

C. In our bakeout

procedure we keep the magnet at 115 Æ

C for 48 h. The temperature is

measured by a platinum resistor sensor on top of the magnet. The signal

of this sensorfeeds a control unit that supplies a ow of cold nitrogen gas

acrossthemagnet ifthetemperatureisabouttosurpassthesetpointvalue.

Thus asafe bakeoutoperation isguaranteed overnight.

Cryostat and UHV Chamber

Theheliumreservoirofthecryostathasausefulcapacityof20lgivingahold

timeinthelowtemperature regimeofapprox.40hbetweensubsequent lls.

The helium reservoir and the magnet are enclosed by a nitrogen radiation

shield. Its20lvolumeprovidesa holdtimeof36 h. At thelowerendwhere

the magnet has its above mentioned openings the shield has an additional

rotating cylinder thepurpose of which is to shut the accesswindows. This

cylinder isthermally coupled to themain partofthe shieldby anumberof

copperbraids. Toavoidvibrationsduetoboilingnitrogen theLN

2

reservoir

ispumped to apressure p<5mbar sothat thenitrogen solidies. To cope

withthe initiallyhugeamount ofgasfromtheboilingliquid weusearotary

vane pump witha nominal pumping speed of 65 m 3

/h. Whenthe nitrogen

has solidied at a temperature of 63 K the rate of exhaust gas is greatly

reduced so that a much smaller pump can be used to hold the pressure.

Thispumpislocatedinanadjacentroomwhichisacousticallyisolatedfrom

the STM laboratory. As thegas ow through thepumping line isvery low

we have no acoustic coupling of the pump. Having a radiation shield at a

temperature aslowas63 Kisof considerableadvantage for minimizing the

heliumboil o.

The outer vacuumchamber of the cryostat unit has a DN350 CF base

Table

Preamp

Titanium

Sublimation

Pump

Titanium

Sublimation

Pump

A

B

UHV Chamber

UHV Chamber

LN Radiation

Shield

2

LN Radiation

Shield

2

_{LHe Bath}

Cryostat

LHe Bath

Cryostat

STM

Magnet Coils

Magnet Coils

Thermal Anchoring

of Electrical Leads

Thermal Anchoring

of Electrical Leads

Viewport

Getter Pump

Getter Pump

Evaporator

Manipulator

Figure 3.1: (a) Schematic drawing of thecryomagnetSTM system (sideview).

TheSTM is insertedfrom the bottom through thebase ange which alsocarries

Cut A - B

Cut A - B

Distribution Chamber

Distribution Chamber

Viewport

Manipulator

Evaporator

Viewports for

MOKE

Viewports for

MOKE

Magnet

Transfer Rod

Transfer Rod

Table

Spare Port

Spare Port

90°

80°

Rotating Ratiation Shield

Rotating Ratiation Shield

Load Lock Port

Load Lock Port

STM with Sample

STM with Sample

Figure3.2: Sectionofthecryomagnetsystematthesampleplane.

titaniumsublimation pump. The basepressureafter bakeoutand cooldown

is < 510 11

mbar. The turn-around time for venting the system from

low temperature, bake-out, and returning to low temperature accounts to

several days. Thus it is essential that samples and tips can be introduced

through the load-lockof the central distribution chamber without breaking

the vacuum.

3.2 STM Design

ThedesignoftheSTMwasgeometricallyrestricted bythe62mmdiameter

of the magnet's core tube. The cylindrical body of the STM, machined

from one piece of the glass ceramic Macor [47] has a diameter of 40 mm

and a height of 110 mm. This body bears all parts of the microscope. It

is mounted on top of an OFHC copper pedestal which serves both as the

microscope's supportandasthethermal anchoringfor allelectricalwirings.

Togetherwiththisstandthemicroscopeisinstalledasaunitintothemagnet

a b

c

d

e

f

f

g

h

Figure 3.3: Photographof themicroscopeon itspedestal. (a) Macor body, (b)

sapphire prism, (c) leaf spring, (d) tube scanner with tip, (e) sample, (f)

ther-malanchoringofelectricalleadsto heliumandnitrogentemperature,respectively.

a

b

c

d

e

f

g

c

f’

h

i

l

n

z

x

y

m

c’

c’

e’

k

Figure 3.4: Schematic drawingof theSTM (not to scale). (a) Macor body, (b)

sapphireprism,(c) and (c') shearpiezo stacks,(d)Macor beam,(e)and (e') ruby

ball,(f)and(f')leafspring,(g)scannerwithtip,(h)statorsforsamplerotation,(i)

rotorwithsample,(k) spring,(l)temperaturesensor,(m)leafspring,(n)bridge.

beryllium.

3.2.1 Approach Mechanism

At the center of the microscope one nds two moving parts, the approach

sledge bearing the scanner tube at its lower end [(b) in Fig. 3.4], and the

samplerecectacle (i)which canberotated about they-axis. Thecoarse

ap-proachmechanismisbasedonPan'sdesign[48]thathasproventobestable

enough to regain a microscopic location on the samplewith an accuracyof

lessthan100nmposteriortoamacroscopicmovementof20mm[49,50]. The

approach sledge is a polished sapphire prism placed in a V-shaped groove

where it is rigidly clamped by two triplets of shear piezo stacks [51] [(c) in

Fig. 3.4]. A 5 mm  5 mm  1 mm Al

2 O

3

pad is glued on top of each

shearpiezo stack. These padsprovide the actual contact areas between the

stacks and the sapphire prism surfaces. Two of the piezo stacks are glued

to aMacorbeam(d)which ispressedonto theprismby meansof a

molyb-denum leaf spring (f) and a ruby ball (e). The Macor beam functions as

a balance and thus warrants an equal distribution of thespring force to all

contactareasofthesixshearpiezostacksandtheprismsurface. Incontrast

topreviouslypresenteddesigns[52 54]wedonotemploywalkersteppingas

aworkingmechanismbutuseinertial movement byapplyinganasymmetric

saw-tooth voltage curveto all sixstackssimultaneously (stick-slip). Onthe