Interaction Mechanisms and Magnetization

Dynamics in Ultrathin Antiferromagnetic Films

and their Correlation with Structure and
Morphology
DISSERTATION

to obtain the academic degree

Doctor rerum naturalium (Dr. rer. nat.)

Im Fachbereich Physik

der Freien Universität Berlin

von

Yasser Shokr

from Cairo, Egypt

2016
1st Reviewer: Prof. Dr. Wolfgang Kuch

2nd Reviewer: Prof. Dr. Holger Dau

Date of defense: 19.10.2016

For my father spirit...................
Abdelmageed Shokr
Cairo, (1953 / 2015)
 Abstract

In this thesis, by the means of Auger electron spectroscopy (AES), low energy electron diffraction (LEED),
medium energy electron diffraction (MEED), X-ray absorption spectroscopy (XAS), magneto-optical Kerr
effect (MOKE), and photoemission electron microscopy (PEEM) the structure and the magnetic properties
of antiferromagnet (AFM) and ferrimagnetic material (FIM) films were investigated. All of the AFM material
was grown and studied in ultra high vacuum (UHV) chambers with base pressure of 2×10−10 mbar. The AFM
material was chosen to be Nix Mn(100−x) ultrathin films and it was studied in contact with two ferromagnetic
(FM) Ni film(s) in exchange-biased bilayers and trilayers on Cu3 Au(001). The Ni films were grown in a
layer-by-layer fashion with a p(1×1) crystal structure on the Cu3 Au(001) substrate. The structure and the
magnetic properties of the Ni films were investigated in relation to the thickness in monolayers (ML), to find
a spin reorientation transition (SRT) from in-plane (IP) to out-of-plane (O O P) which takes place in between 7
ML and 8 ML. At 7 ML up to 15 ML, longitudinal and polar magnetization loops were observed with almost
identical shape and only twice the coercivity. Then an angle-dependent MOKE experiment was designed
and used to investigate the magnetic anisotropy of the Ni film. With the help of the Stoner-Wohlfarth model
(SW), a simulation of the angle-dependent MOKE data was done, to estimate the anisotropy constants, K1 and
K2 . The origin for the continuous transition from IP to O O P-magnetization of the 12 ML Ni/Cu3 Au(001) is
tentatively ascribed to the fourth-order anisotropy, K2 . Later, the Nix Mn(100−x) ultrathin films were grown on
Ni/Cu3 Au(001). A change in the Curie temperature (Tc ) of the Ni layers under the Nix Mn100−x over-layer was
observed. These changes are probably a consequence of a spin frustration at the interface which determines
the overall magnetic properties of FM/AFM systems. This frustration was studied as a function of the
Nix Mn100−x alloy composition, which was divided into Mn-rich, and Ni-rich overlayers. Furthermore, the
magnetic interlayer coupling across the Nix Mn100−x as an AFM spacer layer is investigated using MOKE. First,
the effect of O O P-magnetized top Ni layers on an O O P-magnetized bottom Ni layer through the Nix Mn100−x
was studied by changing the top layer thickness (τ) for different Nix Mn100−x thicknesses with x ≈ 25%. Then
the magnetic interlayer coupling was investigated by measuring minor loops using MOKE for 14 ML Ni/45 ML
Ni25 Mn75 /16 ML Ni. The coupling strength (J) was then calculated from the minor loop measurements and a
positive value was assigned to parallel coupling and a negative value was assigned to antiparallel coupling.
For this sample an important observation is that the interlayer coupling changes from ferromagnetic to
antiferromagnetic when the temperature is increased above 300 K. This sign change is interpreted as the result
of the competition between an antiparallel Ruderman-Kittel-Kasuya-Yosida (RKKY)-type interlayer coupling,
which dominates at high temperature, and a stronger direct exchange coupling across the AFM layer, which is
present only below the Néel temperature of the AFM layer.
The FIM material samples were fabricated in a cluster system consisting of a magnetron sputter deposition
and a surface analysis chamber with base pressure of 1×10−8 mbar, at Gebze Institute, Istanbul, Turkey. Then
the samples were capped with 8 Å Pt layer and transferred to Germany. The FIM material was chosen to be
Fe(100−x) Gd(x) . Two series of Fe(100−x) Gd(x) films were grown, one with 10 Å Co on top and the other without
Co. The magnetic properties of the Fe(100−x) Gd(x) and Co/Fe(100−x) Gd(x) samples were investigated in relation
to the Fe/Gd ratio x. x was chosen to be 15, 25, and 30, since FeGd films with a Gd concentration of around
20% show perpendicular uniaxial magnetic anisotropy and at this range they are FIM with a relatively high
magnetic compensation temperature. The Fe(100−x) Gd(x) were found to be O O P-magnetized samples, while a
SRT in Co/Fe75 Gd25 was found after annealing the samples at 400 K for 30 minutes. This SRT is a temperature
dependent transition with the sample behaving as an O O P-magnetized sample at 50 K and an IP-magnetized
one at room temperature (RT). The SRT starts to occur at around the compensation temperature (Tcom ). This
transition can be due to a diffused interface at the FeGd surface. It was also found that the Tcom for Co/FeGd
sample is reduced compared to the corresponding ones from the FeGd films. This results from the increase of
the total magnetic moment of the 3d elements after evaporating Co on top of FeGd. Furthermore, one example
of laser-induced domain wall (DW) motion is presented in a Co/Fe75 Gd25 system. The single laser pulses were
moving the DWs in the Co/Fe75 Gd25 at a distance of around 4 µm away from the center of the laser pulse
towards the colder region of the sample. The underlying mechanisms of this DW motion were discussed in
terms of a spin Seebeck effect. This was done by estimating the temperature gradient within the spatial profile
of the laser pulse and checking if this temperature gradient is sufficient to generate a spin transfer torque (STT)
to move this DW or not.
 Deutsche Kurzfassung

In dieser Arbeit wird mit Hilfe von Augerelektronenspektroskopie (AES), Beugung niederenergetischer
Elektronen (LEED), Beugung mittelenergetischer Elektronen (MEED), Röntgenabsorptionsspektroskopie
(XAS), Magnetooptischem Kerr-Effekt (MOKE) und Photoemissionselektronenmikroskopie (PEEM) die
Struktur sowie die magnetischen Eigenschaften von antiferromagnetischen (AFM) und ferrimagnetischen
(FIM) Filmen untersucht. Die AFM-Proben wurden in einer Ultrahochvakuum-Kammer (UHV) mit einem
Basisdruck von 2×10−10 mbar hergestellt. Als AFM-Probe wurde Nix Mn(100−x) gewählt, welche in Kontakt mit
zwei ferromagnetischen (FM) Ni-Filmen in „exchange-biased“ Zweifach- und Dreifachlagen auf Cu3 Au(001)
sind. Die Ni-Filme wurden in Dicken zwischen 7 und 15 Monolagen (ML) mit einer p(1 × 1) Kristallstruktur
auf den Cu3 Au(001) Kristall aufgedampft. Es wurden longitudinale- und polare Magnetisierungskurven
mit nahezu identischer Form und doppelter Koerzitivfeldstärke gemessen und dabei in diesem System ein
Spin-Reorientierungsübergang (SRT) von „in-der-Ebene“ (IP) zu „aus-der-Ebene“ (OoP) bei Schichtdicken
zwischen 7 ML und 8 ML gefunden.
Des Weiteren wurde ein Winkelaufgelöstes MOKE-Experiment entwickelt, mit dem die magnetische
Anisotropie (K1 und K2 ) der Ni-Filme bestimmt wurde. Dazu wurden die experimentellen Daten mit einer
Simulation auf der Grundlage des Stoner-Wolfarth-Modells verglichen. Den beobachteten kontinuierlichen
Übergang von IP- zu OoP-Magnetisierung von 12 ML Ni/Cu3 Au(001) kann durch eine magnetische Anisotropie
vierter Ordnung (K2 ) beschrieben werden. Weitere Nix Mn(100−x) -Proben wurden auf Ni/Cu3 Au(001)
aufgedampft.
Bei diesen System wurde eine Veränderung der Curie-Temperatur des Ni-Films beobachtet, welche
wahrscheinlich eine Konsequenz von „Spin-Frustration“ an der Grenzschicht ist. Diese Frustration wurde
in Abhängigkeit der Nix Mn(100−x) -Komposition untersucht und beschreibt die gesamten magnetischet
Eigenschaften des FM/AFM-Systems. Die Proben wurden hierfür nach hohen Ni- und hohen Mn-Anteil
unterteilt. Mittels MOKE wurde die magnetische Zwischenlagen-Kopplung in Abhängigkeit der AFM-Schicht
untersucht. Als erstes wurde festgestellt, welchen Einfluss ein OoP-magnetisierter Ni-Film auf einen ebenfalls
OoP-magnetisierten Ni-Film hat, wenn sich dazwischen ein Nix Mn(100−x) Film mit einer Ni-Konzentration
von x = 25 % befindet. Der Effekt wurde für verschiedene Schichtdicken des oberen Ni-Films sowie für
unterschiedliche Schichtdicken von Nix Mn(100−x) untersucht. Im Anschluss daran, wurde die magnetische
Zwischenlagenkopplung eines 14 ML Ni/45 ML Ni25 Mn75 /16 ML Ni Systems mittels „minor loop“-Messungen
mit MOKE untersucht und daraus die Kopplungsstärke J berechnet. Insbesondere konnte für dieses System
gezeigt werden, dass die Zwischenlagenkopplung oberhalb von T = 300 K von einer FM (J>0)-zu einer AFM
(J<0) Kopplung wechselt. Die Ursache für diesen Vorzeichenwechsel liegt in dem Wechselspiel zwischen einer
antiparallelen- und parallelen Kopplung, der Ruderman-Kittel-Kasuya-Yosida-Wechselwirkung (antiparallel),
welche bei hohen Temperaturen dominiert, und einer starken direkten Austauschwechselwirkung (parallel)
durch die AFM-Schicht hinweg, die jedoch nur unterhalb der Néel-Temperatur des AFM existiert.
Neben diesen Systemen wurden zusätzlich noch FIM-Systeme, Fe(100−x) Gd(x) , näher betrachtet. Diese
wurden im Gebze Institute in Istanbul (Türkei) durch Magnetronzerstäubung hergestellt. Um die
Proben vor Verschmutzung zu schützen, wurden sie mit einer 8 Å dicken Pt-Schicht bedeckt und nach
Deutschland transportiert. Es wurden zwei unterschiedliche Fe(100−x) Gd(x) Systeme, eines mit 10 Å Co
als oberste Schicht und das andere ohne, untersucht. Zuerst wurden die magnetischen Eigenschaften
beider Systeme für unterschiedliche Konzentrationen (x = 15, 25 und 30) an Gd und Eisen mittels
MOKE untersucht. FeGd-Filme besitzen eine senkrechte uniaxiale magnetische Anisotropie mit einer
relativ hohen magnetischen Kompensierungstemperatur (Tcomp ). Während die Fe(100−x) Gd(x) Systeme eine
OoP-Magnetisierung aufweisen, zeigen die Co/Fe75 Gd25 Systeme nach Erwärmung für 30 Minuten auf 400 K,
eine temperaturabhängige SRT. Diese tauchte während nochmaliger Messung bei 50 K bis Raumtemperatur
auf und wurde als SRT von IP- zu OoP-Magnetisierung bei Tcomp definiert. Diese Reorientierung findet bei der
Kompensierungstemperatur statt, welche durch eine diffuse FeGd-Grenzschicht verursacht sein könnte. Auch
konnte gezeigt werden, dass eine Erhöhung des magnetischen Moments der 3d-Elemente durch aufdampfen
auf FeGd, zu einer Reduzierung der Tcomp im Vergleich zu den reinen FeGd-Systemen führt. Als letztes
Ergebnis wird in dieser Arbeit ein Beispiel für Laser-induzierte Domänenwand (DW)-Bewegung in einem
Co/Fe75 Gd25 System gezeigt. Einzelne Laserpulse konnten dabei Domänenwände um 4 µm vom Zentrum des
Laserspots in Richtung der kälteren Regionen verschieben. Als mögliche Ursache wird dazu der spinabhängige
Seebeck-Effekt diskutiert. Dazu wurde der Temperaturgradient innerhalb des Laserprofils simuliert und
abgeschätzt, ob der dadurch entstehende Spinstrom stark genug sein kann, um die DW entsprechend zu
verschieben.
 Contents

List of Figures vii

List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix

List of Tables xi
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi

Glossary xiv

1 Introduction 1
1.1 Data storage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Outline of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2 Experimental techniques 5
2.1 Ultra high vacuum chambers used . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.1 MOKE chambers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.2 Synchrotron radiation facility and X-PEEM chamber . . . . . . . . . . . . 8
2.2 Structure and stoichiometry characterization techniques . . . . . . . . . . . . . 10
2.2.1 Electron spectroscopies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2.2 Electron diffraction techniques . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2.3 Magneto-optic techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3 Theoretical background 27
3.1 Magnetic anisotropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.1.1 Magnetocrystalline anisotropy energy (EC ani ) . . . . . . . . . . . . . . . . 27
3.1.2 Shape anisotropy energy (E Shani ) . . . . . . . . . . . . . . . . . . . . . . . 28
3.1.3 Exchange anisotropy (E E xani ) . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.2 Stoner-Wohlfarth (SW) model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.3 Magnetic interlayer coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.3.1 Rudermann–Kittel–Kasuya–Yosida (RKKY) . . . . . . . . . . . . . . . . . . 31

iii
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3.3.2 Coupling across antiferromagnetic layers . . . . . . . . . . . . . . . . . . . 32

3.3.3 Magnetostatic coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.4 Interaction of laser pulses with thin film . . . . . . . . . . . . . . . . . . . . . . . 33
3.4.1 Two-temperature model (TTM) . . . . . . . . . . . . . . . . . . . . . . . . 35
3.5 Spin Seebeck effect (SSE) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.5.1 Seebeck effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.5.2 Spin Seebeck effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

I Antiferromagnetic samples 41

4 Ultrathin films Ni/Cu3 Au(001) and NiMn/Ni/Cu3 Au(001) 43

4.1 Ni/Cu3 Au(001) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.1.1 Growth and structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.1.2 Magnetic characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.1.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.2 NiMn/Ni/Cu3 Au(001) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.2.1 Growth and structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.2.2 Magnetic characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.2.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

5 Coupling between ultrathin films through an antiferromagnetic layer 63

5.1 Growth and structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.2 Effect of Ni top layer on the coupling across NiMn . . . . . . . . . . . . . . . . . 65
5.2.1 ∼25 ML Ni24 Mn76 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
5.2.2 ∼30 ML Ni22 Mn78 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.3 Interlayer coupling across ∼45 ML Ni25 Mn75 . . . . . . . . . . . . . . . . . . . . . 73
5.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

II Ferrimagnetic samples 79

6 Polycrystalline Fe100−x Gdx samples 83

6.1 Sample fabrication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
6.2 Magnetic characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
6.2.1 MOKE measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
6.2.2 Magnetization investigation by XMCD . . . . . . . . . . . . . . . . . . . . 87
6.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

7 Femtosecond-laser-pulse induced domain wall motion in Co/FeGd 93

7.1 Domain wall motion in Co/FeGd . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
7.2 Two temperature model for multilayer (TTM) . . . . . . . . . . . . . . . . . . . . 100

iv
 v

7.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

8 Summary and conclusion 105

List of publications 111

Appendix 115

Bibliography 135

Acknowledgement 155

v
List of Figures

2.1 Top view MOKE chamber. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.2 Side view for MOKE chamber. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.3 Laser optical path in the MOKE chamber. . . . . . . . . . . . . . . . . . . . . . . . 7
2.4 Synchrotron radiation from a bending magnet and a wiggler or undulator. . . . 8
2.5 PEEM UHV chamber at BESSY II, and the magnetic sample holder. . . . . . . . 9
2.6 Schematic diagram of the Auger electron spectroscopy system. . . . . . . . . . . 11
2.7 Schematic diagram of the process of Auger emission. . . . . . . . . . . . . . . . . 12
2.8 Schematic of XAS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.9 Universal curve. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.10 Schematic digram of LEED system. . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.11 Wood’s notation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.12 MEED set-up. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.13 MEED example. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.14 Decomposition of light polarization. . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.15 A schematic representation of MOKE geometries. . . . . . . . . . . . . . . . . . . 21
2.16 Example of in-plane and out-of-plane MOKE of 8 ML Co/Cu3 Au(001). . . . . . . 22
2.17 Laser optical path in the angle-dependent MOKE. . . . . . . . . . . . . . . . . . . 23
2.18 Example of XAS at PEEM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.19 Electron trajectories in PEEM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.1 Example of exchange biased hysteresis loop. . . . . . . . . . . . . . . . . . . . . . 28

3.2 Angle definition for SW model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.3 Origin of the RKKY interaction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.4 Spin frustration at an FM/AFM interface. . . . . . . . . . . . . . . . . . . . . . . . 32
3.5 Example for magnetostatic coupling . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.6 Light path in multilayer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.7 Laser spot profile. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

vii
viii List of Figures

3.8 Schematic diagram for the spin dependent Seebeck effect (SDSE). . . . . . . . . 39

4.1 Expected LEED pattern for Cu3 Au(001). . . . . . . . . . . . . . . . . . . . . . . . . 45

4.2 LEED, LEED-IV, and MEED for Ni on Cu3 Au(001). . . . . . . . . . . . . . . . . . . 46
4.3 Determination of interlayer spacings by LEED-IV. . . . . . . . . . . . . . . . . . . 47
4.4 IP and OoP MOKE magnetization curve for 9.6 ML Ni/Cu3 Au(001). . . . . . . . 48
4.5 Hc as function of temperature for both configurations for 9.6 ML Ni/Cu3 Au(001). 49
4.6 Curie temperature of Ni/Cu3 Au(001) as a function of Ni thickness. . . . . . . . . 50
4.7 Angle-dependent MOKE for 12 ML Ni/Cu3 Au(001). . . . . . . . . . . . . . . . . . 51
4.8 Angle-dependence of Hc for 12 ML Ni/Cu3 Au(001). . . . . . . . . . . . . . . . . . 52
4.9 Root mean square deviationas as function of K 1 /M s and K 2 /M s . . . . . . . . . . 53
4.10 Total energy surface from the calculated model at φ = 0 and H = 0 mT. . . . . .
◦
54
4.11 MEED for NiMn on 12 ML Ni/Cu3 Au. . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.12 Auger electron intensities for NiMn on Ni/Cu3 Au. . . . . . . . . . . . . . . . . . . 56
4.13 LEED-IV intensities for diffrent NiMn thicknesses on Ni/Cu3 Au(001). . . . . . . 58
4.14 MOKE for 3.4 ML Ni45 Mn55 /7.9 ML Ni/Cu3 Au(001). . . . . . . . . . . . . . . . . . 59
4.15 Ni Tc as a function of the NiMn thickness in Ni-rich regime. . . . . . . . . . . . . 60
4.16 Schematic model for the Ni Tc changes at the NiMn with Ni-rich regime. . . . . 60
4.17 Ni Tc as a function of the NiMn thickness in Mn-rich regime. . . . . . . . . . . . 61
4.18 Schematic model for the Ni Tc changes at the NiMn with Mn-rich regime. . . . 61

5.1 MEED for 12 ML Ni /40 ML Ni25 Mn75 /12 ML Ni. . . . . . . . . . . . . . . . . . . 64

5.2 MOKE for τ ML Ni/25 ML Ni24 Mn76 /12 ML Ni (τ= 0 and 17). . . . . . . . . . . . 67
5.3 HC and Heb for τ ML Ni/25 ML Ni24 Mn76 /12 ML Ni (τ= 0, 12, 17, and 22). . . . . 68
5.4 Change of coercivity HC for τ ML Ni /25 ML Ni24 Mn76 /12 ML Ni. . . . . . . . . 69
5.5 MOKE for τ ML Ni/30 ML Ni22 Mn78 /12 ML Ni (τ= 0 and 12). . . . . . . . . . . . 70
5.6 HC and Heb for τ ML Ni/30 ML Ni22 Mn78 /12 ML Ni (τ= 0, 12, 17, and 22). . . . . 71
5.7 Change of coercivity HC for τ ML Ni /30 ML Ni22 Mn78 /12 ML Ni. . . . . . . . . 72
5.8 Minor loops of 14 ML Ni/45 ML Ni25 Mn75 /16 ML Ni at 240 K. . . . . . . . . . . . 74
5.9 Temperature-dependent minor-loops of 14 ML Ni/45 ML Ni25 Mn75 /16 ML Ni. . 75
5.10 Temperature vs. interlayer coupling in 14 ML Ni/45 ML Ni25 Mn75 /16 ML Ni. . . 76
5.11 HC and Heb for τ ML Ni/45 ML Ni25 Mn75 /16 ML Ni (τ=0 and 14). . . . . . . . . . 77

6.1 Temperature-dependent MOKE hysteresis loops of FeGd25. . . . . . . . . . . . . 85

6.2 Temperature-dependent MOKE hysteresis loops of Co/FeGd25. . . . . . . . . . 86
6.3 XAS spectra of Fe, and Co, and Gd in Co/FeGd25. . . . . . . . . . . . . . . . . . . 88
6.4 XMCD-PEEM images of DW in Fe, Co, and Gd in Co/FeGd25. . . . . . . . . . . . 89
6.5 Element selective hysteresis loops by PEEM. . . . . . . . . . . . . . . . . . . . . . 90
6.6 Temperature-dependent MOKE for Co /FeGd25 IP and OoP. . . . . . . . . . . . . 91

7.1 Fe and Gd hysteresis loops by PEEM at diffrent positions. . . . . . . . . . . . . . 94

viii
List of Figures ix

7.2 Comparing XAS for Co signal inside inside and outsied the laser pulse. . . . . . 95
7.3 Controling the domain wall motion by laser pulse. . . . . . . . . . . . . . . . . . 96
7.4 Domain wall displacement after laser pulse under zero magnetic field. . . . . . 97
7.5 Domain wall motion within the laser pulses under 4 mT. . . . . . . . . . . . . . . 98
7.6 Time history of lattice temperature profile for film depth. . . . . . . . . . . . . . 101
7.7 Lattice temperature profile at z direction at 0.9 ps, with fluence = 38.7 mJ/cm2 . 102
7.8 Lattice temperature profile in x-direction at 900 fs. . . . . . . . . . . . . . . . . . 103
7.9 Time history of the lattice temperature profile for the different interfaces. . . . 103

A.1 Mirror holders designed to perform Angle-dependent MOKE. . . . . . . . . . . . 115

A.2 Magnetic Core for MOKE-II chamber. . . . . . . . . . . . . . . . . . . . . . . . . . 116
A.3 Relay Circuit design for the magnet power supply. . . . . . . . . . . . . . . . . . . 117
A.4 The determination of T AF M and Tb . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
A.5 Magnetic flux simulation for the PEEM sample holder. . . . . . . . . . . . . . . . 121
A.6 XAS and XMCD for Fe, Co, Ni, and Gd pure metals. . . . . . . . . . . . . . . . . . 123
A.7 Comparison between XAS for Fe, Co, Ni (pure material) and there oxides. . . . . 123

ix
List of Tables

2.1 Auger electron spectroscopy parameters. . . . . . . . . . . . . . . . . . . . . . . . 13

4.1 Interlayer spacings calculated from Kinematic LEED-IV. . . . . . . . . . . . . . . 45

5.1 Ts as function of top Ni layer and NiMn layer thickness. . . . . . . . . . . . . . . 72

6.1 Compensation temperatures for the FeGd samples. . . . . . . . . . . . . . . . . . 87

7.1 The parameters used to solve the two-temperature model. . . . . . . . . . . . . 100

7.2 Calculated complex refractive index (n + i k). . . . . . . . . . . . . . . . . . . . . . 100

xi
 Glossary

ρ root mean square deviation. 50, 52

3PPE three photon photoemission. 37

AES Auger electron spectroscopy. i, 5, 10, 11, 13, 43, 54, 55

AFM antiferromagnet. i, 1, 2, 3, 31, 32, 43, 54, 65, 66, 71, 73, 74, 75, 78, 89, 105, 106

DW domain wall. i, 3, 32, 81, 89, 93, 94, 95, 96, 97, 98, 99, 101, 102, 104, 106, 107

EB exchange bias effect. 2, 28, 43, 65, 69, 73

EF Fermi energy. 31

FC field-cooling. 65, 66, 71, 73

FCC face-centered cubic. 44

FIM ferrimagnetic material. i, 3, 4, 83, 84, 105, 106

FM ferromagnetic. i, 1, 2, 3, 31, 32, 43, 54, 65, 69, 71, 72, 73, 74, 75, 78, 105

GMR giant magnetoresistance. 1

Hc coercivity. 30, 47, 65, 66, 69, 71, 72, 73, 76, 89, 90, 106

Heb exchange bias field. 65, 66, 69, 71, 76

IP in-plane. i, 5, 22, 28, 30, 45, 47, 48, 50, 53, 89, 90, 105, 106, 121

LCD left circularly polarized light. 19, 20

LEED low energy electron diffraction. i, 5, 10, 14, 15, 16, 17, 19, 43, 44, 45, 57

MEED medium energy electron diffraction. i, 5, 10, 13, 19, 43, 44, 54, 64, 75

xiii
xiv Glossary

MOKE magneto-optical Kerr effect. i, 5, 7, 10, 19, 20, 21, 22, 29, 43, 45, 47, 49, 53, 64, 65, 66,
71, 73, 83, 84, 89, 90, 105, 106, 115

MR magnetoresistance. 1, 2

O O P out-of-plane. i, 2, 5, 30, 47, 48, 50, 52, 53, 57, 65, 84, 87, 89, 90, 105, 106, 121

PEEM photoemission electron microscopy. i, 9, 10, 14, 23, 37, 83, 87, 89, 96, 121

PEM photoeleastic modulator. 7, 21

RCD right circularly polarized light. 19, 20

RKKY Ruderman-Kittel-Kasuya-Yosida. i, 30, 31, 65, 75, 78, 106

RT room temperature. i, 57, 66, 73

SDSE spin dependent Seebeck effect. 39, 99, 102, 104, 107

SMSE spin magnonic Seebeck effect. 39, 99, 102, 104, 107

SRT spin reorientation transition. i, 44, 45, 47, 48, 53, 105, 106

SSE spin-Seebeck effect. 39, 93, 99

STT spin transfer torque. i, 1, 93, 104

SW Stoner-Wohlfarth model. i, 29, 30, 49, 105

Tb blocking temperature. 66, 69, 71, 76

Tc Curie temperature. i, 45, 53, 54, 57, 58, 59, 60, 62, 105

Tcom compensation temperature. i, 3, 84, 87, 90, 106

TEY total electron yield. 14

TTM two temperature model. 35, 36, 99

UHV ultra high vacuum. i, 5, 7, 105, 115

XAS X-ray absorption spectroscopy. i, 10, 13, 14, 23, 87, 95

XMCD x-ray magnetic circular dichroism. 7, 19, 23, 87

XPS X-ray photoelectron spectroscopy. 10

xiv
 Introduction
1
1.1 Data storage

Data storage is a fundamental aspect of human civilization. The story of data storage
goes back as early as the stone ages when humans tried to record the daily activities
of hunter-gatherers. With the settlement of civilization, the crude cave paintings had
developed into sophisticated records of all aspects of human activity on different materials,
culminating in paper. The early technological turning point in data storage occurred in the
19t h and early 20t h century, when the computer was invented, even when it did not yet have
a role in data storage. It was used only as a machine which could help with small calculations.
it was very limited in the beginning, but this was just the start. For a short time, paper was
able to play an important role in the development of the computer when Charles Babbage in
1837 [1] developed the punched paper and used it to program a computer to make a small
calculation. At this point, papers ceased being involved in the development of computer
data storage; even if it still has an essential role until now regarding data storage in the form of
books. Humanity’s needs and fast life style pushed the scientific community to find another
solution for the development of new data storage devices. This led Reynold Johnson [2] to
the invention of the first magnetic hard disk in 1956. This was the start of a new generation of
data storing devices. IBM introduced this device in 1956 with the IBM 305 RAMAC computer
[3]. It helped in the expansion and the production of many technological applications.
Progress related to data storage devices impacts the development of a very wide range of
technology applications. New data storage devices are continuously required to be smaller,
more stable, and faster in order to fulfill our needs. The thin films technology was followed
by the discovery of the giant magnetoresistance (GMR) by Peter Grünberg [4] and Albert Fert
[5] in 1988. This started a new generation of devices which were stable but not fast enough.
Both inventors shared the Nobel Prize for this achievement in 2007. The magnetoresistance
(MR) means that there is a change of the electrical resistance with applied magnetic field.
The GMR is observed in ferromagnetic (FM) multilayer thin film systems when there are
significant changes in the overall resistance of the FM multilayer. The GMR is low for

1
2 1.1. Data storage

parallel alignment of the magnetic moments of the layers and higher in the antiparallel
case. The most used GMR device is the spin valve structure, which consists of a FM layer, a
conducting spacer layer, and another magnetic layer pinned by an antiferromagnet (AFM).
After the GMR was discovered, Slonczewski [6] discovered the spin transfer torque (STT).
This was the foundation of the spinelectronics which is named spintronics by Berger [7].
With this technology, he tried to exploit the quantum spin states of electrons as well as their
charge states. The primary requirement to make a spintronic device is to have a system
which generate a current of spin polarized electrons, and a system able to detect this spin
polarization. Spintronics is the new vision for the future to increase the data processing
speed which is based on spin manipulation by magnetic and/or electrical fields [8].

In the spin valve structure, which was discovered by Meiklejohn and Bean [9], the AFM is
key in the pinning of the soft FM layer by the exchange coupling between the FM and AFM.
Which gives the FM layer high anisotropy and stable order via the so-called exchange bias
effect (EB). In EB the hysteresis of the FM/AFM structure can be centered about a non-zero
magnetic field. This biasing (exchange bias) is used to pin the spins of one FM layer, while
the spin of the other FM layer is left free to be tuned by any external field. This leads to
a change of the MR of the spin-valve and make it sensitive to the spin state of the film.
Accordingly, the interface between the FM and the AFM layers attracted many researchers
to explore this phenomena [10–14]. So the AFM material can be used in applications, it
should have a reliable and stable pinning effect. This means its exchange field should not
be larger than 500 Oe, blocking temperature should be higher than 500 K, and the effect
should remain strong for more than 10 years [15]. This is why Mn-based alloys are good
candidates. All the Mn alloys are AFM, most of them have high blocking temperature, low
critical thickness and easily attainable Néel temperature. They can be classified into two
groups according to the crystalline structure. One of the groups has face center cubic (fcc)
crystalline structure and comprises FeMn, IrMn, RhMn and RuMn. Among them FeMn
is the most widely studied [16–20], since it has the highest exchange bias and it does not
require post annealing during evaporation. Nonetheless it is unsuitable for read sensor
applications due to its poor corrosion resistance. The other group of Mn alloys comprises
NiMn, PtMn, PdMn that have an f c t crystal structure, which offers the advantage of having
higher blocking temperature, though most of them need post annealing during or after
evaporation to become AFM. From this group, NiMn has some unique characteristics since
it has the highest order and highest blocking temperatures of bulk materials, 1070 K and 723
K, respectively [21, 22]. This makes it interesting for scientists to investigate and study the
magnetic properties of the NiMn alloy. NiMn has been deposited onto both Cu(001) and
Cu3 Au(001). On Cu(001) it shows a non-collinear spin-structure, which was attributed to
the broken symmetry at the surface [23]. The NiMn grows with the a-axis along the film
normal [23–25]. This non-collinear spin-structure could be due to the relatively big lattice
mismatch between NiMn and Cu(001). When NiMn is grown on Co/Cu(001), it starts to show

2
Chapter 1. Introduction 3

equiatomic antiferromagnetism, and an enhancement of the coercivity of the Co layer [25].

We showed at Hagelschuer et al. [26] that Ni0.4 Mn0.6 exhibits a transition in the spin structure
when it grows in between a sandwich of two Ni layers out-of-plane (O O P)-magnetized on
Cu(001). Exploiting this transition of the spin structure could be a way of controlling the
magnetic properties of a multilayered magnetic system by taking advantage of the sudden
onset of interlayer coupling, the corresponding jump in coercivity, or the change in the AFM
spin structure itself. On Cu3 Au(001), Nix Mn1−x shows a layer that grows up to x = 30% Ni
with its c-axis along the film normal, and shows a non-collinear spin structure with very
interesting pinning properties [27–29].
NiMn has fascinating magnetic properties (like high antiferromagnetic ordering
temperature T AF M , high blocking temperature Tb for exchange bias, and large exchange bias
field Heb ), but because it is AFM it is not directly possible to explore and understand the spin
structure. All AFM have a total net magnetic moment of zero which makes investigating
with magnetic measurement techniques difficult. In this thesis the effect of the AFM on
an adjacent FM layer was measured. This data could help in understanding the coupling
phenomena in the multilayer structure and it could also help in developing magnetic storage
devices able to resist self-demagnetization. Some of this data was published in [30] and [31].
The stability of a magnetic storage device is a problem, but how dense and how fast
the data can be accessed is an even more complicated problems. Since the maximum real
density is correlated to the size of the magnetic particles in the surface and with the size
of the reading/writing head, increasing the density could be done by developing both. The
newest technology to increase the density is racetrack memory which uses an array of small
nanoscopic wires arranged in 3D. Each wire holds numerous bits to improve the density and
try to control it with short pulses of spin-polarized current [32], and try to read the data with
two magnetic read/write heads. Although the exact numbers of how dense the final device
has not been revealed yet, IBM news articles talk of 100 fold increases. This solution by IBM
is not the final or the unique solution due to the fact that triggering the magnetization by
femtosecond laser pulses is much faster and could also be smaller in size [33, 34]. Therefore,
the other solution to increase the density of the storage device could be to use materials
which support magneto-optical data storage.
The medium which has the ability to change the polarization state of reflected or
transmitted light by changing its magnetization is defined as magneto-optical medium [35].
It provides the ability to store data magnetically and to read it out optically. Beaurepaire
et al. [36] demonstrated the ability to demagnetize Ni in sub-picoseconds by a 60 fs laser
pulse, for manipulating and controlling magnetization with ultrashort laser pulses. This time
scale is the time corresponding to the equilibrium exchange interaction (∼ 0.01 ps- 0.1 ps),
which is much faster than spin-orbit interaction (1–10 ps) or magnetic precession (100 – 1000
ps) time scales [34]. This finding by Beaurepaire et al. [36] opened a wide field of study in
the ultrafast laser manipulation of magnetic materials, like spin reorientation generated by

3
4 1.2. Outline of the thesis

laser pulses [37], demonstrating the possibility of generating coherent magnetic precession
by ultrafast optical excitation [38, 39], and switching magnetic domains with laser pulses
[40]. Nevertheless, the physics of ultrafast interactions with matter is still poorly understood;
the femtosecond laser pulse excites the material into a non-equilibrium state where all the
theoretical models fail to explain the magnetic phenomena. In this thesis, the moving of
the domain wall (DW) in Co/FeGd films by single laser pulses is discussed can contribute
to reveal some understanding. FeGd is known since the 60’s as a good magneto-optical
medium, which is also a good candidate for the ultrafast magnetic switching [40]. FeGd is
ferrimagnetic material (FIM) which has two ferromagnetic sublattices of different moments
coupled antiparallel with each other. This means that the net magnetization direction is
temperature dependent with a compensation temperature (Tcom ) at the temperature at
which the magnetizations of both sublattices are equal. So it is like an AFM material but
with a net magnetization, it can be coupled as FM and as AFM around Tcom .

1.2 Outline of the thesis

This thesis is composed of seven chapters. The next chapter (chapter two and three)
discusses the experimental techniques and the theories used in this work. This is then
followed by two parts. Chapters four and five make up part one of the thesis and it starts
by investigating the Ni growth on-top of Cu3 Au(001). Then try to estimate the anisotropy
constant of the Ni/Cu3 Au(001). Finally, the coupling across NiMn sandwiched between two
Ni layers is discussed in chapter five. Part two is made up of chapters six and seven. The
preparation and characterization of FeGd with chosen different concentrations as FIM is
presented in chapter six. The experimental results and estimation of the temperature profile
in a multilayer system induced by femtosecond laser pulse is presented in chapter seven,
and finally comes the summary.

4
 Experimental techniques
2
2.1 Ultra high vacuum chambers used

Since this work is about the interface properties for ultra-thin films, all the samples were
prepared and characterized in ultra high vacuum (UHV) chambers. Some of the samples
were protected with Pt as a capping layer, and transferred later to be measured at another
experiment. This part will be divided into four sections: First the used UHV chambers will
be described, then some details about synchrotron radiation and the importance of using
it, then the characterization (structure and stoichiometry) techniques used in these UHV
chambers will be discussed and at last the magnetic characterization techniques used in
this thesis.

2.1.1 MOKE chambers

This chamber is located at the institute of Experimental physics of Freie Universität of Berlin,
at Prof. Wolfgang Kuch’s labs. The chamber consists of three levels. In the evaporation
level we use e-beam evaporation, growth rate monitoring by medium energy electron
diffraction (MEED), sample characterization by low energy electron diffraction (LEED), and
stoichiometry and film purity was tested by Auger electron spectroscopy (AES). A sputtering
gun and (or) flashing stage were used to clean the substrate Fig. 2.1. The second part is for
sample transfer and load lock. The third level is a glass finger settled in between magnetic
poles, a magneto-optical Kerr effect (MOKE) set up Fig. 2.2 is installed at the front of the
magnet for the magnetic measurements, which allows used to perform both longitudinal as
well as polar measurements.
By MOKE one can characterize materials by providing magnetic information in the form
of a hysteresis loop. It relates the magnetization (M) to the applied magnetic field (H). The
MOKE physical principle is the Kerr effect which will be discussed in detail in section 2.2.3,
The sample can be cooled with liquid nitrogen down to about 140 K, and heating of the
sample is accomplished with a tungsten wire up to about 1000 K. The temperature is

5
6 2.1. Ultra high vacuum chambers used

4
1. Turbo pump
2. Valve
3. Cold trap 6 5
4. Ion-getter pump
5. LEED 8 3 2
6. Quadrupole 7
7. Flashing stage
8. Wobble stick 1
9. Window 9
10. Load-lock
11. AES
14
12. Sputter gun
13. 3-cell evaporator 12 13
14. TSP
10 11

Figure 2.1: Experimental setup top view for the sample preparation and surface analysis.

12

1. Turbo pump
11
2. Valve 10
3. Cold trap
4 6
4. Ion-getter pump 2
5. LEED 3
6. Quadrupole
7. Flashing stage
7 9 8
1 5
8. Wobble stick
9. Window
10. x,y micrometer
11. z micrometer
12. Manipulator
13. glass finger
14. Electromagnet 13

14

Figure 2.2: Experimental setup side view for magnetic characterization.

6
Chapter 2. Experimental techniques 7

photodiode for glass finger

angle dependent
MOKE
mirror

mirrors path

sample
quarter-wave-plate

photoelastic
modulator multimeter
lock-in-amplifier
polarizer
laser Glan-Thompson
prism
optical bench photodiode

Figure 2.3: Laser optical path in the MOKE chamber.

measured using a K-type thermocouple attached to the sample holder. The experimental
setup involves laser light passing through a polarizing filter and then reflecting the light off
the sample. The glass-finger is set between the magnetic poles. This gives us the possibility
to do both in-plane (IP) as well as O O P measurements.

A diode laser emits monochromatic linearly polarized light of 1 mW power at a

wavelength of 670 nm, which passes through polarizer then through a photoeleastic
modulator (PEM) operated at 50 kHz at 45◦ , then it is directed onto the sample via mirrors,
can be adjusted by sliding it on the two sides of the magnetic poles, see Fig. 2.3. After the laser
is reflected from the sample, the elliptical polarization will be slightly rotated. A combination
of quarter-wave-plate and Glan-Thompson prism once again ensures the linear polarization
of the reflected elliptically polarized laser beam, which is finally collected by a photo-diode
that is installed with an amplifier. All these optics are fixed on an optical table mounted
into the magnet frame. Later the signal is locked with the PEM frequency to get the AC
component from the measured signal and normalize it later to the DC signal component
measured by multimeter. Slight changes in the plane of polarization cause variations in the
detected light intensity, which is proportional to the magnetization of the sample. By this
MOKE setup the hysteresis loops of thin magnetic films up to the laser penetration depth
within metals at about ∼20 nm could be measured, by studying the slight changes in the laser
light intensity at the photo-diode in terms of rotation or ellipticity (in our case rotation) as a
function of applied magnetic field which will be descused in more detailed in section 2.2.3.

7
8 2.1. Ultra high vacuum chambers used

e
be
m ndin
ag
ne g
ts
mc2/Ee

wig
gler
or
und
ulat
or

Figure 2.4: Synchrotron radiation from a bending magnet and a wiggler or undulator.

2.1.2 Synchrotron radiation facility and X-PEEM chamber

The x-ray magnetic circular dichroism (XMCD) technique requires tunable x rays [41]. The
synchrotron radiation facility we used at this thesis was provided by BESSY II, where part
of the data of this thesis were measured. To generate synchrotron radiation electrons are
primarily accelerated to relativistic energies E e before they are injected in to a UHV storage
ring by means of bending magnets. This acceleration process is carried out by a combination
of linear and synchrotron accelerators. In the BESSY II, the electrons are accelerated up to 1.7
GeV by the alternating field of a cavity resonator. To keep the electrons in a closed orbit inside
the storage ring, strong bending and focusing magnets are mounted in the path of the ring.
In general, all electrons start to radiate when they pass through these bending magnets. This
produces synchrotron radiation, which is directed tangentially outward from the electron
trajectory in a narrow radiation cone with an opening angle given by θ = mc 2 /E e . The
radiation spectrum for bending magnets is very broad, analogous to a white light bulb.
BESSY II is a third generation storage ring to generate more intense synchrotron
radiation, There are insertion devices (multipole wigglers and undulators), which consist
of a periodic array of magnets with alternating polarity. They are placed in magnet-free
sections of the orbit (Fig. 2.4). A wiggler is a designed array of strong magnets to periodically
laterally deflect the electron beam. So when the electron passes through the wiggler devices,
it changes its trajectory at every magnet, resulting in an oscillatory motion characterized
by small angular paths. In each of these oscillatory paths, the electron emits radiation
in each of these curved deflections, the emitted radiation later adds up along the wiggler
to produce a more intense synchrotron radiation. Both the wiggler and the undulator
have the same working principle, the main difference is the strength of the magnet. The
wiggler has a higher magnetic field to bind the electron through a large angle to get very

8
Chapter 2. Experimental techniques 9

Sample
Coil

Magnetic
sample holder PEEM
x-ray

Laser

Prep. chamber

Figure 2.5: PEEM UHV chamber at BESSY II, and the magnetic sample holder.

broad and less brilliant synchrotron radiation. With the relatively weaker bending magnets
in the undulator, the angle of the path is smaller and the resultant is radiation of high
brilliance which is quasi-monochromatic. The final obtained synchrotron radiation is
linearly polarized in the orbital plane of the storage ring. Obtaining elliptically or circularly
polarized radiation is done with special magnet undulator structures such as the APPLE II
type undulator in the UE49 beamline at BESSY II, which provides circular polarization with
different helicities and linear polarization at any angle.
To restore the energy lost by the electrons during emission of the synchrotron radiation,
accelerator radio frequency cavities (RF) are installed in the storage ring path. In the RF
cavity the electrons in phase with the cavity excitation are accelerated, while the ones out
of phase are lost. This causes the electrons to have a time structure that consists of buckets
(bunches) filled with electrons. As a consequence of the electron loss, the total number of
electrons are injected every few hours.
The X-PEEM chamber is located at the UE49 PGM beam line, (Fig. 2.5). It consists

9
10 2.2. Structure and stoichiometry characterization techniques

of two parts. The first part is the preparation chamber with 5 e-beam evaporators for
in-situ evaporation at a pressure of 1 × 10−10 mbar and a quartz balance for precise control
of thickness, sputtering with Ar + for cleaning the substrate and annealing to 1800 K.
Furthermore it contains storage for up to 6 samples. The second part is the SPEEM chamber.
It contains an ELMITEC photoemission electron microscopy (PEEM) Fig. 2.5 (the PEEM
image is from the ELMITEC web site). Such instruments are ideal for a synchrotron radiation
source. The chamber is combined with a Femtosource X L300 system. It is a compact system
producing 800 nm wavelength ultra-short laser pulses < 50 fs with high pulse energy up
to 300 nJ and a peak power larger than 6 MW. It is based on a Ti:Sapphire oscillator with
a repetition rate of 5 MHz. The synchronization of the laser pulses with the synchrotron
punches allows for time resolved studies.

2.2 Structure and stoichiometry characterization

techniques
Preparing ultra-thin films in an ultra high-vacuum chamber requires caring about a lot of
parameters. Starting from choosing a suitable substrate with low lattice mismatch to the
film, to the evaporation parameters and growth rate of this film. One of the important
parameters which one has to take in to account is how clean the substrate is. To clean single
crystals that were used two different methods depending on the substrate were used. In case
of Cu3 Au sputtering technique was used. Where the substrate was sputtered by Ar + ions
with energy of 1 − 2 keV, after this, the substrate was annealed at 800 K for 15 min. In case of
W(110), the surface was cleaned by flash heating under 6×10−10 mbar in oxygen atmosphere
to around 1600 K for 15 min, followed by 5−7 flashes to 2300 K for 10 sec each. To confirm the
substrate cleanness AES and LEED was performed. The sputtering and annealing sequence
was repeated until the sample is clean. The film thickness was monitored by MEED during
growing the film, later it was confirmed with AES. For the polycrystalline samples, X-ray
photoelectron spectroscopy (XPS) was performed to confirm there was no oxidation of the
film.
The stoichiometry characterization techniques used in this thesis are classified into
Electron spectroscopy technique (AES and XPS), and Electron diffraction techniques
(LEED and MEED. Which will be discussed in the next section.

2.2.1 Electron spectroscopies

Electron spectroscopy techniques are analytical techniques which study the electronic
structure and its dynamics [42]. Here two techniques was used : AES and XPS. Both
techniques require an environment at ultra high vacuum, an excitation source and an
electron detector. For AES the excitation source was electrons and it was done at

10
Chapter 2. Experimental techniques 11

MOKE chamber, while for X-ray absorption spectroscopy (XAS) the excitation source was
synchrotron radiation at X-PEEM chamber.

Auger electron spectroscopy

Sweep CMA Shield

supply
Auger
electron

Lock-in
Sample

-amplifier
Electron Gun

Electron
multiplyer

Figure 2.6: Schematic diagram of the Auger electron spectroscopy system.

AES is one of the most commonly used surface analytical techniques for checking the
surface layers and determining their composition. The Auger tube consists of an electron
gun with acceleration of around 3 KV to 5 KV (Fig. 2.6), to focus and accelerate electrons
to the sample, which is positioned at the focal point of the gun. The emitted electrons are
later deflected by a cylindrical mirror analyzer (CMA) which collects the desired energetic
electrons into the detection unit, which multiplies the signal and sends a voltage to the
lock-in-amplifier which is locked to the CMA sweep power supply reference frequency. The
sweep power supply used to tune the electric field on the CMA and collect Auger electrons
as a function of their electron energy. The intensity of collected Auger electrons is plotted as
a function of energy.
After bombarding the sample with accelerated electrons from the electron gun, this
will produce a hole in the core level, then the atoms relax by filling this vacancy by other
upper-level electrons, losing the energy difference, as in the example shown in Fig. 2.7, for
L1 . The excess kinetic energy is either emitted later as x-ray in the so-called x-ray fluorescence
or transferred to another secondary electron. The relaxation by AES is more favorable than
by fluorescence for atoms with atomic number less than 35 (Fig. 2.7 b) [42].
By identifying and measuring the kinetic energies of the emitted Auger electrons, one
can identify the emitting atoms since each element has its characteristic peaks at different
kinetic energies in the Auger spectrum. By analyzing the peaks we get information about the
elemental composition of the sample surface and, after some calibration, one can get the
film thickness.
The film thickness of an evaporated film on a substrate S can be calculated, since the
probability of Auger electron emission from the substrate after traveling the distance τ in the

11
12 2.2. Structure and stoichiometry characterization techniques

Or e-
φ VAC

hv
EF

either
M,etc
L2,3
L1
e-
k
(a) (b) (c)

(d )
A u g e r e le c tr o n e m is s io n
1 ,0
x - r a y flu o r a n c e e m is s io n

0 ,8
P r o b a b ility

0 ,6

0 ,4

0 ,2

0 ,0
5 1 0 1 5 2 0 2 5 3 0 3 5 4 0
A to m ic n u m b e r

Figure 2.7: Schematic diagram of the process of Auger emission, (a) initial state, (b) excitation and
emission state, (c) final state the example shown here is named KL1 L2,3 . (d) Probabilities of atomic
relaxation by AES or x-ray photon emission after creating a hole in the k shell.

film without experiencing any scattering is e −τ/λS , where λS is the effective inelastic mean
free path of the substrate Auger electron in the film, and the probability of emitting Auger
electron from the film to travel the same distance τ is 1 − e −τ/λτ , where λτ is the effective
inelastic mean free path of film Auger electrons in the film. This means that the intensity of
the Auger peaks from the film I τ and the substrate intensity I S are related as follows:

I τ = I 0 S τ (1 − e −τ/λτ ) (2.1)

I S = I 0 S S e −τ/λS (2.2)

where I 0 is the initial intensity of the gun and S τ and S S are the sensitivities of the film and
substrate respectively. This makes the ratio of the substrate and the film peak R τ as follows:

12
Chapter 2. Experimental techniques 13

IS S S e −τ/λS
Rτ = = (2.3)
I τ S τ (1 − e −τ/λτ )
By calibration with any other technique and AES, the values of S and λ for every material
can be obtained. In this thesis the AES was calibrated by using MEED experiments. Table 2.1
shows S and λ for the peaks used in this thesis.

Table 2.1: Auger electron spectroscopy parameters.

Element Energy ± 1 (eV) λ ± 0.15 (ML) S ± 0.01

Cu 920 4.8 0.97
Ni 716 4.2 0.31
Mn 545 4 0.8

X-ray absorption spectroscopy

I0 t

It
µ(E)

E
Figure 2.8: Schematic of incident and transmitted X-ray beam and the absorption coefficient µ(E)
versus photon energy E around an absorption edge.

In x-ray absorption spectroscopy (XAS) we measure the energy-dependence of the

X-ray absorption coefficient near the absorption edge of a particular element. It is a
well-established analytical technique used for elemental characterization. With an x-ray
incident on a sample (Fig. 2.8), the extent of absorption depends on the photon energy E
and sample thickness τ, and the transmitted intensity is given by:

I τ = I 0 e −µ(E )τ (2.4)

where I 0 is the initial intensity, µ(E ) the energy-dependent X-ray absorption coefficient and
τ the film thickness [43]. Over large energy regions, µ(E ) is a smooth function of the photon

13
14 2.2. Structure and stoichiometry characterization techniques

energy, varying approximately with Z and m (the atomic number and mass number of the
element) and the target density (d) as:

d · Z4
µ(E ) ∼ (2.5)
m ·E3

Thus, µ(E ) decreases with increasing photon energy. If the latter equals or exceeds the
binding energy of a core electron, however, a new absorption channel is available in
which the photon is annihilated thereby creating a core-hole. The created holes are then
filled by Auger decay. The intensity of the emitted primary Auger electrons is a direct
measure of the x-ray absorption process and is used in so called Auger electron yield (AEY)
measurements, which are highly surface sensitive [44]. This leads to a sharp increase in
absorption coefficient as shown schematically in Fig. 2.8. Above the absorption edge, the
difference between the photon energy minus the work function and the binding energy
is converted into kinetic energy of the photoelectron and µ(E ) continues to decrease with
increasing photon energy. After a short time of the order of < 10−15 s, the core-hole is filled
by an electron from a higher energy state. The corresponding energy difference is released
mainly via fluorescence X-ray or Auger electron emission (Fig. 2.7). The XAS spectra can be
recorded in different ways. The most common methods are transmission and total electron
yield (TEY) measurements [44]. The transmission technique requires a thin foils to measure
the transmitted x ray. In the electron yield technique measures the photoelectrons that
are created by the absorbed x-rays, which suitable for conventional samples. At X-PEEM
chamber XAS was measured by tuning the x-ray energy around the material absorption
edge, later the measured spectrum compared with the pure material reference spectrum to
check for film thicknesses or compositions or whether the film is oxidized.

2.2.2 Electron diffraction techniques

After the de Broglie hypothesis in 1924 (dual nature of electron), Thomson and Davisson
in 1937 received the Nobel prize in physics for discovering the electron diffraction in
a thin metal film. Since that day electron diffraction is used as a technique to study
ultrathin films and surface structure, since the periodic structure of the crystal functions
as a diffraction grating and the electrons are diffracted in a predictable manner [45]. For
more surface sensitivity only the low energy electrons are considered, since the electrons
inelastic mean-free path λi is energy dependent, which is clearly seen from the universal
curve of the monochromatic primary beam of electrons. Since the main interaction between
a monochromatic electron beam and a solid is plasmon excitation and it fully depends on
the electron density, this gives a quasi-universal dependence of the different materials as
shown in Fig 2.9 (after Seah and Dench [46]). This makes electron diffraction techniques
suitable for ultrathin film structure investigations and characterization.

14
Chapter 2. Experimental techniques 15

Figure 2.9: Electrons mean-free path universal curve in solids as a function of their energy, from Seah
and Dench [46].

Low energy electron diffraction

Low Energy Electron Diffraction (LEED) is structural analysis technique based on the
diffraction of electrons from surfaces. Electrons with an energy range of 0 to 500 eV are
used in this technique. It is based on detecting the elastically scattered electron diffraction
pattern. LEED is highly surface sensitive analysis technique probing depth of only a few
monolayers. The typical experimental setup of LEED is shown in Fig. 2.10.
The LEED system consists of an electron gun, retarding grids, and a fluorescent screen
inside the vacuum. Outside we have a CCD camera for image capture, and electronics. The
electron gun produces a monochromatic electron beam with low electron energy. The beam
is then directed to the sample. The back-diffracted electrons are filtered by the grids, which

Grids
Crystal

Electron Gun

Screen

Figure 2.10: Schematic digram of LEED system.

15
16 2.2. Structure and stoichiometry characterization techniques

Real space LEED Diffraction Pattern

a (11)

b
b*1 (10)
(00) a* 1

b1,2= a1,2 2 2 X 2 R450 Or c(2X2)

Figure 2.11: Example c(2×2) Wood’s notation and the expected LEED pattern, light green spot dark
green is correspond to adsorbate and substrate respectively, from Masel [47].

are adjusted to a potential of 95-99 % of the energy of the incident electrons in order to filter
not all inelastically scattered electrons by stopping the electrons below this energy. Electrons
that pass the grid loose most of their energy and hit the fluorescent screen, leaving bright
spots. The sharpness of the spots depend on the surface uniformity.

In a LEED experiment the beam of electrons is normal to the surface, and if we treat
it as electron waves incident normally on a periodic surface, then highly localized electron
density will act as point scattering and scatter the incoming electron wave. If we consider the
simplest model possible by considering the surface as 1D chain of atoms and the electron
scattered elastically, we will find that the resultant diffracted spots should satisfy Bragg’s
condition nλ = d sin θ. For the two-dimensional lattice crystal (2D overlayer structure),the
Laue condition can be applied, which means the reciprocal lattice vector with Miller indices
~ hk = ~
h and k is G k∥ −~
k ∥ , where ~
k ∥ and ~
k ∥ are the projections of scattered and the incident
0 0
~ hk is a 2D reciprocal surface lattice vector.
wave vectors on the surface and G If we
assume that the structure of the top layer has the same symmetry (same Bravais lattice) or
closely-related symmetries (no big difference in the angle) to the bulk (not necessarily valid
for a surface), but likely fulfilled in layer-by-layer growing films with small lattice mismatch
to the substrate. One could expect the resulting symmetry (Bravais lattice) from the LEED
spots or vise versa, from Wood’s notation. In Wood’s notation, if b1 and b2 are the surface
layer unit cell vectors, for the substrate the parameters are a1 and a2 and the angle between
b1 b2
both systems is "ϕ". Then we can label the structure as ( x( × )Rϕ), where "x" can take
a1 a2
"p" for primitive and "c" for possible centering (in some text books "x" is used as the name
of the material, for example Ni(111)). Figure 2.11 From [47] shows an example in real space:
the gold spheres are the substrate and the blue are adsorbate atoms. Since it is clear that
p p p
b1, b2 = a1, a2 × 2 and ϕ = 45◦ , this makes the Wood’s notation ( 2 × 2)R45◦ or c(2×2).
When there is a direct relation between Wood’s notation and the reciprocal space vector
G hk = ha ∗ + kb ∗ , where a ∗ and b ∗ are related to the primitive translation vectors in real

16
Chapter 2. Experimental techniques 17

space a and b, as follows:

b ×n n×a
a ∗ = 2π and b ∗ = 2π (2.6)
| a ×b | | a ×b |

where "n" is a unit vector normal to the surface. From this equation one can easily see that
a ∗ and "b" are perpendicular to each other as well as b ∗ and "a". All a ∗ , b ∗ , "a" and "b" in
the same surface plane. By taking into account that the top layer spot will be sharper than
the bottom layer, one can predict the LEED spots coming from this surface as in Fig. 2.11.
This is not the only information one can get from LEED. Since the diffraction spots obey
Bragg’s condition, this means that by tuning the electron’s wavelength, the spot position
and intensity will change, which can be used within a kinematic approximation to get the
interlayer spacer distance. This experiment is called LEED-IV, since we plot the intensity of
the (00) spot vs the electron energy.
By considering only the (00) spot for simplicity and by considering the Born
approximation (single scattering), elastic scattering and that the density function of the
structure is periodic (superstructures) the Laue can be found in detail in [45]. One obtains
a relation between the layer distance "d " and the energy of a diffraction maximums E (n) as
the following:

nπh
d= (2.7)
2m e (E (n) − ϕ)
p
si n(θ)

where "θ" is the incident angle (should be around 90◦ ), "n" the order of the corresponding
interference peak, and "ϕ" is the work function (typically a few eV). To use this equation in
practice one should know a starting point (an estimate) for "d " and assume "n" for the higher
energy peaks till "d " matches, and later fit the n 2 vs "E " data to get the exact "d " values, see
Fig. 4.13.

Medium energy electron diffraction

The main differences between Medium Energy Electron Diffraction (MEED) and LEED are
the relatively higher energy of the electrons, the grazing angle of the incident electron beam,
and that the interlayer distance "d " in this experiment is changing (during evaporation).
Consequently the setup changes a bit. In our case we used the Auger system as electron
gun to produce the electron beam and make it incident with grazing angle to the sample.
In the layer-by-layer growth regime, the intensity of the (00) spot coming from the substrate
diffraction is monitored as a function of time. When the topmost layer becomes rough at the
start of the evaporation due to the creation of islands and steps, this leads to reduction in
the spot intensity due to the surface roughness, as the layer grows and the full atomic layer
completes the roughness will be reduced and diffraction spot acquires maximum intensity.

17
18 2.2. Structure and stoichiometry characterization techniques

L
S
a
e

Figure 2.12: MEED set-up in the MOKE chamber. The letter "e" refers to the Auger electron gun, "a"
is the evaporator, "s" substrate, and "L" the LEED screen.

(f)
800

1,0 700
Time (sec.)

600
MEED intensity (arb. units)

Shutter opened

500
0,9 400

300 Time
200
Linear Fit
0,8
0 1 2 3 4 5 6 7 8

Number of Peak
0,7
Shutter closed

0,6

0,5

0,4 16 ML Ni / Cu3Au(001)

Figure 2.13: MEED intensity of the (00) spot for the growth of Ni on Cu3 Au(001) at room temperature.
The inset shows the linear fit of the time of the peak maxima.

18
Chapter 2. Experimental techniques 19

In the final intensity vs. time curve, there are oscillations with a regular periodicity as
a function of time. The peak numbers tell us the actual thickness (ML) of the film. By this
means, an accurate thickness control for the thin film deposition is realized. Figure 2.13
shows an example of the oscillations obtained during the evaporation of Ni on Cu3 Au(001). A
linear fit of the times of the peaks give us the final evaporation rate as in the inset of Fig. 2.13.
In both LEED and MEED, the primary electron beam is actually not an ideal plane
wave, but a mixture of waves with some energy and direction deviations. These deviations
from the ideal plane wave direction and energy are due to the finite energetic width with a
thermal width of about 0.5 eV and the angular spread of the beam. The electrons exhibit
some random phase variations when reaching the sample surface. If two spots on the
surface are separated by a large distance, the incident waves cannot be treated as coherent
waves, such that the phases are not correlated and the scattered waves cannot interfere to
produce any diffraction pattern. Therefore, there is a coherence length (radius) used for
describing the maximum size that can be considered as illuminated by a coherent plane
wave on the sample. Thus waves that are scattered from points with separations larger
than the coherence length can only contribute to the background intensity. Therefore no
diffraction pattern can be formed for surface structures with periodicities larger than the
coherence length [48].

2.2.3 Magneto-optic techniques

Before going into detail about the mechanism behind MOKE, it is helpful to briefly outline
how originally linearly polarized light acquires a rotation and ellipticity. Linearly polarized
light can be represented as a superposition of right circularly polarized light (RCD) and left
left circularly polarized light (LCD) in equal parts, with both components in phase as shown
in Fig. 2.14.

a
= +

b LCP RCP

= +

Figure 2.14: (a) Linearly polarized light decomposed into RCP and LCP. (b) The same for elliptically
polarized light.

When the electromagnetic wave propagates through a magneto-optic material (which

has a correlation between light polarization and magnetic properties), the RCD and LCD
parts will propagate differently within this material with different speed and attenuation

19
20 2.2. Structure and stoichiometry characterization techniques

which results in elliptically polarized light. This effect leads to numerous applications and
measuring techniques. In this thesis two different techniques were used to investigate the
samples, and both depend on magneto optical effects (MOKE and XMCD), which will be
reviewed in this section.

In 1845, Michael Faraday published his observation of the polarization change of light
as it passes through materials under an external magnetic field [49]. Thirty years later, John
J. Kerr discovered the same effect in reflection rather than transmission of the beam [50].
There was no explanation for the mechanism behind MOKE till 1955, by Argyres [51], who
described in detail the mechanism behind the magneto optical Kerr effect. In 1980, Mooge
and Bader demonstrated the sensitivity of the MOKE experiment and measured hysteresis
loops of epitaxial iron monolayers [52]. Since then it has become a standard technique to
measure the magnetism of magnetic thin films.

What does MOKE measure? MOKE measures the magneto-optical response of the
material. The polarization state of the light changes when it is reflected from a surface of
a magnetic material, and this change can be attributed to the in-phase component (Kerr
rotation) and out-of-phase component (Kerr ellipticity). Both are directly proportional to
the magnetization (M) of the sample [53]. The origin of the magneto-optic effect is still not
fully understood. This is due to the fact that treating magneto-optics theoretically is very
complex as one has to take into account spin polarization, relativistic effects, and spin-orbit
coupling. In general the magneto-optical response is described from a macroscopic point
of view by the antisymmetric parts of the medium’s dielectric tensor in a picture based on
dielectric theory [53], which assumes two different refractive indeces within the material,
one for LCD n L = n(1 − 12 Q~ · K̂ ) and one for RCD n R = n(1 + 1 Q ~
2 · K̂ ), where "n" is the
~ = iQ x,y,z are the directions of the magneto-optical effect in Voigt
complex refractive index, Q
magneto-optic vector form, and K̂ is the unit vector in the direction of light propagation. If
the antisymmetric part of the dielectric tensor "ε" is defined as follows:
 
1 −iQ z −iQ y
ε = ε◦ 
 
iQ z 1 −iQ x 
 (2.8)
iQ y iQ x 1

p
while ε = n, this clearly shows that the two circular modes attenuate differently in the
material and travel with different velocities, which together leads to the Kerr rotation and
ellipticity. The problem in this model arises with the sign of the time dependence of
electromagnetic waves, which is not consistent from the definition.

In the microscopic model, which accounts for quantum theory, we consider the
propagation of light to be coupled with the electron spin in the medium through spin-orbit
interaction [54]. Since we can write the Hamiltonian ( Ĥ ) of the electron in an external field
with vector potential ~
A as follows:

20
Chapter 2. Experimental techniques 21

1 e e
Ĥ = p + A~M + A
(~ ~L )2 + V (~
r) (2.9)
2m c c

where p~ is the average atomic polarization, A~M is the vector potential of the applied DC
magnetic field and A ~L is the vector potential of the electromagnetic wave. Since Ĥ can
be written as the sum of an unperturbed term Ĥ0 , the magnetic interaction HˆM , and Ĥ I ,
electron-radiation interaction term. HˆM consists of two parts, spin-orbit and Zeeman
interaction. With considering the dipole approximation (taking just the first term in the
induced electromagnetic radiation term), using perturbation theory and neglecting the
small perturbation terms, considering Fermi’s Golden rule (transition probability by photon
absorption), using Bennett and Stern calculation of the optical conductivity and considering
the Kramers-Kronig relation, we end up by an equation to describe the optical conductivity
tensor σ2xx and σ1x y as the following:

2e 2 $ X | 〈i | πx | j 〉 |2
σ2xx = − (2.10)
}m 2V i j | $i j |2 ($2i j − $2 )

e 2 X | 〈i | π− | j 〉 | 〈i | π+ | j 〉
σ1x y = − (2.11)
2}m 2V i j ($2i j − $2 ) ($2i j − $2 )

where π± is the momentum operator (π± = πx ±i π y ), "e", "m" are the charge and mass of the
electron, "V " the volume of the material, "$" is the light frequency and | j 〉 and 〈i | occupied
initial and empty final states (for more details [55–58]).

Magneto-optical Kerr effect

ne
pla
r i ng
e
att
sc

polar longitudinal transverse

Figure 2.15: A schematic representation of MOKE geometries.

There are three conventional MOKE geometric configurations: polar, longitudinal,

and transverse MOKE, which are defined according to the respective direction of the
magnetization relative to the scattering plane (Fig 2.15). The magnetization direction of

21
22 2.2. Structure and stoichiometry characterization techniques

the magnetic films can be studied by analyzing the hysteresis loops obtained from the
measurements. The diagram of an MOKE setup is schematically shown in figure 2.3 and is
one of the setups employed in this work. For longitudinal and polar MOKE measurements,
the incident beam is s-polarized by a polarizer and the polarization direction of the analyzer
is set away by 45◦ from the s-polarization direction. Directly after the polarizer the laser
beam passes through a PEM (photoelastic modulator) to measure Kerr rotation (at twice
the fundamental frequency 2f) and Kerr ellipticity (at fundamental frequency "f") with the
same geometry. The quarter wave-plate is used to compensate the birefringence of the UHV
window and the ellipticity of the metallic reflection on the substrate. The effects of reflection
and absorption by the employed optics is further neglected. The final data is taken as the
ratio between the modulated component (signal collected by the lock-in amplifier) and the
DC component (signal collected by the multimeter). This makes the final modulation of the
light a function of the magnetization of the sample [59]. A disadvantage of MOKE method is
the fact that it does not measure the magnetization directly.

in - p la n e o u t- o f- p la n e
M O K E S ig n a l (a r b . u n its )

-4 0 -2 0 0 2 0 4 0 -4 0 -2 0 0 2 0 4 0
µ 0H (m T ) µ 0H (m T )

Figure 2.16: Example of in-plane and out-of-plane MOKE of 8 ML Co/Cu3 Au(001).

Figure 2.16 shows an IP easy magnetization axis MOKE curve. With longitudinal MOKE,
square-like hysteresis loops of the IP magnetization are obtained, which corresponds to the
easy axis of magnetization. Along the polar direction, which is a hard axis, the magnetization
can not be aligned with the external field due to the large magnetic anisotropy.
Determining the magnetic anisotropies from the shape of the hysteresis loops is
discussed by Hajjar et al. [60] and Weber et al. [61]. Here the angle-dependent MOKE will be
presented as an approach for determining magnetic anisotropies from the hysteresis loops.
During this work the optical setup was improved to be more flexible by adding a mirror
displacement path attached to the magnet. This path give the opportunity to change the
mirror’s positions and angles to perform angle-dependent MOKE, see Fig. 2.17. This was

22
Chapter 2. Experimental techniques 23

photodiode Glan-Thompson
multimeter
prism
lock-in-amplifier quarter-wave-plate
glass finger
mirrors

mirrors path

sample

photoelastic
modulator
polarizer
laser

optical bench

Figure 2.17: Laser optical path in the angle-dependent MOKE.

the only possible method to obtain some information about the magnetic anisotropy with
our system, with further space for enhancement of the system in the future. There exist
other approaches using also MOKE, which can give direct and more accurate data, but
unfortunately were not possible to implement into our chamber, e.g. the method presented
by Weber et al. [61].

X-ray magnetic circular dichroism PEEM

The term "dichroism" is taken from Greek language, Di (Two) Chro (color) ism (productive
suffix). In optics, it refers to the absorption difference between two light polarizations. Today,
the term dichroism is used more generally to reflect the dependence of photon absorption
of a material on polarization. The dichroism effect is due to anisotropies which come
either from the charge or the spin of the material. In the latter case it is called magnetic
dichroism. The magnetic dichroism effect is detectable only nearby the absorption edge of
the respective element. Figure 2.18 shows the X-ray absorption spectrum of Co for different
helicity of circular polarization. It is clear that there are differences between both XAS signals
at the L2,3 edges, which changes with the respect to sample magnetization direction. The
difference between the absorption for the two helicities (µ+ − µ− ) is defined as the X-ray
magnetic circular dichroism (XMCD).
In this thesis, XMCD was detected with the help of a photo electron emission microscope
(PEEM) at UE 49 at BESSY II to investigate our samples, magnetic domains. PEEM is a
powerful tool in surface physics and chemistry. Historically, invention of PEEM goes back
to the early 1930s, after the introduction of electron lenses. The first photoemission electron

23
24 2.2. Structure and stoichiometry characterization techniques

µ +

X -r a y a b s o r p tio n (a r b . u n its )
-

µ +- µ -

7 7 0 7 7 5 7 8 0 7 8 5 7 9 0 7 9 5 8 0 0 8 0 5

E n e rg y (e V )

Figure 2.18: X-ray absorption by the electron yield for Co with positive and negative helicity done at
PEEM.

microscope was built by Brüche [62] in 1930. The first PEEM used ultraviolet (UV) light from
a mercury lamp focused onto the sample. The emitted photoelectrons were accelerated by a
potential difference of 10–30 kV between the cathode and the anode, the image then focused
onto a phosphor screen by electron lenses. Recent development was done by using of X-rays
instead of UV radiation which was firstly demonstrated by Tonner and Harp in 1988, and
has been called later as X-PEEM. X-PEEM instrumentation developed rapidly during the
past decade, and almost every synchrotron radiation facility employs PEEM instruments.
The lateral resolution of PEEM is limited by the electron lenses, chromatic and spherical
aberrations. A corrected lens can improve the resolution down to 1 nm [41, 63]. This makes
X-PEEM suitable for imaging the magnetic domains at high resolution. Figure 2.19 shows
the electron trajectories inside PEEM with energy analyzer. After the illumination by x ray,
electrons are emitted from the sample, with energies between zero and the energy of the
illumination minus the work function of the microscope. These electrons are the source
of the image aberration in the microscope. In front of PEEM an objective lens and field lens
form a telescopic round lens system. The electron beam is driven into PEEM, then the image
is transfered to the projector optics which magnifies the image into a CCD camera. It can
resolve the kinetic energy of the emitted electrons. It can also perform both X-ray absorption
(XAS) and X-PEEM. With a high lateral resolution and with the help of a magnetic sample
holder it can measure element selective hysteresis loops.

24
Chapter 2. Experimental techniques 25

Z)
MH
r(5
se
-la

projective
fs

CCD

objective

Sample

column energy analyzer

x-
ra
y

Figure 2.19: Sketch of the electron trajectories of the PEEM in UE 49 beam line at BESSY II.

25
 Theoretical background
3
In this chapter the terminology and the theoretical equations used in this thesis will be
summarized and reviewed.

3.1 Magnetic anisotropy

In general, the magnetization "M " of a ferromagnetic material lies in a specific direction
related to different factors like the crystalline axes (magnetocrystalline anisotropy) and/or
external shape of the body (shape anisotropy). The energy needed to rotate this
magnetization towards the hard axis is defined as the magnetic anisotropy energy E ani [64].
In general, the total anisotropy energy may be written as:

E ani = EC ani + E Shani + E E xani (3.1)

where EC ani , E Shani , and E E xani are magnetocrystalline, shape, and exchange anisotropy
energy respectively.

3.1.1 Magnetocrystalline anisotropy energy (E C ani )

The magnetocrystalline anisotropy energy arises from the crystalline structure of the
material. It is mainly resulting from the spin-orbit coupling and with less extent from dipolar
interactions. EC ani can be described as follows [65]:

EC ani = K 1 · sin(α)2 + K 2 · sin(α)4 + K 3 · sin(α)6 (3.2)

where K i (i = 1, 2, 3, .....) are the anisotropy constants (J/m3 ). In thin films, K 1 is usually much
larger than the other terms. "α" is the angle enclosed by "M " and the normal to the surface.

27
28 3.1. Magnetic anisotropy

3.1.2 Shape anisotropy energy (E Shani )

It is the energy resulting from the external shape of the sample due to the dipole-dipole
interaction [65]. It can be expressed as:

V
E Shani = K 1V · cos2 (α) (3.3)

µ0 2
where K 1V results asM where M s is the bulk saturation magnetization. This term
2 s
dominate the total anisotropy in relatively thicker films. "α" is defined as the angle
between the plane normal and the magnetization, this makes the magnetization favor the
IP orientation.

3.1.3 Exchange anisotropy (E E xani )

Heb

0 Hext

Figure 3.1: Example for shifted hysteresis loop due to exchange anisotropy (exchange bias).

Is unidirectional anisotropy in non-uniform samples [64], win which exchange-coupled

ferromagnetic and antiferromagnetic films exist side by side. These examples often show
a magnetization curve that appears displaced along the field axis, after field cooling the
antiferromagnetic phase through its Néel temperature to give a specific order for the coupled
saturated ferromagnet. The result is a displaced hysteresis loop as in Fig. 3.1. This
phenomenon, known as exchange bias effect (EB), was discovered in 1956 by Meiklejohn
and Bean [9]. It could originate from the pinned moments created by the setting field during
the field cooling of the sample. The exchange coupling between the two phases may be
described by an effective field Heb which produces a unidirectional anisotropy constant

28
Chapter 3. Theoretical background 29

K 1eb = Heb M . E E xani can be written as [66]:

E E xani = K 1eb · cos(δ) (3.4)

"δ" is the angle between the magnetization direction and the preferred orientation of the
exchange anisotropy.
Determining anisotropies from hysteresis loops, however, is usually based on the
assumption that magnetization reversal proceeds without domain formation. Tis is fulfilled
only for loops along the hard magnetization axis, where the magnetization reversibly rotates
while sweeping the magnetic field.

3.2 Stoner-Wohlfarth (SW) model

Before going into more detail about the Stoner-Wohlfarth model (SW) model, let us first
focus on the angle definition used in this part. In figure 3.2, "φ" is the angle between the
external magnetic field "H " and the normal to the surface, "α" is the angle between the
magnetization "M " and the normal to the surface, which shows the final angle at which the
magnetization lies after applying the external field "H ", and "θ" is the angle between the
MOKE laser beam and the normal to the surface (MOKE measures the magnetic component
at the laser direction).
Normal to the surface

Sample

Figure 3.2: Coordination system used in the SW model. "φ" is the angle between the external
magnetic field "H " and the normal to the surface, "α" is the angle between the magnetization "M "
and the normal to the surface, and "θ" is the angle between the MOKE laser beam and the normal to
the surface.

The SW is one of the simplest models used to explain the physics of tiny ferromagnetic
grains contains single magnetic domains by using the hysteresis loops. This model was

29
30 3.3. Magnetic interlayer coupling

presented in 1948 by Wolniansky et al. [67]. In this model, the total anisotropy energy express
as:

E ani = −µ0 · H · M s cos(φ − α) + K 1 · sin2 (α) + K 2 · sin4 (α) + K 3 · sin6 (α) (3.5)

where M s is the saturation magnetization. To simulate the magnetization loops one needs
to trace the local minimum for the total anisotropy, which exists at a critical angle. This
angle could be calculated by minimizing the total energy in (3.5), which give the following
conditions:

∂(E /M s )
=0 (3.6)
∂α

∂2 (E /M s )
>0 (3.7)
∂α2
The simplicity of the SW model makes it useful to get the anisotropy constants in the
ultrathin film. However, the ultrathin film does not consist from a single domain; this makes
the SW model falls in representing the coercivity (Hc ). Therefore in this work, the coercivity
was not fitted, and only the line at saturation magnetization was taken into account.

3.3 Magnetic interlayer coupling

The interlayer exchange coupling between two ferromagnetic layers separated either by a
non–magnetic or an antiferromagnetic spacer layer results from a competition between [68].

1. Ruderman-Kittel-Kasuya-Yosida (RKKY) coupling from the correlation energy

between two FM layers through the conduction electrons of the spacer layer [69–71].

2. Direct exchange interaction mediated by the antiferromagnetic exchange interaction

within the AFM spacer layer [12, 72, 73].

3. Magnetostatic interactions like orange peel coupling originating from the presence of
magnetic charges on rough interfaces [74, 75], coupling by stray field due to magnetic
domain structures [76, 77] or from the sample edges in small-sized structures [78].

4. Direct ferromagnetic coupling through pinholes [79, 80].

These interaction mechanisms are active both in IP- and O O P-magnetized films, while
their relative strength may vary. Numerous theoretical and experimental investigations of
the different interlayer coupling mechanisms are found in the literature [12, 69–80]. These
mechanisms are summarized in the next subsections. In this thesis the parallel coupling was
assigned with positive sign and antiparallel as negative.

30
Chapter 3. Theoretical background 31

3.3.1 Rudermann–Kittel–Kasuya–Yosida (RKKY)

RKKY describes the magnetic layer as arrays of localized spin, which interact with
conduction electrons by a contact exchange potential [81, 82]. The dependence of the
interlayer coupling on the spacer layer thickness is interpreted as the result of a quantum
interference effect. The critical spanning vectors of the Fermi surface of the spacer material
determine the oscillation periods of the interlayer coupling. Phenomenologically, the
interlayer coupling energy per unit area is written as [82, 83]:

J RK K Y = −R 1 cos(θ) (3.8)

where "θ" is the angle between the magnetization directions of the two ferromagnetic layers,
and R 1 is the interlayer coupling constant. Its temperature dependence is found in [83]. The

k||
k
E E

n(E)

M M
magnetic transition noble metals
metals

(a) (b)

Figure 3.3: (a) Shows the difference between the density of the states in ferromagnetic 3d transition
metals and in noble metals. (b) Schematic digram to explain the origin of the RKKY interaction.

example density of states of a magnetic 3d transition metal in figure 3.3 shows that the spin
up electron can penetrate the whole stack with little reflection at the interface. The splitting
of the bands in the magnetic films is reducing this transmission for the spin down electrons,
which produces a high reflection for the electrons in the interlayer with spins opposite to
the film magnetization and makes standing waves. Increasing the interlayer thickness shifts
the discrete levels downwards, and new levels come in and are populated upon crossing
the Fermi energy (EF). When such a new level just crosses EF, this will increase the total
electronic energy and will thus force the magnetization direction of one layer to be reversed,
lowering the system energy, which leads to an antiparallel alignment.

31
32 3.3. Magnetic interlayer coupling

3.3.2 Coupling across antiferromagnetic layers

For an AFM as an interlayer spacer, the coupling cannot be understood without taking
into account the proximity effects at the interfaces and the magnetic state of the
antiferromagnetic spacer layer. This means that the exchange coupling of the AFM to
the FM at the interfaces as well as the internal exchange coupling within the AFM must
be considered. In FM/AFM systems, the competition between the intralayer magnetic
interaction and the FM/AFM interfacial interaction can lead to magnetic frustration, where
not all the nearest-neighbor spins can be in their local minimum energy configuration
Slonczewski [84].

(a) (b)

(c) (d)

Figure 3.4: Spin frustration at an FM/AFM interface: (a) No frustration, perfect interface. (b)
Frustration in the AFM. (c) Frustration at the interface. (d) Frustration in the FM, from Slonczewski
[84].

Figure 3.4a is an example of perfect interfaces of simple layerwise AFM spin structure
created after [85]. The spins are aligned in pairs with its preferred spin directions, which gives
a regular change in the AFM spin direction with each additional layer, and all spins in the FM
layer are pointing in the same direction. In the reality there are thickness fluctuations, which
produce competition between the exchange coupling through the odd or the even number
of ML thickness. In figure 3.4b the interface steps frustrates the FM–AFM interactions in
the AFM, while in figure 3.4c and d the frustration is at the interface and in the FM layer,
respectively. Whether this frustration occurs in The AFM or in the FM layer (b, c, or d)
will be determined by the minimum energy of the system which will depend on different
parameters such as the strength of the interactions, thickness of the FM and AFM layers,
interfacial defects, and system temperature [85–87].

32
Chapter 3. Theoretical background 33

3.3.3 Magnetostatic coupling

In a magnetic film with finite lateral extension, “magnetic poles” are generated near its
ends giving rise to a demagnetizing field. The strength of the demagnetizing field depends
on the geometry and the magnetization of the FM layer. The magnetostatic coupling
has different forms. The simplest one is generated in between two FM films due to the
interaction of magnetic moments of one film with the local magnetostatic stray field of the
other film. This leads the two films to orient their magnetizations antiparallel (negative)
to produce a flux closure reducing the Zeeman energy. The magnetostatic coupling can
also yield parallel (positive) alignment, which is generated due to surface roughness (see
Fig 3.5a). This kind of coupling is known as Néel “orange-peel” coupling (J N éel ). Another
form of magnetostatic coupling originates from domain walls (DWs). A DW is defined as
the transition region at which the magnetization changes direction from one domain to the
other (see Fig 3.5b). For thin nonmagnetic layers separating two FM layers, the stray field
of a DW in one FM layer will exert a local force in the region above the DW in the second
layer. In general, the magnetostatic coupling is nonuniform over the area of the interface.
While it is approximately uniform within the central region, it diverges near the edges of the
sample. In devices of submicron lateral dimensions, these stray fields can induce significant
coupling.

(a) (b)
M1
- + - +
t - +
- + - + - +

M2

Figure 3.5: Schematic representation of (a) Néel coupling in ferromagnetic layers separated by
nonmagnetic spacers "t ", and (b) DW coupling in single layer film.

3.4 Interaction of laser pulses with thin film

Laser pulses have the ability to provide a huge amount of energy into a confined place of the
thin film. This energy can be used to achieve a specific local modification in the thin film, like
crystal structure [88], magnetization [89], and/or temperature [90]. One of the advantages of
using laser pulses as a processing tool is the high precision in controlling the spot size and

33
34 3.4. Interaction of laser pulses with thin film

the energy, which gives the ability to choose what to modify in the surface. In this part, the
temperature and magnetization modification induced by laser pulses are covered.

I
II

III

IV
V
Figure 3.6: Schematic diagram for the film layers and the light path, "I" to "V" is the index for the
multilayer.

In general, when light enters to a material surface, a fraction is reflected from the
interface and the rest will be transmitted inside the material, see Fig 3.6. This is due to
the difference in the index of refraction at the interface. The fraction transmitted "t " and
reflected "r " can be exactly calculated. The Matrix formalism is one of the methods to
calculate these fractions in the ultrathin films. It is an algorithm proposed by Ohta and
Ishida [91] to calculate the electric field intensity in multilayered films when the light is
incident on the system. It uses Abeles’s formulas [92] and reformats it in an elegant way
to calculate the partial absorption in certain a depth of the multilayered metal films. The
propagation matrix element is defined as:

e (−i δ j −1 ) r j p e (−i δ j −1 )
à !
Cjp = (3.9)
r j p e (i δ j −1 ) e (i δ j −1 )

where " j " denotes a layer, "p" for p-polarized light, r j p or r j p ar the Fresnel coefficients for
layer " j " with p-polarized light and δ j −1 is the phase difference between the wave at layer
" j " and j − 1 which is defined as:

δ j −1 = 2πν(n j −1 ) cos(θ j −1 )h j −1 . (3.10)

where "ν" is the wavenumber of the incident light, n j −1 is the complex refractive index and
h j −1 is the layer thickness. From the matrix elements C j ’s the amplitudes of the forward E +
j
and backward E −
j
propagating waves of the light below the j-th boundary can be obtained
from:

34
Chapter 3. Theoretical background 35

à +! à !
Ej +
C j +1C j +2 ......C m+1 E m+1
= −
(3.11)
E−
j
t j +1 t j +2 ......t m+1 E m+1

where m is the total number of interfaces between layers. The final partial absorbency at a
certain depth "z" in a layer between z 1 and z 2 is defined as:
Z z2
A(z 1 < z < z 2 ) = β j F (z)d z. (3.12)
z1

where F (z) is the field intensity defined as E 2 , and β is defined as:

β j = 4πνI m(n j cos(θ j )). (3.13)

The underlying principles and equations governing the absorption of laser light and the
transport of heat inside the material is discussed in several articles in literature [91, 93–
99]. They all assume that the laser pulse within a few femtoseconds is absorbed by the
material conduction-band electrons. Then, the laser energy is swiftly thermalized in the
conduction band by diffusing hot electrons. These hot electrons transfer their energy
through electron-phonon coupling to the crystal. This leads to a temperature increase in a
few picoseconds [96]. This model is termed the two temperature model (TTM). An assembly
from the TTM was used to calculate the temperature distribution in our multilayer, which
will be discussed in the next section.

3.4.1 Two-temperature model (TTM)

Starting from a one-dimensional TTM to calculate the temperature distribution in

z-direction, the TTM is given as following [93]:

∂TeI ∂ I ∂TeI
C eI = (k ) −G(TeI − TlI ) + S I (z, t ) (3.14)
∂t ∂z e ∂z

∂TlI ∂ I ∂Tl
I
C lI = (k ) +G(TeI − TlI ) (3.15)
∂t ∂z l ∂z

where (I) is the layer index, C e is the electron heat capacity, taken as γTe , since in this
calculation the electrons temperature Te is much less than the Fermi temperature TF and
γ = π2 n e k B /2TF , n e and k B are the density of the free electrons and the Boltzmann constant,
respectively. k e is the electron heat conductivity considered as k e0 (Te /Tl ). k e0 is the material
heat conductivity and Tl is the lattice temperature. C l is the lattice heat capacity, which is

35
36 3.4. Interaction of laser pulses with thin film

considered as constant since it has only a small variation with Tl . k l is the lattice thermal
conductivity and since the conduction is done mainly by electrons then k l is considered
as 1% of the total heat conductivity of the bulk metal. "G" is the electron-lattice coupling,
taken to be temperature-dependent because of the high-power laser heating, and it is given
by:

A(Te + Tl )
G(Te , Tl ) = G 0 (3.16)
B +1
G 0 is the coupling factor at room temperature. S(z, t ) is the heat source as function of depth
and time, it is considered as a Gaussian temporal profile which is given by:
s
β (1 − R)I · F z t − 2t p 2
S I (z, t ) = · · exp[− − β · ( ) ] (3.17)
π tp · α α tp

where "I " is the layer index, β = 4l n(2), "F " is the incident fluence, t p is the laser pulse
duration, "α" is the penetration depth including the ballistic range and R I is the reflectivity
coefficient for the first layer.

The TTM was used to estimate the temperature at every layer by assuming that initially
the layers are in thermal equilibrium at initial temperature T0 . This implies that the electron
and lattice temperatures for all layers ar equal to T0 = 50K . The time zero (t=0) defined as the
instant at which the pump pulse reaches the sample. The source of heating after the laser
pulse is the amount of light absorbed within the layer from equation (3.12) and the heat
transferee between layers. The energy losses (radiative and convective) at the femtosecond
transit were neglected. This makes the boundary condition at the front, and at the back as
follows:

TeI (z, 0) = TlI (z, 0) = TeI I (z, 0) = TlI I (z, 0) = T0 , and

(3.18)
∂T (z, 0) ¯¯
¯
= 0, everywhere.
∂z ¯z=0

where "I ", "I I " is index for first layer and second layer. Since all the layers are in perfect
thermal contact, this allows us to write the boundary condition at the interface between
layers as follows [99]:

TeI ¯z=L I = TeI I ¯z=L I

¯ ¯
(3.19)

TlI ¯z=L = TlI I ¯z=L

¯ ¯
(3.20)
I I

36
Chapter 3. Theoretical background 37

∂TeI ¯¯ ∂TeI I ¯¯
¯ ¯
k eI = k eI I (3.21)
∂z ¯ z=L I ∂z ¯ z=L I

I¯
∂T ∂TlI I ¯¯
¯ ¯
l ¯
k lI = k lI I (3.22)
∂z ¯ ∂z ¯
¯ ¯
z=L I z=L I

where L I is the thickness of the layer.

0 100 200 300 400 500

0

40
Line scan
Gauss fit
80
photoemission intensity (arb. units)

120

160 Intensity
Intansity

Intensity (I) (arb. units)

200
photoemission intensity (a.u.)

240

280

320
Three photon

360

400
Two photon

440

480

0 4 8 12 16 20

Position (µm)

Figure 3.7: Image of the laser spot on the sample after blocking the X-ray, with 25 µm field of view.
The plot shows a line scan and Gaussian fit for the laser spot at the red line with 30 pixel width.

To further estimate the temperature distribution in the lateral direction, the heating
within the laser pulse was considered. Since the laser spot is very small compared to the
rest of the substrate (≈ 10 mm), the area outside the laser pulse profile can be considered as a
heat sink for the laser spot. To obtain the laser profile, a Gaussian function was fitted to a line
scan average for 30 pixel width along the red line in the laser pulse image (Fig. 3.7). PEEM
is imaging the three photon photoemission (3PPE) process resulting of the interaction
between the exciting intense laser field and surface defects (hot spots at the surface). As the
3PPE process is a nonlinear photoemission process, the overall photoelectron count rate is
finally proportional to cube of the intensity (I 3 ). The final intensity calculated from the fit is
plotted by the red solid line in figure 3.7. Later, the resulting fitting parameter was used to

37
38 3.5. Spin Seebeck effect (SSE)

calculate the power profile inside the laser pulse, which was used to estimate the influence
at every point inside the laser pulse in "x" and y-direction.

3.5 Spin Seebeck effect (SSE)

3.5.1 Seebeck effect

In 1822 Thomas Johann Seebeck, was studying the effect of a temperature gradient to a
conducting material. He found that an electric voltage "V" could be measured between the
hot end and the cold end of the material. This was called later the Seebeck effect, and the
voltage is defined as follows:
V = S · ∆T (3.23)

where "S" denotes the material and size-dependent Seebeck coefficient and ∆T is the
temperature difference between the two ends.
This potential difference is generated since the hot end has more electrons with larger
energy in comparison to the cold end, which creates a spatial diffusion of the charge carriers
between the hot end and the cold end. In the net effect, more charge carriers are moving
from the hot end to the cold end than in the opposite direction. This force is called
electromotive force. Thus, if the charge carriers are not able to leave the material, there
will be a charge accumulation. If the charge carriers are negatively charged electrons, there
will be negative charge at the cold end and a positive charge at the hot end. This difference
will induce an electric field, driving against the electromotive force until an equilibrium is
reached. Additionally, there is another effect, which drives the Seebeck voltage. This effect
is a phonon drag contribution. When the temperature difference is applied, phonons are
propagating from the hot end to the cold end. When they scatter with electrons, momentum
and energy will be transferred to the electrons. Thus, the electrons also start to propagate in
the direction of the cold end. Similarly, there will be a charge accumulation at the cold end
and a lack of charge at the hot end.
One of the applications used for this phenomena is the thermocouple. In the
thermocouple, two different metals are connected thermally at the hot end. The two cold
ends will be at the same temperature, and the voltage between them is measured as in
figure( 3.8a). Thus, one is measuring the difference of the Seebeck voltage in metal "A" and
"B ", after calibration one can get the temperature value.

3.5.2 Spin Seebeck effect

The spin Seebeck effect can defined as the spin voltage caused by a temperature gradient
in a ferromagnet over a macroscopic scale of several millimeters [100, 101] see figure 3.8.
This current is a pure spin current that is unaccompanied by a charge current which has a

38
Chapter 3. Theoretical background 39

Figure 3.8: (a) A thermocouple consists of two conductors "A" and "B " connected to each other.
(b) Spin-dependent chemical potentials generated after applied temperature gradient to a metallic
ferromagnet. from Uchida et al. [100], Adachi et al. [101].

spin-independent velocity υk [102]. So one can defined the spin current (I s ) as:

s kz υk
X
Is = (3.24)
k

where s kz is the z-component of the spin density s k with the z-axis chosen as a
spin-quantizing axis, and υk is the velocity of elementary excitations concomitant to the spin
density s k . The recent theoretical and experimental efforts have shown that the magnon and
phonon degrees of freedom play crucial roles in the spin-Seebeck effect (SSE). Here, the SSE
is divided into charge contribution SSE named as spin dependent Seebeck effect (SDSE)
and spin magnonic Seebeck effect (SMSE). The SDSE can be described as:

µB σ↑ S ↑ − σ↓ S ↓
IS = · 5T · σ (3.25)
e σ↑ + σ↓
where σ↑↓ is spin dependent electric conductivity, S ↑↓ is spin dependent Seebeck coefficient,
and 5T is temperature gradient [103]. This formula is used later to estimate the spin current
generated by SDSE in Co/FeGd film.

39
 Part I

Antiferromagnetic samples

41
 Single-crystalline ultrathin lms Ni/Cu3Au(001) and
4
NiMn/Ni/Cu3Au(001)

part of this chapter is based on result published in (Journal of Magnetism and Magnetic
Materials, 373 151–154, January (2015) [31])

Antiferromagnetic materials are a fascinating class of materials with many interesting

physical properties. In particular, the exchange bias effect (EB) effect [9] gives it a high
potential for many applications. antiferromagnet (AFM) materials are generally used to
define a reference magnetization direction and to control adjacent ferromagnetic (FM)
layers [10]. It has also been proposed to stabilize the magnetization of nanometre-sized
particles at room temperature [104]. Recently, magnetoresistive effects in AFM materials
have moved into the focus of interest [14], with the promise that if the AFM spin structure
could be controlled, this would make it an active component in future spinelectronic devices
since it can then be used to store information [105, 106], analogously to data storage in FM
media.

The investigation and characterization of their spin structure is essential for the use of
AFM materials in devices. However, it is an experimentally difficult task. While for large
AFM samples neutron scattering can be used to detect the spin structure, this is, however,
not possible for thin films and nanostructures because of the lower signal intensity. For
AFM spin structures at surfaces spin-polarized scanning tunneling microscopy has provided
considerable contributions [23, 105, 107–109]. On the other hand it does not sense the spin
structure in the interior of thin films or in buried layers, thus in the latter cases one has to
resort to indirect methods.

In this part, an indirect method will be presented to poke around the spin structure of
Nix Mn100−x as AFM. These investigations were reported in our publications Shokr et al. [30]
and Erkovan et al. [31], and both publications are inclusive in the following sections.

43
44 4.1. Ni/Cu3 Au(001)

4.1 Ni/Cu3 Au(001)

An AFM has zero net magnetic moment, which makes it difficult to detect the spin structure
of such materials. This is done by reporting the change of the magnetic properties in an
FM layer directly or indirectly coupled with the AFM. In this study, we have chosen Ni
as the FM layer, which is directly coupled with the AFM layer (NiMn). We will start here
by discussing the growth mode of Ni on Cu3 Au(001) and its magnetic properties by using
medium energy electron diffraction (MEED), low energy electron diffraction (LEED), Auger
electron spectroscopy (AES), and magneto-optical Kerr effect (MOKE).

4.1.1 Growth and structure

Knowing the precise lattice and exact structural parameters is important for understanding
the magnetic properties, as it is generally known that surface strain, pseudomorphic growth,
and spin reorientation transition (SRT) are mutually correlated. In this work Cu3 Au(001)
was chosen for growing our thin films since the Cu-Au alloys are stable towards surface
reconstructions and it is easy to prepare a well-defined surface. Furthermore, the lattice
parameter ranges from 3.61 Å (Cu) to 4.08 Å (Au), which makes it suitable for epitaxial
ultrathin film growth of the magnetic materials. From these alloys the Cu3 Au (001) single
crystal has a face-centered cubic (FCC) structure with a space group of P m 3̄m, lattice
parameter of a = b = z = 3.749 Å and critical bulk ordering temperature of 663 K [110, 111].
Cu 3 Au
From this one can calculate the mismatch to NiMn, which is ∆a z = [a z − a zN i Mn ] ≈ 0.1
Å. As The crystal exhibits a sharp c(2×2) LEED pattern. One can expect the LEED pattern
as explained in section 2.2.2 (Fig. 4.1), which shows that the Cu3 Au(001) substrate exhibits
c(2×2) electron diffraction pattern. The experimental pattern that is obtained after cleaning
Cu3 Au(001) by several cycles of sputtering with Ar+ by energy of 1.5 keV and annealing at 800
K for 15 min is shown in Fig. 4.2a, which shows a sharp c(2×2) LEED pattern as expected.
Ni deposition was done by an e-beam evaporator. While growing the Ni film, a MEED
experiment was performed by using an e-beam with energy of 2 keV incident to the
Cu3 Au(001) crystal by a grazing angle with the [110] direction allowing for the (00) specularly
reflected spot to be obtained. Then, the spot intensity was recorded and the MEED curve
was obtained. Since Ni/Cu3 Au(001) grows layer by layer, from this curve the exact number
of deposited mono-layers could be obtained. The evaporation rate was fixed during our
experiments to be around 1 ML/min at 300 K. Figure 4.2f shows the MEED signal during
evaporation of Ni onto Cu3 Au(001). The first minimum in the intensity is because the Ni
in the beginning of the evaporation does not wet the Cu3 Au(001) surface, which is due to
the higher surface free energy of Ni (2.08 J/m2 ) compared to Cu (1.57 J/m 2 ) and Au (1,33
J/m2 )[112]. Around 1 ML after this reduction a regular oscillation starts, evidencing the
layer-by-layer growth mode of Ni on Cu3 Au(001)[113, 114]. The reduction of the MEED
signal after ≈5 ML comes from a structural change, which starts to dominate after 8 ML.

44
Chapter 4. Ultrathin films Ni/Cu3 Au(001) and NiMn/Ni/Cu3 Au(001) 45

y
Real space LEED Diffraction Pattern

(001)
Au
(11)

Cu
b
b*1 (10)
(00) a* 1
(001)

[010]
a
x
[100]

b1,2=2a1,2 c(2X2)
z

Figure 4.1: Cu3 Au(001) expected LEED pattern as explained in section 2.2.2.

LEED and LEED-IV was performed at Ni thicknesses 6 ML and 9 ML to get the vertical lattice
parameter of both phases. The LEED images are expressed in Fig. 4.2a and b for Cu3 Au(001),
and 6 ML Ni/Cu3 Au(001), respectively at 235 eV. It shows that the Cu3 Au(001) substrate has
a c(2×2) pattern as expected. At 6 ML these patterns start to disappear and the p(1×1) spots
become more pronounced.

Table 4.1: Interlayer spacings calculated from Kinematic LEED-IV.

Stoichiometry interlayer spacing space group

Cu3 Au(001) 3.78 Å c(2×2)
6 ML Ni/Cu3 Au(001) 3.43 Å p(1×1)
9 ML Ni/Cu3 Au(001) 3.60 Å c(2×2)

LEED-IV was done by scanning the energy of the (00) spot. Figure 4.2d shows that
the Cu3 Au(001) peaks become broader and shift toward higher energy while increasing
the Ni thickness up to 9 ML. The broadening means that the film is in a high degree of
disorder at this interval, while the shift in energy indicates changes in the interlayer spacing.
The kinematic approximation eq (2.7) from section 2.2.2 was used to calculate the average
vertical interplanar distance, by plotting the peak energy E values as a function of n 2
(Fig. 4.3). The data was fitted with a straight line and from the slope, the interlayer spacing
was calculated and listed in table 4.1. There is an increase in the interlayer spacer between
6 and 9 ML from 3.43 Å to 3.6 Å. This increase is in the direction of the structure relaxation
towards the bulk Ni structure [113, 114].

45
46 4.1. Ni/Cu3 Au(001)

(a) (11) (b)

(10)

b1

1
a
b1
(00)
a1

[010]
[100]

(c) Cu3Au(001)

6 ML Ni/Cu3Au(001)

9 ML Ni/Cu3Au(001)

0 100 200 300 400

Energy (eV)

(f)
800

1,0 700
Time (sec.)

600
MEED intensity (arb. units)

Shutter opened

500
0,9 400

300 Time
200
Linear Fit
0,8
0 1 2 3 4 5 6 7 8

Number of Peak
0,7
Shutter closed

0,6

0,5

0,4 16 ML Ni / Cu3Au(001)

Figure 4.2: LEED image at 235 eV for (a) Cu3 Au(001), (b) 6 ML Ni/Cu3 Au(001) (c) LEED-IV for
Cu3 Au(001), 6 ML Ni and 9 ML Ni, and (f) MEED-signal for (00) spot for Ni deposition on Cu3 Au(001).
The inset shows the linear fit of the time of the peak maxima.

46
Chapter 4. Ultrathin films Ni/Cu3 Au(001) and NiMn/Ni/Cu3 Au(001) 47

4 0 0

3 0 0
E n e r g y (e V )

2 0 0

1 0 0

0
0 1 0 2 0 3 0 4 0
2
In te n s ity (a r b . u n its ) n

Figure 4.3: LEED-IV intensities for 9 ML Ni/Cu3 Au(001), 6 ML Ni/Cu3 Au(001) and Cu3 Au(001) (black).
The linear fitting of the energy versus n2 extracted from the LEED-IV curves is shown on the right.

4.1.2 Magnetic characterization

It is well known that epitaxial growth of thin films can lead to elastic strain, which changes
the total energy of a ferromagnet and consequently could produce magnetoelastic effects
and modify the magnetic anisotropy [112]. The changes in magnetic anisotropy could in
turn lead to a spin reorientation transition (SRT) of the magnetization. So first, the SRT of
Ni on Cu3 Au(001) was checked for different Ni thicknesses. This was done by recording the
hysteresis loops for different film thicknesses in both configurations, longitudinal and polar
MOKE. Moreover, we have determined the Curie temperature (Tc ) for both configurations,
by studying the temperature dependence at each thickness starting from 6 ML Ni to 15 ML
Ni. For the film at 6 ML, no signal in polar geometry was detected, but only longitudinal
signals. This gives evidence for in-plane (IP) magnetized samples at this thickness, in
agreement with Braun et al. [112].
SRT from IP to out-of-plane (O O P) easy axis of magnetization with increasing Ni
thickness on Cu3 Au(001) is confirmed as in [29, 112]. For the range of 7.3 up to 15 ML
both longitudinal and polar configurations showed MOKE signals. Figure 4.4a and b show
temperature-dependent hysteresis loops obtained from 9.6 ML Ni/Cu3 Au(001) taken in both
longitudinal and polar configuration. Figure 4.4 shows rectangularly shaped loops for both
IP and O O P, where a coercivity enhancement with decreasing temperature can be observed.
The general behavior of the temperature-dependent hysteresis loops is similar for the IP
and O O P cases. The main difference between the two magnetization directions observed

47
48 4.1. Ni/Cu3 Au(001)

a ) L o n g itu d in a l M O K E 3 0 5 K b ) P o la r M O K E 3 1 0 K

3 1 5 K
3 2 0 K

3 2 5 K
3 3 0 K
M O K E S ig n a l (a r b . u n its )

3 3 5 K
3 4 0 K

3 4 5 K
3 5 0 K

3 5 5 K
3 6 0 K

3 6 5 K
3 7 0 K

3 7 5 K

3 8 0 K
3 8 5 K

3 9 0 K
3 9 5 K

-0 ,0 2 -0 ,0 1 0 ,0 0 0 ,0 1 0 ,0 2 -0 ,0 1 0 ,0 0 0 ,0 1 0 ,0 2

µ 0H (T )

Figure 4.4: MOKE magnetization curve for 9.6 ML Ni/Cu3 Au(001) taken in (a) longitudinal, and (b)
polar geometry as a function of temperature.

here is that the coercivity coercivity (Hc ) of IP magnetization is almost two times that of
O O P magnetization (Fig. 4.5). We define Tc as the temperature at which we cannot see any
hysteresis loops (Hc =0) determined by a linear fit of Hc as a function of T. The values of Tc of
Ni/Cu3 Au(001) as a function of Ni thickness are shown in Fig. 4.6.
Figure 4.6 shows a SRT between 7 ML and 8 ML Ni thickness in Ni/Cu3 Au(001). This
higher SRT thickness compared to Braun et al. [112] could be due to a smoother growth of
the Ni film and a concurrently later start of the onset of misfit dislocations. The existence
of loops in longitudinal geometry at thicknesses above the SRT could be explained as a

48
Chapter 4. Ultrathin films Ni/Cu3 Au(001) and NiMn/Ni/Cu3 Au(001) 49

3,5 (c)
Polar HC
3,0 Longitudinal HC

2,5

2,0
µ0 H c (mT)

1,5

1,0

0,5

0,0

300 320 340 360 380 400

Temperature (K)
Figure 4.5: Hc as function of temperature for both configurations for 9.6 ML Ni/Cu3 Au(001).

magnetic component due to a small misalignment of the applied field. If we assume small
misalignment of θ ≈ 1◦ , according to the projection of the field by sin(θ) and cos(θ) the
coercivities should be around 10 time different, in this case for the IP geometry the loops
should be around 10 times wider than for O O P. However, in our case the coercivities in the
longitudinal geometry are just ≈ 2 times bigger than in the polar geometry. In our geometry
a 26◦ misalignment of the field can be clearly excluded. This indicates that what we measure
in the hard axis is not due to misalignment, of the field but which could be due to more
complex situations where multiple axes and/or saddle points are involved, which depend
on the energy surface of the thin film. In this case we should consider the anisotropy energy
with higher order anisotropy constant terms as discussed in section 3.1.

To check the latter assumption, angle-dependent MOKE measurements were performed

for 12 ML Ni(001)/Cu3 Au(001) to estimate the magnetic anisotropy. The angle-dependent
MOKE measurements shown in figure 4.7 were done by changing the angle φ and fixing the
angle θ to 45◦ (angles definition in section 3.2). In the angle-dependent measurements, one
expects along the easy axis a perfect rectangular loop with a flat plateau (saturation), and a
non-saturated line along the hard axis. However, the perfect rectangular loop can be seen at
0◦ up to 42◦ , which marked in between two green dashed line in Fig. 4.8. Along the hard axis
a loops with rounded corners were seen at 50◦ up to 90◦ , and it was not possible to observe
non-saturated loops.

49
50 4.1. Ni/Cu3 Au(001)

4 8 0

4 6 0

4 4 0

4 2 0

4 0 0
(K )

3 8 0
c
N i T

3 6 0

3 4 0

3 2 0

3 0 0
L o n g itu d in a l
2 8 0 P o la r

4 6 8 1 0 1 2 1 4 1 6
N i T h ic k n e s s (M L )

Figure 4.6: Curie temperature of Ni/Cu3 Au(001) as a function of Ni thickness. The vertical dashed
line marks the SRT between 7 ML and 8 ML Ni thickness. The solid line (red) is a linear fit from 7 ML
to 10 ML used to correlate the Curie temperature variation in NiMn/Ni bilayers with a change of the
effective Ni thickness.

Later, these measurements were used to estimate the anisotropy energy constants and
the local energy minima [60, 61, 115] by using the Stoner-Wohlfarth model (SW) model
discussed in section 3.2. The aim here is to estimate anisotropy energies K 1 and K 2 in
equation (3.5) and show how the total energy surface of the system behaves when the field
is aligned along the hard axis which could explain the existence of loops along the hard axis.
In the SW equations the hard axis loop is more important to fit, since the magnetization
reversal along the easy axis takes place by nucleation and propagation of domains, which is
not included in the SW model. This makes the easy axis measurements unsuitable for these
equations. As is discussed in section 3.2 Hc is not implemented in the SW model. Therefore,
the fit was done only for the slope of the hysteresis loops at the angle φ. The following
equation was used to calculate the MOKE signal data points for every applied field H :

D c = R 1 cos(α) cos(θ) + R 2 sin(α) sin(θ) (4.1)

where R 1 and R 2 are scaling factors between IP and O O P. R 2 was constrained to be 10 × R 1 ,

since there is a ratio of ten in the Kerr signal between the data for O O P and IP.

50
Chapter 4. Ultrathin films Ni/Cu3 Au(001) and NiMn/Ni/Cu3 Au(001) 51

-0 ,1 5 -0 ,1 0 -0 ,0 5 0 ,0 0 0 ,0 5 0 ,1 0 0 ,1 5

1 0 0 °

9 0 °
in -p la n e
8 0 °

7 0 °
M O K E S ig n a l (a r b . u n its )

6 0 °

5 0 °

4 2 °

3 0 °

1 0 °

0 °
o u t-o f-p la n e
-7 °

-0 ,1 5 -0 ,1 0 -0 ,0 5 0 ,0 0 0 ,0 5 0 ,1 0 0 ,1 5

µ 0
H (T )

Figure 4.7: Angle-dependent MOKE for 12 ML Ni/Cu3 Au(001) at different angles for φ with θ = 45◦ .
The straight (red or black) lines are the simulated data compared with the experimental data for every
loop.

51
52 4.1. Ni/Cu3 Au(001)

1 2 M L N i
2 5 S in e F it o f " H c "

2 0

(m T )
1 5
c
µ 0H

E a s y A x is

1 0

-2 0 0 2 0 4 0 6 0 8 0 1 0 0
F (d e g )

Figure 4.8: Angle-dependence of Hc determined from MOKE measurements of 12 ML Ni/Cu3 Au(001).

The red line is a sine fit to the data, and green dashed lines mark the angles at which perfect rectangle
loops are observed.

The model used here has nonlinear equations, poor information about all variables
and is strongly path-dependent. Therefore, the best method for calculating K 1 and k 2 is
by step scanning in the expected range and fitting the scaling factor R 1 . The best solution
was chosen by minimizing the root mean square deviation (ρ) between experimental (D e )
and the calculated data points (D c ). The data shown here was done by varying K 1 /M s and
K 1 /M s with 0.001 step and fit the scaling factor R 1 (step scanning). The value of K 1 /M s for
Ni in literature was found to varying between (-1 to 1 J/A.m2 ), when M s is considered to be
5.1 × 105 A/m [116]. For a total number of data points (n) ρ was defined as:

qX
ρ= (D e − D c )2 /n (4.2)

The fitted data points are plotted as straight red or black lines in figure 4.7, The first run
was designed to get an overview of how the model is changing with K 1 /M s and K 2 /M s in
the range of (-1 to 1 J/A.m2 ). The minimum was found in the range of K 1 /M s = -0.06 to -
0.15 J/A.m2 , K 2 /M s = 0.1 to 0.2 J/A.m2 . In a later step a fine scan was done in this range, see
Fig. 4.9, to get the value of K 1 /M s and K 2 /M s with lowest ρ.
Finally, the anisotropy energy was found to be K 1 = −(36 ± 2) × 103 J/m3 and K 2 =
(77 ± 2) × 103 J/m3 . This value of K 1 agrees well with the value for Ni on Cu(100) (35 ×103
J/m3 ) measured by Schulz and Baberschke [117]. The calculated total energy is shown in
figure 4.10, for φ = 0. The existence of minimum total energy at π/2 gives an indication
that the film favors O O P magnetization for the calculated K 1 and K 2 . When K 2 is very
high, comparable with the shape anisotropy measured value (-17 ×103 J/m3 ), one expects
a contribution from the shape anisotropy in K 1 . The higher value of K 2 calculated for this

52
Chapter 4. Ultrathin films Ni/Cu3 Au(001) and NiMn/Ni/Cu3 Au(001) 53

2 )
.m
K /A
/M
(J
1
(J
/A
.m 2 /M
) K 2

Figure 4.9: ρ as function of K 1 /M s and K 2 /M s , calculated with 0.001 J/A.m2 steps in both axis.

sample is the reason why loops appeared at the hard axis measurements, shown in Fig. 4.7.

4.1.3 Conclusion

A spin reorientation transition (SRT) of the magnetization in Ni/Cu3 Au(001) is identified as a

second- or higher-order phase transition which takes place between 7 and 8 ML. From 7 ML
up to 15 ML longitudinal and polar magnetization loops were observed with almost identical
shape and double the coercivity for O O P compared to IP. The temperature dependences of
the longitudinal and polar loops were studied and both found to have the same features
and the same Tc . Furthermore, a simulation of angle-dependent MOKE data for 12 ML
Ni/Cu3 Au(001) was performed to calculate K1 and K2 . K1 is found to be -(36 ± 2) × 103 J/m3 .
K2 was found to be (77 ± 2) × 103 J/m3 . So the origin for the continuous transition from IP
to OoP magnetization of the 12 ML Ni/Cu3 Au(001) is tentatively ascribed to the fourth-order

53
54 4.2. NiMn/Ni/Cu3 Au(001)

40
at f = 0° , H = 0 mT
Energy (arb. units)

20

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Anglep´ a (Deg)

Figure 4.10: Total energy surface from the calculated model at φ = 0◦ and H = 0 mT.

anisotropy, K2 .

4.2 NiMn/Ni/Cu3 Au(001)

Spin frustration at the interface determines the overall magnetic properties of FM/AFM
systems. For binary alloy AFM materials like NiMn, this frustration may also depend on
the alloy composition. In this study, the magnetic properties of epitaxial Nix Mn100−x /Ni
bilayer film systems in two different concentration regimes of Nix Mn100−x (x between 25 and
50, “Mn-rich”, and x around 70, “Ni-rich”) have been studied. This part is focusing only on
the variation of the Tc of the ferromagnetic Ni layers during the initial stages of deposition
of the Nix Mn100−x overlayer. An opposite behavior in the two concentration regimes was
found, which points towards a strong dependence of interfacial spin frustration on the alloy
composition of NiMn. Here, the origin of this opposite behavior will be discussed.

4.2.1 Growth and structure

Nix Mn100−x films were prepared by co-evaporating Mn and Ni immediately after Ni layer
deposition onto Cu3 Au(001). To control the evaporation flux by using the Tectra 4-pocket

54
Chapter 4. Ultrathin films Ni/Cu3 Au(001) and NiMn/Ni/Cu3 Au(001) 55

evaporator I have modified the flux connection to read the flux of every cell separately.
To obtain the Ni (Mn) composition of the Nix Mn100−x films, AES was used. First, the
Nix Mn100−x composition and evaporation rate was calibrated on Cu3 Au(001), and the
ratio was rechecked after every sample was evaporated by AES. During growing the
Nix Mn100−x film, a MEED experiment was performed as has been previously explained. For
Nix Mn100−x /Ni, a clear MEED oscillation was not observed (Fig 4.11) . For these samples, the
thickness cannot be directly inferred from MEED, instead, the Ni composition was calculated
by fixing the evaporation power (evaporation rate) of Ni and determining the Ni composition
by using AES.

4 ,1
In te n s ity (a r b . u n its )

4 ,0

3 ,9

3 ,8

3 ,7
M E E D

3 ,6

3 ,5

3 ,4
0 5 0 0 1 0 0 0 1 5 0 0 2 0 0 0 2 5 0 0 3 0 0 0 3 5 0 0 4 0 0 0

T im e (s e c )

Figure 4.11: MEED during deposition of NiMn on 12 ML Ni/Cu3 Au. Shutter open at time zero for 58
min.

It is not easy to utilize AES to calculate the Ni composition of Nix Mn100−x on top of
the Ni film. The difficulty lies in getting the real Ni composition, since the recorded Auger
electrons are a superposition of two signals: one coming from the electrons generated from
the Ni in the Ni-layer and attenuated through the NiMn layer, and the second coming from
electrons generated from the Ni atoms in the NiMn layer. From equation (2.3) discussed in
I
section 2.2.1, the Auger electron intensities (ICu ) for Cu from the Cu3 Au substrate, (IN i
) from

55
56 4.2. NiMn/Ni/Cu3 Au(001)

a )

In te n s ity (a r b . u n its )
7 1 6
IN i

9 2 0
IC u

5 8 9
IM n

4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 1 0 0 0

E n e rg y (e V )

b ) 5 8 9
IM n
In te n s ity (a r b . u n its )

7 1 6
IN i

4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 1 0 0 0

E n e rg y (e V )

Figure 4.12: a) AES of 5 ML NiMn/5 ML Ni/Cu3 Au. b) AES of 10 ML NiMn/12 ML Ni/Cu3 Au.

II
Ni in the Ni-layer, (IN i
) from Ni in the NiMn-layer and (IMn ) for the Mn in the NiMn-layer
can be written as the following:

ICu = I 0 · SCu · e −(d N i +d N i Mn )/λCu (4.3)

I NI i = I 0 · S N i · (1 − e −d N i /λN i ) · e −d N i Mn /λN i (4.4)

56
Chapter 4. Ultrathin films Ni/Cu3 Au(001) and NiMn/Ni/Cu3 Au(001) 57

I NI Ii = x I 0 · S N i · (1 − e −d N i Mn /λN i ) (4.5)

I Mn = (1 − x)I 0 · S Mn · (1 − e −d N i Mn /λMn ) (4.6)

where d N i and d N i Mn are the thicknesses of the Ni and NiMn layer, respectively, x is the
concentration of Ni in NiMn layer, and SCu , S N i , and S Mn are the the sensitivities of
Cu3 Au(001), Ni, and Mn respectively. The signal from Cu will be visible in the samples with
smaller thickness of Ni and NiMn, see Fig. 4.12a. In this case one can solve equations (4.7)
and (4.8) for x and d N i Mn :

ICu SCu · e −(d N i +d N i Mn )/λCu

RN i = = (4.7)
I NI Ii + I NI i S N i · ((1 − e −d N i /λN i ) · e −d N i Mn /λN i + x · (1 − e −d N i Mn /λN i ))

ICu SCu · e −(d N i +d N i Mn )/λCu

R Mn = = (4.8)
I Mn S Mn · ((1 − x) · (1 − e −d N i Mn /λMn ))

For samples with thick Ni and NiMn layers, the signal from Cu will not be visible
r N i .t
(Fig. 4.12b). While d N i Mn is equal to , where r N i is the evaporation rate of Ni and t is
x
total time of Nix Mn100−x layer evaporation, then the ratio between Ni and Mn intensities
results as:

I Mn S Mn · ((1 − x) · (1 − e −r N i ·t /x·λMn ))
R N i Mn = = (4.9)
I NI Ii + I NI i S N i · (e −r N i ·t /x·λN i · (1 − e −d N i /λN i ) + x · (1 − e −r N i ·t /x·λN i ))
Therefore, making a pre-calibration to measure the Ni evaporation rate (r N i ) is essential.
Afterwards the composition (x) is calculated by eq.(4.9) by measuring R N i Mn from the AES
spectrum for every sample.

The lattice parameter of the epitaxially grown NiMn on Ni/Cu3 Au(001) was rechecked by
LEED-IV experiments on 40 ML Ni20 Mn80 /14 ML Ni/Cu3 Au(001) and 20 ML Ni24 Mn76 /12
ML Ni/Cu3 Au(001). The LEED-IV experiments were done directly after evaporation at room
temperature (RT). Figure 4.13 shows a comparison between LEED-IV for those samples and
the LEED-IV for Cu3 Au(001). The determination of the perpendicular interlayer spacing
from the E(n2 ) curves is illustrated in the same figure. The straight lines represent linear
regression fittings based on the kinematic approximation of the (00) diffraction beam
intensity, as described in section ( 2.2.2). The interlayer spacings were determined to be
3.43 Å and 3.56 Å for 40 ML Ni20 Mn80 /14 ML Ni/Cu3 Au(001) and 20 ML Ni24 Mn76 /12 ML
Ni/Cu3 Au(001), respectively. This is in agreement with Macedo et al. [27], Khan [29].

57
58 4.2. NiMn/Ni/Cu3 Au(001)

5 0 0

4 0 0
6
E n e r g y (e V )

3 0 0 5 5
5
2 0 0

1 0 0

0
0 1 0 2 0 3 0 4 0 5 0
2
In te n s ity (a r b . u n its ) n

Figure 4.13: LEED-IV intensities for 40 ML Ni20 Mn80 /14 ML Ni/Cu3 Au(001), 20 ML Ni24 Mn76 /12 ML
Ni/Cu3 Au(001) and Cu3 Au(001) (black). The linear fitting of the energy versus n2 extracted from the
LEED-IV curves is shown on the right.

4.2.2 Magnetic characterization

This section is focusing on the variation of Tc of the ferromagnetic Ni layers during the
initial stages of deposition of the Nix Mn100−x overlayer, which was published in 2015 [31].
An opposite behavior was found in the two concentration regimes. Thus this discussion is
divided into two separate parts for the Ni-rich samples and the Mn-rich samples. Fig. 4.14
shows that after evaporating Ni45 Mn55 onto 7.9 ML Ni, the Hc for the longitudinal loop is
10 times larger than the Hc for the polar geometry. This clearly points towards a magnetic
component due to magnetic field misalignment. This difference was not observed for just
7.9 ML Ni/Cu3 Au(001) see section 4.1.2. This indicates that the Ni magnetization is perfectly
O O P after NiMn evaporation.

Ni-rich Nix Mn100−x films

For the Ni-rich samples, Nix Mn100−x films were prepared at x = 68, 71, and 74 % Ni
concentrations. The bottom Ni layer thicknesses were chosen to be 8.2, 9.6, and 12.6 ML.
The dependence of Tc of these films on Nix Mn100−x thickness is shown in Fig. 4.15. For
these Ni concentrations and Nix Mn100−x thicknesses shown there,NiMn is paramagnetic

58
Chapter 4. Ultrathin films Ni/Cu3 Au(001) and NiMn/Ni/Cu3 Au(001) 59

L o n g itu d in a l M O K E
P o la r M O K E

M O K E S ig n a l (a r b . u n its )

-0 ,0 1 0 -0 ,0 0 5 0 ,0 0 0 0 ,0 0 5 0 ,0 1 0
µ 0H (T )

Figure 4.14: MOKE curves of 3.4 ML Ni45 Mn55 /7.9 ML Ni/Cu3 Au(001) taken in IP and OoP geometry.

at or above room temperature [118]. It is observed that Tc increases slightly during the
initial stages of growth of Nix Mn100−x on top of Ni, and partly relaxes back towards the
initial value as the Nix Mn100−x thickness is further increased. This behavior is attributed
to a ferromagnetic polarization of Nix Mn100−x at the interface to Ni. This polarization
increases the effective thickness of the Ni layer in the case of Ni-rich samples in the first few
monolayers of Nix Mn100−x due to the fact that NiMn is paramagnetic at this concentration.
Figure 4.16 shows Ni-rich Nix Mn100−x films. Upon deposition of Nix Mn100−x , the
effective Ni thickness first increases, as shown in Fig. 4.16b, where the Nix Mn100−x layer is
ferromagnetically polarized. For larger Nix Mn100−x thicknesses, the polarization is saturated
only at the interface, as shown in Fig. 4.16c, which leads to a slight reduction in the effective
thickness. A very similar behavior of induced ferromagnetic polarization has been observed
by photoelectron emission microscopy (PEEM) in FeMn on Co [18]. Due to finite-size effects,
a change in the effective thickness of the Ni layer is accompanied by a respective change of
Tc .

Mn-rich Nix Mn100−x films

In order to investigate the effect of Mn-rich Nix Mn100−x layers, films with Ni concentrations
of 25, 43, and 48 % Ni were prepared. The bottom Ni layer thicknesses were 7.9 and 10 ML.
The top NiMn layer thickness was varied from 1.5 to around 10 ML. Figure 4.17 shows the
effect of the Nix Mn100−x layer on Tc of the Ni layer as a function of Nix Mn100−x thickness.
The behavior found here is opposite to that in the Ni-rich concentration regime. Tc is clearly

59
60 4.2. NiMn/Ni/Cu3 Au(001)

(ML)

Figure 4.15: Ni Curie temperature as a function of the Nix Mn100−x thickness at different Ni
concentrations in the Ni-rich regime. The scale bar at the right indicates the difference in Curie
temperature corresponding to a 1 ML change of the effective Ni thickness estimated from the linear
fit in Fig. 4.6, published in [31].

a) b) c)
NiMn
Ni

Figure 4.16: Schematic model for the Ni Curie temperature changes as a function of the Nix Mn100−x
thickness in the Ni-rich regime. (a) Ni layer, (b) thin layer of Nix Mn100−x on top, and (c) thicker
Nix Mn100−x layer, red dotted line indicates the effective Ni layer, published in [31].

reduced with increasing Nix Mn100−x layer thickness. Discussing the effect again in terms
of an effective Ni thickness, the deposition of Mn-rich Nix Mn100−x consequently leads to a
reduction of the effective Ni thickness. Due to the tendency of Mn for antiferromagnetic
exchange interaction, Mn-rich Nix Mn100−x films could lead to partial non-ferromagnetic
behavior of some of the topmost Ni atoms of the Ni layer, possibly enhanced by intermixing
at the interface. This is schematically depicted in Fig. 4.18. Upon initial deposition of
Nix Mn100−x , the effective Ni thickness thus slightly decreases by enhanced fluctuations of
topmost Ni atoms interacting with Mn of the Nix Mn100−x layer, as shown in Fig. 4.18b.
Since the antiferromagnetic ordering temperatures are higher for Mn-rich Nix Mn100−x ,

60
Chapter 4. Ultrathin films Ni/Cu3 Au(001) and NiMn/Ni/Cu3 Au(001) 61

(ML)

Figure 4.17: Ni Curie temperature as a function of the Nix Mn100−x thickness at different Ni
concentrations in the Mn-rich regime. The scale bar at the right indicates the difference in Curie
temperature corresponding to a 1 ML change of the effective Ni thickness estimated from the linear
fit in Fig. 4.6, published in [31].

antiferromagnetic order sets in within the range of thicknesses probed here [119], and the
Nix Mn100−x layer orders antiferromagnetically at higher thicknesses, as schematically shown
in Fig. 4.18c. The steps in the Tc vs. Nix Mn100−x thickness curves around 3–4 ML for
Ni25 Mn75 and around 7 ML for Ni48 Mn52 are attributed to the onset of antiferromagnetic
order in the respective Nix Mn100−x over-layer. A similar influence of antiferromagnetic order
on the transition between paramagnetic and ferromagnetic in an adjacent FM layer has been
reported for FeMn/Co bilayers [120].

a) b) c)
NiMn
Ni

Figure 4.18: Schematic model for the Ni Curie temperature changes as a function of the Nix Mn100−x
thickness in the Mn-rich regime. (a) Ni layer, (b) thin layer of Nix Mn100−x on top, and (c) thicker layer
of Nix Mn100−x with antiferromagnetic order, published in [31].

61
62 4.2. NiMn/Ni/Cu3 Au(001)

4.2.3 Conclusion
In conclusion, a change in the Curie temperature of a Ni layer on Cu3 Au(001) was observed
induced by the presence of a Nix Mn100−x over-layer and the ratio of NiMn composition,
and NiMn thickness. Mn-rich overlayers cause a lowering of the Curie temperature, which
is attributed to the tendency for antiferromagnetic order of Mn. In contrast, the Curie
temperature slightly increases for Ni-rich overlayers, which is probably a consequence
of induced ferromagnetic order in Nix Mn100−x close to the interface with Ni. All these
interpretations are related to direct Ni–Ni, Ni–Mn, and Mn–Mn exchange interactions. A
higher number of Ni–Ni interactions in the vicinity of the interface with the ferromagnetic
Ni layer would increase the Curie temperature of the latter, while a higher number of Ni–Mn
interactions decreases Tc .

62
 Coupling between single-crystalline ultrathin lms
5
through an antiferromagnetic layer:
Ni/NiMn/Ni/Cu3Au(001)

Part of this chapter is based on the results published in Journal of Applied Physics, 117(17)
175302,May (2015) [30]

The interlayer exchange coupling between magnetic ultrathin films across a spacer material
has an important influence on the magnetization reversal in multilayered structures, and
thus on their magneto-resistive properties. Understanding and control of this coupling is
important for many technological applications [121, 122] like two- and three-dimensional
magnetic ratchet memories which were introduced by Franken et al. [123] and Lavrijsen
et al. [124] respectively, controllable transport of magnetic beads introduced by Tierno et al.
[125], and mass memories introduced by Richter [126]. All of these applications consist of
several ferromagnetic, nonmagnetic, and/or antiferromagnetic layers. While in the case of
nonmagnetic spacer layers the interlayer coupling strength depends mainly on the spacer
layer thickness [127], for antiferromagnetic spacer layers the interlayer coupling will also
depend on the magnetic state of the antiferromagnetic material, possibly influenced by
proximity effects [13].
It is shown here that variation of temperature can induce a change of the sign of the
magnetic interlayer coupling. The ability to tailor the coupling direction after sample
preparation might provide new applications of the spin valve. As discussed in section 3.3, the
interlayer exchange coupling between two ferromagnetic layers is a competition between
different coupling terms which can be written as:

J I EC = J RK K Y + J N éel + J d (5.1)

Experimentally, the separation of these contributions is not straightforward. Often different

samples with different spacer layer thicknesses are prepared for that purpose. The

63
64 5.1. Growth and structure

measurement of partial magnetization loops yields information about the presence of

different species in a sample and their interaction [128, 129]. In the simpler case of a
magnetic trilayer with clearly distinguishable coercivities of the two ferromagnetic layers, a
minor-loop measurement is sufficient to extract information about the interlayer coupling,
which is discussed at the end of this chapter.

5.1 Growth and structure

3 4 M E E D s ig n a l 8 0 0

6 0 0
T im e (s e c )

3 2
in te n s ity (a r b . u n its )

4 0 0
3 0
2 0 0 L in e a r fit
2 8
T im e (s e c )
0
2 6 0 1 2 3 4 5 6 7 8 9 1 0

P e a k n u m b e r
2 4

2 2
S h u tte r o p e n e d

2 0
S h u tte r c lo s e d
M E E D

1 8

1 6

1 4

1 2
0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 1 2 0 0

T im e (s e c )

Figure 5.1: MEED during deposition of 12 ML Ni onto 40 ML Ni25 Mn75 /12 ML Ni/Cu3 Au(001).

After the deposition of a Nix Mn100−x /Ni bilayer onto the Cu3 Au(001) surface, the
sample was heated to 480 K and then cooled in a magnetic field of +200 mT to 160
K. Subsequently, temperature-dependent MOKE measurements were performed while

64
Chapter 5. Ni/NiMn/Ni/Cu3 Au(001) trilayer 65

increasing the temperature from 160 K to 420 K in intervals of about 20 K. After that, a top
12 ML Ni layer was evaporated at room temperature, and the same field-cooling and MOKE
measurement procedure was performed again for the trilayer. This step was repeated twice
with 5 ML until the top layer reached 22 ML Ni. The evaporation rate of the Ni layer was
controlled by MEED. A good MEED oscillation was observed as a result, see Fig. 5.1. This
is because the NiMn and Cu3 Au lattice parameters almost match [27]. This means that
the lattice parameter of Ni/NiMn and its structure do not change appreciably from that of
Ni/Cu3 Au(001).

5.2 Effect of Ni top layer on the coupling across NiMn

In this section the temperature dependence of the magnetic interlayer coupling across an
AFM spacer layer is investigated by using MOKE. The growth and structure of epitaxial Ni
films on Nix Mn100−x /12 ML Ni/Cu3 Au(001) are discussed in the next sections. Here all
the hysteresis loops are measured by polar MOKE since the FM layer on top and at the
bottom employed here all are O O P-magnetized. From now on, the top FM layers will be
called FMt with N symbols and the bottom FM layers will be called FMb with N symbols.
The samples without field-cooling (FC) will be termed (as-grown) samples. The samples
with FC were all cooled in the presence of a negative external magnetic field of 200 mT,
by first heating the sample up to 480 K and then cooling under the applied magnetic field.
The measurements were done while increasing the temperature from lower to higher values
after FC. Due to the limited external magnetic field and the large HC of the Ni layers when
coupled to the NiMn layer, the loops could be observed only above a certain temperature.
That is why the magnetic field strength was enhanced in the setup from 200 mT up to 800
mT by modifying the single polar power supply with a designed electric circuit to switch the
field direction to be able to make hysteresis loops at lower temperatures as well. The electric
circuit implemented in the power supply is shown in the Appendix A.3. The Ni composition
of NiMn is chosen to be ≈ 25% since it has the highest EB [29, 119].
How the Ni thickness (τ) on top of the bilayer changes the hysteresis loop, the Hc , and
the exchange bias field (Heb ) will be shown and discussed first. The discussion will be
categorized according to the NiMn thickness (Y ). Then, the magnetic interlayer coupling
between the two ferromagnetic (FMt and FMb ) Ni layers through NiMn as an AFM layer
will be discussed. The influence of this coupling on the exchange bias phenomenon
will be revealed by discussing the interlayer coupling energy of an epitaxial trilayer of 14
atomic mono-layers (ML) Ni/45 ML Ni25 Mn25 /16 ML Ni on Cu3 Au(001). When extracting,
the interlayer coupling from the minor-loop magnetization measurements using MOKE,
the interlayer coupling changes from ferromagnetic (+) to anti-ferromagnetic (-) when
the temperature is increased above 300 K. This sign change is interpreted as the result
of the competition between an anti-parallel Ruderman-Kittel-Kasuya-Yosida (RKKY)-type

65
66 5.2. Effect of Ni top layer on the coupling across NiMn

interlayer coupling, which dominates at high temperature, and a stronger direct exchange
coupling across the AFM layer, which is present only below the Néel temperature of the AFM
layer.

5.2.1 ∼25 ML Ni24 Mn76

A bilayer 25 ML Ni24 Mn76 /12 ML Ni/Cu3 Au(001) was evaporated as explained before, andthe
sample was moved to the MOKE position directly after the evaporation. Then FC and
temperature-dependent polar MOKE measurements were performed. The normalized
magnetization loops are shown in Fig. 5.2a. Typical for AFM/FM bilayer exchanged-coupled
systems is the discontinuity in the Hc vs. T curves [13, 28, 130], the temperature at this
discontinuity is defined as the T AF M , see Appendix 8. Figure 5.3 shows the temperature
dependence of Hc and Heb for the bilayer and the trilayer. The bilayer has T AF M and blocking
temperature (Tb ) of ∼ 410 ± 5 K and 390 ± 5 K, respectively. Later, 12 ML Ni was evaporated
onto the top of the surface at RT. This top layer only results in a reduction of Heb and Hc
without any changes in T AF M and Tb (Fig. 5.3 ).
After temperature-dependent MOKE was finished, another 5 ML Ni was evaporated
at RT on top. Then the sample was again FC under the same conditions as before, and
temperature-dependent MOKE was again performed. The resulting loops are shown in
Fig. 5.2b. First observation is that below ≈ 300 K a two-step magnetization reversal appeared.
This temperature will be defined as Ts (Fig. 5.3HN). At 280 K one of the loops have the same
Hc as the 12 ML Ni / Ni24 Mn76 /12 ML Ni/Cu3 Au(001), and the other loop is around 50 mT
less. The same was behavior was observed for the Heb at the same temperature with ≈ 1.1
mT reduction in the Heb .
By further increasing the FMt thickness to 22 ML, the loops (Fig. 5.3HN) show a two-step
magnetization reversal at around Ts = 300 ± 5 K, one loop with almost the same Hc as that
in 12 ML and 17 ML and the other Hc is further reduced. At temperatures higher than 300 K,
Hc is the same for 12 ML and 17 ML, the same trend was observed for Heb . This increase in
FMt thickness changes T AF M and Tb to ≈ 400 ± 5 K.
The question now, at T < Ts , is which loops belong to FMt and which to FMb . To extract
this information from the hysteresis loops, Hc was plotted as function of top-layer thickness
τ (Fig. 5.4) at 280 K. The coercivity of FMb should not change with evaporation of the top layer
unless there is coupling. Figure 5.4 shows the FMb Hc with (O) and referred by the black line.
The other coercivity was assumed to be from the FMt (M), which could be fitted with 1/τ.
This is consistent with an interface-determined coercivity. According to this assumption we
start to extract the Hc and Heb for FMb , FMt , and represent it with (O) and (M) respectively.
For this trilayer the value of Heb was reduced with respect to the bilayer and both layers
FMb and FMt show different values up to Ts and then, at higher temperatures, the same Heb .
The reduction in Heb has also been observed in a different study for the same system by Khan

66
Chapter 5. Ni/NiMn/Ni/Cu3 Au(001) trilayer 67

(a)
280 K

300 K

320 K

340 K

360 K
Kerr Intensity (arb. units)

380 K

400 K

420 K

(b) 260 K

280 K
300 K
320 K
340 K
360 K
380 K
400 K
420 K
440 K
460 K
480 K
500 K
520 K

-0,20 -0,15 -0,10 -0,05 0,00 0,05 0,10 0,15 0,20

µ0H (T)

Figure 5.2: Temperature-dependent MOKE hysteresis loops of (a) 25 ML Ni24 Mn76 /12 ML
Ni/Cu3 Au(001) and (b) 17 ML Ni/25 ML Ni24 Mn76 /12 ML Ni/Cu3 Au(001).

67
68 5.2. Effect of Ni top layer on the coupling across NiMn

1 8 0

1 6 0

1 4 0

1 2 0
(m T )

1 0 0
c

8 0
µ 0H

6 0

4 0

2 0

-2

-4
(m T )

-6
e b

-8
µ 0H

-1 0

-1 2

-1 4
2 5 0 3 0 0 3 5 0 4 0 0 4 5 0 5 0 0

T e m p e ra tu re (K )
Figure 5.3: HC (solid symbols) and Heb (open symbols) for τ ML Ni/25 ML Ni24 Mn76 /12 ML
Ni/Cu3 Au(001) (τ = 0 (), 12( ), 17(N, H) and 22 ML (N, H).

68
Chapter 5. Ni/NiMn/Ni/Cu3 Au(001) trilayer 69

1 5 0

1 4 0

1 3 0

1 2 0
(m T )

1 1 0
c
µ 0H

1 0 0

9 0

8 0 b o tto m N i la y e r c o e r c iv ity
to p N i la y e r c o e r c iv ity
7 0
1 2 1 4 1 6 1 8 2 0 2 2
T o p N i la y e r th ic k n e s s (M L )
Figure 5.4: Change of coercivity HC for τ ML Ni on top of 25 ML Ni24 Mn76 /12 ML Ni/Cu3 Au(001), at
280 K. The red line is a fit with 1/τ.

[29]. This reduction is due to the sharing of the pinning centers in the AFM bulk [28]. The
slight variation in T AF M could be due to the effective thickness of the AFM having changed
after Ni evaporating on top [31]. This happens because the Ts clearly increases as the FMt
layer increases.

5.2.2 ∼30 ML Ni22 Mn78

Figure 5.5a presents the temperature-dependent normalized hysteresis loops of the bilayer
30 ML Ni22 Mn78 /12 ML Ni/Cu3 Au(001). It shows slightly tilted loops, where a coercivity
enhancement with decreasing temperature can be observed. This is due to coupling with
the AFM layer. Hc and Heb were extracted and plotted as a function of temperature in
Fig. 5.6. A discontinuity in the slope of the Hc curves is found to be at T AF M = 400 ± 5
K, and a discontinuity for EB Teb is found at 420 ± 5 K.
The loops of the trilayer with 12 ML Ni on top is shown in figure 5.5a that exhibits two
steps up to a temperature of 400 ± 5 K (Ts ). For FMt and FMb , the Hc values are different
up to Ts = 380 K (see Fig. 5.6 NH). After this, both layers switch together up to T AF M ≈ 440
± 5 K (Fig. 5.6). For FMb , Heb is plotted in Fig. 5.6 O M. The exchange bias shows a slight
change from negative to positive values at T < 320 K < Ts , which could be due to the coupling

69
70 5.2. Effect of Ni top layer on the coupling across NiMn

(b) 300 K

320 K

340 K

360 K

380 K

400 K
MOKE Signal (arb. units)

420 K

440 K
460 K

280 K

290 K
300 K
320 K

340 K
360 K

380 K

400 K
415 K
430 K

(a) 450 K

-0,20 -0,15 -0,10 -0,05 0,00 0,05 0,10 0,15 0,20

µ0H (T)

Figure 5.5: Temperature-dependent polar MOKE hysteresis loops for (a) 30 ML Ni22 Mn78 /12 ML
Ni/Cu3 Au(001) and (b) 12 ML Ni/30 ML Ni22 Mn78 /12 ML Ni/Cu3 Au(001).

70
Chapter 5. Ni/NiMn/Ni/Cu3 Au(001) trilayer 71

1 8 0

1 6 0

1 4 0

1 2 0
(m T )

1 0 0
c
µ 0H

8 0

6 0

4 0

2 0

0
-1
-2
-3
-4
-5
(m T )

-6
e b

-7
µ 0H

-8
-9
-1 0
-1 1
-1 2
-1 3
-1 4
2 4 0 2 6 0 2 8 0 3 0 0 3 2 0 3 4 0 3 6 0 3 8 0 4 0 0 4 2 0 4 4 0 4 6 0 4 8 0

T e m p e ra tu re (K )

Figure 5.6: HC (solid symbols) and Heb (open symbols) for τ ML Ni/30 ML Ni22 Mn78 /12 ML
Ni/Cu3 Au(001) (τ = 0 (), 12(N H), 17(N H) and 22 ML (N H)).

between the two FM layers [30]. Tb was found to be around 400 ± 5 K for both FMb and FMt .
Figure 5.6 NH shows Hc (solid symbols) and Heb (open symbols) after the FMt thickness
was increased by 5 ML to make the top layer 17 ML Ni. Then the sample is FC. In this case no
second step in the loops is observed up to ≈ 360 ± 5 K (Ts ). This indicates that the two FM
layers have almost the same coercivity, and the coupling between both layers drives them to

71
72 5.2. Effect of Ni top layer on the coupling across NiMn

1 3 0

b o tto m N i c o e r c iv ity
1 2 0 T o p N i c o e r c iv ity

1 1 0

1 0 0
(m T )

9 0
C
µ 0H

8 0

7 0

6 0

1 2 1 4 1 6 1 8 2 0 2 2
T o p N i la y e r th ic k n e s s (M L )

Figure 5.7: Change of coercivity HC for τ ML Ni on top of 30 ML Ni22 Mn78 /12 ML Ni/Cu3 Au(001), at
300 K. The red line is a fit with 1/τ.

have the same magnetization switching field. T AF M and Tb were found to be at around 390
± 5 K and 380 ± 5 K, respectively. After further increasing the FMt thickness to 22 ML and
FC, MOKE was measured and shown in figure 5.6 NH, which shows Ts to be around 340 ±
5 K. Heb in figure 5.6 M O shows a big step at around Ts = 320 K which makes it complicated
to determine Tb . This step could be due to the coupling between the two layers around this
temperature which increases Heb . To confirm the last assumption about the top and bottom
layer signal, Hc was plotted as a function of top FM layer thickness τ which shows that the
Hc of the top layer can be fitted with 1/τ as in the case of the trilayer with AFM thickness 25
ML NiMn.

Table 5.1: Ts as function of top Ni layer and NiMn layer thickness.

top Ni 25 ML NiMn 30 ML NiMn

12 ML (< 280 K) 380 K
17 ML 280 K (< 260 K)
22 ML 300 K 320 K

Table 5.1 is summarizing the change in Ts by increasing the top Ni layer and by increasing
the NiMn thickness. It shows that for 25 ML NiMn and for 12 ML Ni on top, both FMt and

72
Chapter 5. Ni/NiMn/Ni/Cu3 Au(001) trilayer 73

FMb still strongly couple with the same Hc , even at 280 K. By increasing the FMt to 17 ML, it
becomes softer and has different coercivity at lower temperature, with different Hc , up to 280
K, then the coupling forces both to switch together with the same Hc . By further increasing
the top layer to 22 ML, Ts is enhanced to 300 K. At temperatures higher than Ts , the coupling
forces both FM layers to switch together.
In the sample with 30 ML NiMn and 12 ML Ni, FMt has a higher Hc than FMb . This
results in a Ts of 380 K. When reducing the coercivity of FMt by evaporating 5 ML Ni, both
layers had the same coercivity. By evaporating another 5 ML Ni on top, Hc of the FMt reduces
further and Ts reappears at 320 K. At T > Ts the exchange coupling forces both FMt and FMb
to switch together with the same coercivity.
The EB in these samples was reduced by evaporating a top FM layer and also by
increasing its thickness. This is because EB does not only arise from the interface, but also
from pinning centers within the bulk of the AFM [131]. The pressure of the FM layer on top
of the bilayer makes the pinning centers be shared by the two FM layers and reduces the EB
[28].

5.3 Interlayer coupling across ∼45 ML Ni25 Mn75

In this section the temperature dependence of the magnetic interlayer coupling across a 45
ML Ni25 Mn75 as an AFM spacer layer is investigated by measuring minor loops using MOKE,
as published in 2015 [30]. Growth and structure of epitaxial Nix Mn100−x films on Cu3 Au(001)
and on Ni/Cu3 Au(001) are discussed in sections 5.1.
After deposition of a 45 ML Ni25 Mn75 on 16 ML Ni/Cu3 Au(001), the sample was FC as
before. Subsequently, temperature-dependent MOKE measurements were performed from
160 K to 420 K at intervals of 20 K. After that, the top FM layer (14 ML Ni) was evaporated
at RT, and the same FC and MOKE measurement procedure was performed again for the
trilayer. The AFM layer thickness of 45 ML was chosen because the two separate steps in
the magnetization loops can be observed at all temperatures so that the coupling can be
analyzed qualitatively.
Figure 5.8 shows the major loop (black line) and minor loops (red and green lines) of
the trilayer, measured at 240 K. The major loop shows two steps at 107 and 250 mT. From
comparison with the magnetization loop of the bilayer, one can conclude that the bottom
Ni layer is the harder of the two FM layers with the higher coercivity, as observed in 25
and 30 ML NiMn. The minor-loop measurements were acquired by saturating the harder
layer to either the positive or negative field direction, and then ramping the field below the
coercivity of the hard layer. The exchange bias coupling energy Jeb defined as the horizontal
shift of the center of the minor loops away from zero field. It is results from the combined
effect of the interlayer exchange coupling JI EC through the AFM layer and the exchange
bias of the soft layer by the AFM layer. While the former changes sign when the hard-layer

73
74 5.3. Interlayer coupling across ∼45 ML Ni25 Mn75

(arb. units)

Figure 5.8: Major magnetization loop (black) as well as positive (green) and negative (red) minor
loops of 14 ML Ni/45 ML Ni25 Mn75 /16 ML Ni at 240 K. The green curve was taken while the hard
layer was saturated in positive field direction and the red curve was taken while the hard layer was
saturated in negative field, published in [30].

magnetization direction is reversed, the sign of the latter is set during FC and remains
constant. This can be used to separate these two effects. The coupling strength J is then
taken from the product of the field offset and the magnetization of the soft layer, where a
negative value is assigned to antiparallel coupling:

J n = µ0 · M sN i Hn and J p = µ0 · M sN i H p (5.2)

with Hn and H p as the shift field of the negative and positive minor loops, respectively. It is
thus:

J n = J eb + J I EC , J p = J eb –J I EC , and so J I EC = (J n –J p )/2, J eb = (J n + J p )/2 (5.3)

The shift of the positive minor loop to the left with respect to the negative one indicates

74
Chapter 5. Ni/NiMn/Ni/Cu3 Au(001) trilayer 75

(arb. units)

Figure 5.9: Minor-loop measurements of 14 ML Ni/45 ML Ni25 Mn75 /16 ML Ni/Cu3 Au(001) at
different temperatures. The color code is the same as in Fig. 5.8, published in [30].

a ferromagnetic coupling between the two FM layers. Examples of minor loops for different
temperatures are displayed in Fig. 5.9. At low temperatures, J I EC is positive, as in Fig. 5.8.
With increasing temperature the coercivity decreases, and the loop shifts. Eventually J I EC
reverses sign at higher temperatures. The resulting J I EC as a function of temperature is
calculated using equation (5.2) and (5.3), as shown in Fig. 5.10. As can be observed, the
interlayer coupling changes sign at about 325 ± 5 K, corresponding to a change of the
coupling from FM to AFM. The AFM coupling at higher temperatures can also be observed
in the major loops. One example is shown in the inset of Fig. 5.10, where the reduced
remanence of the hysteresis loop at 380 ± 5 K indicates that the two FM layers are AFM
coupled.
As discussed in section 3.3, J I EC is the sum of direct exchange coupling (Jd ) by the spin
structure of the AFM layer and indirect coupling between the two FM layers through the
AFM layer. The latter can be due either to magnetostatic coupling, JNeel , and/or the RKKY
interaction, JRK K Y :

J I EC = J d + J Neel + J RK K Y (5.4)

75
76 5.3. Interlayer coupling across ∼45 ML Ni25 Mn75

Figure 5.10: Temperature-dependence of the interlayer coupling between the top and the bottom
Ni layer in 14 ML Ni/45 ML Ni25 Mn75 /16 ML Ni/Cu3 Au(001). The dashed line is a guide for the eye.
The inset shows the major hysteresis loop measured at 380 K. The non-saturation around zero field
indicates that the two Ni layers are antiferromagnetically coupled, published in [30].

JNeel , Jd , and JRK K Y do not change sign as a function of temperature [132]. This means
that the observed sign change must come from different temperature dependencies of the
different contributions. The direct exchange coupling is strongly temperature-dependent
around the ordering temperature of the AFM, above which this coupling contribution
vanishes, while the RKKY and magnetostatic coupling exhibit a more gradual temperature
dependence [133]. We thus suggest that the indirect coupling, RKKY and magnetostatic
coupling, are dominating at temperatures higher than 340 K. Since the coupling is negative,
an antiparallel RKKY coupling must outweigh a weaker magnetostatic coupling. JNeel for
this sample is very small and could be neglected because MEED oscillations were observed
during deposition of Ni on NiMn, as discussed in section 5.1. The value of the AFM coupling
energy at 380 K is about –0.25 µJ/m2 . This value is within the range expected for RKKY-type
coupling at a spacer-layer thickness of 45 ML. It was calculated using typical values of similar
systems [82, 83, 129] and extrapolating from those values to the ninth antiferromagnetic
coupling maximum using the formula used by Stiles [82], assuming a decay length to account
for nonzero sample temperature of 10 Å. RKKY coupling alone could, hence, be responsible
for the observed antiferromagnetic coupling.

76
Chapter 5. Ni/NiMn/Ni/Cu3 Au(001) trilayer 77

Figure 5.11: Temperature-dependence of the coercivity HC (solid symbols) and exchange bias field
Heb (open symbols) of the 45 ML Ni25 Mn75 / 16 ML Ni/Cu3 Au(001) bilayer ( ) and the 14 ML Ni/45
ML Ni25 Mn75 /16 ML Ni/Cu3 Au(001) trilayer (up- and down-triangles for top and bottom layers,
respectively). ? represents the exchange bias field extracted from the minor loops, published in [30].

Finally, the temperature dependence of the coercivity Hc and the EB field Heb of the
bilayer and the trilayer are presented in Fig. 5.11. T AF M and Tb for the trilayer sample are
360 ± 5 K and 260 ± 5 K, respectively. T AF M of the trilayer as extracted from the temperature
dependence of Hc , is around 360 ± 5 K. This confirms the assumption that the direct
exchange coupling disappears at around this temperature. The temperature-dependent

77
78 5.4. Conclusion

exchange bias field of the top layer extracted from the minor-loop measurements (? in
Fig. 5.11) agrees well with the loop shift of the soft layer extracted from the major loops.

5.4 Conclusion
From the present data, we conclude that there is an increase of T AF M with increasing AFM
layer thickness, which is in agreement with the results for FeMn/Co/Cu(001) by Offi et al.
[130] and (Co/)Ni/FeMn/Cu(001) by Lenz et al. [13]. The observation of two steps in the
loops depends on different parameters. The first parameter is the coercivity of the top and
the bottom layer, and how much they are different from each other. When they are near each
other, the reversal of the soft layer is dragged by the harder layer through the DW switching.
Since the coercivity is enhanced by the coupling with the AFM, this means the appearance
of this second step depends also on the direct exchange coupling with the AFM. For the 45
ML, the coupling through the AFM layer between the bottom and top FM layers, has been
found at this thickness to be a competition between direct exchange coupling through the
AFM layer favoring parallel alignment and an antiparallel RKKY-type coupling. The latter
dominates at high temperatures, leading to an effective antiparallel coupling between the
two Ni layers, while the direct exchange coupling is present at temperatures below the Neel
temperature of the AFM layer, where it prevails over the RKKY coupling. The coupling
strength at temperatures above the ordering temperature of the AFM layer is in the range
of possible RKKY-type coupling energies. These competing interlayer interactions allow
tuning of the magnitude as well as the sign of the total interlayer coupling by variation of
temperature. An AFM material, with a suitable ordering temperature, could therefore not
only serve to enhance the temperature dependence of the coercivity of an adjacent FM layer,
but it could also serve to modulate the interlayer coupling and, thus the remanence of a
trilayer by temperature.

78
 Part II

Ferrimagnetic samples

79
 81

Introduction
A small and fast storage device with contact-less read and write functions with high bit
density is a dream, which may be achieved by combining rare-earth (RE) metals with
transition metals in what is called a magneto-optical storage device. In this device
the information is stored as sequence of small magnetic domains; the writing process
could be achieved by local laser pulses combined with low external magnetic fields and
reading by sensing the polarization change by the magneto-optical Kerr effect. For this
application alloys of Gd and/or Tb combined with Fe and/or Co are highly suitable as
storage media. To improve the read-out efficiency and lifetime of such kind of devices,
the bi- and multilayer structures were studied in the last years for example by Hartmann
[134], Hartmann and McGuire [135], Hartmann et al. [136], Hansen and Hartmann [137],
and Wu et al. [115]. Nowadays FeGdCo alloys started to attract high interest since Rasing
et al. [138] demonstrated how to use ultrafast laser pulses to manipulate the magnetization
direction in such a material by changing the laser helicity.
In this part of the thesis a study on Fe(100−x) Gd(x) will be presented and its coupling with
a Co cover layer. We start by presenting the fabrication and magnetization curves for two
series of samples, namely 8 Å Pt/150 Å Fe(100−x) Gd( x)/10 Å Pt/Si(001) and 8 Å Pt/10 Å Co/150
Å Fe(100−x) Gd( x)/10 Å Pt/Si(001) with different Gd concentration (x) prepared by our partner
M. Erkovan in the Gebze Institute in Istanbul (Turkey). Then we will show how the top Co
layer alloyed with the FeGd layer during heat treatment of the samples to give a very soft
magnetic alloy with higher compensation temperature. Finally we discuss the domain wall
(DW) motion induced by a single laser pulse in one of the samples from this series.

81
 Polycrystalline Fe100−x Gdx samples
6
6.1 Sample fabrication

The samples employed here were fabricated by M. Erkovan in a cluster system consisting of
a magnetron sputter deposition and a surface analysis chamber at Gebze, Istanbul, Turkey.
The deposition chamber was pumped down to below 1×10−8 mbar, and a Gd target was
per-sputtered to remove gettered oxygen. Naturally oxidized SiO(001) wafers were subjected
to a cleaning process by ethanol and methanol, and then transferred into the vacuum for
annealing at 550 °C for 20 min to remove surface contaminations. Argon process gas of
6N purity was given to the system through an Ar-filter during deposition, such that the
growth pressure was 1.2-1.3×10−3 mbar. The substrate was always normal to the target
and the distance between these two was kept at 100 mm. FeGd alloys were grown by an
automated process using Fe (100 W) and Gd (10 W) targets to deposit less than 1 monolayer
sequentially. Deposition periods were calculated using X-ray photoelectron spectroscopy
(XPS) calibration results for each target in order to ensure uniform alloy growth. Fe and
Gd targets were calibrated separately by 10 seconds periods of depositions at the desired
sputtering powers. Then finally 8 Å Pt capping layer was deposited to prevent further
oxidation by ambient conditions.

Two series of Fe(100−x) Gd(x) films were grown, one with 10 Å Co on top and the other
without Co. The layer sequences are 8 Å Pt/10 Å Co/150 Å Fe(100−x) Gdx /10 Å Pt/Si(001)
and 8 Å Pt/150 Å Fe(100−x) Gdx /10 Å Pt/Si(001). Later we will call the samples FeGdx or
Co/FeGdx, where x is the percentage of Gd, which was chosen to be 15, 25, and 30, since
FeGd films with a Gd concentration of around 20% show perpendicular uniaxial magnetic
anisotropy and at this range they are ferrimagnetic material (FIM) with a relatively high
magnetic compensation temperature [134].

83
84 6.2. Magnetic characterization

6.2 Magnetic characterization

After the samples were prepared and capped by Pt to prevent oxidation, the samples were
transferred to Germany and then to the MOKE chamber. Later, temperature-dependent
MOKE was performed to investigate the magnetization compensation temperature and the
coupling properties between FeGd and Co, and after it is characterized, one sample was
moved to BESSY into the X-PEEM chamber for further investigation. We will start here by the
temperature-dependent MOKE. Then we will discus the data obtained by X-photoemission
electron microscopy (PEEM).

6.2.1 MOKE measurements

As grown samples

In this section, all samples were treated by the same way. After loading into the chamber it
was pumped down to 1 × 10−8 mbar, then the sample was moved into the MOKE position
and magnetization loops in longitudinal and polar geometry were acquired to check the easy
axis of the sample. All samples were O O P-magnetized; no magnetization loops have been
observed in longitudinal geometry. Later, the sample was cooled in remanence down to 70
K. Then, temperature-dependent MOKE was performed while increasing the temperature
in steps of ≈ 10 K up to around room temperature.
In figure 6.1a, an example is shown of the magnetization loops obtained from FeGd25.
Tilted loops typical for FIM were obtained up to 160 K. It is hard to obtain loops around
200 K up to 258 K, then tilted magnetization loops show up again up to room temperature.
At the compensation temperature, we expect no loops for a FIM, since around Tcomp the
magnetizations of the two sub-lattices cancel each other such that the sample has zero
net magnetization. That makes it difficult to get loops in MOKE. The same behavior
was observed for FeGd15 and FeGd30 with different temperature ranges. In figure 6.1b
we present the extracted remanence from the loops of the three samples. The coercivity
converges to zero at the magnetic compensation temperature Tcomp . This was observed and
reported for different metallic FIM films by Wu et al. [115], Hartmann [134], Ostoréro et al.
[139], Tsymbal et al. [140], Fishman and Reboredo [141] and Radu et al. [142]. The Tcomp
is defined here as the temperature at which the remanence is extrapolated to zero; it was
found at 160 K ± 15K for FeGd15, 180 K ± 15K for FeGd25 and 200K ± 20 K for FeGd30, which
is in agreement with Hartmann [134] for the corresponding thicknesses. The huge errors at
determining Tcomp for these samples is due to the fact that it was not possible to observe
loops at around these temperatures.
In figure 6.2a the magnetization loops of the Co/FeGdx samples are presented. The loops
behave differently than in FeGdx. In general, one can observe that there is still hysteresis; the
loops appear like the ones presented by Zeper et al. [143] for Co/Pt at this thickness. At lower

84
Chapter 6. FeGd 85

(a )
2 9 0 K
M O K E S ig n a l (a r b . u n its ) 2 7 0 K

2 5 8 K
2 0 5 K

1 6 0 K 1 5 0 K
1 4 0 K 1 3 0 K
1 2 0 K 1 0 0 K
8 0 K 7 4 K
6 4 K
-5 0 0 5 0
µ 0H (m T )
3 ,5
F e G d 3 0
F e G d 2 5
3 ,0
R e m a n e n c e (a r b . u n its )

F e G d 1 5

2 ,5

2 ,0

1 ,5

1 ,0

0 ,5

0 ,0

5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0 3 5 0
T e m p e ra tu re (K )
Figure 6.1: (a) Temperature-dependent MOKE hysteresis loops of FeGd25. (b) The remanence for
FeGd15 (), FeGd25 ( ), and FeGd30 () as a function of temperature. The solid lines are a guides to
the eye.

85
86 6.2. Magnetic characterization

M O K E S ig n a l (a r b . u n its )
8 0 K
(a )
M O K E S ig n a l (a r b . u n its ) 3 4 0 K 3 2 0 K

3 0 9 K 2 9 5 K

2 8 0 K 2 5 9 K
-6 0 -4 0 -2 0 0 2 0 4 0 6 0
2 3 9 K 2 2 0 K µ 0H (m T )

1 9 9 K 1 9 0 K
1 8 0 K

1 6 4 K
1 2 1 K
9 9 K
8 0 K

-6 0 -4 0 -2 0 0 2 0 4 0 6 0 8 0 1 0 0
µ 0H (m T )

(b )
2 5
R e m a n e n c e (a r b . u n its )

2 0

1 5

1 0

C o /F e G d 1 5
5
C o /F e G d 2 5
C o /F e G d 3 0
0

1 0 0 1 5 0 2 0 0 2 5 0 3 0 0 3 5 0 4 0 0
T e m p e ra tu re (K )
Figure 6.2: (a) Temperature-dependent MOKE hysteresis loops of Co/FeGd25. The inset shows the
loop at T = 80 K with a magnified vertical axis. (b) The remanence for Co/FeGd15 (), Co/FeGd25 ( ),
and Co/FeGd30 () as a function of temperature. The solid lines are guides to the eye.

86
Chapter 6. FeGd 87

temperatures, the loop shows strongly tilted loops, which is magnified and shown in the inset
of figure 6.2a. At around compensation temperature (Tcom ), one can still observe hysteresis.
However, it starts to be aligned oppositely to the applied magnetic field. As the temperature
increases, the loops start to be more square and aligned totally with the magnetic field.
In FeGd, one expects that the Gd sublattice aligns with the magnetic field at temperature
T<Tcomp and as the temperature increases so T>Tcomp , the Fe moment would dominate and
align with the field [142]. Here it was observed that the loops direction is switched as the
temperature increases, which indicates the MOKE measurement is more sensitive to the
most top layer Co layer in this case. This gives indication that Co is antiferromagnetically
coupled to the Gd moments, and ferromagnetically to the Fe moments.
Figure 6.2b shows the extracted remanence of the Co/FeGdx loops. Tcomp can be found
at ≈ 150 K, 180 K, and 220 K for Co/FeGd15, Co/FeGd25, and Co/FeGd30 respectively (see
Table 6.1). The Tcom for Co/FeGd samples are reduced compared to the corresponding ones
from the FeGd films. This results from the increment of the total magnetic moment of the 3d
elements after evaporating Co on top of FeGd, which could leads to reduction of the Tcom .

Table 6.1: Compensation temperatures for the FeGd samples.

percentage % FeGd Co/FeGd

15% 160 K ± 15 150 K
25% 180 K ± 15 175 K
30% 200 K ± 20 220 K

6.2.2 Magnetization investigation by XMCD

By PEEM

The Co/FeGd25 sample was moved to the PEEM chamber at BESSY II to study the magnetic
domains and further investigate the coupling between FeGd and the Co on top. Firstly, the
sample was degassed in the preparation chamber before transfer into the X-PEEM chamber.
After transfer, X-ray absorption spectroscopy (XAS) was measured for the Fe, Co L3 and L2
edges and the Gd M5 edge, and then later compared to the spectra of the corresponding
pure materials in the XAS Handbook by Grieken and Markowicz [144]. Figure 6.3 shwos
the XAS spectra, there is no extra peaks appeared for all elements (see the oxides XAS in
Appendix A.6) which indicate that our samples are not oxidized. The exact energy values of
maximum intensity of the edge were determined and used to perform the x-ray magnetic
circular dichroism (XMCD) imaging. The values are 707, 777.8, and 1182.6 eV for Fe, Co, and
Gd, respectively.
XMCD-PEEM images were collected with 20 µm field of view (fig. 6.4) at these energies.
3r d harmonic of the undulator was used for Co and Fe, while for the Gd image and M 5

87
88 6.2. Magnetic characterization

6000

Fe
XAS Fe
Intensity (arb.units)
5500

5000

4500
Intensity (arb. units)

700 710 720 730

Energy (eV)
Intensity (arb.units)

6000

5500
Co
5000

XAS Co
4500

770 775 780 785 790 795 800

Energy (eV)
Intensity (arb.units)

3000

2500
Gd
2000

XAS Gd
1500

1180 1190 1200 1210 1220 1230

Photon energy
Energy (eV) (eV)

Figure 6.3: XAS spectra of the L3 and L2 edges of Fe, and Co, and the Gd M5 and M4 edge of
Co/FeGd25.

88
Chapter 6. FeGd 89

edge the 5t h harmonic was used. In Fig. 6.4 the XMCD difference is presented as gray-scale
contrast as described in section 2.2.3 and by Kuch et al. [41]. In the PEEM chamber the
sample was cooled to 50 K at the O O P sample holder (Fig. 2.19). The XMCD-PEEM images
show that Gd oriented antiferromagnetically with respect to Co and Fe due to the negative
exchange coupling between the 4f in Gd and the 3d in the Fe and Co. The Fe and Co are
ferromagnetically coupled. At 50 K the Gd magnetization dominates and is aligned with the
field direction. Therefore, we only considered Gd XMCD-PEEM images in this part.

0 100 200 Gd 300 400 5000 100 200

Fe 300 400 5000 100 200
Co
300 400 500
0 0

40 40

80 80

120 120

160 160

200 200

240 240

280 280

320 320

360 360

400 400

440 440

480 480

Figure 6.4: XMCD-PEEM images acquired at the M 5 edge of Gd and at the L 3 edges of Fe and Co. The
field of view is 20 µm.

Figure 6.5 shows local element-selective magnetization loops at 50 K obtained from

field-dependent PEEM images, taken at the absorption edge of the corresponding elements
using only one helicity of the x ray as function of the applied magnetic field. Square loop are
observed for all elements, and confirm that Fe and Co sublattices are AFM coupled with the
Gd except for a small range at around -6.53 mT since there is a slightly different switching
field for Fe and Gd. This could mean that at these fields Fe and Gd are FM aligned, but
this was not confirmed by the XMCD-PEEM images at these fields. We rather think that this
difference is due to the irreproducibility of the DW motion. Also one can observe that at the
temperature of ≈ 50 K the coercivity Hc is around 6 mT which is 10 times smaller than Hc
obtained by MOKE at the same temperature. Later the sample was remeasured by MOKE to
confirm the change in the coercivity field.

MOKE after annealing

It was recognized that the coercivity measured by XMCD-PEEM (see Fig. 6.5) is 10 times
smaller compared to the MOKE measurements (see Fig. 6.2a). Also, the shape of the domain
walls suggests that the magnetization is likely to be in the IP direction. This leads to look
for the sample magnetization again by MOKE measurements in both IP and O O P direction.
Figure 6.6 shows temperature-dependent hysteresis loops measured by MOKE for IP and
O O P directions. they confirm that at low temperature the sample has an IP easy axis of

89
90 6.3. Conclusion

PEEM Imagne Brightness (arb. units)

Fe
Gd
Co

-15 -10 -5 0 5 10 15

µ0H (mT)

Figure 6.5: Local remanent hysteresis loops calculated from the field dependent PEEM images
contrast for single helicity at M 5 edge for Gd (1182.6 eV) and L 3 edges for Fe (707 eV), and Co (777.8
eV) at ≈ 50K .

magnetization since it was not possible to observe any O O P loops starting from 80 K up to
180 K (see Fig. 6.6a), and at temperature > 180 K both components can be measured up to
room temperature. This could be due to a spin reorientation transition at around Tcomp
which is reported to be 175 K (see table 6.1). The XMCD-PEEM at BESSY shows that the
coercivity at 50 K is around 6 mT (see Fig. 6.5) which seems consistent with the coercivity
of the same sample measured by O O P MOKE at 100 K (see Fig. 6.6b). This confirm our
expectation that the magnetization direction has changed during measuring MOKE for the
first time after sample fabrication. This could be due to the fact that the sample was annealed
at 400 K for 30 minutes during the first measurement, which could lead to a diffused interface
at the FeGd surface, and reduces the IP anisotropy. Den Broeder et al. [145] were reporting
an anisotropy change from IP to O O P for a Co/Au multilayer after annealing at 523 K for 30
minutes.

6.3 Conclusion
For FeGdx the Hc diverges at Tcomp . This is due to the fact that around this point the two
sublattice magnetizations cancel each other to have zero net magnetic moment [134, 142].
Tcomp was considered as the temperature at which the remanence is tending to zero.
Co/FeGdx samples at lower temperature show strongly tilted loops in polar MOKE while

90
Chapter 6. FeGd 91

(a) OoP
320 K
260 K
MOKE Signa (arb. units)

220 K

180 K

160 K

140 K

120 K
100 K

-200 -150 -100 -50 0 50 100 150 200

µ0H (mT)

(b) IP
MOKE signal (arb. units)

300 K
290 K
260 K

220 K
200 K
180 K
160 K
120 K
100 K

-60 -40 -20 0 20 40 60

µ0 H (mT)
Figure 6.6: (a) Temperature-dependent MOKE hysteresis loops of Co /FeGd25 with out-of-plane
configuration after annealing. (b) Temperature-dependent MOKE hysteresis loops of Co/FeGd25
with in-plane configuration after annealing.

91
92 6.3. Conclusion

no loops were observed IP. The extracted Tcomp are found in Table 6.1. It shows that
there is a slight reduction in the compensation temperature due to the Co evaporation.
This reduction could be due to increasing the net magnetic moment of the Fe sublattices
after Co evaporation which will lead to a reduction of Tcom . The XMCD-PEEM images
show that the Gd is aligned antiferromagnetically to Fe and Co, which was also confirmed
by the element-selective hysteresis loops measured at 50 K. This has to be the result of
a negative exchange coupling between the 4f electrons in Gd and the 3d electrons in Fe
and Co. Annealing the Co/FeGd samples during measuring temperature-dependent MOKE
leads to enhances the IP anisotropy, which can be due to a diffused interface at the FeGd
surface [145], and introduce a spin reorientation transition at around the compensation
temperature. This change in anisotropy was confirmed later by measuring IP and O O P
MOKE.

92
 Femtosecond-laser-pulse induced domain wall
7
motion in Co/FeGd

Ultimately, controlling the motion of a DW via laser pulses without electric current and field
is a key aspect that would pave the way for novel applications. The research on moving
domain walls in artificially engineered materials has experienced an increasing interest
due to their potential applications in computing technology and data storage media [32].
Up-to now DW motion has been demonstrated via field- and current-driven methods. In
2008, Uchida et al. [100] reported moving DWs by the so-called spin-dependent Seebeck
effect (SDSE), where spin currents induce a torque on the DW when propagating from one
domain to the other. This spin current is generated from a temperature gradient – due to
the difference in the conducting electron’s Seebeck coefficients [100]. This phenomenon is
spectacular because this pure spin current is generated without any electric currents over
long distances in the magnetized film [146].
Although this phenomenon extensively investigated, the theoretical understanding of
the underlying mechanisms is still under strong debate since there are contradictions
between the two theoretical models that exist to explain the DW motion by the spin-Seebeck
effect (SSE) [101, 147–155]. The first are the thermodynamic theories (TDT) – which
consider the magnetic DWs as thermodynamic objects moving due to the entropy force
and free energy. These theories conclude that the DW must move toward the regions with
higher temperature while still being far below (TC ) [101, 147–152]. The second model
depends on microscopic magnonic calculations, like the linear momentum transfer theory
and the microscopic angular momentum transfer theory. In these theories, the spin-wave
reflection was considered when dominating, which leads to DW motion against the heat
flow [153–158].
In this chapter, one example of laser-induced DW motion is presented in Co/FeGd as
a ferromagnetic (FM)/ ferrimagnet (FIM) system, where single laser pulses can move DWs
away from the heated region, at a distance of around 1 µm away from the laser pulse towards
the colder region of the sample. The underlying mechanisms of this DW motion will be

93
94 7.1. Domain wall motion in Co/FeGd

Fe Gd

(1.148 , 1.062) mm
PEEM Imagne Intensity (arb. units)

(1.263 , -1.813) mm

(0.957 , 1.051) mm

(0.667 , 1.497) mm

-15 -10 -5 0 5 10 15 -15 -10 -5 0 5 10 15

µ0H (mT) µ0H (mT)

Figure 7.1: Fe hysteresis loops for positive helicity at the Fe L 3 edge with beam energy 707 eV and Gd
hysteresis loops at the Gd M 5 edge at 1182.6 eV obtained at different positions.

discussed in the frame of spin- dependent Seebeck effect. This was done by estimating
the temperature gradient within the spatial profile of the laser pulse and checking if this
temperature gradient is sufficient to generate a spin transfer torque (STT) to move this DW
or not.

7.1 Domain wall motion in Co/FeGd

The X-PEEM chamber at the UE-49 beamline at BESSY II is equipped with a Femtolasers
Scientific XL Ti:sapphire oscillator. This Femtolaser produces pulses with a repetition rate
of 5 MHz and a pulse width from 60 to 500 fs at a central wavelength of 800 nm. In this
experiment, the pulse width was adjusted to 100 fs, with a maximum energy per pulse of 300
nJ. To perform single-shot experiments, the laser system was combined with a Femtolasers
Pulsefinder and set to single shot. With this setup it is possible to select any repetition rate
ranging from 5 MHz down to a single shot. XMCD-PEEM was used to achieve magnetic
contrast and laser sensitivity. The XMCD-PEEM measurements were performed in an
applied magnetic field with a magnetic sample holder (Fig. 2.5).
Figure 7.1 shows the hysteresis loops obtained for positive helicity at the Fe L 3 edge at 707
eV and at the Gd-M 5 edge at 1182.6 eV for different positions. Comparing the loop shift we

94
 Chapter 7. Laser induced Dw motion in Co/FeGd 95

0 100 200 300 400 500

0

40

80

120

7000 160

200

240
units)

280

6000
320

360
(a.u)

400
(arb.

440

480
Intansity

5000
Intensity

onside the
Co XAS Outside thelaser
laserspot
spot
4000

3000
inside the
Co XAS Inside the laser
laser spot

775 780 785 790 795 800

Photon energy
Enargy (eV) (eV)
Figure 7.2: Comparing XAS for Co signal inside #, and outside # the laser spot after 1000 laser pulses
trains, the inset is the XMCD image

can see there are different offset fields changing with the image position. For the DW-motion
experiment the data in Fig. 7.1 was used to estimate the field gradient (µ0 ∂H /∂r ) in the field
of view used (20 µm). µ0 ∂H /∂r was calculated by considering the loop shift at different
positions and dividing it by the distance between these position. It was found that at the
center of the sample holder the value of µ0 ∂H /∂r ≈ 1.7 × 10−3 mT/µm. This value is reduced
as we move further from the center of the sample holder. This field gradient could be due to
the coil remanence or the objective lens of PEEM which has a uniform magnetic field, but
this value is very small and can be neglected inside the field of view. Nonetheless, it was then
essential to measure hysteresis loops for large movements of the sample to correct the field
applied during the scan. Consequently, in this chapter, whenever it is mentioned that the
applied field is zero, this is after correcting for the offset field corresponding to the position
(maximumly was 0.1 mT).

The laser enters the chamber from one side toward the sample holder at a grazing
incidence angle of 16°and the x rays illuminate from the opposite side under the same angle
with both overlapping at the sample surface. The x rays have a spot size (FWHM) of about 20
× 30 µm and a duration of about 50 ps. The laser was focused by an optical lens inside the
vacuum chamber to a spot size of 10 × 3.5 µm (at 1 e 2 ) on the sample. The overlapping
±

of the laser and the x rays can be confirmed by imaging the laser-excited three-photon
photoemission at hot spots at the sample surface. To tune the flux density, a combination of
a λ 2-plate and a polarizer were used. This allowed the fluence, from 0 to 60 mJ/cm2 . The
±

95
96 7.1. Domain wall motion in Co/FeGd

0 100 200 300 400 500 0 100 200 300 400 500 0 100 200 300 400 500
0 0 0

40 a) 40 b) 40 c)
80 80 80

120 120 120

160 160 160

200 200 200

240
1 240 240

280 280 280

320 320 320

360 360 360

400 400 400

440 440 440

480 480 480

0 100 200 300 400 500 0 100 200 300 400 500
0 100 200 300 400
0 0 500

d) f)
0
40 40
40 g)
80 80
80
120 120
120
160 160
160
3
200 200
200
240
1 240
240
280 280
280

2
320 320

360 360
2 320

360
400 400
400
440 440
440
480 480
480

Figure 7.3: (a) Gd XMCD-PEEM images. At the initial position, laser is at position 1 (b,c) and (d) after
first, second, third laser pulse. (f) Domain walls after 10 pulses with the laser at position 2. (g) Domain
wall after 10 pulses with the laser at position 3.

numbers specified in the following always refer to the fluence in the center of the spot on the
sample. The laser power used in this work was adjusted to avoid damaging the sample with a
single pulse. To investigate the effect of the number of pulses on the sample, different pulse
sequences were tested which all had the same pulse energy. It was found that when the laser
setting was changed to a pulse train of more than 7 pulses, the DW randomly moved. This is
probably due to the rapid increase of the local temperature, which increases the mobility of
the DW. Increasing the number of pulses, to pulse trains of around 100 to 1000 pulses, the
sample temperature increases to the extent that the Co evaporated. Figure 7.2 shows a burnt
area after 1000 laser pulses withe 38.7 mJ/cm2 . The XAS inside the burnt area shows that the
Co signal is significantly reduced compared to the XAS outside the burnt area.

Later, the sample was pumped by a linearly polarized femtosecond single laser pulse of
38.7 mJ/cm2 in PEEM and the magnetic domains, probed by XMCD-PEEM. Overall, the DW
was moving as a consequence of the laser pulse. In figure 7.3, two DWs were brought to

96
Chapter 7. Laser induced Dw motion in Co/FeGd 97

15.5
Laser 3 x = 18.8 µm
15.0

14.5

14.0

13.5

13.0
Position (µm)

12.5
Laser
12.0
1
5.8 x = 9.0 µm
5.6
5.4
5.2
5.0 Laser position
4.8 Right domain wall
4.6 Left domain wall
4.4
4.2 Laser 2 x = 0.8 µm

0 2 4 6 8 10 12 14 16 18 20 22
Number of Laser Pulses

Figure 7.4: Domain wall displacement of the two domain walls in Fig. 7.3 by laser pulses at positions
1, 2, and 3. The x’s values are the positions of the laser pulse center, under zero magnetic field.

the field of view by tuning the magnetic field. Then, the laser was adjusted to be almost in
the middle of the two DW (at position 1 in Fig. 7.3a). Later, the sample was subjected to
the single laser pulses and XMCD images were collected after every successive laser pulse.
The collected XMCD-PEEM images are shown in figure 7.3b, c and d. Then, the laser spot
was positioned at position 2 as shown in Fig. 7.3d, and the DW was exposed to a series of 10
single pulses while Gd-PEEM images were collected. The Gd XMCD-PEEM image after this
laser pulse series is presented in figure 7.3f. Finally, the same experiment was repeated with
the laser at position 3 (figure 7.3g).

Figure 7.4 depicts the laser-induced DW motion with respect to the position obtained
from a linescan along the blue line in Fig. 7.3a. The DW on the right started at 5.5 µm and on
the left started at 13.1 µm. These original positions are marked by yellow lines in Fig. 7.3a-f.
After each laser pulse at position 1, the two DW moved away from the original position by
about 0.8 µm and 0.9 µm for the right and left DW, respectively. After the laser spot was
moved to position 2, the right DW moved towards its original position. After the laser pulses,
the final positions exhibited a total displacement of about 1.6 µm and zero µm for the right

97
98 7.1. Domain wall motion in Co/FeGd

0 50 100 150 200 250 300 350 400 450 500

0
1.8 1.8

50
20

100
µm
Domain wall motion ( x) (µm)

150

& first derivative (arb. units)

1.6

200
1.6
250
Domain wall motion (µm)

Laser profile intensity

300
1.4

Laser intensity (a.u.)

0
350

1.4
400

1.2
450
500

1.2
1.0

Displacement
0.8 Laser profile
1.0 Laser profile first derivative
0.6
0.8
0.4

0.6
0.2
Displacement
Laser profile
0.4
0.0
Laser profile
0 2 4 6 8 10 12 14 16 18 20
first derivative
0.2 Position (µm)

0.0
0 4 8 12 16 20
Position (x) (µm)
Figure 7.5: DW motion within the laser pulses under 4 mT. The inset is the start DW image. The blue
line is the reference line for position calculation. The red ellipse is shows the laser spot.

and left DW respectively (orange and green lines at Fig. 7.3f. Finally, the laser was moved into
position 3 to move the left DW back to its original position. However, the left DW was pinned
at some defect, and did not move further. It seems that this place is energetically favorable
for the DW, since it was pinned at the upper edge of the field of view and oscillated between
the green and orange lines in Fig. 7.3g. The DW moves until it reaches a position where the
laser power density is not enough to move it any more.

Further testing of the DW motion was done, with the effect of the laser pulse being
examined under an applied field Bext around 4 mT. This field encourages the growth of
the black domains in the positive helicity images to move from right to left in the XMCD
image. The DW was brought into the field of view and adjusted at the edge of the laser spot
as explained before. The DW was adjusted such that the field applied is assisting the DW
movement towards the laser pulse. The pulse was kept at the same fluence as before (38.7
mJ/cm2 ). A series of single-pulse cycles were pumped into the sample and directly after
every pulse, images were collected. In figure 7.5 inset the starting DW image is presented.
The DW position along the blue line after every pulse is plotted on the x-axis. The laser
spot profile was obtained, as explained before in section 3.4.1 figure 3.7, and plotted as a red
line and its first derivative as a green line. Then the DW displacement on the blue line was
calculated between every two successive images and plotted on the y axis. By comparing
those displacements to the laser profile, one can see that the biggest movement is around

98
Chapter 7. Laser induced Dw motion in Co/FeGd 99

the highest laser profile gradient. This gives an indication that these DW motions could be
due to the temperature gradient.
To move a DW, one needs to exert a torque on the magnetization to manipulate
the electron spin orientation. That could be done by an external magnetic field or by
spin-polarized current [159]. Here the movement of the DWs is only affected by the
laser pulse since the magnetic field was set to zero. That gives an indication of the
existence of spin-polarization generated by the laser pulse. In the case here, a spin current,
propagating in the sample to produce a torque on the DW to move it, should be robust
enough to propagate the DW up to ≈ 4 µm far from the center of the laser spot. In
principle, the spin-polarized current induced by the femtosecond laser pulse could come
from super-diffusion [160]. However, the lifetime of such current is less than 1 ps [160]. If
this model is considered with a fastest DW motion observed till now [161], both will lead to
a maximum mean free path of around 5 nm. One needs spin-polarized currents running for
at least 1 ns to have DW motion at that relatively far distance.
The other possibility is reported by Sandig et al. [162]. The laser-induced depinning of
DW could be reducing the energy barrier for thermal activation. After the DW is depinned,
it could travel by thermal activation over a lower potential landscape until it reaches another
strong pinning site. This could be over longer time scales and relatively low velocities. Also,
in this case the laser fluence is less important and the activation by the base temperature
comes into play. This mechanism cannot fully explain our result since our sample was cooled
down to 50 K, which makes any point outside the laser spot more likely to be pinned than
inside the laser. Here we report systematic DW motion toward, the cooled area with and
without magnetic field. If this mechanism is taken into account, that means all movement
should be constrained by the laser pulse profile and might prefer to move toward the area
with less pinning (hotter region) [149]. However, the depinning of the DW by the laser pulse
can not be excluded, but the direction of the DW motion in the case presented here is not
only due to different pinning properties.
Another mechanism is the existence of spin accumulation in the ferromagnet due to a
temperature gradient. The spin accumulation is defined as spin dependent Seebeck effect
(SDSE) which was firstly observed by Uchida et al. [100] in ferromagnetic material. In
this possibility, the sample was in a temperature gradient which leads to the spin-up and
spin-down moving to opposite ends according to the spins directions. This spin-dependent
diffusion creates a spin accumulation in both ends which can be measured by inverse Hall
effect. Nevertheless, it has been shown that this mechanism alone cannot explain the SSE in
a magnetic insulator, because the absence of conduction electrons [163, 164]. Later, it was
suggested that the SSE is carried by magnons in what is here called spin magnonic Seebeck
effect (SMSE) [165]. Here the possibility of having SDSE will be checked by estimating
the temperature gradient and the corresponding spin current produced in the Co/FeGd25
sample.

99
100 7.2. Two temperature model for multilayer (TTM)

7.2 Two temperature model for multilayer (TTM)

The plausibility of the SDSE hypothesis simulation of the vertical heat flow within the
sample was examined by the two temperature model (TTM) up to the nanosecond time
range. The TTM assumes that the electronic system absorbs the laser pulse within a few
femtoseconds. Then, the energy is swiftly thermalized in the conduction band by diffusing
hot electrons. These hot electrons transfer their energy through electron-phonon coupling
to the crystal. This leads to a temperature increase in a few picoseconds[96]. We start this
from a one-dimensional TTM to investigate the ultrafast laser-material interaction within
the multilayer z direction [91, 93–95, 97–99], using equation (3.14) and (3.15) in Section 3.4.1.
The latin numbers I to V in figure 3.6 are indexes of the layers and refer to 8 Å Pt, 10 Å Co, 150
Å FeGd, 10 Å Pt, and SiO substrate, respectively.

Table 7.1: The parameters used to solve the two-temperature model.

Element Lattice Electron Initial electron Electron lattice

heat capacity heat capacity thermal conductivity coupling factor at
(C l ) coefficient (γ) coefficient (k e ) room temperature
(G 0 )
(J/(m3 K)) (J/(m3 K2 )) (W/(m K)) (J/(m3 sec K))
Pt [166] 2.85×106 750 71 109×1016
Co [166] 2.07×106 662 100 4.05×1018
FeGd [167] 1.8×106 600 80.4 1.7×1018

Table 7.2: Calculated complex refractive index (n + i k).

Material Refractive index n Extinction coefficient k

Pt 2.858 4.962
Co 2.488 4.803
FeGd25 2.66 3.6
SiO 1.4533 0

The values of the lattice heat capacity C l , the electron heat capacity coefficient γ, initial
electron thermal conductivity coefficient k e , and the electron- lattice coupling factor at
room temperature G 0 are given in table 7.1. The complex refractive index (n + i k) was
calculated to get the refractive index n and the extinction coefficient k for every layer by using
IMD-software [168] and recheck the output against the electronic data base available online
at (http://www.refractiveindex.info) [169]. Table 7.2 shows the values of (n) and (k) which are
calculated for the corresponding thicknesses used in our film. To obtain the R I as function
of layers, the values of n and k in table 7.2 were used as the input for the matrix formulation

100
Chapter 7. TTM 101

4 0 0
1 0 5 0

2 0 0 P t
P t C o
F e G d 2 5

1 0 0 8 5 0
8 0
6 0

T e m p e r a tu r e (K )
4 0
T im e (p s )

6 5 0

2 0
4 5 0
4
2
1
2 5 0

5 0
0 2 0 4 0 6 0 8 0 1 0 0 1 2 0 1 4 0 1 6 0
D e p th (A n g s tro m )

Figure 7.6: Time history of lattice temperature profile for film depth, with fluence = 38.7 mJ/cm2 .

equation (3.9). These values were used to calculate S I (z, t ) in every layer (see eq. (3.17)).
Later, all of the data was used to calculate the temperature as a function of z and t up to 550
ps. The MATLAB code used for this calculation is listed in Appendix 8. Figure 7.6 shows the
time evolution of the lattice temperature at the center of the laser pulse as a function of z.
One can see the Co layer has the highest temperature which goes up to ≈ 1125 K in 0.9 ps and
starts to drop to ≈ 200 K in around 1 ns. The different temperature at various layers is due to
the differences in heat conductivity of every material. This high temperature could explain
why Co is removed after the multi-pulse experiment in figure 7.2. To get more familiar with
the temperature distribution inside the multilayer, the time regime at 0.9 ps was extracted,
at which the maximum lattice temperature is observed in Fig. 7.7.
Since the DW moves laterally, the temperature distribution in the lateral direction was
also estimated. The resulting parameters from the Gaussian shape of the laser pulse are
used to calculate the power profile inside the laser pulse which is then used to evaluate the
fluence at every point and then to determine the temperature as a function of x and y inside
the laser pulse at every layer. The x-direction is chosen to be with the DW motion. Figure 7.8
shows the lattice temperature profile in the x-direction for every interface. The maximum
lattice temperature is at the Pt/Co interface, which around the center of the laser pulse
reaches Tlmax =1125 K. The lateral temperature gradient at this interface is around 5T xmax =
178 ×106 K/m. Figure 7.9 shows the time evolution of the lattice temperature at the different

101
102

@ 0 .9 p s
1 2 0 0
P t/C o
C o /F e G d
1 0 0 0
F e G d /P t
T e m p e ra tu re (K )

8 0 0

6 0 0

4 0 0

2 0 0

0
0 2 0 4 0 6 0 8 0 1 0 0 1 2 0 1 4 0 1 6 0 1 8 0 2 0 0
D e p th (A n g s tro m )

Figure 7.7: Lattice temperature profile at z direction at 0.9 ps, with fluence = 38.7 mJ/cm2 .

interfaces, which indicates that the multilayers start to have the same temperature at around
250 ps. After 5 ns the multilayer temperature drops to around 200 K. This gives a temperature
gradient around 25 ×106 K/m at 5 ns.
Out of this temperature gradient calculation, one can see that the maximum spin current
generated by the temperature gradient will come from the Pt/Co interface. For using
equation (3.25) discussed in section 3.5, for the Pt/Co interface σ↑↓ is found to be 2.7×106
σ↑ S ↑ −σ↓ S ↓
Ω−1 m−1 , and σ↑ +σ↓ ≈ 5 µ V K−1 , as reported by Choi et al. [103]. That gives a maximum
estimated spin current density J Smax at 0.9 ps of ≈2.4×107 A/m2 , which is gradually dropping
to ≈ 3.4 ×106 A/m2 at 5 ns.
It is noted that the current density produced from the calculated model is four orders of
magnitude less than the reported spin current density needed for switching DW in metallic
films, which is in between 1011 and 1012 A/m2 [7, 170–172]. A temperature gradient can
produce this SDSE, but also a SMSE [101, 147, 165]. This can explain the long displacement
of DW movement [165]. Moreover, it can explain the direction of the DW motion toward
the cooled region, since the hotter region has higher magnon density, which will diffuse in
the direction of the cooler region [147]. The SMSE, used only to explain the DW motion
in magnetic insulators where there is no chance to have charge assisted DW motion, and

102
Chapter 7. TTM 103

1 2 0 0 1 0 0 0 @ P t/C o

T e m p e ra tu re (K )
1 0 0 0 5 0 0
T e m p e ra tu re (K )

8 0 0 0
0 2 0 0 0 4 0 0 0

T im e (p s )
6 0 0
@ 8 A P t/C o in te r fa c e
@ 1 8 A C o /F e G d in te r fa c e
4 0 0 @ 1 6 8 A F e G d /P t in te r fa c e

2 0 0

0
0 1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5 1 6
x (µ m )

Figure 7.8: Lattice temperature profile in x-direction at 900 fs. The inset shows the time evolution of
the lattice temperature profile for the Pt/Co interface up to 5 ns, with fluence = 38.7 mJ/cm2 .

1 2 0 0
T e m p e ra tu re (K )

1 0 0 0

1 0 0 0
5 0 0
T e m p e ra tu re (K )

8 0 0
0
0 1 2
6 0 0 T im e (p s )
P t/C o
4 0 0 C o /F e G d
F e G d /P t

2 0 0

0
0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 5 0 4 0
T im e (p s )

Figure 7.9: Time history of the lattice temperature profile for the different interfaces, with fluence =
38.7 mJ/cm2 .

103
104 7.3. Conclusion

is disregarded in metallic films, where it must exist in addition to the charge-based spin
current. Since magnons carry angular momentum, the magnon diffusion will be most likely
more effective in the lateral directions [147, 165]. Hence in ferromagnetic metals, one should
expect both types of spin Seebeck effect. That means the magnonic spin current should be
considered in moving the DW under a temperature gradient even in the case of a metal films,
since it is indistinct how big the two contributions are.

7.3 Conclusion
In conclusion, a DW motion induced by a femtosecond laser pulse in Co/FeGd25 is
presented, which moves the DW as far as 4 µm from the center of the laser spot. This DW
motion could be adequately controlled in the absence of magnetic pinning centers. This
movement at this distance cannot be explained by only considering the spin diffusive current
even with estimating the highest possible DW speed. To move the DW in the µm regime, one
needs the current to run for at least 5 ns. The expected model is the thermally assisted DW
motion, where a spin accumulated current could transfer and produce that DW propagation.
A simulation of the sample temperature under a fluence of 38.7 mJ/cm2 shows that the
maximum temperature gradient that can be obtained is found at the Pt/Co interface. At
around 5 ns it could produce electronic spin currents by SDSE up to ≈2.4 ×107 A/m2 , which
is four orders of magnitude less than expected to move DW by STT [7, 170–172]. Including
the magnonic spin current generated by the SMSE with the SDSE might explain both the
high diffusion lengths and the direction of the DW motion reported in this thesis [147].

104
 Summary and conclusion
8
The magnetic properties of NiMn as an antiferromagnet (AFM) and FeGd as a ferrimagnetic
material (FIM) were reported in this work. All of the AFM films were grown and studied
under ultra high vacuum (UHV) conditions with a base pressure of 2×10−10 mbar. The
AFM material was chosen to be Nix Mn(100−x) in thin film form in contact with a Ni single
layer in exchange-biased bilayers and then sandwiching the Nix Mn(100−x) films between two
ferromagnetic (FM) Ni layers in exchange-biased trilayers on Cu3 Au(001). Since the AFM
material has net zero magnetic moment, this makes it difficult to measure its properties.
This is why an indirect method is used to test the effect of these materials on a FM material.
The Ni films were grown in a layer-by-layer fashion with a p(1×1) crustal structure on
the Cu3 Au(001) substrate. The structure and the magnetic properties of the Ni films were
investigated and it was found that a spin reorientation transition (SRT) from in-plane (IP)
to out-of-plane (O O P) takes place between 7 ML and 8 ML, and it was identified to be due
to structural relaxations at this thickness. Longitudinal and polar magnetization loops were
observed with almost identical shape but double the coercivity at 7 ML up to 15 ML Ni. The
temperature-dependence of both IP- and OoP-magnetization of Ni was studied, and it was
found that hysteresis loops in both cases have the same features. Therefore angle-dependent
magneto-optical Kerr effect (MOKE) measurements were required to determine the easy
axis of Ni magnetization. These measurements were used to estimate the anisotropy
constants, K1 and K2 . With the help of the Stoner-Wohlfarth model (SW) model a simulation
was done using the experimental data for 12 ML Ni/Cu3 Au(001). The value of K1 and K2
were found to be −36 ± 2 × 103 J/m3 and 77 ± 2 × 103 J/m3 , respectively. The high value of K2
might be the origin for the continuous transition from IP to O O P magnetization for the 12
ML Ni/Cu3 Au(001).
Nix Mn(100−x) ultrathin films were grown on Ni/Cu3 Au(001). A change in the Curie
temperature (Tc ) of the Ni layers due to the Nix Mn100−x over-layer was observed to be a
function of NiMn composition and NiMn thickness. The Mn-rich overlayers of NiMn cause
a lowering of the Tc , which is attributed to the tendency for the antiferromagnetic order of
Mn. While the Ni-rich overlayers slightly increase the Tc , which is probably a consequence

105
106

of induced ferromagnetic order in Nix Mn100−x close to the interface with Ni. All these
interpretations are related to direct Ni–Ni, Ni–Mn, and Mn–Mn exchange interactions. A
higher number of Ni–Ni interactions in the vicinity of the interface with the ferromagnetic
Ni layer would increase the Tc of the latter, while a higher number of Ni–Mn interactions
decreases Tc .
Furthermore, the magnetic interlayer coupling across the Nix Mn100−x as an AFM spacer
layer was investigated using MOKE. The effect of an O O P-magnetized top Ni layer on an
O O P-magnetized bottom Ni layer through the Nix Mn100−x was studied, by changing the top
layer thickness (τ) for different Nix Mn100−x thicknesses with x ≈ 25%. There is an increase
of T AF M with increasing AFM layer thickness. An existence of two steps in the loops of such
trilayers depends on the coercivity of the top and the bottom layers. Since the coercivity is
enhanced by the coupling with the AFM layer, the appearance of the second step depends
also on the direct exchange coupling with the AFM layer. In general, it was found that
the reversal of the soft layer is dragged by the harder layer through the domain wall (DW)
switching.
Later, the magnetic interlayer coupling was investigated by measuring minor loops
using MOKE for 14 ML Ni/45 ML Ni25 Mn75 /16 ML Ni. The minor loop measurements
were used to calculate coupling strength (J) and assigned the negative value to antiparallel
coupling and positive for parallel coupling. It was reported for this sample that the
interlayer coupling changes from ferromagnetic to antiferromagnetic at T > 300 K. This
sign change is interpreted as the result of the competition between an antiparallel
Ruderman-Kittel-Kasuya-Yosida (RKKY)-type interlayer coupling, and a stronger direct
exchange coupling across the AFM layer.
The FIM material samples were fabricated in a cluster system consisting of a magnetron
sputter deposition and a surface analysis chamber with base pressure of 1×10−8 mbar.
The FIM material was chosen to be Fe(100−x) Gd(x) . Two series of Fe(100−x) Gd(x) films were
grown, one with 10 Å Co on top and the other without Co. The magnetic properties of the
Fe(100−x) Gd(x) and Co/Fe(100−x) Gd(x) samples were investigated in relation to the Fe/Gd ratio,
x. x was chosen to be 15, 25, and 30, since FeGd films with a Gd concentration of around
20% show perpendicular uniaxial magnetic anisotropy and, at this range, they are FIM with
a relatively high magnetic compensation temperature.
For FeGdx, the remanence converges to zero and coercivity (Hc ) diverges at
compensation temperature (Tcom ). This is due to the fact that around this point the
two sublattices magnetization cancel each other out to have zero net magnetic moments.
The easy-axes of magnetization for the Fe(100−x) Gd(x) were found to be O O P-magnetized
samples. The Tcom was defined as the temperature at which the remanence is tending to
zero. The Co/FeGdx after annealing at 400 K shows an SRT as temperature dependent with
O O P at high temperature and IP at low temperature. This SRT starts to occur at around
Tcom . This change due to annealing might occur due to the diffused interface at the FeGd

106
Chapter 8. Summary and conclusion 107

surface which forms after annealing. The extracted Tcom found for FeGdx and Co/FeGdx
samples shows that there is a slight reduction in the compensation temperature due to
the Co overlayer. This reduction is due to the rise of the net magnetic moment of the Fe
superlattices after Co evaporation which leads to a reduction for the Tcom . The XMCD-PEEM
images show that the Gd is aligned antiferromagnetically to Fe and Co, which was also
confirmed by the element selective hysteresis loop measurements at 50 K. This clearly occurs
as a result of the negative exchange coupling between the 4f(5d) electrons in Gd and the 3d
electrons in Fe and Co.
Furthermore, the DW motion on the Co/Fe75 Gd25 sample was tested by a single
femtosecond laser pulse. Single laser pulses were moving the DWs in Co/Fe75 Gd25 at a
distance of around 4 µm away from the center of the laser pulse towards the colder region
of the sample. This DW motion could be adequately controlled in the absence of magnetic
pinning centers. The underlying mechanisms of this DW motion were discussed in the frame
of thermally assisted DW motion, where a spin accumulated current could transfer and
produce that DW propagation. The temperature gradient within the laser pulse profile was
estimated and spin dependent Seebeck effect (SDSE) was calculated at the Pt/Co interface.
This is why it was recommended to include the spin magnonic Seebeck effect (SMSE) with
the SDSE, which might explain both the far away DW motion and its’ direction.

107
 Erklärung

Die Arbeit ist nicht schon einmal in einem früheren Promotionsverfahren angenommen
oder als ungenügend beurteilt worden. Hiermit versichere ich, dass ich die Arbeit
selbstständig verfasst und keine anderen als die angegebenen Quellen und Hilfsmittel
genutzt habe.

Berlin, 2016

Yasser Shokr
 List of publications

Paper during PHD thesis

• Shokr, Y. A.; Erkovan, M.; Wu, C.-B; Zhang, B.; Sandig, O. ; Kuch, W.;
’Temperature-induced sign change of the magnetic interlayer coupling in
Ni/Ni25 Mn75 /Ni trilayers on Cu3 Au(001)’ Journal of Applied Physics, Volume 117,
Issue 17, 04 May 2015, Pages 175302. http://dx.doi.org/10.1063/1.4919597

• Sandig, O.; Shokr, Y. A.; Vogel, J.; Valencia, S.; Kronast,F.; Kuch, W.; ’Movement of
magnetic domain walls induced by single femtosecond laser pulses’ Physical Review
B 94, 054414 – Published 11 August 2016. http://dx.doi.org/10.1103/PhysRevB.
93.054428

• Hagelschuer, T.; Shokr, Y. A.; Kuch, W.; ’Spin-state transition in antiferromagnetic

Ni0.4 Mn0.4 films in Ni/NiMn/Ni trilayers on Cu(001)’ Physical Review B 93, 054428 –
26 February 2016. http://dx.doi.org/10.1103/PhysRevB.93.054428

• Erkovan, M.; Shokr, Y. A.; Schiestl, D.; Wu, C.-B; Kuch, W.; ’Influence of Nix Mn1−x
thickness and composition on the Curie temperature of Ni in Nix Mn1−x /Ni bilayers on
Cu3 Au(001)’ Journal of Magnetism and Magnetic Materials, Volume 373, 1 January
2015, Pages 151–154. http://dx.doi.org/10.1016/j.jmmm.2014.02.017
112

Paper in preparation

• Shokr, Y. A.; Erkovan, M.; Vogel, J.; Ünal A.; Sandig, O.; Kronast,F.; Kuch, W.;
’Temperature gradient generated by femtolaser pulse induces Domain Wall Motion’.

Paper during Master thesis

• El-Hagary, M.; Shokr, Y. A.; Emam-Ismail, M.; Moustafa, A.M.; Abd El-Aal, A.;
Ramadan, A.A.; ’Magnetocaloric effect in manganite perovskites La0.77 Sr0.23 Mn(1−x)
Cu( x) O3 (0.1≤ x≤ 0.3)’ Solid State Communications, Volume 149, Issue 5, February
2009, Pages 184-187. http://dx.doi.org/10.1016/j.ssc.2008.11.023

• El-Hagary, M.; Shokr, Y. A.; Mohammad, S.; Moustafa, A.M.; Abd El-Aal, A. ; Michor,
H.; Reissner, M.; Hilscher, G.; Ramadan, A.A.; ’Structural and magnetic properties of
polycrystalline La0.77 Sr0.23 Mn(1−x) ( x) O3 (0≤ x≤ 0.5) manganites’ Journal of Alloys
and Compounds, Volume 468, Issue 1, 22 January 2009, Pages 47-53. http://dx.doi.
org/10.1016/j.jallcom.2008.01.048

112
Appendix

113
 Technical modication

Angle-dependent MOKE mirrors holder.

This is the mirror holder system designed for MOKE experiment to allow changing the
mirror tilting angle. By the help of the right mirror tilting angle one can keep the angle
between the light and the sample fixed and change the sample angle to the field to perform
angle-dependent MOKE.

Sample Mirrors
Mirrors
holder

Hall sensor

Figure A.1: Mirror holders designed to perform Angle-dependent MOKE.

115
116

Magnetic Core for the MOKE-II chamber.

This is a magnetic core designed to perform MOKE under UHV condition.

Hall
Magnetic sensor
Core

Figure A.2: Magnetic Core for MOKE-II chamber.

Relay circuit digram.

This is the circuit designed to control two relays, which allowed us to switch the polarity of
the magnet power supply by the help of ± 5 V from PNC cable.

116
Chapter 8. List of publications 117

Figure A.3: Relay Circuit design for the magnet power supply.

117
Determination of T AF M and Teb

180

160 Hc

140

120

100 TAFM
Hc (mT)

80

60

40

20

-14
-20

HBe
-12

-10

-8
Heb (mT)

Tb
-6

-4

-2

2
260 280 300 320 340 360 380 400 420 440 460

Temperature (K)

Figure A.4: The determination of T AF M and Tb .

119
 Magnetic sample holder

Magnetic flux simulation for the photoemission electron microscopy (PEEM) sample holder,
To show the magnetic field flux line at 1 mm over the sample holder. If the sample is 0.5 mm
off from the center of the sample holder both IP and O O P magnetic field component will be
existed.

core

0 0.5 1 1.5
Distance from the sample holder center (mm)

Figure A.5: Magnetic flux simulation for the PEEM sample holder.

121
 X-ray absorption spectroscopy for Fe, Co, and Gd

Figure A.6: XAS and XMCD for Fe, Co, Ni, and Gd pure metals, figure from Stöhr and Siegmann [64].

Figure A.7: Comparison between XAS for Fe, Co, Ni (pure material) and there oxides, figure from Stöhr
and Siegmann [64]

123
 Matlab codes

Matlab code for two-temperature model (TTM)

The detail of the equations were discussed at section 3.2, the equation used
are equations (3.14), (3.15),(3.17), (3.19), (3.20), (3.21), and (3.22)

125
function L18APt

close all;

global kin1 kin2 kin3 kin4 gama1 gama2 gama3 gama4 Gin1 Gin2 Gin3 Gin4 uin1 Cl4
global Ab1 Ab2 Ab3 Ab4 Ab5 F1 alpha1 tp1 Cl1 Cl2 Cl3 L1 L2 L3 L4

%Pt input data%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

L1=0.8*10^-9; %Thickness of thin layer (m)
kin1=71; %initial Electron thermal conductivity
cofficient (W/m-K)
gama1=750; %Electron heat capacity coefficient (J/(m^3
K^2))
Cl1=2.85*10^6; %lattice heat capacity (J/(m^3 K))
Gin1=109*10^16; %Electron lattice coupling factor at rom
temperature (J/(m^3 Sec K))
%Co input data%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
L2=1*10^-9; %Thickness of thin layer (m)
kin2=100; %initial Electron thermal conductivity
cofficient (W/m-K)
Cl2=2.07*10^6; %lattice heat capacity (J/(m^3 K))
Gin2=4.05*10^18; %Electron lattice coupling factor at rom
temperature (J/(m^3 Sec K))
gama2=662; %Electron heat capacity coefficient (J/(m^3
K^2))
%FeGd input data%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
L3=15*10^-9; %Thickness of thin layer (m)
kin3=80.4; %initial Electron thermal conductivity
cofficient (W/m-K)
Cl3=2.2*10^6; %lattice heat capacity (J/(m^3 K))
Gin3=4.05*10^18; %Electron lattice coupling factor at rom
temperature (J/(m^3 Sec K))
gama3=670; %Electron heat capacity coefficient (J/(m^3
K^2))
%Pt layer input data%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%the same data used from layer 1
%SiO supestrate input data.%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
L4=100.4*10^-9; %Thickness of thin layer (m)
kin4=1.4; %initial Electron thermal conductivity
cofficient (W/m-K)
Cl4=1.9*10^6; %lattice heat capacity (J/(m^3 K))
Gin4=4.05*10^18; %Electron lattice coupling factor at rom
temperature (J/(m^3 Sec K))
gama4=733; %Electron heat capacity coefficient (J/(m^3
K^2))
%absorption data.%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Ab1=0.0328; %8 A Pt Absorption
Ab2=0.0373; %10 A Co Absorption
Ab3=0.2924; %150A FeGd 25Absorption
Ab4=0.0197; %10 A Pt Absorption
Ab5=0.0820; %0,5 mm SiO Absorption

126
%laser data%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
F1=4.982498179; %Fluance (J/m^2)
alpha1= 15.3*10^-9; %pentration depth (m)
tp1=100*10^-15; %Full Width at Half-Maxmum (FWHM)
(sec)
%initial temperatuer%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
uin1=50; %(K)
%grid information%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
xend=L1+2*L2+L3+L4; %Maximum lenghth (m)
tend=1*10^-9; %Final time (Sec)
xpoints=10^4; %Number of point in x direction
tpoints=10^4; %Time of point in x direction
%vector to solve%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
m = 0; %cartiziean cordinat (x,t)
x = linspace(0,xend,xpoints); %vector in x dirction (start,
end, number of point)
t = linspace(0,tend,tpoints); %vector in t dirction (start,
end, number of point)
sol = pdepe(m,@pdex6pde,@pdex6ic,@pdex6bc,x,t);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%n12=exp(-x/alpha1); % distance atenation factor.
%w12=exp(-2.773*(t-(2*tp1)).^2/tp1.^2); % time atenation factor
%S=0.939*Ab1*F1*n12.*w12/(tp1*alpha1)*2.2*10^-19; % laser as heating source
gaussian temporal profile.
% Extract solutions components.%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
TE= sol(:,:,1); %Extracte Temperature of Electron
Data
TL= sol(:,:,2); %Extracte Temperature of Lattice
Data
TEM=max(max(TE)); %Extracte Maxmum Electron
Temperature
TLM=max(max(TL)); %Extracte Maxmum Lattice
Temperature
%save data%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
save(sprintf('run1nano-295.mat'));
save TE-X0295.dat TE -ascii
save TL-X0295.dat TL -ascii
%load('runxtherdtime080.mat')
% Electron Temperature Solution and lattice temperature at endtime.%%%%%%%%
%figure, plot(x,TE1(end,:));hold on;plot(x,TL1(end,:))
%title(strcat('Electron Temperature Solution and lattice temperature at t = ',
num2str(tend)))
%xlabel('Distance x (m)')
%ylabel('Temperature (K)')
%Plot surface temperature vs. time%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%figure, plot(t,TE(:,1));hold on;plot(t,TL(:,1))%;hold on;plot(t,S)
%title('Surface Temperature')
%xlabel('Time (sec)')
%ylabel('Temperature (K)')
%Plot surface temperature vs. time%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%figure, plot(t,S)

127
%title('Surface Electron Temperature')
%xlabel('Time (sec)')
%ylabel('Temperature (K)')
%figure,plot(t,TL(:,1))
%title('Surface Lattice Temperature')
%xlabel('Time (sec)')
%ylabel('Temperature (k)')
%Plot contor plot for temperature (x vs t)%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%figure,
%contour(x,t,TL1,'ShowText','on')
%title('Contour plot for lattice temperature depth profile')
%xlabel('depth (m)')
%ylabel('time (sec)')
% --------------------------------------------------------------

function [c,f,s] = pdex6pde(x,t,u,DuDx)

global Gin1 gama1 ke1 F1 Cl1 alpha1 tp1 Laser1 EF1 deltT1 kin1 n1 w1 EF3 Laser2
Laser3 Laser4
global Ab1 gama2 Cl2 ke2 kin2 Gin2 EF2 L1 L2 gama3 Cl3 ke3 kin3 kin4 Gin4 gama4
Gin3 L3 Ab2 Ab3 Ab4 EF4
global deltT2 deltT3 deltT4 ke4 Cl4

if x <=L1;

c =[gama1.*u(1); Cl1];

ke1= kin1.*u(1)./u(2); % electron heat

condactivity as function of temperature
f =[ke1; 0.01*kin1].*DuDx;

deltT1= u(1)-u(2); % Temperature diffrent.

EF1=Gin1.*deltT1; % electron lattice
coupling factor as function of temperature diffrent on the laser term.
n1=exp(-x/alpha1); % distance atenation
factor.
w1=exp(-2.773*(t-(2*tp1))^2/tp1^2); % time atenation factor
Laser1=0.939.*Ab1.*F1.*n1.*w1/(tp1.*alpha1); % laser as heating source
gaussian temporal profile.
s =[Laser1-EF1;EF1];

elseif L1<x&&x<=L1+L2;

c =[gama2.*u(1); Cl2];

ke2= kin2.*u(1)./u(2); %electron heat

condactivity as function of temperature
%electron lattice
coupling factor as function of temperature diffrent on the laser term.
f = [ke2; 0.01*kin2].*DuDx;
deltT2= u(1)-u(2); % Temperature diffrent.
EF2=Gin2.*deltT2;

128
 n1=exp(-x/alpha1); % distance atenation
factor.
w1=exp(-2.773*(t-(2*tp1))^2/tp1^2); % time atenation factor
Laser2=0.939.*Ab2.*F1.*n1.*w1/(tp1.*alpha1); % laser as heating source
gaussian temporal profile.

s =[Laser2-EF2;EF2];

elseif L1+L2<x&&x<=L1+L2+L3;

c =[gama3.*u(1); Cl3];

ke3= kin3.*u(1)./u(2); %electron heat

condactivity as function of temperature
f = [ke3; 0.01*kin3].*DuDx;

deltT3= u(1)-u(2); % Temperature diffrent.

EF3=Gin3.*deltT3; %electron lattice
coupling factor as function of temperature diffrent on the laser term.
n1=exp(-x/alpha1); % distance atenation
factor.
w1=exp(-2.773*(t-(2*tp1))^2/tp1^2); % time atenation factor
Laser3=0.939.*Ab3.*F1.*n1.*w1/(tp1.*alpha1); % laser as heating source
gaussian temporal profile.

s =[Laser3-EF3;EF3];
elseif L1+L2+L3<x&&x<=L1+2*L2+L3;
c =[gama1.*u(1); Cl1];

ke1= kin1.*u(1)./u(2); % electron heat

condactivity as function of temperature
f =[ke1; 0.01*kin1].*DuDx;

deltT4= u(1)-u(2);
EF4=Gin1.*deltT4;
n1=exp(-x/alpha1); % distance atenation
factor.
w1=exp(-2.773*(t-(2*tp1))^2/tp1^2); % time atenation factor
Laser4=0.939.*Ab4.*F1.*n1.*w1/(tp1.*alpha1); % laser as heating source
gaussian temporal profile.

s =[Laser4-EF4;EF4];
else

c =[gama4.*u(1); Cl4];

ke4= kin4.*u(1)./u(2); % electron heat

condactivity as function of temperature
f =[ke4; 0.01*kin4].*DuDx;

deltT4= u(1)-u(2);

129
 EF4=Gin4.*deltT4;
n1=exp(-x/alpha1); % distance atenation
factor.
w1=exp(-2.773*(t-(2*tp1))^2/tp1^2); % time atenation factor
Laser4=0.939.*Ab4.*F1.*n1.*w1/(tp1.*alpha1); % laser as heating source
gaussian temporal profile.

s =[Laser4-EF4;EF4];
end
% --------------------------------------------------------------

function u0 = pdex6ic(~)
global uin1

u0 = [uin1;uin1];

% --------------------------------------------------------------

function [pl,ql,pr,qr] = pdex6bc(~,~,~,~,~)

pl = [0;0];
ql = [1;1];
pr = [0;0];
qr = [1;1];

% --------------------------------------------------------------

Published with MATLAB® R2015a

130
Chapter 8. List of publications 131

Matlab code for Stoner Wohlfarth Model (SW).

The detail of the equations were discussed at section 3.4.1, the equation
used are equations (3.5), (3.6), (3.7), and (4.1)

131
%read data
format long
filename = 'C:\Users\Admin\Dropbox\hossam_yasser\matlab SW\data for 90\90.dat';
delimiter = '\t';
formatSpec = '%f%f%[^\n\r]';
fileID = fopen(filename,'r');
dataArray = textscan(fileID, formatSpec, 'Delimiter', delimiter, 'ReturnOnError', fa
lse);
fclose(fileID);
H = dataArray{:, 1};
D = dataArray{:, 2};
clearvars filename delimiter formatSpec fileID dataArray ans;

% generate Monte Carlo models

MCSIZE=10; % Monte Carlo steps. 10 for just Publish probably 10,000 is enough.

%Array models will hold the estimated variables

%col1 col2 col3 co4 col5
%k1 k2 r1 r2 ssq=(sum of squared erros)
models = zeros(MCSIZE,5);

%extracting data and solve

for j=1:MCSIZE
fprintf('Monte Carlo step %d out of %d\n',j,MCSIZE);
C1= unifrnd(0,0.1);
C2= unifrnd(0,0.1);
R1= 0.0166;
R2= R1*10;
alpha=pi/2;
ssq=0.0;
A=0;
for i=1:size(H,1)

syms x;
h=H(i);
Ex= 2*C1*sin(x)*cos(x) + 4*C2*sin(x).^3*cos(x) - h*sin(alpha-x);
xm=double(solve(Ex == 0, 'Real', true));
xm_pi = xm(xm <= pi/2 & xm >= 0.0);
Exx = 2*C1*cos(x).^2 - 2*C1*sin(x).^2 - 4*C2*sin(x).^4 + h*cos(alpha - x) + 12*C2
*cos(x).^2*sin(x).^2;
Exxm=subs(Exx, xm_pi);
ind1=find(Exxm>0);
xm1=xm_pi(ind1);

if(size(xm1,1) > 1)
A=2;
if A==2
fprintf('more than 1 xm SSQ: %f.\n',ssq);
fprintf('%f %f %f %f %f\n\n', A,C1,C2,R1,R2);
end
break;
end

A=0;
Dg= R1*cos(xm1)*cos(pi/4)+R2*sin(xm1)*sin(pi/4); % clculated data

132
 ssq = ssq + (D(i)-Dg).^2; %sum of squared erros f
or all values
end
if A==0
fprintf('Found good MC model with SSQ: %f.\n',ssq);
fprintf('%f %f %f %f %f\n\n', A,C1,C2,R1,R2);
end
% Lsqu=sum(deltasqu);
models(j,1)=C1;
models(j,2)=C2;
models(j,3)=R1;
models(j,4)=R2;
models(j,5)=ssq;

end

%find model with least RMSD

[minval, minidx] = min(models(:,5));
%models(minidx,1);

% output parameters of best model and display histogram of all models' ssq
disp ('C1:'), disp (models(minidx,1));
disp ('C2:'), disp (models(minidx,2));
disp ('R1:'), disp (models(minidx,3));
disp ('R1:'), disp (models(minidx,4));
disp ('RMSD:'), disp (sqrt(models(minidx,5)));
hist (models(:,5), 30);
%save data as text withe this format
%col1 col2 col3 co4 col5
%k1 k2 r1 r2 ssq
dlmwrite('Mymodel1000-04-12-01-2015.txt',models,'-append','delimiter','\t')

Monte Carlo step 1 out of 10

Found good MC model with SSQ: 0.024845.
0.000000 0.060284 0.071122 0.016600 0.166000

Monte Carlo step 2 out of 10

Found good MC model with SSQ: 0.003129.
0.000000 0.022175 0.011742 0.016600 0.166000

Monte Carlo step 3 out of 10

Found good MC model with SSQ: 0.003159.
0.000000 0.029668 0.031878 0.016600 0.166000

Monte Carlo step 4 out of 10

Found good MC model with SSQ: 0.012644.
0.000000 0.042417 0.050786 0.016600 0.166000

Monte Carlo step 5 out of 10

Found good MC model with SSQ: 0.001248.
0.000000 0.008552 0.026248 0.016600 0.166000

Published with MATLAB® R2013a

133
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 Acknowledgments

I would like to express my sincere gratitude to my advisor Prof. Dr. Wolfgang Kuch not
only for the successfully supervised this work, his competence, knowledge, and his ability to
discuss physical problems down to the very details were for me precious, but also for opening
an opportunity for me to work in his group and for giving me the freedom to realize many of
the experiments I was dreaming up.

Besides my advisor, I would also like to thank Prof. Dr. Holger Dau for being my second
advisor and offering me opportunity for discussing with him about my thesis, and his time
to write a reports and recommendations for me every year.

On the domestic front, encouragement always came from my parents, my in-laws, my

brothers and my sisters, but most important, from my lovely wife, Amany, who cheerfully
stood by me throughout, and did a wonderful job raising up our kids Abdelrahman, Mariam
and Menatullah, at times when I was far too busy to contribute more than a few hours a day.
I want to thank my friend Associated Prof. Dr. Mustafa Erkovan, he is just like a brother for
me, I never knew the meaning of unconditional support until we work together. Thanks for
promoting me the FeGd samples, and establishing the fruitful collaboration with Prof. Dr.
Osman Öztürk in Gebze, Istanbul, Turkey.

I am deeply indebted to Dr. Matthias Bernien for his help during all stages of this work,
and my best friend Dr. Hossam Elgabartiy for his insightful comments, discussions and
supports. My sincere thanks also go to Prof. Dr. Chii-Bin Wu whom teach me as a beginner
in the lab. I was lucky to learn from him when he was post Dr. in Ag. kuch. I owe them a
lot, and to Olivar Sandig, and Dr. Bin Zhang my friends and Co-partner who join with me
the beam times and facing up the hard times together. Working at a synchrotron is always
156

a matter of team work, many people are needed to operate the beamline, and carry out the
measurements. I want especially to thank the UE49-SPEEM beamline scientist: Dr.Florian
Kronast, Dr. Akin Ünal, and Dr. Sergio Valencia Molina.
I would like to also thank deeply my four musketeers, Daniela Schiestl (Diploma), Till
Hagelschuer (Bachelor and Master), Patrick-Axel Zitzke (Bachelor), and Silvio Künstner
(Bachelor), who we were together fought our way through many problems in the chamber,
carrying out repairs of the equipment on the fly, fighting with leaks, the noise in the MOKE,
preparing films, and collecting data. All of you are somebody to count on. I enjoyed our
discussion about physics and other stuffs.
I appreciate and thank for the great help from Ms. Marion Badow, and Mr. Hans Badow
for all supports me from my first days in the group until now.
Great thanks also goes to Dr. Yaqoob Khan, and Dr. Yin-Ming Chang for their friendship,
for guiding me through MOKE lab in my first day, and supporting me by the all means
whenever i need help. For my roommate Fabian Nickel, he was always there for helping,
supporting, and discussing not only about physics and technical aspects but also in all life
fields, it was my honor to share with him the office. Many thanks goes to eng. Uwe Lipowski
about the technical supports, his smart ideas and the wonderful designs which helped me a
lot to finish this work, and Dr. Julia Kurde for guiding me and introducing me to the X-PEEM
experiment in my first days, and Dr. Andrew Britton for his final revise of some parts of the
thesis. I want to express my sincere thanks for all members of Kuch research group in Berlin
great thanks to Dr. Barbra Sandow, Dr. Felix Hermanns, Dr. Alex Krüger, Dr. Jiaming
Song, Lalminthang Kipgen, Lucas Arruda, and Tauqir Khan for the great teamwork and the
excellent atmosphere.
I also want to thank Detlef Müller at Feinwerktechnik, Martin Rust and Wolfgang
Schimank at Fachabteilung Elektronik, and Cihan Dede at Materiallager for their help
during my Ph.D project.
I appreciate the financial support from Ministry of Higher Education of the Arab Republic
of Egypt (MoHE) and the Deutscher Akademischer Austauschdienst (DAAD) for supporting
me four years in Berlin.

Yasser Shokr

156