Digital Comprehensive Summaries of Uppsala Dissertations fromthe Faculty of Science and Technology 840

Magnetism and Structure of Thin3d Transition Metal Films

XMCD and EXAFS using Polarized Soft X-Rays

BY

ANDERS HAHLIN

ACTA UNIVERSITATIS UPSALIENSISUPPSALA 2003

Dissertation for the Degree of Doctor of Philosophy in Physics presented at Uppsala Universityin 2003

ABSTRACT

Hahlin, A. 2003. Magnetism and Structure of Thin 3d Transition Metal Films: XMCD andEXAFS using Polarized Soft X-Rays. Acta Universitatis Upsaliensis. Digital ComprehensiveSummaries of Uppsala Dissertations from the Faculty of Science and Technology840. 64pp.Uppsala. ISBN 91-554-5632-4

In this Thesis the magnetic and structural properties of thin epitaxial Fe, Co, and Ni filmsare discussed. Some of the in-situ prepared samples were used to characterize the degree ofcircular polarization of the newly installed beamline D1011 at MAX-lab. By means of x-raymagnetic circular dichroism (XMCD) and utilizing the associated magneto optic sum rules, theorbital (ml) and spin (ms) moments are determined directly in µB/atom with elemental speci-ficity. The extended x-ray absorption fine structure (EXAFS) measurements yield site specificinformation on the local crystallographic structure.

These measurements were performed using the circular x-rays of several beamlines. Theinfluence of the degree of spatial source coherence (lspat) of the x-rays was characterized bymeans of Fresnel diffractometry. A correlation between enhanced XAS white line intensitiesand higher values of lspat was established for 20 ML Fe, Co, and Ni films on Cu(100).

The degree of circularly polarized x-rays (Pc) at beamline D1011 at MAX-lab was char-acterized by studying Fe films on Cu(100) by means of XMCD. The maximum value of Pc isexperimentally determined to Pc = 0.85.

The Au/Co/Au trilayer system was studied as a function of Co thickness, temperature, andAu cap thickness. A 10 mono-layer (ML) Co film, with an Au cap of 20 A , shows a spin reori-entation transition (SRT) from an in-plane to an out-of-plane easy direction as the temperatureis lowered from 300 K to 200 K. The magnetic properities of these Co films are very differentto what is found for bulk samples due to, in particular, the broken symmetry at the interfaces.

The thickness dependent spin reorientation transition in the Fe/Ag(100) system was charac-terized by means of XMCD and EXAFS measurements. 3 ML Fe films show an out-of-planeeasy direction with an 125% enhanced orbital moment as compared to the 25 ML Fe in-planefilm. Simulations of the Fe L-edge EXAFS indicate the bulk Fe bcc structure for film thick-nesses of 6 − 25 ML Fe. For 3 ML Fe strong deviations from this bcc phase is observed.

Ultrathin Co films deposited on flat and vicinal Cu(111) in the thickness region 1 − 25ML were studied by means of XMCD and scanning tunneling microscopy (STM). The vicinalCu(111) Co deposition leads to the formation of elongated islands preferentially oriented alongthe step edges. In connection to this particular Co growth mode we observe an increase of boththe orbital and the spin moment on the vicinal Cu(111) of about 25% relative to what was ob-served for Co on flat Cu(111).

Anders Hahlin. Department of Physics. Uppsala University. Lagerhyddsvagen 1, SE-751 20Uppsala, Sweden (anders.hahlin@fysik.uu.se)

c© Anders Hahlin 2003

ISBN 91-554-5632-4ISSN 1104-232X

Printed in Sweden by Kopieringshuset AB, Uppsala, 2003

Till mamma och pappa

List of papers

This thesis is based on the following papers. Reprints were made with permis-sion from the publishers.

I. A comparative study of x-ray absorption spectroscopy at varioussynchrotron facilities and the effect of transverse source coherenceJ. Hunter Dunn, D. Arvanitis, K. Baberschke, A. Hahlin, O. Karis, R. Carr,and N. MartenssonJ. Electr. Spectr. Rel. Phen. 113, 67, 2000.

II. Magnetic x-ray circular dichroism on in situ grown 3d magnetic thinfilms on surfacesD. Arvanitis, J. Hunter Dunn, O. Karis, A. Hahlin, B. Brena, R. Carr,and N. MartenssonJ. Synchr. Rad. 8, 120, 2001.

III. Quantitative analysis of L-edge white line intensities: the influenceof saturation and transverse coherenceA. Hahlin, O. Karis, B. Brena, J. Hunter Dunn, and D. ArvanitisJ. Synchr. Rad. 8, 437, 2001.

IV. A circularly polarized x-ray study of the temperature-dependentspin-reorientation transition of thin Co filmsJ. Langer, R. Sellmann, J. Hunter Dunn, A. Hahlin, O. Karis, D. Arvani-tis, and H. MalettaJ. Magn. Magn. Mater. 226-230, 1675, 2001.

V. Cap layer influence on the spin reorientation transition in Au/Co/AuJ. Langer, J. Hunter Dunn, A. Hahlin, O. Karis, R. Sellmann, D. Arvani-tis, and H. MalettaPhys. Rev. B 66, 172401, 2002.

VI. Ultrathin Co films on flat and vicinal Cu(111) surfaces: Determina-tion of per atom orbital and spin momentsA. Hahlin, O. Karis, J. Hunter Dunn, and D. ArvanitisJ. Appl. Phys. 91, 6881, 2002.

iii

VII. Structure and magnetism on in-situ ultrathin epitaxial films: XMCDand EXAFS on Fe/Ag(100)A. Hahlin, C. Andersson, J. Hunter Dunn, O. Karis, and D. ArvanitisSurf. Sci. (in press)

VIII. Ultrathin Co films on flat and vicinal Cu(111) surfaces: per atomdetermination of orbital and spin momentsA. Hahlin, J. Hunter Dunn, O. Karis, P. Poulopoulos, R. Nunthel, J. Lind-ner, and D. ArvanitisJ. Phys. Cond. Mater. 15, S573, 2003.

IX. The temperature-driven transition to perpendicular magnetizationin a Co film studied by XMCD and XRMS based magnetometryA. Hahlin, E. Holub-Krappe, H. Maletta, C. Andersson, O. Karis, J. Hunter Dunn,and D. Arvanitis(In manuscript)

X. Structure and magnetism for ultra-thin epitaxial Fe on Ag(100)A. Hahlin, C. Andersson, J. Hunter Dunn, O. Karis, and D. Arvanitis(In manuscript)

XI. Elliptically polarized soft x-rays produced using a local bump inMAX II - Characterization of the degree of polarizationA. Hahlin, O. Karis, D. Arvanitis, J. Hunter Dunn, G. LeBlanc, andA. Andersson(In manuscript)

The following paper is not included in the thesis as it goes beyond the scopeof the thesis.

Observation of excitation-energy-dependent Xe 4d−15/2,3/2 lifetime

widthsA. Ausmees, A. Hahlin, S. L. Sorensen, S. Sundin, I. Hjelte, O. Bjorne-holm, and S. SvenssonJ. Phys. B 32, L197, 1999.

Conference contributions

Quantitative analysis of L-edge white line intensities: the influenceof saturation and transverse coherence (Poster contribution)A. Hahlin, O. Karis, B. Brena, J. Hunter Dunn, and D. ArvanitisXAFS XI, July 26-31, 2000 Ako, Japan

iv

Tutorial on use of Synchrotron Radiation Sources (Invited talk)A. HahlinThe 1st Workshop on Correlation of Structure and Magnetism in No-vel Nanoscale Magnetic Particles, October 27-31, 2000 Smolenice, Slo-vakia

Magnetic moment determination and the reorientation transition inultra-thin films: Fe/Ag(100) and Fe/Cu(100) (Oral presentation)A. Hahlin, C. Andersson, O. Karis, J. Hunter Dunn, and D. ArvanitisJMMM, November, Seattle, 2001 USA

Structure and magnetism for in-situ epitaxial films: XMCD andEXAFS on Fe/Ag(100) (Oral presentation)A. Hahlin, C. Andersson, O. Karis, J. Hunter Dunn, and D. ArvanitisNano-7/Ecoss-21, June 24-28, 2002 Malmo, Sweden

Comments on my own participation

The research area of experimental physics contains many facets including theservice of experimental equipment, instrumentation development, sample prepa-ration, carrying through the measurements, and finally analyzing and present-ing the data for the community. This work is usually not done by one persononly. In the work presented here my role has more been active in the latersteps, that is to carry through the experimental work and to extract the physicsout of the experimental data. My contribution in the published work is to someextent reflected by my position in the author list.

v

Contents

List of papers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiConference contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivComments on my own participation . . . . . . . . . . . . . . . . . . . . . . . . . . . . v1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Magnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.1 The atom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.2 The solid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.2.1 Localized magnetism associated with the ion cores . . . . . . 72.2.2 Magnetism associated with electron bands . . . . . . . . . . . . . 92.2.3 Magnetic anisotropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3 Light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.1 Polarization of light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.2 Coherence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

4 Experimental work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194.1 Synchrotron radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

4.1.1 MAX-laboratory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224.1.2 The Stanford Synchrotron Radiation Laboratory (SSRL) . . 23

4.2 Sample preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255 Investigation techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

5.1 X-ray absorption spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . 285.1.1 Depth sensitivity in the electron yield . . . . . . . . . . . . . . . . . 305.1.2 Saturation effect in XA spectroscopy . . . . . . . . . . . . . . . . . 30

5.2 Extended x-ray absorption fine structure . . . . . . . . . . . . . . . . . . 325.3 X-ray magnetic circular dichroism . . . . . . . . . . . . . . . . . . . . . . . 34

5.3.1 The XMCD sum rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365.3.2 The Bruno approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375.3.3 Depth sensitivity in the XMCD . . . . . . . . . . . . . . . . . . . . . 37

5.4 Soft x-ray resonant reflectivity . . . . . . . . . . . . . . . . . . . . . . . . . . 385.5 Photoelectron spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

5.5.1 Magnetic information from PES . . . . . . . . . . . . . . . . . . . . . 406 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

6.1 Characterization work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 426.1.1 The degree of circular polarization (Pc) at beamline D1011 42

vi

6.1.2 The degree of spatial coherence and its effect in XA spec-troscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

6.2 Magnetization reversal in thin films . . . . . . . . . . . . . . . . . . . . . . 486.2.1 Thickness and structural dependence . . . . . . . . . . . . . . . . . 486.2.2 Temperature dependence . . . . . . . . . . . . . . . . . . . . . . . . . . 536.2.3 The influence of the cap thickness . . . . . . . . . . . . . . . . . . . 56

6.3 Enhancement of magnetization when lowering the symmetry . . . 57Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

vii

Introduction

Mankind has always been eager to explain the world in which she is living, andhow this beautiful complex machinery actually works. Imagine, e.g., dividinga grain of sand (or anything) into two halves, and one of theses halves into twohalves, ....... how long can one continue like that? Does one ever reach thecore? Questions like this are one of the main driving forces of science. Thephenomenon of magnetism is a question of this form.

When thinking of magnetism most people probably have in mind the com-pass needle or the magnet holder on the refrigerator. The compass needle tendsto align its internal magnetization direction to the external magnetic field (inthis case the earth magnetic field), and the magnet holder moves as close aspossible to the refrigerator wall. If one travels back in time one finds that theearliest text mentioning magnetic compasses dates back to Shen Kua, China(1088). A simple device such as the compass secured a day and night westerlycourse for Christopher Columbus and brought him to the coast of Hispaniola(1492).

Magnetism has also been used for medical purposes. Anton Mesmer setup a practice in Paris in 1784 healing his patience by magnetic means (“ani-mal magnetism”). The method was based on the belief that living beings hadmagnetic fields running through them that could be manipulated. The idea thatmagnetic fields may have some therapeutic value lives on. Magnetic plasterscan be purchased in any Japanese pharmacy, magnetic insoles, bracelets andbandages sell well everywhere. Magnetic cups for treating drinking water arepopular in China, while in Western hospitals pulsed fields have been used tohelp treat bone fractures for the past 20 years.

Our technology of magnetic data storage dates back to 1898 when ValdemarPoulsen demonstrated his telegraphone for magnetic recording. His inventionwas refined by Germans in the 20’s and 30’s using plastic tapes coated with amagnetic oxide, which led the development further to modern tape and videorecorders.

The application of magnetic recording to computing soon followed that ofaudio and video recording. In 1953 the magnetic core memory was introduced,where arrays of thousands of magnets could store and manipulate data bits.Nowadays the primary random access memory (RAM) in which most of thecomputing is done is semi-conductor based, but magnetic media provide the

1

secondary storage on the hard disk. A future prospect is to replace both thesemiconductor memory and the hard disk by magnetic random access memory(MRAM) consisting of arrays of magnetic tunnel junctions.

The archetypal magnet is no longer a horseshoe, but small disc’s of metalfound inside every electric device. There are a myriad of uses of these mag-nets: numerous types of small motors, magnetic separators, magnetrons forradars and domestic microwaves, flux sources for nuclear magnetic resonanceimaging (MRI), oil and water treatment, ..the list goes on and on. Whereas theaverage family in the 1950’s owned two magnets, one in the bicycle dynamo,the other in the windscreen washer motor of the family car, the same familynow owns hundreds of them.

Although magnetism was known long before the concept of research wasborn, it was not until the development of quantum mechanics in the early 20th

century that a deeper understanding was reached. In the formalism of quantummechanics the purely quantum mechanically electron spin plays an importantrole, and is the basis for our understanding of magnetism. The electron spincan be viewed as a spinning top that spins in either a clockwise or a counterclockwise direction. We denote these spin states as spin up and spin down elec-tron states. The way the spins are distributed in matter determines its magneticproperties. Questions like why a piece of magnetic iron clamps to another ironbar but not to a bar of copper, observed but unanswered for thousand’s of year,is now understood and can even be simulated from calculations.

In this Thesis the magnetic and structural properties of thin films of Fe andCo deposited on single crystal substrates such as Cu or Ag have been inves-tigated using polarized soft x-rays. These systems have magnetic propertiesvery different from the free atom or the bulk system. Here the size and thedirection of the magnetization are influenced by, e.g., the film thickness, thechosen substrate, the cap layer, and the temperature. The goal for such stud-ies is not only to design new materials for future advance in technology ormedicine, but also just because we need to know.

2

Magnetism

In this chapter my intention is to introduce the basic consept of magnetismand describe what is governing an element’s magnetic properties. For furtherreading I refer to standard textbooks in magnetism and solid state physics [1,2].

2.1 The atomOur fundamental knowledge of the electronic and structural properties of mat-ter is based on what we know from the atom itself. The atom concept datesback more than two thousand years back, but the atomic model as we knowit today was founded less than 100 years ago. Two giant steps were the dis-covery of the electron (J. J. Thompson 1892) and the nucleus (E. Rutherford1910). Later Bohr established the relationship between wavelengths measuredin spectra and energy levels in the atom, and also proposed a mechanical modelof the hydrogen atom. Also after the introduction of quantum mechanics thismodel serves as a conceptual starting point of our understanding of the small-est building blocks of matter. Nowadays we know that even the atom can bedivided into its constituent part, but for this thesis the atom is the starting pointof the discussion.

In the classical picture of an atom the negatively charged electrons are di-vided into the shells denoted K,L,M, . . ., surrounding the positively chargednucleus consisting of protons and neutrons. In quantum mechanics each elec-tron (as well as the proton and the neutron) can be described as a wavefunctioncarrying properties: charge, mass, angular momentum and spin. To the wave-function we assign four quantum numbers: n, l, ml, and ms representing theprincipal, the angular momentum, the magnetic, and the spin quantum num-ber, respectively. Two electrons are forbidden to carry identical sets quantumnumbers. This fact is known as the Pauli exclusion principle. The Pauli exclu-sion principle implies that the relative direction of two interacting spins cannotbe changed without changing the spatial distribution of charge. The resultingchange in the Coulomb electrostatic energy of the whole system acts as thoughthere is a direct coupling between the directions of the spin involved [3].

The magnetic properties of the atom are defined as the size and the direc-tion of its magnetic moment. The magnetic moment of a free atom has three

3

where c is the speed of light. Diamagnetism leads to a weak magnetic fieldanti-parallel to the applied field. All elements in the periodic table exhibit dia-magnetism but, as the diamagnetism is so much weaker compared to what isfound for atoms with an intrinsic magnetic moment, it can often be neglected.

H M

v-=v0-cHv+=v0+cH

Figure 2.2:Diamagnetic response under the applied magnetic field H . Thecounterclockwise orbiting electron increases its velocity whereasthe clockwise orbiting electron slowes down. This leads to a netangular momentum within the atom. Still the net spin moment iszero.

The atoms with an intrinsic magnetic moment are found among the atomsthat have un-paired electrons, but also in atoms where the Pauli principle canbe fulfilled without a complete pairing of the electrons. For many-electron sys-tems, the net magnetic moment is actually determined by the vector sum of thespin and orbital angular momentum of its electrons. A closed shell of electronsalways gives a zero net magnetic moment. The total angular momentum J isexpressed as a vector sum

J = L + S . (2.1)

The way the individual electrons order within a ground state atom is set by theempirical Hund rules [4]. These rules apply to the spin S, the orbital angularmomentum L, and the total angular momentum J such that:

1. the maximum total atomic spin quantum number S =∑ms is obtained

without violating the Pauli exclusion principle,

2. the maximum value of total atomic orbital quantum number L =∑ml

is obtained, while remaining consistent with the given value of S,

3. the total atomic angular momentum J is equal to |L−S| when the shellis less than half-filled, and is equal to |L+S| when the shell is more thanhalf-filled. When the shell is exactly half-filled L = 0 so that J = S.

5

This means that the electrons as far as possible will occupy states with all spinsparallel within a shell. They will also start by occupying the state with thelargest orbital angular momentum followed by the state with the next largestorbital angular momentum, and so on. The values of L and S according tothe Hund rules for the elements in the 3d transition metal series are shown inFig. 2.3.

5

4

3

2

1

0

J,L,andS

1086420Number of 3d-electrons

J=|L-S| J=|L+S|

Figure 2.3:Values of L (circles) and S (triangles) according to Hund rules forthe elements in the 3d transition metal series.

2.2 The solidIn the previous section we discussed the foundation of magnetism within theatom. If we instead let the individual atoms form a solid, what will then governthe magnetic properties? We will see that although the individual atom carriesa magnetic moment, the solid that is formed does not necessarily show a netmagnetization. However, the solid always shows a magnetic response in thepresence of an applied magnetic field. This is described within the Langevintheory of paramagnetism for localized magnetic moments. Most metals cannotbe described within the Langevin model because they do not fulfill the criteriaof localized magnetic moments. For such systems the itinerant electron theoryis applied. In the itinerant model energy bands are formed where the electronsare treated collectively as waves traveling through the whole crystalline solid.Of course, magnetism also has to be considered as an collective phenomena inthe itinerant model.

6

The localized model is valid when the individual atomic moments only in-teract weakly with the environment. This approach works well for rare earthmetals where the unfilled electron shell is localized on the atoms. The itinerantmodel describe the magnetic properties of 3d transition metals and their alloysquite well, where the electrons in the unfilled shell no longer are localized tothe atom but instead form energy bands.

2.2.1 Localized magnetism associated with the ion coresFor atoms (or ions) with an un-filled electron shell localized on the atomiccore, a localized model for magnetism can often be applied. The essential in-teraction is then addressed to the molecular field2 between the atoms in thesolid. In the presence of an applied magnetic field the paramagnetic suscep-tibility3 varies markedly with temperature, ideally following the Curie law orthe Curie-Weiss law. Both these relations will be described later in the text.Solids that have a permanent magnetic moment have a positive magnetic sus-

1.0

0.8

0.6

0.4

0.2

0.0

Magnetization

100a

IVIII

I II

IV

III

II

I

82 4 6

Figure 2.4:The magnetization following the Langevin theory of paramag-netism. At α= 0 the individual localized spins I are randomlydistributed due to thermal motion. As an external field is applied( II and III ) the spins start to align along the field direction. Fi-nally ( IV ), at sufficient field strength all spins point in the samedirection and the saturation magnetization has been reached.

ceptibility (χ), leading to an alignment of the individual spin moments along

2Originally denoted as a “molecular field”, but perhaps more accurate as an “atomic field”.3Susceptibility is a measure on how a material responds to an applied magnetic field.

7

the direction of an external magnetic field (H). At low fields and finite temper-atures the susceptibility is linear (in Fig. 2.4, the region I and II ), and thethermal energy tends to randomize the direction of the individual moments. Inthe Langevin theory of paramagnetism the potential energy (E) of an atomicmagnetic moment (m) in the applied magnetic field is expressed as

E = −µ0m·H , (2.2)

where the constant µ0 is defined as the Bohr magneton4. Supposing that theindividual moments are non-interacting, classical Boltzmann statistics are usedto express the probability of a given system occupying the energy state E

p(E) = e−E/kBT , (2.3)

where T and kB denotes the temperature and the Boltzmann constant, respec-tively. Solving for the total magnetization M gives

M = Nm(coth (µ0m · HkBT

) − kBT

µ0m · H ) , (2.4)

which for (µ0m · H/kBT ) � 1 leads to the Curie law of susceptibility

χ =M

H=Nµ0m

2

3kBT=C

T. (2.5)

A more general law for the temperature dependence of the paramagnetic sus-ceptibility is known as the Curie-Weiss law

χ =C

T − Tc, (2.6)

where Tc denotes the Curie temperature. Three cases can be identified: Tc > 0where the solid undergoes the transition between the paramagnetic and ferro-magnetic phase, Tc = 0 corresponds to the simple Curie law, and Tc < 0applies for solids that undergo the paramagnetic to anti-ferromagnetic transi-tion. In Fig. 2.4, the Langevin paramagnetic behavior is shown, where α=M ·H/kT . At α= 0, the individual spins are randomly distributed as the en-ergy of the thermal motion overcomes the electrostatic energy. As α increasesthe spins align, but to perfectly align all the spins extremely high fields andlow temperatures are required. However, experimentally this is not the ob-served behavior below the Curie temperature. Considerably weaker fields areneeded to reach saturation magnetization for ferromagnets than the fields ex-pected from the Langevin theory. Here, the individual atomic magnetic mo-ments interact strongly with each other through an exchange field He, and

4The Bohr magneton is defined as µ0 = e�/2m.

8

spontaneously align. Below the Curie temperature Tc the thermal energy is in-sufficient to cause random paramagnetic alignment because of the dominatingexchange field He. The origin of He can be discussed within two approaches:the mean-field approximation and through nearest neighbor interaction. If wesuppose that each magnetic moment mi experiences an effective field He,i

from its nearest neighbors mj than the total exchange interaction field can beexpressed as

He,i =∑j

Jijmj , (2.7)

where Jij is the exchange integral. Here the assumption is that all momentsinteract equally with each other so that J = α, leading to

He = α∑j

mj�αMs . (2.8)

The interaction energy of the spin can then be expressed as

Ee = −µ0αmi · Ms . (2.9)

For a zero external field the exchange field will be the only field present. Fol-lowing the argument analogous to that of the Langevin theory of paramag-netism, the temperature dependent magnetization can be expressed as

Ms

M0= coth (

µ0αm · Ms

kBT) − kBT

µ0αm · Ms. (2.10)

In Fig. 2.5, a perfect alignment of the magnetic moments occurs as the temper-ature approaches absolute zero. As T increases the magnetization decreasesand will, close to Tc, rapidly decrease to zero. Here the thermal energy over-comes the exchange energy and the spins are randomly distributed. For tem-peratures above Tc, Eq. 2.10 is no longer valid. Instead the Langevin theoryof paramagnetism (Eq. 2.4) describes the magnetization of the system moreaccurately.

2.2.2 Magnetism associated with electron bandsIt should be remembered that the above discussion requires the magnetic mo-ments to be localized on the atomic sites. This is not the case for most metals,since their outer electrons that carry the magnetic properties are not localizedat the atomic cores. Besides paramagnetism there exist a number of orderedmagnetic structures such as ferromagnetism, anti-ferromagnetism, ferrimag-netism, and helimagnetism. However, these ordered states undergo the tran-sition to the paramagnetic state at the Curie temperature where the thermalenergy overcomes the ordering energy. This results in a random alignment ofthe individual magnetic moments.

9

1.0

0.8

0.6

0.4

0.2

0.0

Ms(T)/Ms(0)

1.00T/Tc

0.80.60.40.2

Figure 2.5:Mean field approximation for the temperature dependent magne-tization of the ferromagnetic localized atomic magnetic moments.As the temperature increases, thermal energy is introduced into thesystem. This results in a lowered spontaneous magnetization as thespins fluctuate. At the Curie temperature (T/Tc = 1) the thermalenergy and the exchange energy are comparable in size. Abovethis temperature all the spins are randomly distributed.

In metals, the least bound states, often denoted valence states, correspond toelectrons traveling throughout the whole crystalline solid. Here energy bandsare formed, instead of the discrete energy states within the atom. Also themagnetism must then be considered as a collective phenomena. In the Paulitheory of paramagnetism [3] the introduction of a Fermi-Dirac distribution ofthe electrons adjusts the expression of the paramagnetic susceptibility in thelocal model to be applicable for band magnetism. The concentration of thespin up, N+, and the spin down, N−, electrons at the Fermi energy, EF , isthen expressed as

N±�12

∫ EF

odεD(ε)±1

2µHD(EF ) , (2.11)

whereH is the magnetic field and D is the electron density of states. The mag-netization, M , is expressed as M = µ(N+ − N−) and denoted as the Paulispin magnetization (see Fig. 2.6). To describe ferromagnetism within the bandpicture the most straightforward way is to consider the electrons to be entirelyfree following a parabolic energy distribution. The next step is to introducethe exchange interaction between the electrons that favor an alignment of thespins. The exchange interaction gives rise to an excess of electrons with spinspointing in one direction, which results in a spontaneous magnetization. The

10

Fermi level

H 2mH

Energy

Density ofstates

(b)

Fermi level

H=0

Energy

Density ofstates

(a)

Figure 2.6:Distribution of spin up and spin down electrons in a paramagnet atthe Fermi energy within a band. To the left the spin up and spindown density of states are balanced. Under the applied magneticfield H an energy dependent shift between spin up and spin downdensity of states proportional to 2µH takes place.

equilibrium magnetization depends on the number of electrons, the magnitudeof the exchange interaction, and the temperature. A ferromagnetic order hasa net magnetization even at zero applied magnetic field. The simplest case iswhen all individual magnetic moments spontaneously align in the same direc-tion. This system is then mono-domain and has reached its saturation moment.

To understand spontaneous magnetic ordering we have to understand theconcept of exchange interaction. Exchange interaction is an electrostatic effectfavoring the individual spin moments in a system to order in various waysdependent on e.g. the temperature and the structure. In the Heisenberg modelof ferromagnetism the exchange field gives an approximate representation ofthe quantum mechanical exchange interaction. The energy of the interactionbetween sites i and j carrying electron spins si and sj contains a term

U = −2Jexsi·sj , (2.12)

where Jex is the exchange integral. We notice from Eq. 2.12 that the mini-mization of U leads to two cases: Jex > 0 that favors a ferromagnetic orderand Jex < 0 that favors an anti-ferromagnetic order. In the Bethe-Slater curve(see Fig. 2.7) Jex > 0 for the ferromagnetic 3d transition metals Fe, Co, andNi. On the other hand, the anti-ferromagnetic Mn shows a Jex < 0. Above thecritical temperature the paramagnetic behavior is described within the Pauliparamagnetism as expressed in Eq. 2.11.

Although the itinerant model of ferromagnetism is an appealing approachfor explaining non-integral values of atomic magnetic moments and to predict

11

FeCo

Ni

Mn

1.5 2.0

ExchangeinteractionJ ex

D/d

D = interatomic distance (Å)d = diameter of d-shell (Å)

Figure 2.7:The Bethe-Slater curve describing the value of the exchange inter-action Jex dependent on the ratio D/d where D and d denotes theinter-atomic distance and the diameter of the d-shell, respectively.A positive Jex favors a ferromagnetic order, whereas a negativeJex favors a anti-ferromagnetic order.

anti-ferromagnetism and ferromagnetism within the 3d series it has its draw-backs.

2.2.3 Magnetic anisotropyIn a solid it is often found that the spontaneous magnetization prefers certaindirections. The magnetic anisotropy describes how the internal energy of thespecimen depends on the direction of the spontaneous magnetization. Themagnetic anisotropy in a solid can, for instance, be modified by applying me-chanical stress, or varying the temperature. In the case of thin films, we willlater consider how film thickness and capping layers play important roles in themagnetic anisotropy. In a solid with an ordered crystal structure a significantcontribution to the magnetic anisotropy is given by the magneto-crystallineanisotropy, which is linked to the crystal structure of the solid. In such an or-dered crystal structure the internal energy is minimized as the magnetizationdirection lies in what is denoted the easy direction. The magneto-crystallineenergy, Ek, of a uniaxial ferromagnet is written empirically in a series of pow-ers of sin2 θ

K = K0 +K1 sin2 θ +K2 sin4 θ +(K3 +K ′

3 cos(6φ))sin6 θ + . . . (2.13)

where K0, K1, K2 . . . are empirical constants which vary with temperatureand material. θ is the angle between the magnetization vector and the directionof the easy axis and φ represents the azimuthal angle. For the ferromagnetic

12

bcc Fe fcc Nihcp Co

Figure 2.8:The easy direction in the three ferromagnetic elements in the 3dtransition metal series: bcc Fe, hcp Co and fcc Ni.

metals in the 3d series the easy direction is found as shown in Fig. 2.8. Ironhas a body centered cubic (bcc) structure with the easy axis in a six-foldedsymmetry along its principal axis, e.g. [100]. Cobalt has a hexagonal closepacked (hcp) structure with a twofold easy axis symmetry along the c-axis. Nihas a face centered cubic (fcc) structure with an eightfold easy axis symmetrydiagonal through the cube, e.g. along the [111] direction.

The spontaneous direction of the magnetization within a solid is also af-fected by the demagnetizing field inside the body. An illustration of the effectof the demagnetizing field is illustrated for a bar magnet in Fig. 2.9. The totalfield acting inside such a ferromagnetic body, Hi, with saturating field H0 isexpressed as

Hi = H0 − M · D , (2.14)

where D is the demagnetizing tensor and M the saturation magnetization.D is entirely dependent on the shape of the specimen. If, e.g., the specimenhas a spherical shape D is isotropic in all directions. However, for a thindisc, D has much larger elements in the direction perpendicular to the planeof the disc compared to in the plane of the disc. In this case the spontaneousmagnetization would favor an in-plane direction over an out-of-plane directionbecause of the demagnetization factor. On the other hand, imagine a thin discof Co with the c-axis normal to the disc surface. Here the demagnetizationfactor strives for an in-plane magnetization whereas the magneto-crystallineanisotropy prefers the out-of-plane magnetization direction. What is the easydirection in this case?

The magneto-static energy, Em, per unit volume in an external field Hext

is

Em = −12Hi · M − Hext · M . (2.15)

13

Without the external field Eq. 2.15 is reduced to

Em =12(H0 · M − M · D · M) . (2.16)

In cases where these quantities strive in different magnetization directions,

S N S N

(a) (b)

Figure 2.9: (a) Magnetic field inside and outside a ferromagnet. (b) The mag-netic induction inside and outside a ferromagnet. Outside the mag-net the magnetic field lines and the induction field lines are iden-tical. However, inside the magnet the magnetic field opposes theinduction field.

the magneto-crystalline anisotropy generally dominates. However, in extremecases as for ultra thin magnetic films, the demagnetizing factor plays an im-portant role in determining the easy direction.

14

Light

To describe the nature of light historically two classical approaches has beenused: the wave approach; and the corpuscular approach. Both descriptionshave manifested great success in describing physical phenomena. On the onehand stand all the phenomena of interference, diffraction and polarization,which are well described within the wave theory. On the other hand, the photontheory is required to explain the black body radiation1 and the photo electriceffect. However, in the electromagnetic wave approach there is no place forthe photons, and in the particle theory waves have no meaning, yet both are re-quired to give a complete description of the phenomena we observe in nature.In quantum mechanics the formalism for an unified particle-wave theory wasdeveloped in the early 20th century, where the particle and wave description oflight appear as complementary rather than as exclusive conceptions. Perhaps adeeper understanding concerning the fundamental aspects of light has not beenachieved, but the explanation of the wide range of phenomena it covers showsits strength.

Fig. 3.1 shows the electromagnetic spectrum over a broad energy interval.To the left we find the infrared light at photon energies �ω ≤ 1 eV that corre-sponds to a wavelength of λ≥1.2 µm. On the high energy side to the right inFig. 3.1 we find hard x-rays at �ω ≥ 10 keV that corresponds to λ≤1.2 A. In

10 keV1 keV100 eV10 eV1 eV

0.1 nm1 nm10 nm100 nm1 mm

UV

soft x-rays

hard x-rays

VUV

extreme ultraviolet

infra red

visible light

Wavelenght

Photon energy

Figure 3.1:The electromagnetic spectrum for energies from the infra red re-gion up to the hard x-ray region. The infrared region is found≤ 1 eV corresponding to wavelengths ≥ 1µm. The hard x-rays isfound at ≥ 10 keV corresponding to wavelengths ≤ 0.1 nm.

1All bodies emit radiation with the intensity peak at the wavelength λ ∝ 1/T .

15

the experiment work presented in this thesis photons in the soft x-ray regimehave been used, corresponding to wavelengths of ∼ 1 − 5 nm (or alternativelyenergies ∼ 300− 1500 eV). Additional to the wavelength and the energy lightalso carry properties like intensity, polarization, and coherence. In the exper-imental work presented here all these parameters has shown to be important,and especially the two latter needs some extra attention.

3.1 Polarization of lightThe polarization state of light is an intrinsic property of light that describeshow the direction of the electric field E varies with time. Essentially we candivide the polarization state into two extreme cases where, on the one handstand unpolarized light, and on the other 100% polarized light. In the formercase the E-field is randomly distributed in space and no predictions about theorientation of E can be done. In the latter case we find the elliptical polarizedlight, again with the extreme cases: circularly polarized light; and linearlypolarized light. We know that photons are generated as charge is accelerated.The photons exhibit spin angular momentum directed parallel or anti-parallelto its propagation direction, corresponding to helicity σ+ and σ−, respectively.σ+ and σ− photons correspond to right-, and left-handed circularly polarizedlight. A coherent superposition of equal amount of σ+ and σ− photons yieldslinearly polarized light.

A general expression for an electric field (E) propagating in the ∓z-directioncan be be written in terms of cosinusoidal function as

E(z, t) = Ex(cos(ω(t∓z/c) + ∆ϕ)x + Ey(cosω(t∓z/c)y (3.1)

with Ex and Ey representing the amplitude of the electric field in the x andy direction, respectively (see Fig. 3.2). ∆ϕ is the relative phase shift betweenthe two electric fields. The polarization state of a beam of light is describedin terms of the Stokes parameters. These represent four quantities that arefunctions only of observables and can be expressed as

S0 = (E2x + E2

y)/2ζ0 (3.2)

S1 = (E2x − E2

y)/2ζ0 (3.3)

S2 = ExEycos(∆ϕ)/ζ0 (3.4)

S3 = ExEysin(∆ϕ)/ζ0 , (3.5)

where ζ0 is a normalization factor. The first parameter (S0) simply describesthe total intensity of the electric field. S1 and S2 describe the degree of linearlypolarized light in the horizontal plane and at 45◦ versus the horizontal plane,

16

y

xz

ExEy

Ey

Ex

E(a)

ExEy

y

xzE

Ey

Ex

(b)

Dj=0 Dj=p/2

Figure 3.2:A super position of two linearly polarized electric field leads to:(a) a linearly polarized field if the phase difference, ∆ϕ, betweenthe two interfering field is a multiple of π: or (b) to a circularlypolarized field if ∆ϕ is a multiple of π/2. For other values of ∆ϕthe resulting field will be elliptically polarized with the axes alongy and x.

respectively. The last parameter (S3) describe the degree of circular polarizedlight. The Stokes parameter’s are related to each other through

S20 =

S21 + S2

2 + S23

V 2, (3.6)

where V is a measure of the degree of polarization. V = 1 characterize com-pletely polarized light and V < 1 indicate the degree of partial polarization.

3.2 CoherenceTwo beams of light are said to be coherent when the phase difference betweenthe waves by which they are represented is constant during the period normallycovered by observations. Two beams are said to be non-coherent when thephase difference changes many times and in an irregular way during the short-est period of observation. Mathematically we can define a coherence functionwhich describes to what degree the information of the electrical field at a pointcan be predicted by knowing its properties at a second point, as a function oftheir separation in space and time. Real light sources are neither fully coherentnor fully incoherent, but partially coherent. In the direction of propagation wecan define a temporal coherence length, ltemp, as the length over which thephase relationship is maintained. For a source with bandwidth, ∆λ, we have

ltemp =λ2

2∆λ, (3.7)

17

that is, ltemp is entirely related to ∆λ and the wave length λ. In the directionorthogonal to the propagation direction we define the spatial coherence lengthlspat which depends on the size of the source and the angle of observation.Starting from the Heisenberg’s uncertainty principle ∆x∆p � �/2 we obtain,for small θ setting |∆p| = �k∆θ, the limiting relationship

∆θ = λ/2πd , (3.8)

where d and θ represent the diameter of the source and the angle of observa-tion, respectively. If we now define the spatial coherence length lspat = z∆θ,Eq. 3.8 can be expressed as

lspat =zλ

2πd. (3.9)

It is evident that the lspat is linearly dependent to the distance of observa-

Dq

l

d=2Dx z

Figure 3.3:The degree of spatial (or transverse) coherence of a wave at dis-tance z is dependent on the wavelength λ and the source size d.

tion, which means that one can achieve relatively high spatial coherence for allsources, when moving far away from the light source. Moreover, the lspat isalso linearly dependent to the wavelength.

Combining the two defined coherence quantities enables the determinationof an coherence volume

lvol = lspat·ltemp . (3.10)

This would mean that by knowing the phase at point (x1, y1, z1) one wouldalso know the phase at point (x2, y2, z2) as long as one moves around withinlvol.

18

Experimental work

Most of the experimental work presented here were done at two synchrotronfacilities: the MAX-lab in Lund, Sweden and the Stanford Synchrotron Radia-tion Laboratory (SSRL) at Stanford, California. The requirement for perform-ing x-ray absorption (XA) spectroscopy measurements is a stable tuneablyx-ray source with a high brilliance1. For x-ray magnetic circular dichroism(XMCD) an additional requirement is the availability of circular polarized x-rays. These requirements are, at present, only fulfilled at synchrotron facilitiesand a short presentation of their characteristics follows here.

The sample preparation work was mainly done in-situ ultra high vacuum(UHV). This is to ensure a high cleanness and high quality of the samplewhich is of essence in this work. The preparation work includes cleaningand characterization of the surface substrate, and film deposition using elec-tron beam evaporation. Here follows a description of the experimental setupand the preparation work at the two synchrotron facilities (MAX-lab, and theSSRL) and the characteristics of the x-rays provided. For a more thoroughpresentation of synchrotron radiation I refer to the textbooks of Als Nielsenand McMorrow [5], and Attwod [6].

4.1 Synchrotron radiationElectromagnetic radiation is created as charged particles change velocity ordirection, i.e, as they are accelerated. As all matter contains charged particles(electrons and protons) it will continuously emit electromagnetic radiation of abroad spectrum of frequencies when accelerated. This is actually the concep-tual explanation of the black body radiation. One way to create radiation in acontrolled way is to keep negatively charged electrons2 at high velocity in anorbit, a storage ring. This is practically done at synchrotron facilities by accel-erating the electrons to high velocities and then steering them with magnets.The storage of the electron beam has to be done under high vacuum condi-tions to avoid the electrons colliding with atoms and molecules present in therest-gas. This is achieved by using different stages of vacuum pumps through-

1The brilliance is defined as proportional to the ratio between the intensity and the line-widthof the x-rays.

2Some sources also operate with positively charged particles such as positrons.

19

out the vacuum system. In the reference system of a staionary observer theelectrons must be accelerated towards the ring center to maintain the circulartrajectory, and thus radiate as a consequence of energy and angular momentaconservation. If the velocity of the electrons is low the emitted radiation isnearly monochromatic3 and preferentially directed orthogonal the acceleratingdirection. Close to the speed of light the wavelength of the radiation is a broadspectra with the intensity maxima shifted to shorter wavelength, directed in acollimated narrow cone4 tangentially to the electron orbit in the storage ring.The half angle of the cone θ is inversely proportional to the relativistic factor5

γ as θ = 1/2γ, see Fig. 4.1. Each time the electron bunch passes the pointof observation a short radiation pulse of intensity I and duration time 2∆τ isemitted. I and 2∆τ depends on the current and the velocity of the electronsin the storage ring, respectively. The radiation in the plane of the electron

AB

R sinq

B'q= 2g

1

q= 2g1

Radius R

2Dt

Time

Intensity

RadiationPulse

(b)(a)

Figure 4.1: (a) Radiation from the electron beam in the storage ring is emit-ted as the electron beam is bent by a dipole magnet. The time oftraveling from point A to point B sets the (b) pulse time and is de-pendent on the energy of the electron beam through the relativisticfactor γ.

beam orbit is ideally plane polarized with the E-field in the plane of the beamorbit. As we move out of this plane a vertical component of the E-field ap-pears, with magnitude dependent on the wavelength and the angle to the plane.From Fig. 4.1(a) we notice that the electron beam has a non-vanishing angularmomentum: from above clockwise; and from below counterclockwise. Wecan define a degree of circular polarization with the helicity positive (σ+) ornegative (σ−) when viewing the orbiting plane of the electrons from above orbelow, respectively.

3Monochromatic means only one wavelength.4The Lorenz transformation of the observed angle between the rest system of the electron

and the rest system of the observer gives rise to this collimation.5The relativistic factor γ is defined as γ = 1√

1−v2/c2, where v is the velocity in the system

of the observer.

20

e-

NS

N

N

N

S

S

S

Undulatorradiation

Figure 4.2:The undulator consists of a periodic array of magnets arranged insuch a way as to induce regular oscillations in the electron beam.The resulting x-rays produced generally have higher intensity andbrilliance than the bending magnet radiation.

To achieve a higher photon intensity than is possible from bending mag-net radiation, so called insertion devices can be introduced. At present threemain types of insertion device exist: wigglers, undulators, and free electronlasers. The first two are today commonly used at various synchrotron facili-ties, whereas the free electron laser is a device still under development. Theyall have in common that they consist of periodic arrays of magnets which arearranged in such a way as to induce regular oscillations in the electron beamorbiting in the ring (see Fig. 4.2). The resulting x-rays produced generally havehigher intensity and brilliance than the bending magnet radiation.

So far only the production of photons has been discussed, but to make theradiation useful for experimental purposes we need to transfer the x-rays to ourexperiment end station. In Fig. 4.3 a schematic view over the SX-700 basedbeamline D1011 at MAX-lab is shown. The beamline is operated at ultra highvacuum (UHV) conditions (pressure < 10−9 mbar) and consists of several op-tical elements, starting from the light source (the electron storage ring) andending at the experimental chamber. In Fig. 4.3(a) and (b) we can trace thephoton beam path in the vertical and horizontal plane, respectively. From thesource the beam is diverging and has a broad energy spectrum. Mirror 1 is aplane-elliptical mirror that focuses the beam onto the exit slit in the horizontalplane. Mirror 2 is a plane rotatable mirror that reflects the light onto the dis-persive rotatable grating. At the grating, the x-rays, that until here consist ofa broad energy range, are dispersed in the vertical plane and reflected onto themirror 3. The rotatable elliptical-plane mirror (mirror 3) focuses the beam inthe vertical plane onto the exit slit. At the end station the beam is monochrom-atized and slightly defocused (as the focus lies on the exit slit ∼ 200 mm fromthe sample position). The wave-length at the end station is controlled by therelative positioning of the elements in the monochromator (mirror 2, grating 1,and mirror 3).

21

mirror 1 mirror 2

mirror 3grating 1

lightsource

lightsource

mirror 1 mirror 2 mirror 3grating 1

endstation

endstation

exitslit

exitslit

Beamline D1011

(b) View from above

(a) View from the side

Figure 4.3:Schematic view of the beamline optics in the modified SX700beamline D1011 at MAX-lab. This optical setup ensures that thephoton beam focus is found at the exit slit for energies between30 − 1500 eV.

4.1.1 MAX-laboratoryAt MAX-lab today there exist two operating storage rings: MAX I (550 MeV)and MAX II (1.5 GeV). MAX III is still under build up. The characteristicsof MAX I and MAX II are partly described in the PhD theses of Werin [7]and Andersson [8]. The results presented here are obtained using the beamlineD1011 at MAX II. Beamline D1011 is a bending magnet beamline coveringthe energy range 30 to 1500 eV, meaning that for example the 2p core elec-trons for the 3d transition metals are easily reached. The monochromator is amodified SX-700 [9] (see Fig. 4.3) with the energy dependent intensity and res-olution shown in Fig. 4.4. Characteristic for such a bending magnet beamlineis the fairly smooth photon intensity distribution for the whole energy interval(30 − 1500 eV). This is important for the local structure investigation method(EXAFS studies) introduced in Section 5.2. What really devotes this beam-line to magnetic research is the possibility to vary the polarization state of thelight. This is done by providing for an adjustable local bump of the electronbeam in the vertical direction as is sketched in Fig. 4.5. As the beamline, byintroducing this local electron bump, now views the light cone at an angle Θrelative to, defined in Fig. 4.5, the plane of the electron beam, the x-rays at theoptical path of the beamline has a degree of circular polarization, which makesthe work of XMCD possible.

The end station at beamline D1011 consists of an ultra high vacuum (UHV)chamber split into a lower measuring chamber and an upper preparation cham-ber, separated with a manual valve. The sample holder is mounted on a rodthat is attached to a manipulator mounted on top of the upper chamber. This

22

Figure 4.4:The photon flux and the energy resolution for various exit slitwidths in the photon energy interval 30 − 1500 eV at beamlineD1011 at MAX-lab.

enables the transfer of the sample between the two chambers, as well as rota-tion around the vertical axis and movement in the horizontal. The preparationchamber is equipped with an ion sputtering gun for surface cleaning, a gas in-let system, and low energy electron diffraction (LEED) equipment for surfacestructural analysis. In the preparation chamber there is also a possibility to at-tach extra UHV compatible equipment such as evaporators for the film growthand coils for the magnetization of the samples.

The measuring chamber is always kept at low pressure (around 2 · 10−10

mbar) to ensure highest possible cleanness during the data collection.

4.1.2 The Stanford Synchrotron Radiation Laboratory (SSRL)At beamline 5 at the Stanford Synchrotron Radiation Laboratory (SSRL) thex-rays are produced in a slightly different way. Instead of utilizing the dipoleinduced synchrotron radiation, an undulator is installed in the straight sectionof the ring just before beamline 5. The specially tailored elliptically polarizingundulator (EPU) of beamline 5 consists of four beds of magnets. A schematicsketch of an EPU is shown in Fig. 4.6. The four magnetic beds can be po-sitioned to produce either linearly polarized light in the horizontal or vertical

23

netization are mounted from below and are independently rotatable around thevertical axis, which enables magnetization directions in the horizontal plane.The channel-plate detector for electron yield measurements is mounted hori-zontally from below and can be moved in the vertical direction to approachthe sample. The photo diode, mounted on the coils, enables specular reflectiv-ity measurements at different incident x-ray beam angles. This UHV chamberwas moved from SSRL to MAX-lab the autumn 2001, and has been operating,in parallel with the D1011 end-station, at beamline D1011 since April 2002.

4.2 Sample preparationSingle crystal surfaces were used as substrates for the in-situ prepared ultra-thin films. The crystals were delivered from different manufactures with a cho-sen specific crystal orientation, with a miscut of less than 0.5◦ and a surfaceroughness < 0.03µm. The surface was further cleaned and polished by ar-gon ion bombardment and annealing cycles until sharp diffraction spots weredetected by means of LEED. These spots are only seen if the surface has awell defined long range order crystallographic structure. Typical parametersfor these cycles were argon ion sputtering for 20 minutes at 2.0 keV and 5µA,followed by annealing the crystal at 900 K for 2 minutes. The last sputteringcycle before film deposition was done at a lower power and at a shorter time,e.g, 5 minutes argon sputtering at 1.0 keV and 2µA. The argon pressure duringthe sputtering process was typically ∼ 10−5 mbar.

The metal films were deposited by means of electron beam evaporation ata rate of typically 0.5 layer per minute at a pressure of < 4·10−9 mbar. Theevaporators are “home made” and shown in Fig. 4.7. The principle idea is to re-sistively heat up two W filaments (current If ) that eventually release electrons.The material of evaporation are ultra-pure metal rods (usually of Fe, Co, or Ni)of diameter D = 5 mm and length L = 50 mm. The rod is set on high voltageU, and by measuring the current in the rod Ir the total power P (P = UIr)is determined and controlled by the filament current. The temperature of themetal rod is dependent on P .

To ensure a high cleanness the base pressure in the chamber was kept <2·10−10 mbar. Depending on the system studied, the film growth was done attemperatures between 100−300 K. Film growth at low temperatures were donefor systems where the risk of intermixing between the two elements (substrateand film) was expected. For the low temperature film depositions (substratetemperature � 100 K), the sample was shortly annealed to 300 K directly afterthe film deposition. This was done to increase the mobility of the atoms at thesurface in order to improve the structure of the film. The annealing time wasalways kept short to prevent intermixing.

25

e-

e-

e-

If Ir

+1.2 kV

e-

e-

If

Figure 4.7:Schematic drawing of our “home made” electron beam evaporatorfor thin film deposition. The metal rod is put on a positive highpotential and is bombarded with electrons emitted from the W fil-aments. The power delivered to the rod is P = UIr.

The film thickness was controlled by the time and power for evaporation,and characterized by means of x-ray absorption measurements (the spectroscopymethods are described in Section 5.1) by studying the ratio of the film/substrateabsorption signal. The total electron yield Y from a thin film sample can beassigned to a yield contribution from both the film and the substrate

Y =∫ lf

0dYf +

∫ lf+ls

lf

dYs , (4.1)

where the integration limits lf and the ls represent the film thickness and thesubstrate thickness, respectively. The individual electron yield contributionfrom the film (dYf ) and the substrate (dYs) are expressed as

dYf = I0µf exp (−xfµf )exp

(−xf

λf

)dxf (4.2)

dYs = I0µs exp (−(lfµf + xsµs))exp

(−(xs

λs+lfλf

)

)dxs . (4.3)

Here λf , λs and µf , µs represent the electron escape depths and the absorptioncoefficients in the film and in the substrate, respectively. The incident intensityof the x-rays is described by I0. If we combine Eq. 4.2 and 4.3 with Eq. 4.1,and assuming a very thick substrate compared to the film (ls → ∞) the totalelectron yield reduces to

Y = I0µs

exp

((− 1

λf+ µf )lf

)1λs

+ µs

+I0µf

1 − exp

(−( 1

λf+ µf )lf

)1

λf+ µf

.

(4.4)

26

20

15

10

5

0

Absorption(arb.units)

1000900800700600Photon energy (eV)

FeCo

Ni Cu

W Ag Au

Figure 4.8:The absorption coefficient µ versus photon energy for Fe, Co, Ni,Cu, W, Ag, and Au. The data were taken from the tabulated valuespresented at the Center of X-Ray and Optics (CXRO) homepage.

In Fig. 4.8 tabulated values for the absorption coefficient µ versus photonenergy are shown. These data were obtained from the CXRO homepage, seealso Ref. [10].

We observe that the 3d transition metals Fe, Co, Ni and Cu all have largecharacteristic edge jumps in the energy range presented in Fig. 4.8. The in-crease in the absorption cross section, given these “jumps”, corresponds to the2p3/2,1/2 → 3d, 4s excitations. In Fig. 4.8 the white lines6 are not present.Interesting is that the commonly used substrate Cu has a low absorption crosssection for photon energies below the 2p3/2,1/2 threshold, whereas the othersubstrate candidates W, Ag, Au, have a smooth and stronger absorption coef-ficient throughout this energy interval.

The XAS edge jump ratio for a thick film (> 50 ML) is independently ofsubstrate as the electron yield contribution from the substrate, due to the lowelectron escape depth, is negligible. However, for a thin film the situation isvery different. Here the XA spectra has a non-negligible contribution fromthe substrate. By combining the absorption coefficients from Fig. 4.8 withtabulated values of the electron escape depth, the electron yield contributionsfrom the film and substrate can be simulated with Eq. 4.4, and thus the filmthickness can be determined.

In the case for 3d transition metal films with Cu as the substrate a morestraightforward method in calibrating the thickness were used. Here we di-rectly used the experimentally determined edge jump ratio [11], that is validfor Fe, Co, and Ni.

6“White lines” is the historical name of the edge resonances as they appeared as white lineson photographic films used in the early x-ray experiments.

27

Investigation techniques

The investigation techniques used throughout this thesis are mainly based oncore electron spectroscopy using synchrotron radiation. The main advantageworking with core electrons is the element specific outcome, as the core elec-trons serves as fingerprints for the elements. Here mainly the x-ray investi-gations probing magnetic and structural properties based on x-ray absorption(XA) spectroscopy has been used. But also the techniques based on surfacex-ray resonant reflectivity (SXRR) and photoelectron spectroscopy (PES) arepresented to yield useful information on the magnetic properties.

5.1 X-ray absorption spectroscopyIn x-ray absorption (XA) spectroscopy we aim to determine the absorptioncoefficient µ. XA spectroscopy is an experimental technique that yields in-formation about the electronic structure in the sample, and can also, as willbe shown, give both magnetic and structural information. In principle (seeFig. 5.1) we let a monochromatized x-ray beam of intensity I0 impinge on asample with thickness x, and then measure the transmitted intensity I . Fromthe relation

I = I0·e−µx , (5.1)

the absorption coefficient µ is determined. However, for ultra-thin transitionmetal films deposited on single crystal surfaces, µ cannot be measured directlyin the way described above. Here, due to the thickness of the samples, includ-ing substrates, and the high absorption of the photons at these energies, thetransmitted intensity is not measurable. Instead the secondary electron yieldchannel, reflecting the µ indirectly, is measured. Every absorption of a photonis most likely followed by emission of one or several electrons. It is generallyaccepted in the literature that the amount of emitted electrons is directly pro-portional to µ, see, e.g., Ref. [12]. The size of µ is mainly determined by theelectronic structure within the specimen, and is proportional to the sum of thetransition probabilities Pi,f from the initial state |i〉 to the final state |f〉

Pi,f =2π�|〈f |V |i〉|2ρf (E) , (5.2)

28

where V and ρf (E) are the time-dependent perturbation and the density offinal states, respectively. To determine the total XA cross section at the photonenergy �ω we have to sum over all initial states |i〉 with binding energy lowerthan �ω.

In Fig. 5.1 a typical energy dependent XA spectrum for Fe recorded withlinearly polarized x-rays is shown. The relative intensity is proportional to the

4

3

2

1

0Relative

intensity(arb.units)

120011001000900800700Photon energy (eV)

EXAFS * 10

Fe L3,2 I0 I

I=I0.e-mx

Figure 5.1:The most straightforward XA measurement is to let x-rays impingeon a sample and measure how much of the x-rays penetrates. Bythe simple expression above we solve for µ for different energies.Above, the background corrected relative µ is plotted versus thephoton energy. Alternatively µ is measured as the amount of elec-trons emitted in the secondary electron yield process.

absorption coefficient µ and dominated by the sharp L3,2 edges at 708 eV and721 eV, reflecting the excitation of the 2p3/2 and 2p1/2 core levels, respec-tively. The energy region in the vicinity of these transition is defined as thenear edge x-ray absorption fine structure(NEXAFS) region. In this example(Fig. 5.1) the data was obtained using linearly polarized x-rays. By using cir-cularly polarized x-rays this electronic structure information can be resolvedin a spin-up and spin-down fashion, and thus give us magnetic information. Athigher photon energies the characteristic EXAFS appears. In Fig. 5.1, the EX-AFS oscillations are shown multiplied with a factor of 10. The origin of theseoscillations is that the final state cannot be treated as only the core hole andthe escaping photoelectron, but one has to take into account constructive and

29

destructive interference from the surrounding backscattering atoms. A carefulanalysis of this effect (see section 5.2) will enable element specific real spacestructural information and is a powerful spectroscopic tool to determine thelocal structure.

5.1.1 Depth sensitivity in the electron yieldIn the total electron yield Y measurements we, due to the finite electron escapedepth, mainly probe the surface region. The energy dependent electron yieldY (E) can be expressed as

Y (E) =∫ ∞

0I(x,E)µ(E)e−

xλdx , (5.3)

where x, µ(E) and λ are the depth of the absorption process, the photon ab-sorption coefficient, and the electron escape depth, respectively. I(x,E) rep-resent the intensity of the x-rays for the photon energy E at the depth x, and isexpressed as

I(x,E) = I0Ee−xµ(E) , (5.4)

where I0(E) is the incident x-ray intensity. That is, although the photonspenetrate several hundred Angstroms deep into the sample, the depth depen-dent contribution to the electron yield signal decreases rapidly with increasingdepth, as is visualized in Fig. 5.2. Here the depth dependence of the electronyield is plotted where the mean electron escape depth was set to λ = 17 A.As λ�(1/µ) the x-ray intensity I(x,E) is often set to I0(E) for thin films.At the depth x1 most of the emitted electrons penetrates to the surface and aredetected in the experiment. However, at the depth x2 only a few electrons pen-etrate to the surface and the contribution to the measured signal is low. If oneinstead would detect photons this effect is less significant, as the photons havea much larger penetration depth.

5.1.2 Saturation effect in XA spectroscopyIn most cases the photon penetration depth λ is much larger than the electronescape depth λ. However, if the condition λ� λ is not fulfilled the measuredtotal electron yield Y does not any longer reflect the absorption coefficient µ,but is suppressed. From Fig. 5.1 we observe a strong variation in µ in thevicinity of the L3,2 peaks at 708 eV and 721 eV compared to what is found atother energies. For such a sample, measurements at low angles do not fulfillλ� λ which might lead to saturation effects in the vicinity of the peaks. Herea correction procedure to compensate this effect is needed. The electron yieldcan be described as

Y (E) =µ(E)

µ(E) + 1λsin θ

, (5.5)

30

1.0

0.8

0.6

0.4

0.2

Contributedyield(arb.units)

806040200Probing depth (Å)

100

e-e-

hninhnout hnout

q

x 1x 2

Figure 5.2:X-ray absorption spectroscopy measured with electron yieldmainly probes the surface of the sample. The emitted electronsfrom depth x reach the surface of the sample with probability pro-portional to e−x/λ, where lambda represent the electron escapedepth. The photons have a much larger penetration depth.

where θ is the measuring angle relative to the sample surface. The normalizedyield Ynorm is scaled to the experimental yield Yexp using

Ynorm = a+ bYexp . (5.6)

From here the correction is done in four steps:1. From Eq. 5.6 we construct two equations: one for the pre edge and

one for the post edge. We introduce the terms: Y prenorm, Y post

norm, Y preexp

and Y postexp . The first two terms are obtained from tables, e.g., the

CXRO homepage, and the latter two terms are obtained from the XASmeasurement. Using Eq. 5.6 and these terms the constants a and b arecalculated.

2. We know focus on another energy, e.g., the L3 peak maximum andcalculate Y L3

norm from Eq. 5.6 using the above determined a and b. AsYexp we use the measured intensity at the L3 peak, obtained from thesame spectra as Y pre

exp and Y postexp .

3. Using Eq. 5.5 with Y (E) = Y L3norm, and θ as the x-ray incidence

angle, the corrected µ is obtained.4. Finally the corrected yield Y corr

L3is obtained using the corrected µ in

Eq. 5.5 with θ set to 90◦.It should be noticed that the procedure above only describes the correction atone energy point, i.e., the procedure has to be repeated for all energy points inthe XAS spectra. Sometimes a thin film cap layer is put on top of the measuredfilm (see Section 6.2.3). The cap do not alter the saturation correction proce-dure as long as the cap has a smooth µ over the photon energy range used in

31

the measurements. However, Eq. 5.5 can easily be extended to bi- and tri-layersaturation corrections.

5.2 Extended x-ray absorption fine structureAt photon energies above the threshold energy for the resonant excitation theextended x-ray absorption fine structure(EXAFS) region starts. This regionis characterized by weak oscillations of low frequency arising from backscat-tering of photoelectrons from the first neighboring atoms. From EXAFS ex-periment we obtain inter-atomic distance information, coordination number,and information about the static and dynamic disorder for the first neighboringatoms. The EXAFS oscillations can be written in the form

χ(E) =µ(E) − µ(0)

µ(0), (5.7)

where µ(E) is the measured absorption and µ(0) the ideal absorption of thefree atom. In the EXAFS scattering theory χ(E) is expressed as the sum of

constructive inteferencedestructive inteference

hn

Figure 5.3: In the extended x-ray fine structure process (EXAFS) the final statecannot be viewed as a core hole and an escaping photoelectrononly. One has to take into account interference effects from thebackscattering from the neighboring atoms also.

modified sine waves with different frequency and phase from each backscat-tering coordination shell j, around the central atom i

χi(k) =∑j

Aj(k) sin(ψij(k)) , (5.8)

where Aj(k) is the total backscattering amplitude of the jth shell of backscat-tering atom and ψij(k) is the corresponding total phase function. As both

32

Aj(k) and ψij(k) contain structural information the expression of Eq. 5.8 isdecomposed to an expression where we can identify more physical parameters

χi(k) =∑j

NjS20(k)

kR2j

|feff(k)|je−(2k2σ2j)e−(2Ri/Λ(k)) sin(2kRi + ψij(k)) ,

(5.9)where

Nj= number of back-scatterers in the jth shell.Rj= the distance between the absorbing atom i and the backscatteringjth shell in single scattering.S2

0(k)= the amplitude reduction factor due to multiple excitations,etc..feff(k)= the effective amplitude function for each scattering path.e−2σj

2k2= the Debye-Waller factor in the harmonic approximation.

σj= the Debye-Waller parameter accounting for thermal and staticdisorder.Λ(k)= the photoelectron mean free path.e−2Rj/Λ(k)= the mean free path factor.(2kRi + ψij(k))= the total phase.ψij(k))= the phase shift due to the Coulomb potential of the centralatom i and of the backscattering jth shell.

A typical example of the different steps in an EXAFS analysis is shown inFig. 5.4. Here I present Fe L3,2 XA spectra with the photon energy coveringthe energies 650 − 1400 eV. At 708 and 721 eV the characteristic L3 and L2

peaks appear, relating from the 2p3/2,1/2 → 3d core excitations. At higherphoton energies we can follow the EXAFS oscillations at energies up to 1400eV. The EXAFS oscillations are magnified up with a factor of 10. To isolatethe EXAFS from the background a function representing the atomic absorptionis subtracted from the XA spectra as described in Eq. 5.7. Down to the left weshow the pure EXAFS (χ) times the wavevector k plotted against k. Finallyafter Fourier-transforming k · χ we can present the modulus of the Fourier-transform versus the distance (in real space) down to the right in Fig. 5.4.

The EXAFS measurement are support by calculations performed using theFEFF 8.10 software [13]. The FEFF 8.10 calculations are based on ab initioself-consistent real space Greeen’s function approach for clusters of atoms andyields e.g. the theoretical EXAFS. By building a cluster-model, the experi-mental spectra can be simulated and local crystallographic information suchas nearest neighbor distances and coordination number are ideally obtained.The cluster input files were generated from ATOMS 3.0 program developed byBruce Ravel.

33

5

4

3

2

1

0

Relativeintensity(arb.units)

14001300120011001000900800700Photon energy (eV)

3 AL25 AL

EXAFS x 10Fe on Ag(100)Normal incidenceT = 120K

0.4

0.2

0.0

-0.2

-0.4

k·c(k)

121110987654k (Å-1)

0.4

0.3

0.2

0.1

Mod

ulus

FT(k

·c(k))

76543210R (Å)

(a)

(c)(b)

Figure 5.4:The EXAFS analysis involves different steps: (a) the EXAFS areisolated by subtracting a function reflecting the atomic absorption;(b) the EXAFS are expressed as k·χ in the reciprocal space; (c) k·χis Fourier-transformed and the modulus of the Fourier-transform inreal space reflects the real space interatomic distance of the nearestneighbors.

5.3 X-ray magnetic circular dichroismX-ray magnetic circular dichroism (XMCD) is an experimental technique that,in an element specific way, enables quantitative determination of the size anddirection of the spin and orbital moments. Moreover, the technique is very sen-sitive to small quantities of material which makes it possible to study highlydiluted samples, such as ultra thin magnetic films and magnetic nano struc-tures. In the band picture of itinerant ferromagnetism the majority spin bandis more populated than the minority spin band, due to the exchange splitting∆Ex (as described in Section 2.2). By using the above described technique ofXA spectroscopy in a spin selective way, the amount of spin up and spin downpopulation can be determined, and the spin momentms can be calculated fromthe relation

ms = (N+ −N−)µB , (5.10)

where N+ and N− reflect the average number of majority and minority d-electron spins per atom, respectively.

In the itinerant band picture of Stoner, the magnetic moment is solely due tothe electron spin, without an orbital moment contribution. For an orbital mo-ment to exist a net orbital current from the unfilled d-shell electrons is needed.

34

EF

Energy

2p3/22p1/2

4s

3d

hu

s+

600

400

200

0

-200Intensity(arb.units)

750740730720710700690Photon energy (eV)

minoritymajority

XMCD diff.

3 AL Fe on Ag(100)T=120 Kelvin

DAL3

DAL3

half sum

(a) (b)

Figure 5.5: (a) Using x-rays with a degree of circularly polarization a spinselective excitation from the spin-orbit split 2p3/2,1/2 to the ex-change split 3d band is performed. (b) The XMCD differencespectra is achieved by subtracting the minority spectra from themajority spectra. Using the magneto optic sum rules and introduc-ing the double step function, the orbital (ml) and the spin (ms)moment can be determined directly in µB per atom with elementalspecificity.

This would imply a broken time symmetry such that the motion of the orbit-ing electrons, on average, is larger in one direction compared to the oppositedirection. In magnetic materials, such symmetry breaking, is induced by thespin-orbit coupling. The angle dependent orbital magnetic moment ml of thed-shell is given by

ml = −µB

�〈L〉 , (5.11)

where the orbital moment is calculated by summing the matrix elements

〈ψ(k)|L|Φn〉 , (5.12)

over all unoccupied electronic states ψ(k).The mechanism driving the electronic excitation is the interaction of the

photon field and the and the atom. This interaction can for our purpose oftenbe approximated with dipolar type interactions only. This can be representedby the dipolar operator 〈eR〉, where e and R represent the charge and posi-tion, respectively. The only non-vanishing matrix element is obtained when

35

∆l = ±1 as the parity of the final and initial state is determined by their or-bital quantum number l. In the absorption process the angular momentum ofthe photon must be transfered to the sample, and for circularly polarized x-rays this gives the additional selection rule ∆m = ±0, where a positive ornegative value of m is dependent on which helicity that is involved. The ab-sorption as described by Eq. 5.1 has to be modified to account for the magneticcontribution and will get the following form

I± = I±0 ·e−µ±x , (5.13)

where µ+ and µ− represent the absorption coefficient for right and left handedcircularly polarized x-rays, respectively.

In an one-electron picture, the XMCD effect for the 3d transition metals canbe explained within a two step model. If we assume that the magnetization,M , and the wave vector, k, are collinear, the circularly polarized x-rays haveits spin parallel, +�, or anti-parallel, −�, to M . From atomic physics we havethe dipole selection rules for conservation of angular momentum as: ∆l = ±1and ∆m = 0. As the 2p state is split by the spin-orbit interaction to 2p3/2,1/2 itis no longer a pure spin state, and the photon angular momentum is transferredto both the spin and orbital degrees of freedom of the excited electron. For the2p3/2 state the proportion “spin up” and “spin down” excitations are 5:3 and1:3 for +� and −� photons, respectively.

In the second step, the exchange split valence band acts as a detector forthe excited core electrons. The imbalance of empty states in the 3d band willlead to a spin selective excitation process, and yield information about thespin polarization of the d-states. The XMCD effect is especially strong forferromagnets with a strong absorption edge. For further reading I refer to thetextbooks of Lovesey and Collins [14], and Als-Nielsen and McMorrow [5].

5.3.1 The XMCD sum rulesBy applying the magneto optical sum rules [15, 16] the orbital (ml) and spin(ms) moments can be determined from the data of Fig. 5.5(b) using the rela-tions

∆L3 + ∆L2 = − C

−2µBml , (5.14)

and

∆L3 − 2∆L2 = − C

−3µB(ms − 7mT ) = − C

−3µB(meff

s ) , (5.15)

where ∆L3 and ∆L2 are the areas of theL3 andL2 asymmetries of Fig. 5.5(b),respectively. The scaling constant C is govern by the half sum of the minority-and majority spectra, the number of empty d-states (nd), and the degree of

36

the circular polarization of the x-rays. The number of empty d-states are mostoften obtained from theory, and the degree of circular polarization is a beam-line specific quantity. The term mT = 〈T 〉µB/� is the component of the delectron expectation value of the intra-atomic magnetic dipole operator [15,16].

5.3.2 The Bruno approachThe anisotropy of the orbital moment is closely related to the magneto crys-talline anisotropy when the magnetization direction is changed from the easyto the hard axis. For a uni-axial anisotropy with the exchange splitting largerthan the band width, this relation is according to Bruno [17] expressed as

∆Eso = E⊥so − E‖

so = − ξ

4µB(m⊥

l −m‖l ) , (5.16)

where the spin-orbit constant, ξ, is of the order ∼ 0.05 eV.

5.3.3 Depth sensitivity in the XMCDIn the XMCD method the average orbital (ml) and spin moments (ms) aredetermined directly in µB per atom. Due to the finite electron escape depth themeasured moments Have a large contribution from the surface region. Thiseffect can be modeled by constructing a layer weighted sum. For example, forthe orbital moment (ml) we obtain

ml =

∑Ni=0ml,i exp

(−di

λ

)∑N

i=0 exp(−di

λ

) , (5.17)

where ml and ml,i represent the average and the orbital moment for layer i,respectively. In this expression we assume that we know how to decompose afilm into slices so that a unique ml,i can be identified with slice i. The electronescape depth (λ) has to be determined experimentally and is found to be ∼ 17Afor the 3d transition metals [11]. That is, although the photons penetrate sev-eral hundreds Angstrom into the sample, the layer dependent contribution tothe electron yield signal decreases rapidly with increasing depth. Already ata depth of di = λ the excited electrons that reach the detector are only of theamount e−1 � 0.37. Assuming bulk properties concerning the magnetic mo-ments for the deeper buried layers, the magnitude of the uppermost layers canthen be estimated from Eq. 5.17. For 3d transition metals the mT contributionis only a few percent of the total magnetic moment and is often neglected inthe analysis process.

37

5.4 Soft x-ray resonant reflectivityWhen an electromagnetic field interacts with matter, electrons within the atomsand molecules are excited to a higher energetic state. The following de-excitationprocess will either involve emission of photons or electrons. In XA spec-troscopy the latter case is studied (see Section 5.1), but additional informationcan be obtained by also studying the scattered photons. The basic principlebehind soft x-ray resonant reflectivity (SXRR)1 reflectivity is to let x-rays im-pinge on the sample at an angle θ relative to the sample surface and detect thereflected x-ray intensity at the specular angle 2θ with, e.g., a photo diode.

M

k

Diode

Figure 5.6:The basic principle of the surface x-ray resonant reflectivity mea-suring setup. The incident x-rays (k) are reflected from the sampleand detected at a specular geometry. Seen in the figure are also thecoils for magnetization.

In Fig. 5.7, XMCD (a) and SXRR (b) spectra are shown for a Co/Fe bi-layerfilm on Ag(100). As in the case of the XMCD measurements, the SXRR spec-tra are dominated by sharp features coinciding in energy with the 2p3/2,1/2 →3d transitions. Using x-rays with controlable polarization state one can mon-itor how the scattered intensity depends on the coupling between the samplemagnetization and the polarization vector of the x-rays. The magnetic con-trast in the reflectivity channel in SXRR often exceeds in magnitude of whatis seen for XMCD, and thus appears as an excellent complementary tool formagnetic investigations. Especially for thicker samples, where XMCD spec-troscopy is hampered by its inherent surface sensitivity due to the electronescape depth (λe), the probing depth for the x-rays in SXRR enables magneticinformation several hundred Angstrom beneath the surface region. However,no straightforward sum rules for SXRR data have been used in the literaturefor determination of, e.g., magnetic moments.

1For hard x-rays often denoted as x-ray resonant magnetic scattering (XRMS)

38

6

5

4

3

2

1

Relativeintensity(arb.units)

820800780760740720700680Photon energy (eV)

3ML Co / 10ML Fe on Ag(100)

majorityminority

10

8

6

4

2

Relativeintensity(arb.units)

820800780760740720700680Photon energy (eV)

majorityminority

3ML Co / 10ML Fe on Ag(100)

Figure 5.7: (a) XMCD spectra for a Fe/Co bilayer film on Ag(100). The mag-netic properties can be studied for Fe and Co independently. (b)The magnetic contrast in SXRR measurement is stronger and giveselemental specific magnetic information as XMCD.

In Fig. 5.7, the difference in surface sensitivity is obvious when comparingthe Co-Fe peak ratio in the XMCD and the SXRR channels. In (a), the 3ML Co L3 peak is almost as strong as the L3 peak from the buried 10 MLFe layers, whereas in (b) the average L3 peak intensity half sum of majorityand minority peaks for Co scales ∼ 1 : 3 to the average Fe L3 peak. Thisindeed indicates that the buried layers contribute less to the overall electronyield signal, whereas the 1 : 3 SXRR peak ratio also shows that atoms fromthe buried layers contribute to the SXRR signal.

In Fig. 5.8, SXRR based hysteresis curves are shown. Here the photon en-ergy was fixed to the Co L3 peak maximum of the SXRR spectra of Fig. 5.7(b).It is evident that the SXRR hysteresis technique is an element specific probe,meaning that for a bilayer (or even an alloy) the excitation can be tuned toprobe the magnetic hysteresis for the chosen element. By slowly varying theapplied magnetic field, the reflected photon intensity is measured as a func-tion of the applied field. This method enables hysteresis measurements underthe identical experimental conditions as are used for the moment determina-tion (XMCD) and the local structure measurements (EXAFS). However, due tovery small reflection coefficients at large angles, only measurements at grazingincidence are possible. This means that only in-plane magnetization hysteresisloops can be recorded. A SXRR based hysteresis measurement typically takesfive minutes.

39

1.0

0.5

0

-0.5

-1.0

Relativeintensity(arb.units)

-80 -60 -40 -20 0 20 40 60 80Applied field (Gauss)

hn=778 eV

Figure 5.8:SXRR based hysteresis measurements. The photon energy wasfixed to the Co intensity maxima from the SXRR data in Fig. 5.7,and the applied magnetic field was varied.

5.5 Photoelectron spectroscopyPhoto electron spectroscopy (PES) has not been extensively used in the presentwork, therefore a deeper discussion of the details in PES won’t be presentedhere. For further reading I refer to the textbook of Hufner [18] and referencestherein.

In PES a photon with energy hν is absorbed by the system that emits a coreelectron as described in the photoelectric effect

Ek = hν − Eb + Φ , (5.18)

where the Eb and Ek reflects the binding energy and the kinetic energy of theemitted electron, respectively. The Φ represents the work function and can formetallic system be calibrated to the Fermi level. However, as the techniquealso can be applied for magnetic investigations the special features of mag-netic linear dichroism [19] and magnetic circular dichroism will be shortlypresented.

5.5.1 Magnetic information from PESIn magnetic linear dichroism (MLD) and magnetic circular dichroism (MCD)the angular distribution of the photoelectrons are studied for magnetic pur-poses. In Fig. 5.9, the experimental geometries for MLD and MCD are sketched.If spin-orbit interactions are present, the photo-excitation in the MLD geome-try as shown in Fig. 5.9a, leads to spin polarized photoelectrons with the quan-tization axis parallel to E×k. This geometry is chosen in such way that E×kis parallel or anti-parallel to M . The interplay between the spin-orbit interac-tion and the magnetic interactions causes a dependence of the spectra on the

40

x

yz

x

yz

MM

E hn hns+ s-

e- e-

(a) (b)

Figure 5.9:The experimental geometry for (a) MLD and (b) MCD in photo-electron spectroscopy. The photoelectrons are spin polarized de-pendent on the polarization state of the incident x-rays.

direction of sample magnetization. The lines with spin polarization originatingfrom exchange are either enhanced or suppressed, depending on whether ex-change and spin-orbit induced spin polarization’s are parallel or anti-parallel.In MLD the maximal dichroic contrast is obtained when M⊥E and M⊥k,where M , E, and k are the sample magnetization, the electric field vector,and the direction of the photoelectron wave to the detector, respectively. InFig. 5.9b, the experimental setup for MCD using circularly polarized x-raysis shown. Here the escaping photoelectrons are spin-polarized in the horizon-tal plane, which means that the sample has to be magnetized in the horizontalplane in order to achieve maximum magnetic contrast.

41

Experimental results

Here follows a condensate of the results throughout the publications in thesecond part of this thesis.

6.1 Characterization workThe x-ray produced and used at the various synchrotron facilities are not al-ways that well defined. Especially the polarization state of the x-rays, and thedegree of spatial coherence are two parameters that often are taken for grantedto have certain characteristics or being totally neglected in the experimentalwork. Here I will show examples on the importance of those parameters andhow they can be determined (see Paper I, III, and XI). Part of the work inthis thesis has been devoted to the characterization of the degree of the circularpolarization of the x-rays at the beamline D1011 at MAX-lab. Also attemptsto determine the visible effect in XA spectra related to the degree of spatialcoherence is discussed.

6.1.1 The degree of circular polarization (Pc) at beamline D1011Maxlab has introduced a local perturbation to the electron orbit in one of thedipole magnets of MAX II, providing the user at the SX700 based dipole mag-net beamline D1011 with elliptically polarized x-rays. To confirm the potentialof this approach, we have calculated and measured the degree of circular po-larization, Pc.

Radiation from a dipole magnet in a synchrotron ring is rather well un-derstood [5, 6]. In the plane of the storage ring the radiation is horizontallypolarized. With the relative phase of the vertical and horizontal componentspreserved, the resulting polarization state becomes increasingly circular thefurther out of the storage ring plane one observes the radiation. Due to therelativistic nature of the orbiting electrons the emitted radiation is contained ina narrow cone (see Sec. 4.1). Higher degrees of circular polarization thereforecome at the expense of the photon flux.

From calculations, the intensity of the vertical, I⊥, and the horizontal, I‖,polarization components are determined as a function of Θ and photon en-ergy [20]. Θ is defined as the of-plane angle relative to the electron storage

42

ring. Using the Stokes formalism for quasi-monochromatic light, the circularpolarization component Pc may be written,

Pc =S3

S0=

2E⊥E‖ sin2 (∆φ)E2

⊥ + E2‖

, (6.1)

where ∆φ denotes the phase shift between the vertical (E⊥) and the horizontal(E‖) E-field. In the calculations we have used the relations: I⊥ = E2

⊥ andI‖ = E2

‖ , and assumed that ∆φ = π/2. Figure 6.1 shows the calculated Pc

based on Equation 6.1 for a photon energy of 715 eV. It is clear that for Θ = 0,we only have a horizontal polarization component, i.e, Pc=0. The degree ofcircularly polarized light increases as Θ is increased above or below the orbitplane.

-1 -0.5 0 0.5 10

0.2

0.4

0.6

0.8

1.0

Degreeofcircularpolarisation

Degree of circularpolarisation

Vertical observation angle, Q (mrad)

Figure 6.1:The calculated degree of circular polarization at 715 eV as a func-tion of the out-of-plane angle, Θ, for the photon energy 715 eV.This curve is the result of using I⊥ and I‖ obtained from calcula-tions combined with Equation 6.1.

To experimentally verify the predictions presented in Fig. 6.1, we have usedthe XMCD technique to investigate a previously characterized 25 ML bccFe on Cu(100). By comparing the XMCD results obtained at this beamlinesource, with earlier results obtained with x-rays of a well known polarizationstate [21], Pc can be determined for various Θ. Once ms,Θ is calculated, Pc

can be determined from the relation

Pc =ms,Θ

ms,ref, (6.2)

where ms,ref (see, e.g., Sec. 5.3.1) is reported in the literature to ms = 2.25µB

43

[21]. In Table 6.1 the experimental and the calculated Pc is presented forvarious values of Θ.

Table 6.1:Measured and calculated values of Pc at ∼ 715 eV at beamlineD1011 at MAX-lab.

Θ (mrad) Pc (measured) Pc (calculated)

+0.50 +0.85 +0.95

+0.25 +0.63 +0.75

±0.00 ±0.0 ±0.00

−0.25 −0.63 −0.75

−0.50 −0.85 −0.95

We observe a deviation of ∼15 % between the measured and calculated val-ues of Pc at 715 eV. The larger calculated Pc can be attributed to assumptionsmade in our application of the Stokes formalism. Specifically, our applica-tion of the Stokes formalism is identical to an assumption of fully coherentmonochromatic radiation, which is certainly not the case for bending magnetradiation [22]. The assumption ∆φ = π/2 is not necessarily valid for thedipole source and thus only yields the upper limit of S3. In addition, the cal-culation also assumes 100% polarized light which is not strictly true at thesample position due to the optical components of the beamline. The degreeof polarization varies little, of order 0.5%, over the energy intervals of interestwhen investigating the L3,2 edges of the late transition metals.

In Fig. 6.2 Co 3p PES spectra at photon energy hν=160 eV from a 25 MLCo film on Cu(100) recorded at various value of Θ are shown. The experimen-tal geometry was described in Section 5.5.1 with the sample surface positionedat an angle of 45◦ versus the incident x-rays, and the PES detector positionednormal to the sample surface. The magnetic field pulses were here applied inthe vertical direction to fulfill the requirements of the MLD experimental ge-ometry. In (a) (Θ = 0.50 mrad) the dichroic contrast is small indicating thatthe degree of linear light in the plane of the electron beam is low. This is whatto be expected if the x-rays either have a high degree of linear polarization inthe vertical direction, or alternatively no defined polarization at all. However,more probable is a higher degree of circular polarization, as is predicted fromcalculations [20]. At Θ = 0.25 mrad (b) the MLD dichroic contrast is higher,meaning that the degree of linear polarization in the horizontal plane has in-creased. Finally at Θ = 0.00 mrad (c) MLD the dichroic contrast has reached

44

6

4

2

0

-2

Relativeintensity(arb.units)

70 60 50

(+) - (-)

(+)(-)

Q=0.5 mrad

70 60 50Binding energy (eV)

Q=0.25 mrad

70 60 50

Q=0.0 mrad

(+) - (-)

(+)(-)

(+) - (-)

(+)(-)

(a) (c)(b)

Figure 6.2:Co 3p PES spectra at photon energy hν=160 eV with the PES de-tector positioned normal to the sample surface. The dotted and thesolid lines representing data taken for reversed remanent magneti-zation in the vertical plane. The dashed line represent the dichroicresponse after subtraction of the dashed from the solid spectra.

its maximum value, which is expected from the discussion in Section 5.5.1.This serves as an independent investigation to verify that the degree of polar-ization vary with Θ also at lower energies (in this case hν = 160 eV).

6.1.2 The degree of spatial coherence and its effect in XA spec-troscopy

Most theoretical models describing the scattering processes make the assump-tions that the spatial and temporal coherence lengths are infinite. For syn-chrotron radiation and other “real” light sources this is not the case. The ques-tion is to what extent this assumption is valid when it comes to the point of dataevaluation. The spatial coherence has already been shown to have an influencein imaging [23], structural [24], and dynamic studies [25]. In these studies theeffect is addressed to interference effects. Hunter Dunn et al. [26] reported anincrease of the XA signal linked to the degree of the spatial coherence of thex-rays. Here I present findings from experiments showing how the influence

45

of spatial coherence manifests itself as an important parameter when analyzingdata from XA measurements. These investigations are found in Paper I and III.

1000

800

600

400

200

0

Norm

alized

inte

nsity

(arb.u

nits)

3020100-10E-E(L3) (eV)

fct Ni/Cu(100)

fct Co/Cu(100)

bcc Fe/Cu(100)

(a)

(c)

(b)

1.2

1.0

0.8

0.6

0.4

0.2

Intensity(arb.units)

-0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1Vertical distance (mm)

SSRLMAX-Lab

Figure 6.3:To the left L3,2 edge XA absorption spectra for 20 ML Fe, Co, andNi on Cu(100) recorded at beamline 5.2 at the SSRL (solid line)and at a SX700 beamline at BESSY-I (dashed line). To the rightFresnel diffraction from the wires of a Au mesh recorded with 600eV photon energy at the SSRL (solid line) and MAX-lab (dashedline).

In Fig. 6.3(a), L3,2 XA spectra for 20 ML Fe, Co, and Ni on Cu(100)recorded at beamline 5.2 at the SSRL (solid line) and at a SX700 beamlineat BESSY-I (dashed line) are shown. The XA intensity were plotted versusE−E(L3), where E(L3) is the threshold energy of the 2p3,2 → 3d transition.The spectra were subtracted with a 2 : 1 continuum step function in order iso-late mostly the 3d final states (as described in Section 5.3.1). We observe howthe L3,2 peak intensities obtained at the SSRL consistently are enhanced with∼ 20% compared to what is found for the BESSY-I spectra. We contribute thisenhancement to the difference in the degree of spatial coherence of the x-raysproduced at the two synchrotron facilities.

Section 3.2 describes how the coherence length is defined. For the x-rays thetemporal coherence is determined by the wavelength and the bandwidth, i.e.,it is determined by the resolution. From Eq. 3.7 we have ltemp = λ2/2∆λ.

46

However, the spatial coherence length is more complicated to determine ex-perimentally as we need to know the characteristics of the source and how thesource is imaged at the sample position by the beamline. Due to the character-istics of the sources used in today’s synchrotron raidation facilities, any degreeof spatial coherence at the sample is predominantly due to the imaging proper-ties of the beamline, i.e, coherence is obtained through propagation. We havechosen to directly measure the manifestation of the degree of coherence byrecording the diffraction pattern from an Au mesh. Most modeling tools usedin beamline design are inadequate for analysis of such parameters for variousreasons.

In Fig. 6.3(b), Fresnel diffraction from the wires of a Au mesh recorded at600 eV photon energy at beamline 5.2 at SSRL (solid line) and at beamline 22at MAX-lab (dashed line) are shown. The x-ray energy resolution was 0.9 eVand 1.0 eV at SSRL and MAX-lab, respectively. The data were obtained byusing a photo diode positioned behind a 10 µm pinhole. The pinhole and thephoto diode were scanned in the vertical direction, mapping the diffraction pat-tern from the Au wire. From the diffraction pattern recorded at MAX-lab only

l Au wirespin hole

photo diode

Figure 6.4:The schematically setup for measuring the diffraction from an Aumesh by using a photo diode behind a pinhole.

weak oscillations are visible. However, the diffraction pattern obtained fromthe SSRL x-ray source shows strong oscillations indicating that the degree ofcoherence in this case is stronger. The temporal coherence length is similarfor the two cases, as ltemp is determined by λ and ∆λ. Therefore we concludethat the stronger fringes observed in the diffraction measurement made at theSSRL are the result of a larger spatial coherence length for the x-rays producedat beamline 5.2 at SSRL compared with the x-rays produced at the beamline22 at MAX-lab.

The spatial coherence is determined (see Section 3.2 and the discussion inthe previous paragraph) from the ratio of the distance from the x-ray sourceand the source diameter. As the SX700 beamlines at BESSY-I and beamline22 at MAX-lab have the identical optical setup and the almost identical sourcedistance, the spatial coherence between the two should be very similar. In

47

Paper I a comparison of Fe XA data recorded at beamline 22 at MAX-lab anda SX700 beamline at BESSY-I show almost the identical shape. We thereforeconclude that a comparison between XAS data from BESSY-I and SSRL basedon our coherence findings from MAX-lab and SSRL is justified.

What is then the microscopic origin of the observed spatial coherence de-pendence in the XA absorption spectra? This effect has not yet been exten-sively explored, neither in XA reported measurements nor in theoretical calcu-lations. However, the starting point in the discussion could be to incorporatethe whole scattering process in the analysis. The real and imaginary part of thetotal scattering factor are complementary components of the same phenomena.Therefore, if effects from the degree of spatial coherence have been observedin, e.g., scattering experiments involving reflective x-rays, they should also inprinciple be present in XA measurements.

The core levels studied in the XA and SXRR measurements are generallyassumed to predominantly give local atomic electronic structure information.For coherent illumination one approach could perhaps be to consider the totalelectric field Etot at the site of the scattering process, as being the sum of theincident field Ei and the dielectric field Ed response from within the spatialcoherence length. In this picture one would expect an enhancement of the ob-served absorption coefficient, µ, in the vicinity of the resonant excitation. It istherefore clear that this phenomenon requires further efforts both of theoreticaland experimental nature.

6.2 Magnetization reversal in thin filmsThe easy axis for the magnetization direction in thin films is govern by inwhich direction the anisotropy energy has its lowest value. Here I will showexamples where the direction of the easy magnetization can be manipulatedby varying the temperature, the film thickness, and the cap thickness (see Pa-per IV, V, VII, IX and X).

6.2.1 Thickness and structural dependenceWe have made in-situ investigations of ultrathin Fe grown on Ag(100). Thissystem is known to exhibit a reorientation of the magnetization, dependent onFe thickness and temperature [27, 28]. The x-ray absorption fine structure hasbeen recorded in-situ both in the near edge as well as in the extended x-rayabsorption fine structure (EXAFS) range. Using XMCD we find that, below300 K, films between 2− 5 ML show an out-of-plane remanent magnetizationwhereas for thicker films the magnetization lies in-plane. By applying themagneto optic sum rules we determine the orbital (ml) and spin (ml) moments.These are presented in Table 6.2 for 3, 6, 8 and 25 ML Fe on Ag(100).

48

Table 6.2:Orbital (ml) and spin (ms) magnetic moments for 3, 6, 8, and 25ML Fe on Ag(100). The 3 ML Fe film show out-of-plane mag-netization, whereas the thicker films (8 and 25 ML Fe) show in-plane magnetization. The 6 ML Fe film show only a minor in-planemagnetization. Relative errors of 10% and absolute errors of 25 %should be for the data.

Fe/Ag(100) ml (µB) ms (µB) ml/ms easy dir.

3 ML 0.45 2.35 0.19 ⊥6 ML 0.04 0.37 0.10 ‖?8 ML 0.23 2.28 0.10 ‖25 ML 0.20 2.25 0.09 ‖

The orbital moment ml is increased by 125% when the Fe film thicknessis decreased from 25 ML to 3 ML. However, only a small increase (of ∼ 5%)in the spin moment ms is found. At 6 ML the remanent magnetization is veryweak as we are in the vicinity of the transition region from out-of-plane to in-plane magnetization [28], but by adding two additional layers (now 8 ML) theFe film becomes strongly ferromagnetic again.

In addition to the moment determination, we performed L-edge EXAFSmeasurements on the Fe films in Table 6.2, to probe the local crystallographicstructure of the Fe atoms. As the lattice mismatch between the Ag(100) surfaceand the Fe(100) film rotated 45◦ is only 0.8% (starting from the bulk values ofthe lattice constants for both Ag and Fe), Fe is initially expected to adopt theAg(100) surface structure. This would most likely result in the bulk like bccFe growth phase [29, 30, 31]. However, our EXAFS measurements show thatthis is not necessarily the case. In Fig. 6.5(a), the k-weighted modulus of theFourier transformed kχ(k) is shown in real space for the 3 ML (dotted line)and the 25 ML (solid line) Fe film. The original kχ(k) has been presentedearlier [33]. The data were recorded at 120 K with the polarization vector ofthe x-rays in the horizontal plane at two incidence angles: 30◦ and 90◦. InFig. 6.5(a), only the data recorded at 90◦ x-ray incidence angle are shown. At90◦, we mainly probe the local structure within the plane of the sample surface,whereas at 30◦ we mainly probe the structure perpendicular the sample surface.The 25 ML film has its main peak at 2.30 A and shows the characteristic doublepeak structure with sharp features at 3.76 A and 4.56 A, which can be takenas a fingerprint for bulk Fe bcc structure [32]. However, for the 3 ML Fe filmthe interpretation of the EXAFS result is not that straightforward. The mainpeak maximum is here shifted to 2.15 A, with the double peak features found

49

0.4

0.3

0.2

0.1ModulusFT

(k·c(k))

76543210R (Å)

3 ML25 ML

Fe onAg(100)Normalincidence

(a)a

b

gd

0.3

0.2

0.1

76543210R (Å)

8 ML6 ML

Fe onAg(100)Normalincidence

a

b d

Figure 6.5:The k-weighted modulus of the Fourier transform χ(k) of the Feon Ag(100) films from Tabel 6.2. (a) The 25 ML film show themain feature at 2.30 A and the characteristic double peak structureat 3.76 A and 4.56 A, a fingerprint for bcc Fe [32]. For the 3 MLFe film the double peak features are now shifted to 3.63 A and 4.64A, with an additional feature appearing at 4.17 A. (b) The 6 and8 ML Fe films both show the double peak structure characteristicfor a bcc structure.

at 3.63 A and 4.64 A. Additional to these features an extra peak appears at4.17 A that should not be present in case of a pure bcc phase. The maxima ofthe peak positions are presented in Table 6.3. However, these peak positionscannot directly be viewed as the interatomic distances.

In Fig. 6.6, EXAFS simulations using the FEFF 8.10 [13] code are shown.The inset (to the left) shows the lattice structure of the bcc cell with sides(a, a, a), which can also be viewed as a fct structure (to the right) with thesides (

√2a,

√2a, a). In the simulation, the Fe cell has been expanded from the

pure bcc phase, to the fcc phase in three steps. The expansion was done in sucha way that the nearest neighbor distance was kept constant. The final structurewas that of an fcc unit cell with a side of a = 3.52 A. The temperature was inthe simulations set to 120 K (as in the experiment) with the Debye temperatureat 477 K, as for bulk Fe. The simulation for pure bcc agrees well to what wasfound for the 25 ML Fe film in Fig. 6.5, and what was already reported forbcc Fe L-edge EXAFS by Lemke et al. [32]. The simulated peaks, for the bccstructure in Fig. 6.6, were found at 2.27 A , 3.74 A , and 4.56 A. For the 3

50

0.0

ModulusFT

(k·c(k))

1.4

1.2

1.0

0.8

0.6

0.4

0.2

76543210R (Å)

bcc (fct c/a=1.41)fct c/a=1.21fct c/a=1.1fcc (bct c/a=1.41)

bcc fct

a÷2•a

aa

a ÷2•a

Figure 6.6:EXAFS simulations using the FEFF 8.10 [13] code show the k-weighted modulus of the Fourier transform for a bulk bcc phaseand various degrees of an extended bct (or fct) phase. The simula-tions were done for Fe clusters with radius of 10 A.

ML Fe film, the intepretation of the EXAFS results is more complicated. Theexperimental EXAFS of the 3 ML Fe film does not match the simulations forthe bcc → fcc transition. However, the feature at 4.18 A from Fig. 6.5 appearsin the fcc simulation (here at ∼ 4.02 A) which could lead us to the idea of amixed phase for the 3 ML Fe case, as discussed by Biedermann et al. [34, 35]for the Fe/Cu(100) system. Furthermore, the fcc simulation shows the mainpeak at 2.21 A compared with the experimental peak at 2.15 A, and a featureat 4.61 A that is experimentally found at 4.64 A. However, the experimentalpeak at 3.62 A does not agree that well with the simulated one at 3.37 A. Thepeak maxima positions for the simulations described above are presented inTable 6.3.

In Fig. 6.7, site resolved EXAFS simulations for 3 ML Fe on Ag(100) usingthe FEFF 8.10 code are presented. The different sites A, B, and C, defined inthe inset in Fig. 6.7 represents the Fe/Ag interface, the second Fe layer, andthe Fe/vacuum interface, respectively. Here we have assumed a pure bcc Feinitially adopting the fourfold hollow sites of the Ag, as described by Canepaet al. [30]. The intra-atomic spacing between the Fe layers and the Fe/Aginterface was set to 2.87 A (the bcc bulk value for Fe) in the vertical direction.For the site A, representing the Fe/Ag interface, the main peak is now foundat 2.15 A, and we also find peaks at 3.74 A, 4.11 A, and 4.54 A. At site B,representing the middle layer the main peak is found at 2.24 A and is stronger

51

Table 6.3:Peak positions for the most pronounced features obtained from EX-AFS measurements of the 3, 6, 8, and 25 ML Fe films on Ag(100)for the 30◦ and 90◦ x-ray incidence angles. The peak positions:α, β, γ, δ, are defined in Fig. 6.5. In addition, the results fromsimulations using the FEFF 8.10 code are given. Relative errors of0.02 A and absolute errors of 0.04 A are realistic here for distancedetermination.

Fe on Ag(100) Peak positions (A)

t Angle α β γ δ

30◦ 2.15 3.66 4.18 4.643 ML

90◦ 2.15 3.63 4.17 4.64

30◦ 2.21 3.68 −− 4.676 ML

90◦ 2.23 3.69 −− 4.66

30◦ 2.21 3.69 −− 4.708 ML

90◦ 2.25 3.68 −− 4.66

30◦ 2.30 3.76 −− 4.5625 ML

90◦ 2.30 3.76 −− 4.56

bulk bcc1 2.27 3.74 −− 4.56

bulk fcc2 2.21 3.37 4.02 4.61

bulk fcc3 2.69 3.89 4.76 5.68

because of the higher coordination number. Additional peaks are found at 3.43A, which we attribute to the nearest Ag neighbors, and at 4.42 A. The third andtop-most site C, representing the Fe/vacuum interface, has a suppressed mainpeak due to the low coordination number. The main peak is here found at 2.36A, which is 0.21 A and 0.12 A shifted to the larger distance compared to whatwas found for the interface and the middle layer, respectively. Moreover, thedouble peaks are here found at 3.71 A and 4.63 A. The solid line represent aweighted sum of the three individual layers taking into account the electronescape depth. Here the three main features are found at 2.21 A, 3.68 A, and4.50 A.

Canepa et al. [30] reported that island formation starts already within thesecond layer for Fe on Ag(100), with a typical island size ∼ 15 − 20 A, and

52

1.0

0.8

0.6

0.4

0.2

0.076543210

R(Å)

A, Fe-Ag interfaceB, Fe middle layerC, Fe-vacuum interfaceA+B+C

Ag

FeModulusFT

(k·c(k))

AB

C

Figure 6.7:Site resolved EXAFS simulations for site A, B, and C for a 3 MLFe/Ag(100). The solid line represent the weighted sum of the threesites.

thus cannot be simulated as layers. Furthermore, the above mentioned authorssuggest that although precautions are taken during the film deposition, Fe andAg atoms exchange positions during deposition leading to combinations ofFe/Ag, Fe/Fe, and Ag/Fe structures in the film. Considering the small hori-zontal lattice mismatch, the lattice spacing should then only be affected in thevertical direction. The limited success to reproduce the experimental EXAFSfor the 3 ML Fe film strengthen this suggestion, and show that the proposedmodel such as the one found in the inset of Fig. 6.7 is maybe to naive. Insteadmodels taking into account various degrees of intermixing and correspondinglattice spacing should in that case also be examined.

6.2.2 Temperature dependenceThe Au/Co/Au tri-layer system is known to exhibit a magnetization reversalfrom in-plane to out-of-plane magnetization (or vice versa) depending on theCo thickness [36, 37, 38, 39], the temperature [40, 41, 42], and the Au capthickness [43]. For thin films, the magnetization reversal is usually a conse-quence of the competing magneto-crystalline anisotropy favoring out-of-planemagnetization, and the shape anisotropy that favors an in-plane magnetization.

We performed a series of angular dependent XMCD measurements at dif-ferent temperatures (see Paper IX) on the Au/Co/Au trilayer system. In addi-tion to the XMCD data, we also recorded SXRR based hysteresis loops (see

53

1.5

1.0

0.5

0.0

Magneticmoment(mB/atom)

300280260240220200180Temperature (Kelvin)

In-plane msIn-plane meffOut-of-plane msOut-of-plane meff

Co L3,2 edge XMCD onAu/Co/Au/W(110)

s

s

Figure 6.8:Co L3,2 XMCD results on Au/Co/Au/W(110). In- and out-of-plane spin moment (ms) versus measuring temperature. The dia-monds and the triangles represent the meff

s for in-plane and out-of-plane magnetic moment, respectively. The squares and the circlesrepresent the ms for in-plane and out-of-plane magnetic moment.

Section 5.4). In Fig. 6.8 the Co ms for the in-plane and out-of-plane compo-nents are shown as a function of temperature. At 300 K, the Co film has itseasy direction entirely in-plane. When lowering the temperature the in-planevalue of the ms decreases simultaneously as the out-of plane ms appears. At200 K the in-plane ms is zero and instead the out-of-plane ms has reachedits maximum value. The reorientation process takes place in the temperaturerange 200 − 300 K. In this temperature interval the magnetization could bestabilized both in-plane and out-of-plane, but not at the same time. That is,no remanent magnetization was detected perpendicular to the direction of themagnetic field pulse. This excludes the possibility of a canted magnetizationas was reported by other investigators [44] (see Paper IX). The smooth mag-netization reversal found in Fig. 6.8 has been explained theoretically withinthe mean-field approach by Jensen et al. [45]. The main assumption in theirapproach is to distinguish between the anisotropy in the second order expan-sion term of the anisotropy energy K2: (i) the interfaces (K2,s) and (ii) theinterior of the film (K2,v). The stronger decrease of the surface magnetization,

54

as compared with the interior of the film, causes a larger decrease of the effec-tive surface anisotropy as compared with the effective dipole coupling throughK2(T ) = K2(m(T )) [45]. That is, the interfaces serves as the driving force in

1.0

0.8

0.6

0.4

0.2

0.0

Relativemagnetization(arb.units)

300280260240220200Temperature (Kelvin)

ms from XMCDArea hysteresis curvesRemanence at H=0 fromthe hysteresis curves

Au

Co

Au

e-e-

hnin

hnouthnout

Figure 6.9:Comparison between the relative in-plane magnetization versustemperature measured by means of XMCD (diamonds) and SXRR(squares and circles).

the temperature dependent magnetization reversal.In addition to the XMCD experiments, we also performed SXRR based hys-

teresis measurements as described in Section 5.4. As SXRR probes deeper intothe sample compared to XMCD, we made the attempt to investigate the rela-tive surface-bulk effect in the temperature dependent decrease of the in-planemagnetization. In Fig. 6.9 the relative in-plane magnetization for the surface(circles) and the interior (diamonds) of the film is shown versus temperature.It is evident that the surface contribution decrease faster when lowering thetemperature which is in accordance to the findings by Ref. [45]. We addressthe observed reorientation of the easy axis from in-plane to out-of-plane, whenlowering the temperature, to the fast decrease of the surface magnetization.

55

6.2.3 The influence of the cap thicknessIn Section 6.2.2, the temperature dependent magnetization reversal from in-plane to out-of-plane magnetization was presented. Here I will show that alsothe cap layer thickness influences the magnetic anisotropy in such way thatthe Co easy direction changes from in-plane to out-of-plane as the Au capthickness is lowered. This effect is presented in Paper V. In Fig. 6.10, a

19 Å Co

50 Å Au(111)

10 Å 13 Å20 Å17 Å

Au

Figure 6.10:A schematic sketch of the Au/Co/Au tri-layer sample. A 19 A Cofilm is sandwiched in-between 50 A Au below and a staircase of10 A, 13 A, 17 A, and 20 A Au on top.

schematic sketch of the trilayer system is shown. A 19 A Co film is sandwichedin-between 50 A Au below and a staircase of 10 A, 13 A, 17 A, and 20 A Auon-top. The films were deposited by means of electron beam evaporation asdescribed in Section 4.2.

The XMCD measurements performed at 300 K show a full in-plane mag-netization for the region with the 20 A Au cap, whereas the Co region with the10 A Au cap both exhibit an in-plane as an out-of-plane magnetization. TheCo regions with the 13 A and 17 A Au caps falls in-between the above results.When cooling the sample down to 90◦ K all four regions of the sample showonly out-of-plane magnetization. By applying the magneto optic sum rules, theorbital (ml) and spin (mc) moments were obtained, as presented in Table 6.4.We link the increase of ml to the spin reorientation as the Au cap thickness

Table 6.4:Orbital (ml) and spin (ms) Co magnetic moments for 17 A Cocapped with different thickness of Au.

Au cap (A) ml (µB) ms (µB)

10 0.18 1.7

13 0.15 1.7

17 0.13 1.7

20 0.13 1.7

56

is decreased. By applying the Bruno approach Eq. 5.16 [17], the increase ofml of 0.05 µB yield a spin-orbit magnetic anisotropy energy of 1.25·10−4 eVper Co atom, which is larger than the spin-spin dipole interaction of 9·10−5

eV per Co atom. Within this simple qualitative model, the enhancement ofml for thinner Au caps would explain the reason for the cap thickness inducedmagnetization reversal in the Au/Co/Au system.

6.3 Enhancement of magnetization when lowering thesymmetry

In previous sections we have seen how the reduction of the film thickness canmake the magnetic properties change, such as reversing the easy axis fromin-plane to out-of-plane magnetization (Section 6.2.1). Recently, the trend hasbeen to further decrease the dimensionality aiming at magnetic nano structures,such as small magnetic particles and magnetic wires. Here I will show howwe by making use of a vicinal (high index) surface, could force the film topreferentially grow along the surface terraces, and how the magnetic propertiesof the sample is affected by doing so. These findings are presented in Paper VIand VIII.

The sample chosen for this study was Co on flat and vicinal Cu(111). Thevicinal surface had a miscut of 1.25◦, which results in mean terrace width of110 A along the [110] direction. The lattice mismatch between Co and theCu(111) surface is ∼ 2%, judging from the bulk lattice constants: 2.51 A forhcp Co and 3.61 A for fcc Cu. The initial growth of Co on Cu(111) starts atthe atomic steps and the Co will eventually coalesce into islands preferentiallyalong the step edges. This holds for both vicinal and “flat” surfaces as thelatter ones cannot strictly be considered flat as they also exhibit atomic steps.The difference between the two surfaces is rather that the vicinal surface hasa miscut resulting in a higher density of oriented atomic steps, whereas in thecase of the flat surface the atomic steps are distributed randomly in all direc-tions. In Fig. 6.11 scanning tunneling microscopy (STM) pictures are shownfor 10 ML of Co deposited on: (a) a flat Cu(111); and (b) a vicinal Cu(111). Inboth Fig. 6.11(a) and (b) the Co films have a rough surface structure consist-ing of Co islands. However, it should be noted that the islands on the vicinalsurface are smaller and elongated in the direction of the step edges, which is tobe expected because of the limitation induced by the terraces in one direction.Thus, the initial growth of Co on Cu(111) influences the Co growth even atthicknesses up to 10 ML.

In Fig. 6.12, the in-plane Co orbital moment ml obtained from XMCDis shown versus Co coverage for both the flat (circles) and vicinal (squares)Cu(111) substrates. At this temperature (300 K) and these thicknesses only anin-plane magnetization component was evident. The inset shows SXRR hys-

57

b

40nm

a

20nm

Figure 6.11:Topographic image of 10 ML Co on flat (a) and vicinal (b)Cu(111). The size of the image is 1200×1200 A and 2000×2000A for (a) and (b) , respectively.

teresis measurements where the 25 ML Co film on flat and vicinal Cu(111)are represented by the solid and dashed line, respectively. We observe an in-crease of the orbital moment ml for both the flat and vicinal surface as theCo thickness is lowered. This effect has already been reported by Tischer etal. [46], for Co on the flat Cu(100) surface, and is attributed to the loweringof the symmetry at the surface. What is more striking for the present data isthe overall enhancement of ml when comparing Co deposited on the vicinalsurface to the flat Cu(111). The ml for the vicinal surface is enhanced with30% for all thicknesses. A possible explanation for the higher ml present onthe vicinal surface could be the introduction of bi-axial strain related to the“uni-axial” island formation. However, a magneto optic based study on a sim-ilar system, Co on Cu(100) Ref. [47], shows that the step induced anisotropydepends linearly on the step density, and do not originate from the volume-type bi-axial strain. It is therefore also unlikely to be the explanation for a stepinduced increased orbital moment for the present system. Another explanationof the big enhancement of ml on the vicinal surface could be that we observe acanted magnetization, meaning that the measured moment is just a cosα pro-jection of the real ml. However, no XMCD was detected in the out-of-planedirection, and the hysteresis loops in the inset of Fig. 6.12 indicate saturationmagnetization at zero applied field for both the flat and the vicinal surface.

As previously stated, Co on the vicinal Cu(111) surface exhibits island for-mation along the step edges. The lattice mismatch of about 2% [48], has beenfound to result in changes in the magnetic anisotropy. The structural modifi-cations due to the presence of step edges can be assumed to lead to tetragonaldistortions along the edges of the terraces but also perpendicular to the sur-

58

-1.0

-0.5

0

0.5

1.0

Diodecurrent(arb.units)

500-50Magnetic field (Gauss)

100-100

-100 -60

0

1.0

-1.0

vicinalflat

Co on Cu(111)

0.22

0.20

0.18

0.16

0.14

0.12

ml(mB/atom)

252015105Co coverage (ML)

0

0.24

Figure 6.12:Orbital moment versus Co coverage. The squares and the cir-cles represent the Co coverage dependent orbital moments for Coon vicinal and flat Cu(111) respectively. SXRR based hysteresisloops indicate full saturation magnetization for both the flat (solidline) and the vicinal film (dashed line). We also observe a highercoercive field in the case of the vicinal film.

face in the vicinity of the steps. Due to both reduced symmetry and magneto-elastic coupling this will indeed influence the orbital moments. The correlatedenhancement observed for the spin moment would, in this simplistic picture,be a consequence of a strong spin-orbit coupling. High moments for cobalthave been reported earlier. Bucher et al. [49] reported an internal magneticmomentof 2.08µB per atom for cobalt clusters containing 20 − 200 atoms.This enhancement of the magnetic moment was later confirmed by other in-vestigators [50, 51, 52]. Our present results allow us to correlate also the pref-erential growth directionwe observe here for the vicinal surface per sewithmodifications in the magnetic anisotropy observed in such surfaces. We fi-nally note, that the orbital and spin moment enhancement is observed over thewhole thickness range, much as the step induced anisotropy on vicinal surfaces[47], indicating a correlation with the island formation along the step edges weobserve here.

59

Acknowledgements

Thanks for all support Dimitri. Your door has always been open when I neededyour input, whether it concerned questions about physics or just friendly advicein general. Especially what I know about physics and coffee I have learnt fromyou. And to you Charlie, besides that you have tortured me with your badsense of humor for five years, I really appreciate your friendship and support.Our nights in California, what would we have done without carrots, computers,and Callas..... Jonathan, I have benefit a lot from your experimental skills, andthat I will not forget.

I am also grateful to all present and former colleagues at the department forcreating a friendly atmosphere, which makes the daily work more joyful. Thestaff at MAX-lab should also be acknowledged.

Uppsala, 11 April, 2003

Anders Hahlin

60

References

[1] S. Chikazumi, Physics of magnetism, reprint ed. (John Wiley & Sons, Inc.,Malabar, 1964).

[2] C. Kittel, Introduction to solid state physics, 6th ed. (John Wiley & Sons,Inc., Chichester, 1986).

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