Measurements of Linear and Circular Birefringence in ... · Optically induced transient linear and...

Measurements of Linear and Circular

Birefringence in Metals by Femtosecond

Optical Pump-Probe Spectroscopy

by

Ralph Wilks

Submitted to the University of Exeter as a thesis

for the degree of Doctor of Philosophy in Physics,

December 2002.

This thesis is available for the library use on the understanding that it is copyright

material and that no quotation from the thesis may be published without proper

acknowledgment.

I certify that all material in this thesis which is not my own work has been identified

and that no material has been previously submitted and approved for the award of

a degree by this or any other university.

ii

Fur meine Eltern

Acknowledgements

First of all I like to thank my supervisor Dr. Rob Hicken for giving me the oppor-

tunity to conduct this interesting and exciting research project in his group. I am

extremely grateful for the large amount of time and interest he continuously dedi-

cated to support and discuss my research. My further thanks go to the former group

members Mr. Norman Hughes and Dr. Jing Wu for welcoming me and helping me

settle quickly in both the new workplace and the new country, and to Dr. David

Schmool who has been a very good colleague and friend. Thanks to all the other

members of my group who kindly granted me support and help.

I like to acknowledge the valuable support of the whole staff of the School of

Physics. I experienced friendlyness and helpfulness beyond what I believe can usu-

ally be expected. Special mentioning deserve the research technicians Mr. Melvyn

Gear and Mr. Russel Edge as well as Mr. Kevyn White in the main workshop who

made and mended countless bits of equipment. Thanks also to all other members

of the mechanical end electrical workshops. A special mention deserves the “cheese

and wine” gang: Mr. Kevyn White, Mr. Pete Cann, Mr. Dave Jarvis, Mr. John

Meakin and Miss Karen Gannon. You guys thoroughly improved my colloquial En-

iii

ACKNOWLEDGEMENTS iv

glish. Pete deserves further thanks for introducing me to the delights of Dartmoor

walking and Karen for being that “mad cow” with the big heart!

A big hug goes to my perpetual lunch date and founder of the interdisciplinary

“phud support group”, Mrs. Rosemary Baines in the Maths department. Thanks

for distracting and motivating me again, again and yet again. Good luck with

your PhD! Many thanks to all the other mad folkies of the Exeter Univerity Folk

Society. Here I found the right environment to relax from and find new energy for

my work. Thanks also to all the friends and nice people I met in the International

Society, Globe Cafe, Guild of Students and various other university organisations

who helped making Exeter a home to me. Special mention for friendship and support

deserve Mrs. Anna-Sophia Alklind Taylor, Miss Ginni Lam, Mr. Roger Barden, Mrs.

Rosemary and Mr. Simon Bourne, Miss Jenny Sibbons and Mr. Christian “Bobby”

Bopf. And Miss Jo Robinson who boosted my motivation for writing up during the

final weeks.

Back home in Germany I wish to thank my friend Dr. Petra Maier who strongly

encouraged me to take up this doctoral study abroad. And last but not least I like

to thank my family, especially my parents and my sister, who always supported me

and who I missed a lot during those years.

My final thank goes to the Engineering and Physical Sciences Research Council

(EPSRC) for funding my research and my studentship.

Abstract

Optically induced transient linear and circular birefringence has been studied in

three different materials: ferromagnetic Ni, semiconducting GaAs and the non-

magnetic metal Al. A pump-probe experiment with sub-ps resolution was set up

for this purpose. The time-resolved reflectivity, rotation and ellipticity of the re-

flected probe beam were recorded after pumping with light of variable helicity. In

the Ni sample an ultrafast demagnetisation effect was observed and the variation

of the rotation and ellipticity on sub-picosecond time scales was compared. Rota-

tion and ellipticity were found to have a similar time dependence. In GaAs, optical

orientation of spin was achieved and the subsequent spin relaxation was measured

for different pump powers. Fitting of the optical rotation data has revealed the

power dependence of the various decay constants. In the Al sample a small sig-

nal was observed that decays on ps time scales. This was attributed to a linear

birefringence effect resulting from a cubic optical nonlinearity. In all three samples

the dependence of the birefringence upon the pump polarisation was studied. A

sharp peak was observed at zero delay with a width that was determined by the

laser pulse width. The peak observed in GaAs showed a behaviour characteristic

v

ABSTRACT vi

of the specular inverse Faraday effect (SIFE, a circular birefringence), while that of

Ni and Al is characteristic of a combination of the SIFE and the specular optical

Kerr effect (SOKE, a linear birefringence). The Al measurements also showed a tail,

that decays within a few ps, and that is characteristic of the SOKE. It is suggested

that a lattice excitation provides the most likely mechanism for the long-lived lin-

ear birefringence. No clear evidence was found for optical orientation of spin in Al

although a small but poorly resolved tail in the ellipticity data gives an indication

of the existence of such an effect.

Contents

Acknowledgements iii

Abstract v

Contents vii

List of Figures xi

List of Tables xv

1 Introduction 1

2 Background 6

2.1 Electronic Structure and Magnetism . . . . . . . . . . . . . . . . . . 6

2.2 Time-Resolved Measurement Techniques . . . . . . . . . . . . . . . . 14

2.2.1 Magneto-Optical Kerr Effect . . . . . . . . . . . . . . . . . . . 15

2.2.2 Second-Harmonic Generation . . . . . . . . . . . . . . . . . . 18

2.2.3 Two-Photon Photoemission . . . . . . . . . . . . . . . . . . . 20

2.3 Ultrafast Electron and Spin Dynamics . . . . . . . . . . . . . . . . . 21

vii

CONTENTS viii

2.3.1 Electron and Lattice Dynamics . . . . . . . . . . . . . . . . . 21

2.3.2 Ultrafast Demagnetisation Effects . . . . . . . . . . . . . . . . 28

2.3.3 Spin Orientation and Spin Relaxation . . . . . . . . . . . . . . 33

2.3.4 Transient Linear and Circular Birefringence . . . . . . . . . . 37

2.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

3 Experimental Methods 43

3.1 Optical Pump-Probe Set-Up . . . . . . . . . . . . . . . . . . . . . . . 43

3.1.1 General Description of the Set-Up . . . . . . . . . . . . . . . . 44

3.1.2 Detailed Descriptions of Selected Components . . . . . . . . . 49

3.1.3 Measuring the Time-Resolved Signals . . . . . . . . . . . . . . 60

3.2 Pulse Width Control and Measurement . . . . . . . . . . . . . . . . . 66

3.2.1 Group Velocity Dispersion (GVD) . . . . . . . . . . . . . . . . 66

3.2.2 Pulse Width Measurements . . . . . . . . . . . . . . . . . . . 67

3.2.3 GVD Compensation . . . . . . . . . . . . . . . . . . . . . . . 70

3.3 The Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

4 Ultrafast Demagnetisation in Nickel 76

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

4.2 Experiment and Results . . . . . . . . . . . . . . . . . . . . . . . . . 77

4.2.1 Static Hysteresis Loops . . . . . . . . . . . . . . . . . . . . . . 77

4.2.2 Time-Resolved Reflectivity and Magnetisation Measurements . 80

4.2.3 Dynamic Hysteresis Loops . . . . . . . . . . . . . . . . . . . . 84

CONTENTS ix

4.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

5 Circular Pump in GaAs, Ni and Al 90

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

5.2 Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

5.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

5.3.1 Gallium Arsenide . . . . . . . . . . . . . . . . . . . . . . . . . 94

5.3.2 Nickel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

5.3.3 Aluminum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

5.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

5.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

6 Al SIFE and SOKE Measurements 114

6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

6.2 Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

6.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

6.3.1 Reflectivity Data . . . . . . . . . . . . . . . . . . . . . . . . . 117

6.3.2 Rotation and Ellipticity Data . . . . . . . . . . . . . . . . . . 125

6.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

6.4.1 Reflectivity Data . . . . . . . . . . . . . . . . . . . . . . . . . 138

6.4.2 Rotation and Ellipticity Data . . . . . . . . . . . . . . . . . . 140

6.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

CONTENTS x

7 Summary 143

Bibliography 150

List of Figures

2.1 Temperature dependence of the magnetisation . . . . . . . . . . . . . 9

2.2 Typical hysteresis loop . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.3 Magnetisation of a single crystal . . . . . . . . . . . . . . . . . . . . . 11

2.4 Spin-split density of states of Ni . . . . . . . . . . . . . . . . . . . . . 14

2.5 Definition of the rotation Θ and ellipticity η . . . . . . . . . . . . . . 16

2.6 MOKE geometries . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.7 The time-resolved two-photon photoemission process . . . . . . . . . 20

2.8 Electronic band structure of Al . . . . . . . . . . . . . . . . . . . . . 26

2.9 Electronic band structure of GaAs . . . . . . . . . . . . . . . . . . . . 34

3.1 Set-up of the optical pump-probe experiment . . . . . . . . . . . . . . 45

3.2 CCD camera and lenses for sample observation . . . . . . . . . . . . . 48

3.3 Expansion and focusing optics . . . . . . . . . . . . . . . . . . . . . . 51

3.4 Autocorrelator set-up . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

3.5 Field calibration of the electromagnet . . . . . . . . . . . . . . . . . . 59

3.6 Probe polariser and detector alignment . . . . . . . . . . . . . . . . . 65

xi

LIST OF FIGURES xii

3.7 Calculated fringe-resolved autocorrelation curves . . . . . . . . . . . . 71

3.8 Example of a measured fringe-resolved autocorrelation curve . . . . . 72

3.9 Calibration of the autocorrelation curves . . . . . . . . . . . . . . . . 72

3.10 Chirp compensation with Brewster prisms . . . . . . . . . . . . . . . 73

3.11 Pulse width for different prism spacings . . . . . . . . . . . . . . . . . 75

4.1 Ni: Static hysteresis loop (rotation) . . . . . . . . . . . . . . . . . . . 78

4.2 Ni: Static hysteresis loop (ellipticity) . . . . . . . . . . . . . . . . . . 79

4.3 Ni: Calculated MOKE rotation and ellipticity . . . . . . . . . . . . . 79

4.4 Ni: Time-dependent reflectivity change . . . . . . . . . . . . . . . . . 81

4.5 Ni: Ultrafast demagnetisation signal for up to 30 ps . . . . . . . . . . 82

4.6 Ni: Ultrafast demagnetisation signals close to zero delay . . . . . . . 83

4.7 Ni: Comparison of the reflectivity and average sum signals . . . . . . 84

4.8 Ni: Dynamic hysteresis loops for different time delays . . . . . . . . . 85

4.9 Ni: Comparison of the rotation and ellipticity signal . . . . . . . . . . 87

5.1 GaAs: Rotation signal for linear and circular pump . . . . . . . . . . 94

5.2 GaAs: Reflectivity change and rotation for different pump intensities 96

5.3 GaAs: Fitted rotation parameters for varying pump intensity . . . . . 97

5.4 GaAs: Angular dependence of the rotation peak height . . . . . . . . 98

5.5 Ni: Reflectivity and rotation for circular pump . . . . . . . . . . . . . 99

5.6 Ni: Static hysteresis loop (rotation) . . . . . . . . . . . . . . . . . . . 100

5.7 Ni: Rotation signal for circular pump in a transverse field . . . . . . . 102

LIST OF FIGURES xiii

5.8 Ni: Angular dependence of the rotation peak height . . . . . . . . . . 103

5.9 Al: Reflectivity and MOKE rotation close to zero delay . . . . . . . . 104

5.10 Al: Reflectivity and MOKE rotation up to 80 ps . . . . . . . . . . . . 105

5.11 Al: Angular dependence of the rotation peak height . . . . . . . . . . 106

6.1 Al: Pump power dependence of reflectivity and rotation . . . . . . . . 118

6.2 Al: Reflectivity and rotation signals for linear pump . . . . . . . . . . 119

6.3 Al: Reflectivity and ellipticity signals for linear pump . . . . . . . . . 120

6.4 Al: Reflectivity and rotation signals for elliptical pump . . . . . . . . 121

6.5 Al: Reflectivity and ellipticity signals for elliptical pump . . . . . . . 122

6.6 Al: Exponential decay of the reflectivity signal . . . . . . . . . . . . . 123

6.7 Al: Angular dependence of the reflectivity peak height . . . . . . . . 124

6.8 Al: Reflectivity scans for linearly s-polarised probe . . . . . . . . . . 125

6.9 Al: Rotation signal for linear pump up to 60 ps . . . . . . . . . . . . 126

6.10 Al: Ellipticity signal for linear pump up to 60 ps . . . . . . . . . . . . 126

6.11 Al: Rotation signal for elliptical pump up to 60 ps . . . . . . . . . . . 128

6.12 Al: Shapes of the ellipticity signal for different elliptical pump polar-

siations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

6.13 Al: Ellipticity signal for elliptical pump up to 60 ps . . . . . . . . . . 130

6.14 Al: Fitted parameters for rotation measurements with linear pump

polarisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

6.15 Al: Fitted parameters for ellipticity measurements with linear pump

polarisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

LIST OF FIGURES xiv

6.16 Al: Fitted parameters for rotation measurements with elliptical pump

polarisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132

6.17 Al: Fitted parameters for ellipticity measurements with elliptical

pump polarisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132

6.18 Method for separating the SIFE and the SOKE . . . . . . . . . . . . 136

6.19 Al: Separation of SIFE and SOKE in the ellipticity signal . . . . . . 137

List of Tables

6.1 Al: SIFE/SOKE fits . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

xv

Chapter 1

Introduction

A fundamental understanding of spin dynamics including the knowledge of spin

relaxation times is essential in the rapidly growing data storage and telecommu-

nications industries. In magnetic storage devices the storage density continues to

grow rapidly and as the bit size decreases the read and write transducers must also

become smaller. New technologies have been incorporated such as read heads using

sensors based on the Giant Magneto-Resistance (GMR) effect where spin relaxation

effects play an essential role and relaxation times need to be known. New electronic

devices such as the spin-valve transistor also incorporate spin effects into traditional

electronics and make use of spin relaxation effects. The speed of recording is also a

critical issue. Presently the reorientation of magnetisation in the recording medium,

in write heads and in the sense layer in the spin valve sensor are limited by the time

required for precessional motion. There is great potential to speed up recording by

using intense laser pulses to demagnetise the storage medium and then reverse it

1

CHAPTER 1. INTRODUCTION 2

in an external field while the electron system cools. This could reduce write times

in magneto-optical technologies by 3 orders of magnitude moving them into the fs

regime. In the telecommunications industry, and especially within fibre optics, new

fast optical devices are sought, and the incorporation of magnetic devices could

lead to new capabilities such as the direct integration of the communication and

information storage functions.

The aim of this research project was to study demagnetisation processes and

spin dynamics on sub-picosecond time scales by means of an optical pump-probe

experiment. At the beginning of the project in 1999 the ultrafast demagnetisation

effect in ferromagnets had recently been discovered in Ni samples (1; 2) and only a

few other materials such as CoPt3 (3; 4) had been studied. Theoretical investigation

of the effect had only just begun (5; 6). The ultrafast demagnetisation was attributed

to the creation of a hot electron distribution in which spin relaxation may occur

many orders of magnitude faster than by lattice heating. It was not clear what

mechanism coupled the laser field to the spin system and whether a separate spin

temperature should to be assigned for the hot electrons in addition to the electronic

temperature. There were conflicting reports about whether the demagnetisation

occured within the electron thermalisation time or after a longer delay. During

the present project more published reports contributed to our understanding of the

effect but more questions also arose. For example some doubts arose as to whether

the effects observed in magneto-optical studies were purely due to magnetic effects.

Time-resolved magneto-optical Kerr effect (MOKE) (7; 8) and Magnetic Second-


Harmonic Generation (SHG) measurements (9) indicated that other contributions

to the signal arose from modification of the optical constants on time scales less than

500 fs. It seemed that such effects might reduce the usefulness of these techniques

for magnetic studies. Nonmagnetic samples were also examined in the past. For

example spin orientation and relaxation in GaAs were systematically studied at

room temperature using a pump-probe apparatus (10). Other effects such as an

ultrafast collapse of the band structure in Al due to ultrafast heating of the electron

system were observed (11). A more thorough review of these studies will be given

in the chapter 2. Some of these findings stimulated further research and influenced

the course of the present study.

Within this research project a pump-probe experiment was set up for the mea-

surement of ultrafast changes in the reflectivity and the magneto-optical response

of samples after excitation with intense unltrashort laser pulses. The experimental

apparatus will be described in detail in chapter 3 along with some techniques for its

alignment. Particularly important for the success of this project were the focusing

and overlapping of the pump and probe spots in order to achieve a sufficient pulse

energy for the sample excitation. Also the control of the pulse width was essential

and a fringe-resolved autocorrelator was set up to measure the pulse width.

The original aim of this project was to measure ultrafast demagnetisation effects

in ferromagnetic samples. Initial measurements were performed on a Ni sample and

the results are presented in chapter 4. This sample had been studied before by others

but some questions remained unanswered. After the first successful observation of


the effect in measurements of the optical rotation signal, it was then of interest to

determine whether a difference could be observed between the rotation and ellipticity

signals obtained from the Ni sample on sub-picosecond time scales. Also dynamic

hysteresis loops were taken in order to examine the effect of the static applied field

upon the transient optical response.

The question then arose as to whether it was possible to affect the demagnetisa-

tion signal by using a circularly polarised pump beam to control the spin orientation

of the excited electrons. Similar control of spin orientation in semiconductors had

previously been studied by means of the Hanle effect and more recently by optical

pump probe experiments. In chapter 5 the experiment was modified to allow exci-

tation with an elliptically polarised pump and measurements were performed on the

Ni sample. The next question to be addressed was whether the experiment could be

used to create a non-equilibrium spin orientation in a non-magnetic metal and mea-

sure its subsequent decay. It seemed likely that a metal with an interband transition

would be required and Al seemed to be a good candidate with parallel bands leading

to a strong absorption peak close to 800 nm. At first such measurements were made

upon GaAs. The dependence of the magneto-optical rotation signal upon the pump

power and the pump polarisation was investigated. Then measurements were made

with elliptical pump polarisation upon the Al sample. Finally the response of the

magneto-optical rotation of the probe beam in all three samples was compared.

Initial observations of a long-lived optical rotation signal from the Al sample

after excitation with elliptically polarised light was first thought to be the result of


a spin orientation that decayed on ps time scales. However, it was than found that

the dependence upon the pump polarisation was instead characteristic of a laser

induced linear birefringence effect. In chapter 6 a systematic approach was taken

to fully charaterise the contributions of the specular optical Kerr effect (SOKE, a

linear birefringence effect) and the specular inverse Faraday effect (SOKE, a cir-

cular birefringence effect) to the reflectivity signal and the magneto-optical signal.

From these measurements both non-vanishing components of the cubic nonlinear

susceptibility tensor of Al were calculated.

Finally in chapter 7 the results and conclusions from the experimental chapters 4-6

will be summarised and some suggestions will be given for possible further research

within this area.

Chapter 2

Background

In this chapter a short introduction of the theoretical background relevant to the

experiments will be given. After a brief introduction into the electronic structure

and the origin of ferromagnetism the Magneto-optical Kerr effect will be introduced

being the main experimental technique used. Afterwards a review of the rapidly

growing field of ultrafast electron and spin dynamics will be given. This has to be

limited to aspects relevant to this project. Also some formulae for the description of

the observed transient effects will be introduced for the later use in the experimental

chapters.

2.1 Electronic Structure and Magnetism

Within the class of condensed matter, different solids can exhibit very different op-

tical, electrical and magnetic properties. They are determined by the electronic

stucture of the material which is determined by the Coulomb interaction in com-

6

CHAPTER 2. BACKGROUND 7

bination with the Pauli exclusion principle. The Pauli exclusion principle does not

allow two electrons (Fermions) to occupy identical states within the electronic sys-

tem. In condensed matter this leads to the formation of energy bands and it also

determines the filling of the bands. The position of the Fermi edge (upper band

filling level at 0 K) within the band structure determines different classes of conduc-

tors: insulators, semiconductors and metals. In metals the Fermi edge lies within

a partly filled band (conduction band) so that an electrical field can easily excite

the electrons and cause an electrical current. Semiconductors and insulators have

the Fermi edge in between a filled valence band and an empty conduction band. In

semiconductors the band gap is small enough to allow electrons from the valence

band to be thermally or optically excited into the conduction band so that electrical

conduction becomes possible. Insulators have a band gap too big to allow those

transitions and cannot conduct electrical currents.

In addition to the electrical properties, condensed matter can exhibit a variety

of different magnetic properties. The magnetization M of a sample is defined as

the ratio of the magnetic moment of a small volume devided by the volume. The

magnetic induction is B = H + 4πM . If M is parallel to the magnetic field H then

the magnetic susceptibility χ is defined by M = χH . All materials exhibit diamag-

netic behaviour for which −1 < χdia < 0. This can be understood qualitatively by

considering Lenz’s law: If the electrons in the atomic orbitals are considered as a

current loop, then applying an external field will change the flux through the loop

and this will induce a current in such a direction that its magnetic field opposes the


original field. As a consequence, the resulting magnetic induction is reduced or even

zero as in superconductors. If the material posesses a net spin angular momentum

per atom, the diamagnetic response may be smaller than the additional paramag-

netic or ferromagnetic effects. In paragnetic substances external fields can align

the magnetic moments and the magnetisation will be proportional to the applied

field. Many substances follow the Curie-Weiss law with 0 < χpara = CT−Θ

where

Θ is a constant. In ferromagnetic substances the magnetic moments are strongly

coupled and even small fields usually produce a much larger magnetisation than

that produced in a paramagnetic substance. Also it does not need to disappear in

a zero external field. This behaviour was phenomenologically explained by Weiss

by introducing an internal magnetic field called molecular field Hm which is respon-

sibe for aligning the magnetic moments. The thermal agitation of the atoms or

molecules acts against the ordering. Above a critical temperature TC , the Curie

temperature, the ferromagnetic order is lost and the material undergoes a phase

transition from the ferromagnetic to the paramegnetic state. Figure 2.1 shows the

relative magnetisation M(T )/M(T = 0) plotted agains the reduced temperature

T/TC . A ferromagnetic sample does not need to show a resulting magnetisation.

The magnetisation usually splits up into domains of uniform magnetisation sepa-

rated by domain walls. The magnetisations of the domains can point into different

directions can macroscopically cancel out each other so that the sample appears to

be unmagnetised. A sufficiently strong external field will align them and lead to

a resulting magnetisation. When all moments are aligned parallel to the external


Figure 2.1: The figure shows the dependence of the spontaneous magnetisation

M(T )/M(0) on the reduced temperature T/TC (taken from ref. (12)).

field then the magnet reaches its saturation magnetisation MS. The magnetisation

M plotted against the external field HExt is called hysteresis curve and is shown

in figure 2.2. Characteristic magnitudes are the saturation magnetisation MS, the

remanent magnetisation (remanence) MR in zero external field and the coercive field

HC for which the magnetisation is zero. The shape of the hysteresis loop depends

on many factors such as the reversal processes involved and the magnetic anisotropy

of the sample. Two main effects contribute to the magnetisation alignment: domain

wall movement and rotation of the magnetic moments. The latter requires more

energy and occurs at higher fields. The magnetisation process of a macroscopically

unmagnetised sample is shown schematically in figure 2.3. If the external field is big


Figure 2.2: The figure shows the magnetisation M versus an externally applied field H

(hysteresis loop). Figure taken from (13)

enough it can move domain walls and magnetic domains with magnetisation similar

to the external field will grow in favour of those of opposite alignment (2.3b). At

higher fields the magnetisation of the domains will rotate (2.3c) in order to align

the magnetic moments parallel to the external field (2.3d). The gradient of the

hysteresis curve depends on the magnetic anisotropy. The most important are the

magnetocrystalline and the shape anisotropy. The magnetocrysatlline anisotropy

results from the spin-orbit coupling. Depending on the symmetry of the crystal

the orientation of the magnetic moments along certain (“easy”) axes is energeti-

cally more favourable than along other (“hard”) axes. The shape anisotropy results

from the dipole-dipole interaction. It tries to minimise the stray fields outside the


Figure 2.3: The figure shows schematically the magnetisation of a macroscopically un-

magnetised crystal (a). At first domain walls move and domains in favour of the external

field grow, the others shrink(b). Then at higher fields the magnetisation in the domains

rotates (c) until the crystal is fully magnetised(d) (taken from (14)).

sample. For a thin film it is energetically favourable to keep the magnetisation in

plane rather than perpendicular to the plane. Further anisotropies can e.g. result

from strain in the sample, surface roughness, etc. The anisotropy of surfaces and

interfaces can differ considerably from bulk values.

The origin of the strong coupling in Weiss’ molecular field cannot be explained

by classical models. Heisenberg showed that it was a consequence of the quantum

mechanical exchange interaction. Heisenberg followed the Heitler-London method

develloped for the hydrogen molecule (see e.g. (12)). Considering two electrons

moving in the same molecular field, their wave function ψ(1, 2) has to satisfy the

equation

|ψ(1, 2)|2 = |ψ(2, 1)|2 (2.1)


since the electrons are indistinguishable. Furthermore the Pauli principle requires

the wave function to be antisymmetric in respect to exchanging their coordinates

because the probability of both electrons being at the same position at the same

time must be zero. The only possible linear combination of the single electron wave

functions ψa and ψb is:

ψanti(1, 2) =1√2

[ψa(1)ψb(2) − ψa(2)ψb(1)] . (2.2)

Single electron wave functions are products of the spatial and spin wave functions:

ψ = φ(r)χ. This allows two possible combinations for an antisymmetrical wave func-

tion: φsym(1, 2)χanti(1, 2) and φanti(1, 2)χsym(1, 2) which lead lead to the following

solutions:

ψI = A [φa(1)φb(2) + φa(2)φb(1)] [χα(1)χβ(2) − χα(2)χβ(1)] (2.3a)

ψII = B [φa(1)φb(2) − φa(2)φb(1)]

χα(1) χα(2)

χα(1)χβ(2) + χα(2)χβ(1)

χβ(1) χβ(2)

(2.3b)

ψI represents the singlet state with antiparallel spins (S=0, MS=0), ψII the triplet

state with parallel spins (S=1, MS=1,0,-1). The interaction between two hydrogen

atoms is given by the Hamiltonian

H12 =e2

rab

+e2

r12− e2

r1b

− e2

r2a

(2.4)

where rab is the distance between the nuclei, r12 is the distance between the electrons

and r1b and r2a are the distances between a given nucleus and the electron of the


other atom. The values of the additional energies due to this Hamiltonian are given

by E =∫

ψ∗H12ψdτ :

EI = A2(K12 + J12) (2.5a)

EII = B2(K12 − J12) (2.5b)

where

K12 =

∫

φ∗a(1)φ∗

b(2)H12φa(1)φb(2)dτ1dτ2 (2.6)

J12 =

∫

φ∗a(1)φ∗

b(2)H12φa(2)φb(1)dτ1dτ2. (2.7)

HereK12 is the average Coulomb interaction energy whereas J12 is called an exchange

integral and occurs as a direct result of the requirement that the electrons be indis-

tinguishable. For the hydrogen atom J12 is negative and hence in the ground state

the electrons are aligned antiparallel. In order to have ferromagnetism J12 needs to

be positive, i.e. spins parallel. This formalism can be extended to systems with more

electrons. Heisenberg’s theory requires the electrons to be localised as e.g. in rare

earths such as Gd. In the transition metals like Fe, Co and Ni the electrons respon-

sible for the ferromagnetic behaviour are itinerant. Stoner develloped a collective

electron theory calculating the interactions between the electrons of an electron gas.

The band structure diagram of the itinerant ferromagnet Ni is shown in figure 2.4.

The magnetisation results from a shift of the bands for spin up and spin down. As

a result one spin orientation (majority) is preferred to the other (minority) and the

energy dependent density of states (DOS) is different for the two spins. This affects

the absorption of electromagnetical waves associated with excitation of minority and


majority spin.

Figure 2.4: Density of states for minority and majority spins in Nickel according to

Callaway and Wang (15). Figure taken from (2)

2.2 Time-Resolved Measurement Techniques

The effects studied in this work take place on sub-picosecond time scales. Real time

measurements on these time scales are extremely difficult to perform. In order to

achieve the temporal resolution one can apply pump-probe techniques. The sample

is excited by a first ultrashort laser pulse. After a set time delay the effect to be

observed is probed by a second ultrashort laser pulse. A variety of effects can be

used to measure the changed properties of the sample. Reflectivity or transmittivity

changes or the emission of photoelectrons is used to measure changes in the electronic

population. The linear magneto-optical Kerr effect or higher order magneto-optical

effect such as second-harmonic generation as well as spin-resolved photoelectron

emission are used to measure changes in the magnetisation or spin population of

samples. Those techniques will be briefly described. The emphasis will be on the


magneto-optical Kerr effect which is the main experimental technique used in this

study.

2.2.1 Magneto-Optical Kerr Effect

In ferromagnetic substances a variety of magneto-optical effects can be observed.

The magneto-optical Kerr effect (MOKE) is observed in reflection from the surface

of a magnetised sample. When linearly polarised light is incident on a metal surface

the reflected beam is usually elliptically polarised. Only s- and p-polarised light

retain their polarisation. However, if the sample is magnetised the reflected light

will be elliptically polarised with its main axis rotated with respect to the incident

polarisation axis. The complex rotation

θ = Θ + iη (2.8)

is shown in figure 2.5. The real part Θ is the rotation of the main axis and η describes

the ellipticity. To lowest order the effect is proportional to the magnetisation M and

the rotation is typically of the order of 10−1 to 10−2 degrees for ferromagnetic bulk

samples. Figure 2.6 shows three different MOKE configurations:

polar: The sample is magnetised perpendicular to the surface. The effect is max-

imum for perpendicular incidence and vanishes for glancing incidence of the

light. The polar effect is the strongest among the three effects.

longitudinal: The sample is magnetised in the plane of the surface and in the plane

of incidence. It vanishes for perpendicular and glancing incidence and reaches


Figure 2.5: The figure shows the definition of the polarisation azimuth Θ and the ellip-

ticity angle η of elliptically polarised light wave propagating in the Z-direction (taken from

(16)).

Figure 2.6: The figure shows the three different geometries of the magneto-optical Kerr

effect: (a) polar, (b) longitudinal and (c) transverse).


its maximum for an intermediate angle depending on the material constants.

transverse: The sample is magnetised in the plane of the surface and perpendicular

to the plane of incidence. The effect can only be observed for p-polarised light.

Instead of a rotation only a magnetisation-dependent change in the intensity

of the reflected light occurs.

MOKE only probes the magnetisation in the surface region within the optical pene-

tration depth. If the sample thickness is smaller, then the effect is thickness depen-

dent. A related effect, the Faraday effect (circular magnetic birefringence), can be

observed for transmission through a magnetised sample. The magnetisation com-

ponent parallel to the direction of propagation leads to a rotation effect linear in

M .

Magneto-optical effects of ferromagnetical materials are produced by the com-

bined effect of spin-orbit coupling and exchange interaction. As shown by Argyres

(17) the resulting action on the polarisation of the electrons by an electric field can

be described by an effective magnetic field. This acts as a ‘Lorentz force’ on the

electron currents induced by the incident electromagnetic wave. A rotation of the

induced electron current results, which in turn leads to a rotation of the elctric field

vector of the reflected wave depending linearly on the magnetisation M . Argyres

calculated the rotation and ellipticity for the polar effect at normal incidence from


the Maxwell equations:

Θ = −ℑ[

N+ −N−

N+N− − 1

]

(2.9)

η = −ℜ[

N+ −N−

N+N− − 1

]

(2.10)

where

N+ −N−

N+N− − 1= −4π

σ1

ω+ iα1

(n− ik) [(n− ik)2 − 1]. (2.11)

σ1 and α1 are the off-diagonal elements of the conductivity and polarisability tensors

and linearly depend on M . N = n + ik is the complex index of refraction of the

medium in absence of any spin-orbit interaction. These equations can be used to

calculate the magnitude of the Kerr rotation and ellipticity.

MOKE can be used for time-dependent studies of ultrafast magnetisation dy-

namics. The magnetisation is influenced by excitation of the sample with an intense

femtosecond laser pulse (e.g. ultrafast demagnetisation effect). After a variable time

delay a second weaker probe laser pulse measures the magnetisation-dependent Kerr

rotation or ellipticity and hence the change in magnetisation. A review of real ex-

periments will be given in e.g. (18).

2.2.2 Second-Harmonic Generation

Similarly to the linear MOKE described in the previous section the presence of

magnetisation changes and/or the intensity of the reflected light can also be observed

in the frequency-doubled light. This effect is called nonlinear Kerr effect although to

first approximation it is also linear in the magnetisation. However, the (magnetic)


second harmonic generation [(M)SHG] is described by a third rank tensor instead

of a second rank tensor as for the linear reflected light. The nonlinear polarisation

P (2ω) induced by an incident laser field E(ω) can be written as:

P (2ω) = χ(2)E(ω)E(ω) + χ(Q)E(ω)∇E(ω) + · · · . (2.12)

The lowest order term describes an electric dipole source and vanishes in centrosym-

metric systems. Only surfaces and interfaces where the inversion symmetry is broken

contribute to the signal. The second term describes bulk quadropole-like contribu-

tions that are usually small in metals but can become important e.g. in insulating

materials and semiconductors. The presence of the magnetisation will not affect the

inversion symmetry but will introduce extra nonzero surface tensor elements which

will change sign when M is reversed:

P (2ω,±M) =(χ(2),+ ± χ(2),−)E(ω)E(ω)

+ (χ(Q),+ ± χ(Q),−)E(ω)∇E(ω) + · · · .(2.13)

The presence of the new tensor components that are odd in the magnetisation will

lead to the phenomenon of magnetisation-induced second harmonic generation. SHG

can be used in a time-resolved way similar to linear MOKE in order to measure ul-

trafast magnetisation effects. Light intensities involved in the SHG process are much

smaller and require more sensitive detection schemes but the rotation magnitudes

are usually larger than in the linear effect. For a review see e.g. chapters in (18).


2.2.3 Two-Photon Photoemission

The principle of the time-resolved two-photon photoemission (TR-2PPE) experi-

ment is schematically shown in figure 2.7. An ultrashort pump pulse excites elec-

Figure 2.7: The figure shows the time-resolved two-photon photoemission process (taken

from (19)).

trons from the valence band within the optical penetration depth. The pulse energy

has to be smaller than the vacuum energy so that one pulse alone is not sufficient to

create photoelectrons. The transient population is then probed by a delayed second

ultrashort laser pulse which promotes the still excited electrons to the vacuum where

their energy is analysed. By varying the time delay, information about the depopu-

lation time of the intermediate states is obtained. The experiment can be performed

spin-resolved in order to measure magnetic effects. For reviews of electron dynamics

in metals see e.g. (19; 20).


2.3 Ultrafast Electron and Spin Dynamics

In recent years the technological progress and the availability of femtosecond laser

systems enabled researchers to examine electron and magnetisation dynamics follow-

ing excitation by ultrashort laser pulses on sub-picosecond time scales. Consequently

new effects were discovered such as ultrafast demagnetisation effects of ferromag-

netic samples. Important parameters such as ultrashort spin relaxation times can

now be measured. This section will give an overview of recent research of electron

and spin dynamics on sup-picosecond time scales. It will focus on publications re-

lated to the materials Ni, GaAs and Al that were examined in this study. Also some

theory required for the understanding of the underlying processes will be presented

as well as equations for the analysis of the experimental data.

2.3.1 Electron and Lattice Dynamics

The excitation of solids with ultrashort laser pulses leads to a variety of effects that

are very different to excitations by cw light or longer pulses such as ns pulses. For

example in a metal, an absorbed pulse energy of 1 µJ/ps excites about one conduc-

tion electron per atom. Electron-electron collisions lead to thermalisation of the hot

electrons. The resulting “warm” electron population has a temperature that may

be very different from the lattice temperature. For a cw laser of the same average

power each excited electron forms a hot spot and cools individually and does not

interact with the hot spot of another excited electron. No collective electron tem-

perature can develop. The initial hot electron distribution leads to various effects


that have to be considered in the relaxation process (21; 22). For subpicosecond

laser pulses three time intervals have to be distinguished: (1) Immediately after

excitation the electrons are in a highly nonequilibrium state. Two competing pro-

cesses take place. One is ballistic motion of the excited electrons with velocities

close to the Fermi velocity which take them into deeper parts of the sample and

potentially out of the surface area which is probed (e.g. skin depth for reflectivity

measurements). The other more general process is the development of an electron

temperature by collisions between excited electrons and electrons around the Fermi

level. (2) Once thermal equilibrium among the electrons is reached the population

is described by a Fermi distribution and an electron temperature Te is established

that lies considerably above the lattice temperature Tl. Driven by the temperature

gradient the electrons diffuse into deeper parts of the bulk at a speed considerably

lower than the ballistic motion. The diffusion length is determined by the thermal

conductivity of the electrons κe and the electron-phonon coupling which cools the

electron bath. (3) Electrons and lattice have reached thermal equilibrium. Due to

the significantly different heat capacities of electrons and lattice the excess temper-

ature of the electrons and lattice after reaching equilibrium is generally one to two

orders of magnitude lower than the excess temperature of the electrons immediately

after thermalisation. The lattice will cool to the bulk temperature, driven by the

remaining temperature gradient and the thermal conductivity of the lattice. This

process will be slow.

The heating of the electrons and the interaction with the lattice can be described


by the two temperature model (23):

Ce(Te)dTe

dt= −Gel(Te − Tl) + P (t) (2.14a)

Cl(Tl)dTl

dt= −Gel(Tl − Te) (2.14b)

where Ce and Cl are the electronic and lattice contributions to the specific heat and

Gel describes the electron-lattice interaction. Only the electron system is excited

by the external laser pulse. By solving the system of coupled differential equations

the evolution of the electron and lattice temperature and the relaxation times and

coupling constants can be determined. Experimentally the development of the elec-

tron temperature can be measured by recording transient reflectivity or transmission

changes of the sample. In noble metals the absorbed part of the probe beam excites

electrons from the d to the s/p band. Changes in the electronic occupancy of the

target states change the reflectivity. Heating of the electrons broadens the Fermi

distribution and depletes states below the Fermi level EF and excites states above.

Depending on the wavelength of the probe this results in either a decrease of the

reflectivity (more electrons get excited into states below EF ) or an increase (less

electrons get excited into states above EF ). From the reflectivity change

∆R

R=R(Te) − R0

R0(2.15)

the electron temperature can be determined. For a variety of noble metals, such

as Au, measurements have been performed and the reflectivity spectra have been

successfully modelled (24; 21). It is more difficult for transition metals due to the

more complex band structure near the Fermi level.


The two temperature model in equation 2.14 is in its simplest form. More terms

have to be added in in order to account for additional interactions as appropriate,

e.g. a heat conductivity term to account for heat diffusion. Another effect is the

ballistic electron transport away from the excited surface region. This is negligible

in thin films but gets important for bulk samples. Some samples have a large piezo-

thermal effect. Picosecond acoustic waves can be excited by the fast creation of

thermal stress due to electron excitation either directly or indirectly after electron

energy transfer to the lattice. In optically thick samples the stress pulse can travel

away from the surface and get reflected at a buried interface depending on the

accoustic impedance and come back to the surface to be measured as an echo in the

reflectivity curve. Those picosecond accoustic pulses have indeed been observed and

the speed of sound has been determined, e.g. in W films (25) or Al samples (26).

Measurements of Ni and semiconductor samples toghether with some theory can be

found in (27).

Some research has been done on ultrafast effects in the electronic structure of

Al following the excitation by intense ultrashort laser pulses. Bauer et al. (28)

investigated the electron dynamics in Al by means of time-resolved photoemission.

With no d electrons Al should be well described within a free electron gas (FEG)

model. However, the measured wavelength-dependent lifetimes were considerably

smaller than the theoretical values calculated from a Fermi liquid theory (FLT). By

accounting for secondary processes such as cascade and Auger processes and also

for transport effects a good agreement was found. According to Matthiesen’s rule


the measured life time Tmeas can be calculated from the electron-electron relaxation

time τee and the lifetime correction due to transport TTrans by

1

TMeas

=1

τee+

1

TTrans

(2.16)

leading to a transport time Ttrans=23 fs. However, the authors doubted that the

magnitude of this contribution of the transport effect was reasonable. A small

transport time corresponds to a lage transport contribution and this value seems

too small when comparing with values determined for noble metals. A closer look

at the band structure reveals the existence of two parallel bands (FIGURE!!!) not

only close to the Fermi level but also extended over a large energy range above EF

(figure 2.8). Interband transitions between the bands lead to a strong absorption

peak close to 800nm. Also a multitude of decay channels is possible so that an

increased scattering rate can be expected which can shorten the life time of excited

electrons considerably. Within their paper the authors could not distinguish between

transport effects and additional scattering due to the parallel bands. The life time

T2 of electrons with (E −EF )=1.5eV was measured to be just over 10 fs. Schone et

al. (29) calculated the lifetime of hot electrons in crystalline Al. Their calculations

are in very good agreement with the experimental data by Bauer et al. and the

contributions of the individual bands to the decay channels could be identified. They

state the transport correction TTrans to be 49.9 fs which is obtained by involving a

more realistic band structure than the s/p like FLT applied by Bauer et al. This

value seems more realistic when compared with results for noble metals. Campillo et

al. (30) performed a full ab initio evaluation of relaxation lifetimes in Al. At 1.5 eV


Figure 2.8: Electronic band structure of Al. (a) The empty lattice free-electron bands

are shown on the left. Splitting and appearance of parallel bands due to a small, effective

crystal potential is shown on the right. (b) The parallel bands offer excitation channels for

optical transitions and lead to a peak in the optical conductivity. Figure taken from (28).


they calculate a life time of ≈ 15 fs within a full random phase approximation (RPA)

as compared to over 20 fs for a FEG. Rethfeld et al. (31) theoretically investigated

the transient evolution of the distribution function of the electron gas in a model

free from phenomenological parameters. For a pulse (rectangular intensity profile)

of 100 fs duration and wavelength λ=630 nm (hω=1.97 eV) they introduced and

calculated electron cooling and thermalisation times. The cooling time is similar

to the electron-phonon relaxation time but also considers the characteristics of the

pulse. They define the thermalisation time as the time after which the electron

gas acts the same way as a Fermi-distributed electron gas. A 100 fs laser pulse of

intensity 7 × 109 W/cm2 absorbs an amount of energy of δue = 6.7 × 108 J/m3

resulting in a cooling time of τcool ≈ 700 fs corresponding to a electron-phonon

relaxation time of τrel ≈ 750 fs for an electron gas described by a Fermi-Dirac

distribution and a thermalisation time τtherm of the order of 10 fs.

Guo et al. (11) studied the dynamics of a structural phase transition in Al in-

duced by a direct electronic interband excitation generated by 130 fs laser pulses at

1.55 eV by measuring the time evolution of its dielectric constant. The threshold

laser fluence of 34 mJ/cm2 and the time scale about 500 fs required for melting

the Al were found to be much less than than the values required for ultrafast heat-

induced melting (about 200 mJ/cm2). The authors explained this by an ultrafast

band structure collapse due to the heating of the electron gas. Due to the band

structure of Al at 800 nm a significant number of electrons can be excited into an

upper antibonding band and thus weaken the lattice structure leading to structural


instabilities and melting. As a control experiment they performed the measurements

with a photon energy of 3.1 eV (400 nm). Here the calculated threshold of (about

310 mJ/cm2) for ultrafast heat-induced melting agreed with the measurements in-

dicating the importance of the band structure.

A further consequence of the interband transition in Al is a strong piezo-optic

response at a wavelength of 800 nm (32). Richardson and Spicer (26) observed

thermoelastic transients in the reflectivity signal of Al films (50 nm, 200 nm and

1600 nm) during the first few ps after absorption of a sub-ps laser pulse. They

modelled the electron dynamics using the two-temperature model and found that

thermal and elastic contributions have to be considered at all times in order to

reproduce the rise of the transient reflectivity signal that reaches its peak after

about 5 ps. This rather long time is a consequence of the thermoelastic contribution

and cannot be explained by the electron-phonon coupling alone.

2.3.2 Ultrafast Demagnetisation Effects

In 1991 Vaterlaus et al. (33) found a rapid decay of the spin polarisation of pho-

toelectrons emitted from a Gadolinium sample after thermal excitation by a laser

pulse (pump: 10ns, probe: 60ps). This decay time of 100 ± 80 ps was interpreted

as spin-lattice relaxation time. In 1996 Hubner and Bennemann (34) presented a

microscopic theory for the spin lattice relaxation in rare earths and calculated the

spin-lattice relaxation time in Gd to be 48 ps. In this paper they also predicted a

breakdown of magnetisation on fs time scales after excitation with intense fs laser


pulses via electron-electron correlations bypassing the lattice and thus reduce lat-

tice heating. In the same year the first measurements of a partial demagnetisation

in a 22 nm Ni film were presented by Beaurepaire et al. (1). Using a 60 fs laser

they measured the electron and spin dynamics by time-resolved transmission and

linear MOKE measurements. The maximum change in transmission was reached

after 260 fs determining the electron thermalisation time. The change in magneti-

sation reaches its maximum at about 2 ps delay, long after the electronic system

thermalised. From their measurements they postulated the existence of separate

electron and spin temperatures which they calculated from the transmission and ro-

tation data. They extended the two temperature model introduced in the previous

section (equation 2.14) by adding a spin system and appropriate additional electron-

spin and spin-lattice interaction to a three temperature model. From that they cal-

culated electron and spin temperatures as well as coupling constants. Hohlfeld et al.

(2) measured pump-probe SHG on polycrystalline Ni for several pump fluences but

did not find any delay between the formation of an electron temperature and the

breakdown of the magnetisation. The authors also found that the recovery of the

magnetisation was governed by the classical M(T ) dependence (as shown in figure

2.1), provided the electron temperature Te was used, as long as electrons and lat-

tice were out of equilibrium. Using time- and spin-resolved pump-probe two-photon

photoemission Scholl et al. (35) observed two different demagnetisation processes

in Ni on two different time scales. The first is a fast demagnetisation process below

300 fs which they attribute to the excitation of Stoner pairs by the hot electron gas.


Secondly they find a change in slope at 500 ps for a 6 A film that they explain the

spin temperature to have reached the macroscopic Curie temperature following a

spin lattice relaxation.

Using a CoPt3 sample Beaurepaire et al. (3) achieved complete demagnetisation

to the paramagnetic state. Also the demagnetisation occured within the electron

thermalisation time. Even with a significantly increased temporal resolution of 40 fs

Hohlfeld et al. (36) could not detect any delay between the initial electron heating

and the demagnetisation of polycrystaline Ni using SHG. The electron temperature

data perfectly matched the cooling expected from thermal diffusion and the magneti-

sation recovery did not show any sign of a second demagnetisation step as reported

in (35). Conrad et al. (37) achieved complete demagnetisation to the paramagnetic

state in an ultrathin Ni film for up to 2 ps with their highest fluence due to the

reduced Curie temperature relative to that of the bulk metal.

Some doubts have arisen about whether magneto-optical measurements truly

reflect the magnetic state of the sample at ultrashort time delays. Koopmans et

al. (7; 8) simultaneously measured the transient rotation and ellipticity signals of

epitaxially grown Cu/Ni/Cu wedges. Assuming the MO signal would scale linearly

with the magnetisation one would expect

∆Θ

Θ0

=∆η

η0

(2.17)

where Θ = Θ0+∆Θ and η = η0+∆η are the real and imaginary part of the complex

polarisation rotation. On time scales longer than 2ps equation 2.17 was found to

be true. However, on times up to 400 fs a large discrepancy in the behaviour of


the rotation and ellipticity signals was found giving evidence for nonmagnetic con-

tributions in the MO response of ferromagnetic Ni. These findings were supported

by time-resolved SHG studies on a Ni(110) single crystal by Regensburger et al.

(9) who concluded that the magnetisation-induced odd SH field is strongly affected

by electronic changes induced by the pump pulse and therefore does not reflect the

magnetisation on a sub-picosecond time scale. This has also been discussed in (38).

However, the most recent MO measurements made by Guidoni et al. (39) on a

CoPt3 film with 20 fs pulses show that ultrafast spin dynamics occur within the

thermalisation of the electronic populations with a characteristic time of about 50fs.

The magneto-optical signal does indeed represent the magnetic state afterwards and

the spins follow the dynamics of the electronic temperature. A SHG study in poly-

crystalline Ni and permalloy films by Melnikov et al. (40) indicated that transient

odd SHG fields reflect the spin dynamics whereas even fields monitor the electron

dynamics. They did not find any indication for the existence of a spin temperature

in Ni but found a delay between the even and odd fields in permalloy which they

attributed to a spin inertia caused by the large magnetic moment of the Fe ions and

which might justify introducing the concept of a separate spin temperature.

Kise et al. (41) observed extremely long spin-relaxation times up to some 100ps

depending on the temperature in the half-metallic ferromagnet Sr6FeMoO6. Finally

Hohlfeld et al. (42) were able to observe a fast femtosecond pump-pulse induced

magnetisation reversal in amorphous Gd23.1Fe71.9Co5.0 within (190±40) ps following

a subpicosecond magnetisation collapse. In this study they found a delay of about


500 fs of the magnetisation breakdown with respect to the increase of the electron

temperature Te. So far only a few studies of ultrafast demagnetisation have been

performed with a circularly polarised pump. Ju et al. (4) performed measurements

on a 20nm CoPt3 crystalline film and were able to distinguish between nonthermal

spin-polarised electrons observable below 1 ps and a thermalised disordered spin

bath on a time scale of 10 ps.

Some theoretical work to explain the effects has been done by Hubner and Zhang

(5; 6; 43; 44). Their calculations for Ni suggest that the high-speed limit of intrinsic

spin dynamics is about 10 fs (6). Measurements made on Ni with a magnetic SHG

probe provide some support for this claim (45) showing a complete magnetisation

breakdown within 50 fs for a 65 fs pump puls. According to Hubner and Zhang the

demagnetisation results from exchange interaction and spin-orbit coupling and does

not involve the lattice. The spin-lattice relaxation time was calculated to be 304 ps.

Four different relaxation processes have to be distinguished:

• (a) momentum relaxation of the electrons, ∼1 fs, due to electron-electron

interactions

• (b) electron-spin relaxation, a few fs, due to exchange interaction and spin-

orbit coupling

• (c) electron-lattice thermalisation, ∼1 ps due to electron-phonon coupling

• (d) spin-lattice relaxation, ∼100 ps, due to spin-orbit coupling plus anisotropic

crystal-field fluctuations.


They also found that although both intrinsic spin and charge dynamics occur on

a time scale of 10 fs, a clear time delay of the spin dynamics with respect to the

charge dynamics was observed (5). A later calculation for a monolayer of Ni revealed

that a cooperative process between the laser field and the spin-orbit coupling on the

femtosecond time scale is necessary to achieve the demagnetisation. This underly-

ing mechanism is qualitatively different from the conventional one where thermally

or magnetically driven processes are quasistatic where a spin temperature is well

defined. The ultrafast demagnetisation process occurs on femtosecond time scales

where the concept of temperature is questionable.

In summary the results so far are contradictory and more systematic studies are

required to clarify the situation. The questions whether and to what extent the

spin system can be separated from the electronic system (two or three temperature

model) and whether time-resolved magneto-optical measurements on femtosecond

time scales reliably show pump-induced demagnetisation are not answered yet. In

order to resolve this the structural and electronic properties of the samples in the

different experiments have to be considered and different techniques should be used

on the same sample.

2.3.3 Spin Orientation and Spin Relaxation

The previous section described ultrafast demagnetisation effects in ferromagnets in

which there is a spin polarisation associated with the spontaneous magnetisation.

Spin relaxation times were measured by exciting the electrons. Similarly to magnetic


Figure 2.9: The figure shows the electronic band structure of GaAs at the Γ point (left)

and the allowed electric dipole transitions for left and right circularly polarised light (right).

The numbers in the circles indicate the relative transition probablilities leading to a pref-

erential excitation of one spin species (taken from (46)).

materials spin relaxation times are of interest in non-magnetic samples. In those

materials a spin orientation must be created prior to spin relaxation measurements.

Optical pump-probe spectroscopy is an appropriate experimental technique.

Semiconductors

In certain semiconductors, due to the spin-orbit splitting of the valence band, a cir-

cularly polarised pump can selectively excite spin-polarised electrons. For example,

spin-polarised electrons have been excited from GaAs to the vacuum level and used

in Inverse Photoemission experiments (46). The schematic electronic band structure

and the corresponding dipolar transitions for circularly polarised light are shown in

figure 2.9. The subsequent relaxation of the spin polarisation can be measured by

pump-probe spectroscopy. By pumping close to the band gap, non-equilibrium spin


polarisations may be created that persist for times in excess of 1 ns and hence give

rise to long-lived circular birefringence (47). Spin relaxation effects in semiconduc-

tors and quantum well structures have been intensively studied (48). The coherent

control of spin orientation has been demonstrated in experiments performed at low

temperatures and in high magnetic fields, and using the optical Stark effect (49).

Recently spin relaxation has also been studied at room temperature in the ab-

sence of external fields in experiments performed with ultrashort laser pulses e.g.

in GaAs (50; 10) and CdTe (51). These studies have revealed a more complicated

magneto-optical response on sub-picosecond timescales. Three separate processes

were identified and the physical origin of two of these was inferred by studying their

dependence upon the wavelength of the pump beam (10). The process with the

longest relaxation time is associated with the spin polarisation of the thermalised

electron distribution. A faster signal results from bleaching of the spin-selective

optical transition prior to thermalisation. Finally a strong peak, centred at zero

time delay, is observed within the overlap of the pump and probe pulses. This is

associated with the orbital and spin angular momentum of the optically excited

hot electrons. In (10) Kimel et al. derived an expression for the magneto-optical

Kerr rotation by relating the complex Kerr rotation to the photo-induced electron

and hole densities. The same expression can be found by convolving the functional

form of each expected component with the pump and probe pulse intensity profiles.

The life time of the peak is much shorter than the experimental pulse duration

and is therefore approximated by a δ function. The two slower decaying functions


are assumed to decay exponentially. Pump and probe pulse are approximated with

Gaussian profiles with the rms width w:

I(t) ∝ 1√2πw

exp

(

− t2

2w2

)

. (2.18)

This yields the following expression:

∆Θ = offs + A exp

(

− t2

4w2

)

+B

2exp

(

w2

τ 21

− t

τ1

)(

1 − erf

(

w

τ1− t

2w

))

+C

2exp

(

w2

τ 22

− t

τ2

)(

1 − erf

(

w

τ2− t

2w

))

,

(2.19)

in which A, B and C are the amplitudes of the three components, τ1 and τ2 are

the decay constants of the exponential terms, and t is the time delay between the

centers of the pump and probe pulses. This equation will be used in the following

experimental chapters to fit the experimentally recorded pump-probe scans.

Metals

Pumping of non-magnetic metals with circularly polarised light is potentially of great

interest since the optical orientation of a non-equilibrium spin population would

allow the spin relaxation time of conduction electrons to be determined from the

transient rotation signal. For cubic metals at room temperature, where dephasing

is insignificant due to motional narrowing, the transverse spin relaxation time T2

is expected to be equal to the longitudinal spin relaxation time T1. The theory

of spin relaxation in metals is well established (52; 53) and involves the influence

of spin-orbit coupling during momentum scattering. However detailed quantitative


calculations have only recently become available and these highlight the importance

of spin ”hot-spots” on the Fermi surface (54) in reducing the value of T1 for certain

metals.

In the case of Al the value of T1 was calculated to be of the order of 100 ps at

room temperature (55), in good agreement with room temperature Conduction Elec-

tron Spin Resonance (CESR) data (56), and should be measurable in a femtosecond

pump-probe experiment. Al is an excellent candidate for optical orientation ex-

periments by virtue of its band structure. A direct interband transition between

parallel bands on the square face of the Brillouin zone (57) leads to a strong optical

absorption at a wavelength of about 800nm that is well matched to the peak output

of a mode-locked Ti:sapphire laser. In previous measurements made on metals such

as Au (58), only intraband transitions were excited, and so no comparison could be

made with the interband pumping mechanism that is used to optically orient spins

in GaAs. Also the strong absorption peak, the rapid band structure collapse and

thermoelastic effects might also indicate ultrafast excitations of the lattice.

2.3.4 Transient Linear and Circular Birefringence

Pumping with linearly (circularly) polarised light may be used to transfer linear

(angular) momentum to the electrons in a solid and induce a transient linear (cir-

cular) birefringence that causes the polarisation state of a time-delayed probe beam

to be modified. To lowest order the pump-probe process may be regarded as a cu-

bic non-linearity, involving two pump photons and one probe photon. The effect


is predicted to exist from symmetry arguments (16) and the resulting peak at zero

delay has been observed in semiconductors (50), and both non-magnetic (58) and

ferromagnetic (59) metals. The observation of the peak in Ni led to suggestions that

the effect might be used in an optical autocorrelator (60).

A general theory of pump-probe polarisation-sensitive phenomena in non-linear

media was developed by Svirko and Zheludev in (16). Pump and probe beams are

assumed to be of the same frequency and incident normal to the surface of the solid.

The measurements made in this study have a different angle of incidence. However,

refraction inside the medium leads to an angle inside the medium close to the normal

so that the theory will be used unchanged as an approximation.

In this work the pump-induced change of the probe polarisation azimuth Θ and

ellipticity angle η was measured. The definition is shown in figure 2.5. The polar-

isation of the incoming and reflected light is described using the Stokes formalism

where the polarisation of the light wave is represented by a point on the Poincare

sphere by four parameters S0, S1, S2, S3. S0 describes the light wave intensity

I = cS0

2πwhere c is the speed of light. S1 describes the intensity difference of the

linear polarisation components along the X and Y axes and S2 describes the in-

tensity difference of the linear polarisation components along the bisector of the X

and Y axes and the perpendicular direction. S3 describes the circular polarisation

component of the light. If the Stokes parameters are known then the polarization

azimuth Θ and the ellipticity angle η may be calculated as follows:

tan 2Θ =S2

S1(2.20)


and

sin 2η =S3

S0(2.21)

For the reflected wave Svirko and Zheludev obtain

ΘR − Θ =1

s20 cos2 2η

ℜ

JR

1 − n2

(2.22)

ηR − η =1

s20 cos 2η

ℑ

JR

1 − n2

(2.23)

where n is the refractive index of the medium and JR contains the magnitudes of the

electric fields of the pump and probe beam and the susceptibility tensor χijkl. Si and

si denote Stokes parameters of the pump and probe beams respectively. In isotropic

media two major nonlinear pump-probe polarisation effects are possible: the optical

Kerr effect (OKE) and the inverse Faraday effect (IFE). In case of the optical Kerr

effect a rapidly oscillating electrical field is applied to the sample perpendicular to the

direction of light propagation. In an isotropic sample this induces linear birefringence

quadratic in the applied field (i.e. independent of its sign). In the pump-probe

experiment the strong pump provides the field and induces the birefringence which

affects the probe beam. The electrical field of the probe is assumed to be weak

compared to the pump effect. In case of the IFE a weakly linearly polarised wave

acts as the probe while the pump is circularly polarised. The medium may be

magnetised optically by an intense circularly polarised light wave which is detected

by the probe. The effect is the inverse of the conventional magneto-optical Faraday

effect where a static magnetic field, applied along the direction of light propagation,

induces circular birefringence and dichroism in isotropic nongyrotropic media. If the


pump induces circular birefringence/dichroism in the nonlinear medium a change in

the polarisation of the reflected initially linearly polarised probe wave will result.

Assuming only isotropic nongyrotropic media and neglecting spatial dispersion,

the expression for JR simplifies and can be expressed by only two independent

nonzero components of the local susceptibility tensor χijkl. Svirko and Zheludev

derive the formula for linearly polarised pump (Θ1) and probe (Θ2) beams:

JR = − 16πS0s20

n |1 + n|2(χxxyy + χxyyx) sin 2(Θ1 − Θ2) (2.24)

resulting in

(

ΘR2 − Θ2

ηR2

)

= −32π2Ipump

c |1 − n|2

sin 2(Θ1 − Θ2)

(ℜℑ

)

χxxyy + χxyyx

n (1 − n2)

. (2.25)

Only the difference of (Θ1) and (Θ2) is important. In the experiment the pump and

probe beams are incident at angles of 25 and 47, there is a well defined plane of

incidence, and the angles are taken relative to this plane. A similar analysis can be

done for the more general case of initially elliptically polarised pump (Θ1, η1) and

probe (Θ2, η2) beams:

JR = − 16πS0s20

n |1 + n|2cos 2η1 cos 2η2 [sin 2Θ1 (cos 2Θ2 − i sin 2η2 sin 2Θ2)

− cos 2Θ1 (sin 2Θ2 − i sin 2η2 cos 2Θ2)] (χxxyy + χxyyx)

+i sin 2η1 cos2 2η2 (χxxyy − χxyyx)

.

(2.26)

For an initially linearly polarised probe beam (η2 = 0) one obtains

(

ΘR2 − Θ2

ηR2

)

= −32π2Ipump

c |1 − n|2

sin 2(Θ1 − Θ2) cos 2η1

(ℜℑ

)

χxxyy + χxyyx

n (1 − n2)

+ sin 2η1

(−ℑℜ

)

χxxyy − χxyyx

n (1 − n2)

.

(2.27)


For a linear pump beam this simplifies to equation 2.25. In case of a linear probe

beam and an elliptically polarised pump beam that results from an initially p-

polarised pump passing through a by an angle φ rotated λ4

plate one obtains:

(

ΘR2 − Θ2

ηR2

)

= −32π2Ipump

c |1 − n|2

1

2sin 4φ

(ℜℑ

)

χxxyy + χxyyx

n (1 − n2)

+ sin 2φ

(−ℑℜ

)

χxxyy − χxyyx

n (1 − n2)

.

(2.28)

Equations 2.25 and 2.28 will be used in chapter 6 in order to analyse the angular

data sets for the contributions of OKE and IFE in Al. In case of a linear pump

polarisation only the OKE can occur. In case of an elliptically polarised pump both

effects can contribute and the first term in equation 2.28 corresponds to the OKE

contribution and the second to the IFE contribution. When measuring the effects in

reflection they are also refered to as the specular inverse Faraday effect (SIFE) and

the specular optical Kerr effect (SOKE). The formulae in equation 2.25 and 2.28

are strictly only valid for continuous pump and probe waves. However, when the

induced polarisation decays quickly compared to the laser pulse width, we may use

the formulae in considering the zero delay peak amplitudes.

2.4 Summary

In this background chapter a general introduction was given into the electronic

structure and the origin of ferromagnetism in solids. Magnetisation processes have

been briefly discussed and time-resolved measurement techniques for the observation

of ultrafast electron and spin dynamics have been introduced. The magneto-optical


Kerr effect used as main measurement technique in this study was presented. Then

a review of the current research on ultrafast electron and spin dynamics was given

with emphasis on research on Ni and Al. Finally some formulae have been derived

for the later use in the evaluation of the experimental data.

Chapter 3

Experimental Methods

3.1 Optical Pump-Probe Set-Up

The first aim of this project was to set up an optical pump-probe experiment for

sub-picosecond time-resolved measurements of magnetisation and spin dynamics.

As a first test the optically induced demagnetisation of a ferromagnetic sample was

measured. For that purpose an existing set-up for ferromagnetic resonance exper-

iments (FMR) was modified in such a way that both types of experiments could

be performed with only minimal changes. Due to the more demanding nature of

the optical pump experiment, several additional components had to be introduced

and new alignment procedures had to be developed. These include the focusing

and overlapping of the pump and probe spots on the sample, the construction of

an autocorrelator for pulse width measurements, the introduction of group velocity

dispersion compensation with prism pairs (i.e. pulse width control), and a modula-

43

CHAPTER 3. EXPERIMENTAL METHODS 44

tion technique to detect the small reflectivity and rotation changes induced by the

pump. A few techniques will be mentioned that were tried but did not work as well.

Some preliminary optical pump experiments were performed in co-operation with

Dr. Jing Wu. They gave the first indications that the demagnetsiation effect could

be observed and are reported in (61; 62). All further work presented was conducted

by myself.

3.1.1 General Description of the Set-Up

During the course of the project the experimental set-up was continuously modified

and improved. Figure 3.1 shows the set-up in its final form. The experiment was

controlled by a computer and LabView software was written for the data acquisition.

In the following the individual parts of the set-up will be described.

The Laser The laser system consists of a 82 MHz mode-locked Titanium:Sapphire

laser (Spectra-Physics Tsunami) pumped by a continuous wave (cw) diode laser

(Spectra-Physics Millenia). The Tsunami output could in principle be tuned be-

tween 692-990 nm in wavelength. It was mainly used close to 790 nm (1.57 eV)

where its output power is at its maximum of 600 mW (cw equivalent). When tun-

ing away from this wave length the power decreases. The bandwidth-limited pulse

width was set to 80 fs corresponding to a spectral width of 8.5 nm (assuming a sech2

pulse shape) which was monitored by a spectrum analyser (IST-REES E201) at the

output coupler of the laser cavity. The vertically polarised laser output is changed

to a horizontal polarisation using two height changing mirrors. A beam sampler


delayline

B

intensity stabiliser

probe beam

pump beam

+

chopper

Ti:Sa laser800nm, 82Mhz

5W diode pump laser

-

camera(x600)

magnet

lock-in amp:rotation/ellipticity

lock-in amp:reflectivity

pulse width 120fs

λ/4 waveplate in probe:rotation → ellipticity

focus and overlap15 µm spots

GVD compensation

λ/4 plate

probe polarisationmodified bymagneto-opticalKerr effect(MOKE)

Figure 3.1: The set-up of the time-resolved optical pump-probe experiment is shown.

then divides it into a weak probe beam with approximately 4% of the intensity

and a strong pump beam with 96%. The laser power at different positions in the

experiment was measured by a laser power meter (Spectra-Physics 407A).

The pump beam path The pump beam travels through a variable delay line

consisting of a corner cube retro-reflector mounted on a translation stage driven by

a computer-controlled stepper motor. The translation stage has a length of 30 cm

corresponding to a maximum delay of 2 ns in time. The minimum step size is

0.25 µm, which corresponds to 1.67 fs. The total lengths of the pump and probe

optical paths were adjusted so that for minimum delay the probe pulse arrives just

before the pump pulse, i.e. giving a “negative” delay. In fact this negative delay


corresponds to a positive delay of 12 ns with respect to the previous pulse. One has

to keep this in mind when dealing with signals that do not entirely decay within

this repetition time and therefore establish a background level. The correct length

and approximate zero delay position was found by measuring the time-resolved

reflectivity signal from GaAs while scanning the delay line through its full length.

Zero delay corresponds to the sharp rise of the signal when the pump excites the

sample. GaAs reflectivity data will be shown in a later chapter. A small DC

motor was attached to the mount of the the retro-reflector. When switched on,

the oscillations of the motor move the retro-reflector through a few wavelengths at

high frequency, i.e. modulate the pump path length with a period which is small

compared to the lock-in time constant. This is a very simple and effective method to

remove coherence oscillations around the zero delay position that mainly result from

interference of the probe beam with diffusely scattered pump light. For the time-

dependent measurements a lock-in detection technique was used and a mechanical

chopper wheel was placed in the beam and run at a frequency close to 2 kHz.

The glass of the corner cube causes a considerable temporal broadening of the

pump pulses (chirp) due to the group velocity dispersion (GVD) in the material

which will be discussed in detail below. The pulse width after the corner cube

was measured to be about 250 fs. A fringe-resolved autocorrelator was set up for

this purpose. In order to compensate for the GVD and re-compress the pulses a

pair of Brewster prisms was introduced into the beam path. After passing through

the prism line the pump pulses have a temporal width of approximately 120 fs.


The beam is now focused down onto the sample to a diameter of 15 µm using a

special configuration of expansion and focusing optics. With a typical pump power

of 280 mW this results in a pulse energy of 3.4 nJ. The reflected part of the pump

beam is then blocked by a beam dump.

The probe beam path After division from the main beam the probe beam passes

through an electro-optical cell and some additional optics that were used as part of

an intensity stabiliser in a different experiment. While the stabiliser worked reliably

in static experiments, it turned out to cause problems when used in combination

with optical chopping of the pump beam as will be described later. Therefore it was

not used in the experiments described in this work but it remained in the set-up.

Similarly to the corner cube the EO cell added a considerable chirp to the pulses.

The pulse width after the EO cell was measured to be approximately 320 fs. The

probe pulses were also re-compressed by a second prism line and then focused onto

the sample by a set of optics, similar to that used for the pump beam.

The sample area The sample was mounted on a sample holder which could

be translated and finely adjusted in the x, y and z directions. For the magnetic

measurements, an electro-magnet with square pole pieces and a gap of 36 mm was

used. A CCD camera with a tele-zoom lens (RS 625-772) was placed above the

optical plane to monitor the sample. An extension tube containing a ×10 microscope

objective (Melles Griot 04OAS010) was used to increase the magnification to ×600.

The set-up is shown in figure 3.2. The two lenses were arranged so that the object


zoom lens

x2 lens

extension tube

microscope lens

CCD camera

Figure 3.2: The set-up of the CCD camera and lenses for the sample observation is

shown. An optical magnification of ×600 is achieved.

plane of the microscope objective coincides with the image plane of the tele-zoom

lens. The mounting flange of the microscope objective was set about 16 cm from the

CCD chip, i.e. to the standard tube length used in optical microscopes. A spatial

filter was placed between the two lenses to reduce the stray light reaching the CCD

chip. The CCD chip is sensitive in the near infra-red, so the camera could be used

for focusing and overlapping the pump and probe sports on the sample. The pump

and probe beams were incident on the sample at angles of 25 and 47 respectively.

The detector path After reflection from the sample, the probe beam is collimated

by a set of lenses and then sensed by an optical bridge detector. Both, the intensity

of the probe beam and the rotation of the polarisation can be measured at the same

time. The detector is insensitive to the ellipticity of the beam. By introducing a

quarter wave plate into the beam, a rotation is converted into an ellipticity and an

ellipticity is converted into a rotation. This configuration may hence be used to

measure the ellipticity induced by the sample.

When recording static magnetisation loops (hysteresis curves) from the Nickel


sample, the relatively large variation of the angle of incidence associated with focus-

ing the beam onto the sample was problematic. For those measurements an aperture

was introduced in front of the detector in order to narrow the angular range.

3.1.2 Detailed Descriptions of Selected Components

In this section some important parts of the set-up are described in more detail. Some

alignment methods are described and some things to avoid are listed for the benefit

of future users of the experiment.

Intensity stabiliser

Previous experiments featured an additional HeNe laser as well as the Ti:sapphire

laser. An intensity stabiliser was introduced into the experiment to reduce intensity

fluctuations (mainly slow drifts) of the HeNe laser beam. It consists of an electro-

optical cell, a polariser, a beam splitter, a photo diode and some feedback electronics

and is described in more detail in (62). In the experiments presented in this thesis

only the Ti:sapphire laser was used. It has a better intensity stability and therefore

the stabiliser is not needed. It was even found that, when switched on, the stabiliser

had a negative effect since it increased the background signal considerably. Tests

showed that, when chopping the pump beam, there was a component with the chop-

ping frequency apparent in the probe beam intensity. It was carefully investigated

where this background could originate from. Care was taken that the chopper blade

did not scatter pump light into the probe beam path. Scattered pump light reflected


from the sample back into the probe beam was not the reason for the effect either.

Considering the set-up of the optics the most likely cause is a back scatter of pump

light into the laser and then into the probe beam. This component in the probe beam

at the pump chopping frequency is then somehow amplified by the feedback circuit

rather than being eliminated. This might be due to the fact that the stabiliser was

designed to counter low frequency drifts. Switching off the stabiliser immediately

removed the effect. It must therefore be due to active stabiliser feedback rather than

passive scattering of pump light. The stabiliser was not used, and in view of the

chirp introduced by the electro-optical cell, the intention is to remove it completely

for future experiments.

Prism lines for GVD compensation

A pair of prisms was introduced into both the pump and probe beams in order to

compensate for the chirp and re-compress the broadenend pulses before they are

focused onto the sample. A more detailed description is given below.

Focusing optics and sample alignment procedures

The 82 MHz repetition rate of the laser is quite high and therefore the energy per

pulse is quite low. In order to achieve sufficient fluence for demagnetisation effects

to be observed the pump beam must be focused down considerably. The probe

beam should ideally be considerably smaller in diameter than the pump beam to

ensure a homogeneous excitation across the probe area. However, a compromise


d = 225mm d = 160mm

f = -25mm

f = +250mm f = +160mm

Sampleposition

from theLaser

Figure 3.3: Set-up of the expansion and focusing optics for the pump and probe beams.

By expanding the beam prior to focusing, the beam divergence is reduced and a smaller

spot size can be achieved. The converx lenses used are achromatic doublets. For optimum

performance the flat (or less curved) side must face the focus and the curved side must

face the infinite conjugate.

was made in order to achieve maximum pump fluence and so the pump and probe

were focused to the same minimum size. The achievable spot size is determined

by the beam divergence and the focal length of the focusing lens. The full beam

divergence of the laser is less than 0.6 mrad. In order to achieve a spot size of the

order of 10 µm a focal length of 16.7 mm is required. This leads to a space problem

for the set-up. Therefore the beams are expanded prior to focusing down in order

to reduce the beam divergence. The set-up of the expansion and focusing optics is

shown in figure 3.3. Assuming ideal lenses the focal lengths of the expansion optics

of -25 mm (Newport KPC043) and +250 mm (Comar 250DQ50) lead to a reduction

of the beam divergence by a factor of ten. With the +160 mm focusing lens (Comar

160DQ40) the achievable minimum spot size is then 9.6 µm. Formulae for these


calculations can be found in the application notes in (63).

For alignment purposes a 12.5 µm pin hole was initially used with a photo detec-

tor placed behind. By optimizing the transmission through the pin hole the position

and size of the spot could be controlled. This method was slow and inconvenient

since it involved movement of the sample. Therefore a clean piece of intrinsic GaAs

wafer was used as a test sample. GaAs has a direct band gap of 1.42 eV (873 nm)

at room temperature, and is photoluminescent when irradiated. A clean, flat sur-

face does not scatter light diffusely and so a nice image of the focused spot can be

observed with the CCD camera. A Si wafer does not work in this respect because of

its indirect band gap. Recombination in Si is non-radiative and on a clean surface

no spot could be observed.

The expansion and focusing optics for the pump and probe beam are set up in

the same way. At first the pump and the probe beam are overlapped on the sample

without using the lenses. The position is marked on the monitor. Then one beam

is blocked while the other is aligned. The final lens is put in first and positioned

so that the sample lies in the focal plane. Then the lens is moved laterally to get

the spot into its original position. Back reflections from the lens surface are checked

in order to avoid a tilt of the lens. Then the negative lens is put in. Again it is

positioned so as to avoid tilt and to position the spot correctly. Also the profile of

the expanded beam is checked. Finally the middle lens is put in and moved laterally

to get the right spot position. It is then moved along the optical axis to minimise

the spot size. The same procedure is then repeated with the second beam.


Another criterion for optimum focusing and overlap is the measurement of the

reflectivity change of GaAs. Best alignment should coincide with a maximum signal.

Indeed the fine focusing and overlap was done by maximising the lock-in signal at

zero delay. Checking the CCD monitor confirmed good alignment. Alternatively,

purely visual alignment led to a reflectivity signal very close to the optimum, con-

firming the validity of the alignment procedure with the CCD camera.

After aligning the spots on GaAs the sample can be changed. Optimum focusing

on the new sample is achieved simply by moving the sample until the two spots

appear overlapped. It is not advisable to attempt alignment directly on a sputtered

sample. The surface quality is crucial for this procedure. Even good sputtered

samples still show an amount of scatter that increases the apparent spot size on the

monitor screen. The scatter can also be misleading in terms of the true spot position

and hence the degree of overlap. If the sample does not luminesce then only scatter

from dust and defects is visible and this may not come from the spot centre.

A smooth surface is essential for pump-probe measurements. A rough surface

scatters pump light into the detector giving rise to a high background level. This

background has the same frequency as the pump-probe effect to be measured, and

is detected by the lock-in detector. It can easily obscure the small signal. The

samples from the Exeter sputtering system are of sufficient quality, but even then

some care has to be taken to find a suitable spot on the sample. A first indication is

given by looking for a nicely shaped spot without bright scater on the CCD camera

image. It is then necessary to move the stage to zero delay and monitor the lock-in


signal. The difference signal is more sensitively affected than the sum signal. Large

random changes in magnitude and phase indicate a bad spot, while stable signals

with high amplitude indicate a good spot. The signal input to the lock-in amlifier can

be monitored on the oscilloscope after passing through the initial low pass filters.

In the presence of scattered pump light the signal shows large fluctuations due

to constructive interference of the probe with the randomly scattered pump light.

When the scatter is small, the oscilloscope signal is almost stable. By monitoring

the lock in detector signal in this way, a good sample position may be found on a

reasonably good but not very smooth sample. This can reduce the time taken to

find a good spot to just a few minutes compared to several hours if not days, when

the spot is chosen by making scans at different positions chosen by trial and error.

The bridge detector

A detailed description of the bridge detector set-up including the optics and the

amplifier circuitry can be found in (62). Here only a brief description will be given.

The incoming beam is split into orthogonal linearly polarized parts. Each part is

measured by a photo diode (A and B). Op-amp circuits provide the outputs -A,

B, (A+B)/10 and (A-B)*10. The sum signal measures the total intensity of the

incoming light and corresponds to the reflectivity of the sample. The difference

signal measures the polarisation rotation when aligned accordingly. The detector is

insensitive to the ellipticity of the incoming light. The detector can be rotated and

used in different configurations. It was usually used in the balanced position where


mirror

pulse

mirror

loudspeaker

non-lineardetector

beam splitter

focusing lens

(foralignment)

Figure 3.4: Set-up of the fringe-resolved autocorrelator based on a Michelson interfer-

rometer design.

the signals A and B are of the same size and the difference is zero. Small changes in

rotation are directly measured with the appropriate sign. Another possibility is the

crossed polariser setting where initially one channel (e.g. A) has maximum signal

and the other (e.g. B) is zeroed. Then B measures the magnitude of the rotation

but its sign is lost. However, if the incident probe intensity is increased in order to

achieve a sufficiently large B signal the A channel may become overloaded and then

no reflectivity information can be recorded.

The fringe-resolved autocorrelator

A fringe-resolved autocorrellator was built for use at different positions in the exper-

ment. The set-up is shown in figure 3.4. The main advantages of the design are that

it is easy to build, it yields self-calibrating curves, makes measurements quickly and


can be constructed at low cost. It is based on a Michelson interferometer set-up.

The incoming pulsed beam is split into two equal parts at the beam splitter. The

two parts travel forward and back along the two arms of the interferometer and

are then spatially overlapped on the detector. One of the mirrors is mounted on

a loudspeaker cone. When a sinusoidal voltage is applied, the length of the inter-

ferometer arm changes periodically and therefore the temporal overlap of the two

pulses on the detector changes periodically. The speaker voltage (describing the

temporal delay between the pulses) and the detector voltage describe the autocor-

relation curve. Both are recorded and displayed by a digital oscilloscope (Le Croy

Waverunner LT342) and later processed by a LabView computer program. As will

be described below, the detector must be non-linear in order to measure chirp. In

our case we use a quadratic intensity respose provided by a two-photon effect. The

first design, using a reverse-biased LED (64), worked quite well. However, due to the

small active area it was difficult to align the beam on the detector. Also there was

some concern about the chirp introduced by the plastic cap. After some attempts

at removing the cap, the LED was replaced by a GaAsP photodiode (Hamamatsu

G1115) with a spectral response range of 300-680 nm and a peak wavelength of

640 nm. A photodiode of the same type (Hamamatsu G1117) was characterised

by Ranka et al. (65). Some commercial semiconductor devices for two photon ab-

sorption autocorrelation measurements are listed in (66). At 800 nm two photons

are needed in order to create an electron-hole. In order to obtain a large enough

quadratic signal above the remaining linear background, a 2 cm focusing lens was


introduced to increase the power density.

The advantages of the fringe-resolved autocorrelator are an intrinsic calibration

and unambiguous alignment. The autocorrelation width is determined simply by

counting the number of fringes that are higher than the half height, since the width

of the fringes is determined by the wave length. There is no need for external calibra-

tion and it is not essential to have a perfectly linear dependence of the loudspeaker

displacement upon the driving voltage. Also the intensity ratio of peak (zero delay

between the pulses from the two arms) to background (pulses do not overlapp at all)

should be 8:1. Achieving this ratio confirms a proper alignment. Typical autocorre-

lation curves and fringe calibrations will be given below. When using these one has

to keep in mind that the autocorrelator optics (beam splitter, lens) also contribute

to the total chirp measured.

The alignment of the autocorrelator is straightforward. A voltmeter and an

oscilloscope are used. The driving voltage of the speaker is used as the x-axis and

the detector voltage as the y-axis. Firstly the beam from the arm with fixed length

is blocked and the moving mirror is adjusted so that the detector response is a flat

line. This ensures that the beam is normally incident on the moving mirror and does

not move across or off the detector as a result of the mirror movement. Then the

beam from the moving arm is blocked and the mirror in the fixed arm is aligned to

give maximum intensity on the detector. Now both beams should be focused on the

same spot, i.e. spacially overlapped. Then the length of the fixed arm is varied until

there are signs of constructive interference. This adjustment should be necessary


only once for the initial set-up and only fine adjustment is needed when using the

autocorrelator again at a later time. Finally the fixed mirror is fine-adjusted to

achieve the typical autocorrelation curve with the 8:1 intensity ratio.

With the current electronics the autocorrelator should not be used with frequen-

cies above a few Hertz. The detector electronics act as a low pass filter and in order

to achieve a high gain the feedback resistor was chosen to be very large (10 MΩ).

In combination with the smallest capacitor available at the time, this results in a

frequency bandwidth that is insufficient to resolve the fringes when operating at a

high scan rate. However this limited bandwidth does not really limit the measure-

ments. LabView software was written to read the traces from the oscilloscope into

the computer and determine the peak to pedestal ratio and the number of fringes.

The magnet

For the magnetic measurements an electromagnet was used. The sample was usually

centred between the pole pieces in the lateral and vertical directions, but was rather

close to the front edge of the gap region (position 3 in figure 3.5). A constant voltage

supply with a programming voltage input was used to drive the magnet. Therefore

the current could drift as the magnet warmed up. In order to measure the field a

Hall probe was attached to one of the pole shoes. Calibration curves were taken

with a Gaussmeter for different positions within the gap as shown in figure 3.5.


-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0Y =0.033+0.853 X

Gau

ssm

eter

Sig

nal (

kOe)

Hall Probe Signal (kOe)

H

12

3

4

H Hall probe position

Gaussmeter calibrationfactors:

1 0.99

2 0.97

3 0.85

4 0.80

Figure 3.5: Field calibration curve (top) and calibration factors for different positions in

the gap of the electromagnet (bottom). The curve shows the field calibration for position

(3). The line through the data points is a straight line fit. The fit parameters are indicated.


Circular pumping

Normally the pump beam is linearly p-polarised. Some of the measurements were

performed with elliptical polarisation. Therefore a quarter wave plate in a rotary

mount was inserted into the pump beam between the final polariser and the focusing

optics. When the wave plate is rotated the polarisation changes continously between

linear p-polarisation for a wave plate setting of 0 and circular polarisation at ±90.

At the same time the principal polarisation axis rotates.

3.1.3 Measuring the Time-Resolved Signals

Although the observed signals are in principle large enough to be measured directly

by the bridge detector (a few mV), the noise on the signal is far too large. Some

attempts were made to measure the signal directly with some signal averaging but

those attempts failed. Therefore a phase-sensitive technique using lock-in amplifiers

was developed. This method yields an excellent signal-to-noise ratio for good quality

samples. However, the drawback of this method is that, due to a phase factor

that depends on various experimental parameters in a complicated way, a direct

statement can be made only about the magnitude of the effects but not about the

sign (e.g. increase or decrease of the reflectivity). Additional experiments had to be

made in order to determine the correct phase. These will be described later.

Four different modulation techniques were tested. Three involved optical chop-

ping of the laser beam, one involved a modulation of the applied external magnetic

field. The latter was the first to give indications of a demagnetisation signal. How-


ever, it is the least desirable method for various reasons. Firstly it only works for the

magnetic measurements on ferromagnetic samples. Reflectivity changes, or spin ori-

entation measurements attempted later with a circular pump beam, are not possible.

Also modulating the field means working with an effective average magnetisation

rather than a well-defined magnetic state. The advantage of this method is that it

is insenstitive to stray pump light. The optical chopping methods are

1. chopping the probe beam,

2. chopping the pump beam,

3. chopping pump and probe beams at different but phase-locked frequencies

(dual chopping) and locking into the sum or difference frequency.

Chopping the probe beam did not work at all. This was to be expected since the

pump beam is responsible for the effects to be measured. Chopping the probe

would eliminate stray pump light. A considerable part of the noise comes from

intensity fluctuations of the probe beam, and these continue to be detected by this

method. Chopping the pump beam results in a good signal to noise ratio. It

yields the signal itself plus any background from stray pump light that also reaches

the detector optics. Since this technique works well it was thought that the dual

chopping method should improve the signal even further because it should eliminate

the effect of scattered pump light. However, the signal to noise ratio from this

method was rather poor. This is probably because the amplitude of the chopped

probe signal is much larger (approximately 1 Volt) than the pump-induced change


in the probe signal (order of mV), so that a much larger signal than the signal to be

measured will pass through the low pass filter to the input stage of the lock in. This

method works, but is inferior to pump chopping. Consequently all phase sensitive

measurements were made by chopping the pump beam only.

In order to calibrate the signals two factors have to be taken into account. Firstly

the desired quantity is the amplitude of the modulated signal. The lock-in outputs

the rms value of the signal component at the modulation frequency. This must

be multiplied by a factor of√

2π

to obtain the correct square wave amplitude. In

the case of reflectivity measurements this value has to be divided by the dc output

voltage of the detector in order to obtain the percentage signal change. In the

case of rotation measurements, the voltage is converted into an angle by applying a

calibration factor. This factor is found by rotating the detector by a known angle

(e.g. 1) and measuring the change in the rotation signal.

The signals can also contain other contributions. With the method of pump

chopping, not only the pump-induced change of the probe signal is detected, but

also stray pump light that is scattered into the detector. Therefore there are also

some unwanted pump contributions in the signal. Furthermore it is possible that the

intensity signal breaks through into the rotation signal (see below), while birefringent

focusing optics can make a nominally linear pump slightly elliptically polarised.

Also the repetitive nature of the experiment can lead to background signals due to

incomplete relaxation in the available time of 12 ns between two successive pulses.

These can be real physical signals for example due to periodic lattice heating effects


(and therefore changing material constants) that arise from the periodic opening and

closing of the pump chopper which happens on time scales that are slow compared

to the laser repetition rate.

Intensity break through and probe polarisation alignment

When making time-resolved rotation and ellipticity measurements it was noticed

that the scans for opposite magnetisation orientation (reverse magnetic field) or

opposite spin orientation (opposite pump helicity) did not always appear to be

symmetric. This was the result of additional contributions to the signal. The most

prominent contribution was a breakthrough of the reflectivity signal due to a slightly

inaccurate alignment of the probe polarisation and the detector orientation. When

the sample plane is not exactly vertical then the plane of incidence is slightly tilted

with respect to the horizontal plane of the optical table. As a consequence the

probe polarisation was slightly misaligned from p-polarisation and different pump-

induced changes in the reflection coefficients rss and rpp result in a time-dependent

contribution to the difference signal. When the detector is close to the balance

condition, the difference signal S varies as

S ∝ (I + δI)(

θoff + δθ)

, (3.1)

where I is the intensity of the probe without the pump, θoff is the angle by which the

detector is mis-aligned from the balanced position, and δI and δθ are the changes in

intensity and rotation induced by the pump beam. To first order, the lock-in signal

is proportional to δI · θoff + I · δθ. Therefore if θoff 6= 0, changes in the reflected


probe intensity δI may contribute to the signal. These changes are independent of

the orientation of the magnetisation. Therefore to obtain the true magneto-optical

signal, half the difference of the signals obtained for the two magnetisation directions

(“average difference”) can be taken. This will be done for the Ni measurements in

the following chapters.

However, if there is no time-dependent magnetic background signal as in the

Ni sample, then the probe polarisation and detector orientation can be adjusted to

remove the intensity contributions. If the incoming pump beam is p-polarised, then

no time-dependent difference signal should be observed in Al or GaAs. Figure 3.6

shows measurements from the Al sample for different probe-polariser settings and

detector orientations. It can be seen that by rotating the detector the difference sig-

nal can be levelled. Depending on the probe polariser setting the detector DC signal

can be quite large, indicating an unbalanced bridge. By choosing the appropriate

probe polariser setting, the DC background can be zeroed. In the present case it

was found to be zero for a probe polariser setting of 311.5. In all panels the flat

line appears at a signal offset of about 60 units. The offset is not affected by the

polariser or detector setting. This indicates an additional background signal from a

different source, e.g. stray pump light that gets into the detector or pump induced

average heating effects that change the optical properties of the sample on longer

time scales.

After aligning the probe polariser setting with this method, the difference sig-

nals for GaAs and Al appeared to be symmetrical upon inversion of the the pump


-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5-150

-100

-50

0

50

100

150

a) probe: 313o

b) probe: 314o

c) probe: 315o

d) probe: 316o

Diff

eren

ce S

igna

l (ar

b. u

nits

)

Pump-Probe Delay (ps)

-4 turns, DC=-9.1V -3 turns, DC=-6.7V -2 turns, DC=-3.9V -1 turn, DC=-1.3V 0 turns, DC=+1.6V 1 turn, DC=+4.5V

-250

-200

-150

-100

-50

0

50

100

150

Diff

eren

ce S

igna

l (ar

b. u

nits

)

-5 turns, DC=-7.8V -4 turns, DC=-4.9V -3 turns, DC=-2.2V -2 turns, DC=+0.5V -1 turn, DC=+3.3V 0 turns, DC=+6.2V +1 turn, DC=+8.9V

-50

0

50

100

150

Diff

eren

ce S

igna

l (ar

b. u

nits

) -6 turns, DC=-6.3V -5 turns, DC=-3.4V -4 turns, DC=-0.7V -3 turns, DC=+2.2V

-150

-100

-50

0

50

100

150

Diff

eren

ce S

igna

l (ar

b. u

nits

) -7 turns, DC=-4.7V -6 turns, DC=-1.9V -5 turns, DC=+1.0V -4 turns, DC=+4.1V -3 turns, DC=+6.9V

Figure 3.6: Scans of the difference signal from the Al sample for p-polarised pump light.

The panels show different probe polariser settings close to p-polarisation. Within each

panel the detector angle was varied to find a flat signal. The legends show the detector

angle (1 turn=1 degree) and the DC voltage from the difference output. From these mea-

surements the polariser and detector setting for a flat signal with zero DC offset can be

found. The constant offset in the lock-in signal of about 60 units does not depend on those

settings, indicating an additional background of different source such as stray pump light

or average heating effects.


polarisation or helicity. Also it was found that for deliberate coarse misalignment of

the probe polarisation the difference signal looked exactly like the sum signal. This

clearly supports the interpretation of the background as an intensity breakthrough.

3.2 Pulse Width Control and Measurement

Many of the excitation and relaxation processes investigated in this thesis occur

on time scales of a few fs up to some ps. The temporal width of the laser pulse, of

about 100 fs, determines the temporal resolution in those experiments and knowledge

of the pulse width is essential if conclusions are to be drawn from the measured

data. Also it is desirable to use short laser pulses in order to increase the temporal

resolution of the experiment. In this section it is described how the pulse width

can be measured using an autocorrelator. Also it will be explained how ultrashort

pulses are broadened by group velocity dispersion and how this broadening can be

at least partly compensated using a set-up with two prisms.

3.2.1 Group Velocity Dispersion (GVD)

In a dispersive medium the index of refraction n(ω) is a function of the frequency of

the light. Therefore the wave vector k, the phase velocity ωk

and the group velocity

dωdk

are also frequency dependent. Ultrashort laser pulses have a broad spectral

profile according to the uncertainty principle. In a dispersive medium, different

frequency components of the pulse will travel at different speeds. Therefore the


different frequency components of the pulse acquire different phase shifts

Φ (ω) = Φ (ω0) +dΦ

dω

∣

∣

∣

∣

ω0

(ω − ω0) +1

2

d2Φ

dω2

∣

∣

∣

∣

ω0

(ω − ω0)2 + . . . . (3.2)

As a consequence the pulse will be increasingly broadened in time while passing

through the medium and there will also be a variation of spectral density across the

temporal envelope. This effect is called “chirp”. A positive chirp corresponds to

an observer experiencing an increasing frequency with time. Accordingly a negative

chirp corresponds to a decrease in frequency with time. The linear term in equation

3.2 simply causes a delay in time of the whole pulse. The quadratic and higher order

terms cause the broadening. This effect is called GVD. In our pulse width range the

quadratic term is the most important. It can be compensated as described below.

Higher order terms are more difficult to deal with but only become important for

shorter pulse widths.

3.2.2 Pulse Width Measurements

Transform-Limited Pulses

In the absence of chirp the pulse is transform limited and has its minimum temporal

width. In this case the temporal width can be calculated from the spectral width

from the time-bandwidth product ∆τ∆ν, which is given by the uncertainty principle.

The value of the produvt depends upon the pulse shape. Most commonly a Gaussian

(for ease of calculation) or a hyperbolic secant (more realistic for ultrafast laser

pulses) is assumed. Strictly speaking a hyperbolic secant pulse does not keep its


shape while a Gaussian remains a Gaussian under the influence of GVD.

Gaussian:

∆τ∆ν = 0.441, I(t) = exp

(−4 ln 2t2

τ 2

)

(3.3)

Hyperbolic secant:

∆τ∆ν = 0.315, I(t) = sech2

(

1.76t

τ

)

(3.4)

where ∆τ is the full width at the half maximum (FWHM) of the intensity envelope

of the pulse and ∆ν is the FWHM of the frequency spectrum of the pulse. The

pulses emerging from the output coupler of our laser system are transform limited.

Therefore the temporal pulse width of the laser in the experiment is conveniently

measured with a spectrum analyser. At a wave length of 800 nm a sech2 pulse

width of 80 fs corresponds to a spectral width of 8.5 nm. However, the spectral

width will remain the same when the pulses are broadened in time due to their pas-

sage through external optical components. Since we measure the spectral intensity

distribution and not the phase distribution, spectral measurements are not suitable

for the determination of the width of chirped pulses.

Autocorrelation measurements

Several techniques for the characterisation of ultrashort laser pulses have been re-

ported in the literature (see e.g. (67)). As part of this thesis a fringe-resolved

autocorrelator using a non-linear photo diode as a detector was built and used. It


has been already described above. Now the theory required to calculate the auto-

correlation signal and calibration curves will be introduced.

There are two types of autocorrelation, intensity and interferometric autocor-

relations. They are also refered to as slow and fast autocorrelations respectively.

In the case of a detector with a quadratic intensity dependence the second order

autocorrelation function can be written as

g2(τ) =

∫ +∞−∞

∣

∣E(t) + E(t− τ)2∣

∣

2dt

2∫ +∞−∞ E4(t)dt

. (3.5)

Expanding the integrand yields the interferometric or fringe-resolved autocorrelation

g2(τ) = 1 + 2

∫ +∞−∞ E3(t)E(t− τ)dt∫ +∞−∞ E4(t)dt

+ 3

∫ +∞−∞ E2(t)E2(t− τ)dt∫ +∞−∞ E4(t)dt

+ 2

∫ +∞−∞ E(t)E3(t− τ)dt∫ +∞−∞ E4(t)dt

,

(3.6)

where E(t) = ξ(t) [cosωt+ φ(t)] is the time dependent electric field, τ is the delay

between the pulses and the constant term represents the background level. For non-

overlapping pulses (τ → ∞) the terms containing the electrical fields become zero

and the signal is equal to 1, establishing the background level. If the pulses overlap

perfectly (τ = 0), the integral ratios all are equal to 1 resulting in a signal of 8.

This establishes the 8:1 peak to background ratio. If however the response of the

autocorrelator is slow compared to the time taken to sweep through one fringe, then

the autocorrelation function will be time averaged to

g2(τ) = 1 +2∫ +∞−∞ E2(t)E2(t− τ)dt∫ +∞−∞ E4(t)dt

. (3.7)

This is called the intensity autocorrelation. The peak to background ratio is then


3:1. When measuring intensity autocorrelation curves a calibration has to be made

as there is no intrinsic calibration as in the fringe-resolved autocorrelation curves.

Figure 3.7 shows calculated fringe-resolved autocorrelation curves for an initially

transform-limited 80 fs pulse at 800 nm with second order chirp of (a) 0 fs2 and (b)

20000 fs2. Figure 3.8 shows a curve obtained with the fringe-resolved autocorrelator.

Figure 3.9 shows the calibration of the number of fringes versus the width of the

broadened pulse for an initially 80 fs long 800 nm pulse.

3.2.3 GVD Compensation

Methods of GVD compensation

In order to re-compress broadened pulses one has to introduce negative chirp to

compensate the positive chirp that broadened the pulse. For the second order chirp

which is usually the most important contribution, this can be achieved using inter-

ferometers, prism sequences or diffraction gratings. In general an angular dispersion

produces a second order GVD contribution (67)

d2φ

dω2= −ω0L

c

(

dα

dω

∣

∣

∣

∣

ω=ω0

)2

(3.8)

where L is the distance from the input to the output of the dispersive system and α is

the dispersion angle. The method used in the present experiment is based on a pair

of Brewster prisms and a mirror as shown in the experimental set-up in figure 3.1.

It works in a similar way to a set-up with four prisms introduced by Fork et al. (68)

which is shown in figure 3.10. The first prism provides the angular dispersion and


-1000 -500 0 500 1000

0

2

4

6

8

b) 20000 fs2

a) 0 fs2

Auto

corre

latio

n Si

gnal

(arb

. uni

ts)

-1000 -500 0 500 1000

0

2

4

6

8

Auto

corre

latio

n Si

gnal

(arb

. uni

ts)

Time (fs)

Figure 3.7: Fringe-resolved autocorrelation curves calculated for an initially transform-

limited pulse of 80 fs at 800 nm with a second order chirp of (a) 0 fs2 and (b) 20000 fs2.


-0.4 -0.2 0.0 0.2 0.4

0.0

0.5

1.0

1.5

Auto

corre

latio

n Si

gnal

(arb

. uni

ts)

Speaker Voltage (V)

Peak: 1.44VBackground: 0.18VRatio: 8:1

Fringes at FWHM: 67

Figure 3.8: Example of an autocorrelation curve measured with the fringe-resolved auto-

correlator.

50 60 70 80 90 100 110 120 130 140 1500

100

200

300

400

500

600

Puls

e w

idth

at F

WH

M (f

s)

Number of fringes at FWHM

Figure 3.9: Fringe calibration for autocorrelation curves of initially transform-limited

80 fs pulses at 800 nm.


lα(ω)

blue

red

(mirror)move tochange GVD

1

2

4

3

Figure 3.10: Four prism set-up for the correction of second order chirp. Due to the

angular dispersion of the pulse spectrum in the prism material the wavelengths that were

advanced have to travel a longer path and are so subject to retardation. When inserting a

mirror in between prisms (2) and (3) a similar set-up can be realised with only two prisms.

the second prism recollimates the spectral components. A mirror sends the beam

back along almost the original path in order to cancel out the lateral displacement

and recover the original beam profile. Due to the slightly different optical path

back through the prisms the beam may not be perfectly circular any more. If more

space were available on the optical table a symmetrical set of four prisms could be

used to avoid this drawback. In addition to the negative chirp resulting from the

angular dispersion, the material of the prisms also adds positive chirp. The amount

of positive chirp depends upon the amount of material in the beam. Therefore by

sliding a prism in or out along its symmetry axis the total amount of chirp can be

finely adjusted. The total amount of GVD arising from both the angular and the


material dispersion is given by

d2φ

dω2= − λ3

2πc24l

[

d2n

dλ2+

(

dn

dλ

)2(

2n− 1

n3

)

]

sin β

−2

(

dn

dλ

)2

cos β

(3.9)

where β is the angular deviation of the dispersed light from a reference ray drawn

from the apices of each prism. The first term is the positive GVD contribution from

the prism material and the second is the negative contribution from the angular

dispersion. The quantity l sin β determines the amount of prism glass in the beam

path. Usually the angle β is small and cosβ ∼ 1. The required prism spacing can be

estimated by adding up all the positive chirp caused by the optics in the experiment

and then using the second term in equation 3.9 to calculate l. The experimental

determination of the position with minimal pulse width is shown in figure 3.11.

3.3 The Samples

Three kinds of samples were used in this thesis. The semiconductor sample is simply

a part of an intrinsic GaAs(100) wafer as supplied by Wafer Technology Ltd., Milton

Keynes. Different wafers were used with Hall mobilities of 7000-8000 cm2 V−1 s−1

and carrier densities of 1.5 − 6.5 × 107 cm−3.

The metallic samples were polycrystalline films of Ni and Al which were grown

by Mr. Norman Hughes. They were grown on pieces of clean Si wafer by DC

magnetron sputtering. The base pressure was of the order of 2× 10−7 Torr and the

calibrated growth rates were 3.5 A s−1 and 0.6 A s−1 for Ni and Al respectively.


300 350 400 450 500 550 600 650 700 75040

50

60

70

80

90

Num

ber o

f Aut

ocor

rela

tion

Frin

ges

Prism Separation (mm)

80fs (8.5nm) 45fs (15nm)

Figure 3.11: Dependence of the pulse width of the pump beam, after passing through the

prisms, on the prism spacing. Measurements were made for initially 80 fs (∆λ = 8.5 nm)

and 45 fs (∆λ = 15 nm) pulses.

The nominal thickness was 500A in both cases. The Si substrate was chosen for its

flatness, to ensure smooth films, and also because its superior thermal conductivity

(compared e.g. with glass) promotes the removal of energy deposited by the pump

laser. Previous experiments with thin metallic films grown on glass led to damage

of the films by the laser.

Chapter 4

Ultrafast Demagnetisation in

Nickel

4.1 Introduction

When setting up the experiment the first aim was to observe the ultrafast demag-

netisation effect reported by Beaurepaire et al. (1) and Hohlfeld et al. (2). Some

first measurements were performed using a polished nickel foil of high purity. Dif-

ferent detection schemes were tried as described in the previous chapter. Some

encouraging first results were achieved as reported in (62). However, the surface of

the foil was not very smooth and also some experimental problems such as the GVD

compensation remained to be solved. After improving the experiment and after

some attempts with different samples (Ni foil, Ni/Cu/Si, Ni/Si) a smooth 500 A Ni

film was grown on a silicon wafer. This finally allowed good quality measurements

76

CHAPTER 4. ULTRAFAST DEMAGNETISATION IN NICKEL 77

of the ultrafast demagnetisation and reflectivity changes.

Different kinds of measurements were made. First of all some static hysteresis

loops were taken with the pump beam blocked in order to characterise the sample

and determine the saturation magnetisation signals for both, rotation and elliptic-

ity. Then time-resolved rotation and ellipticity scans were performed to measure the

pump-induced demagnetisation effect. The behaviour of the rotation and ellipticity

signals will be compared in order to find out whether they show different behaviour

on sub-ps time scales. Finally at several fixed time delays so-called dynamic hys-

teresis loops were taken which reflect how the magnetisation change induced by the

pump depends upon the applied field.

4.2 Experiment and Results

The experimental set-up is mainly as described in the previous chapter but only one

lock-in amplifier was available. The results in this chapter are the first measurements

of ultrafast reflectivity changes and demagnetisation effects after the set-up of the

experiment was finished. All measurements involved p-polarised pump and probe

beams.

4.2.1 Static Hysteresis Loops

At 800 nm the magneto-optical response of Ni is rather small. Static measurements

of the hysteresis loop were taken with the probe beam for both the rotation and

ellipticity signal in order to characterise the sample. Typical curves are shown in


-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6-1.0

-0.5

0.0

0.5

1.0

Rot

atio

n Si

gnal

(mde

g)

Applied Field (kOe)

Figure 4.1: Static magnetisation curve of Ni obtained from the longitudinal MOKE

rotation signal.

figures 4.1 and 4.2. A linear background was subtracted in case of the rotation signal.

The ellipticity signal with a loop height of about 30 mdeg is an order of magnitude

larger than the rotation signal with a loop height of only 1 mdeg. Calculations of

the longitudinal MOKE signal expected from a saturated sample were performed

using published optical and magneto-optical constants of bulk Ni (69; 70). Formulae

for the calculation are given in (71). The angular dependence of the longitudinal

MOKE rotation and ellipticity is shown in figure 4.3. At 47 values of about 18 mdeg

for the ellipticity and 4 mdeg for rotation were obtained. These values correspond

to half the loop height. The calculated value for the ellipticity agrees rather well

with the measurement. The measured rotation loop however appears to be about

one order of magnitude too small.

Some care had to be taken in order to obtain the magnetisation loops. The first


-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5-20

-10

0

10

20

Ellip

ticity

Sig

nal (

mde

g)

Applied Field (kOe)

Figure 4.2: Static magnetisation curve of Ni obtained from the longitudinal MOKE

ellipticity signal.

0 10 20 30 40 50 60 70 80 90-20

-15

-10

-5

0

5

10

15

20

25

30

Rot

atio

n, E

lliptic

ity (m

deg)

Angle of incidence (deg)

Rotation Ellipticity

Figure 4.3: Angular dependence of the MOKE rotation and ellipticity calculated from

published optical and magneto-optical constants of bulk Ni at 800 nm.


attempt at measuring the loops did not work well for the rotation signal. Only very

small signals could be measured on steep linear backgrounds. As can be seen in

figure 4.3 the rotation changes sign at an angle of incidence of about 60. Since the

values of the optical constants used for the calculation were obtained from samples

of dubious surface quality, there is some uncertainty about the exact angle at which

the zero crossing occurs. It may well be close to the angle of incidence used in our

experiment. The large cone of incidence introduced by the expansion optics may

be problematic since it averages the signal over a range of angles close to the zero

crossing. The MOKE rotation will be small anyway and there may also be a partial

cancellation of the Kerr signal from rays at angles of incidence that lie on opposite

sides of the zero crossing point. Therefore an aperture was introduced into the

expanded detector beam in order to select a smaller range of angles. This improved

the signal quality considerably. The time-dependent scans were performed without

the aperture. They were taken at constant field so that the background slope was

not critical. The aperture degraded the time-dependent signals and better curves

were measured without aperture. This could be because a different ratio of probe

signal and scattered pump light was transmitted through the aperture.

4.2.2 Time-Resolved Reflectivity and Magnetisation Mea-

surements

Time-resolved measurements of the effect of the pump upon the reflectivity, the

rotation and the ellipticity signal were taken. In the first configuration of the ex-


-1 0 1 2 3 4 5-20

-15

-10

-5

0

Ref

lect

ivity

Cha

nge

(arb

. uni

ts)


Figure 4.4: Pump-induced change in the Ni reflectivity signal.

periment, when the data for this chapter was taken, only one lock-in amplifier was

available. Therefore only one type of measurement could be performed at a time.

Since the translation stage does not possess encoders there is some uncertainty about

its absolute position. As a consequence the zero delay point might shift somewhat

between different scans if the motor misses any steps. It is therefore somewhat dif-

ficult to relate scans, especially when comparing scans of opposite magnetisation.

This problem was solved later by using a second lock in amplifier to always measure

time-resolved scans of rotation or ellipticity together with the time-resolved reflec-

tivity signal. The reflectivity signal then acts as a reference for other time dependent

measurements.

Figure 4.4 shows a typical pump-induced time-dependent change of the reflectiv-

ity signal at zero external field. Figure 4.5 shows the ellipticity signals in opposite

static external fields of ±860 Oe for a time delay up to 30 ps. Reversing the orienta-


-250

-200

-150

-100

-50

0

50

100

-5 0 5 10 15 20 25 30 35

Pum p-Probe D elay (ps )

Elli

ptic

ity C

hang

e (a

rb. u

nits

)

-860 O e

+860 O e

average d iffe rence

Figure 4.5: Ultrafast demagnetisation effect in Ni obtained from the magneto-optical

ellipticity signal for longer time delays.

tion of the static magnetisation should cause the sign of the demagnetisation signal

to change as is indeed observed. The observed asymmetry is due to a breakthrough

of the reflectivity in the difference signal as has been described in the previous chap-

ter. The true magneto-optical signal was obtained from the average difference of the

two magnetisation directions which is also shown in the figure. The demagnetisation

effect at shorter time delays up to 1.2 ps is shown in figure 4.6 for both rotation (a)

and ellipticity (b). The maximum time dependent ellipticity can be compared with

the static rotation and ellipticity loops. In the case of the ellipticity it corresponds

to a 7% demagnetisation. For the rotation data one would obtain a demagnetisation

of about 80%. However, it was already pointed out that the measured static rota-

tion seemed to be an order of magnitude too small compared with the calculations.

Taking this factor into account one obtains a demagnetisation value of 8%, similar


-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2Pump-Probe Delay (ps)

Cha

nge

in R

ota

tio

n (m

deg

)

+860Oe

-860Oe

average difference

a)

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2Pump-Probe Delay (ps)

Cha

nge

in E

llip

tici

ty (

md

eg)

b)+860Oe

-860Oe

average difference

Figure 4.6: Demagnetisation signals measured in (a) rotation and (b) ellipticity. The

open circles represent the average difference of the two signals measured in opposite exter-

nal field.


-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

-0.5 0 0.5 1 1.5 2 2.5Pump-Probe Delay (ps)

Sig

nals

(ar

b. u

nits

)

reflectivity

average sum

Figure 4.7: Comparison of the time-dependent reflectivity with the average sum of the

ellipticity signals. The curves look similar, suggesting that the major part of the non-

symmetric contribution to the magneto-optical signal is due to a reflectivity break through.

to the ellipticity value.

The magnitude of the magneto-optical signal is expected to be unchanged when

the orientation of the magnetisation is reversed. Therefore we may obtain the non-

magnetic background signal by averaging the magneto-optical signals obtained for

the two field directions (“average sum”) so that the magnetic contributions cancel.

This background signal from the ellipticity is plotted in figure 4.7. It looks similar

in shape to the time dependent reflectivity signal that is also plotted in the figure.

4.2.3 Dynamic Hysteresis Loops

Figure 4.8 shows a series of dynamic hysteresis measurements taken for different

fixed time delays. These loops show the change in magnetisation induced by the


-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

-0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2Pump-Probe Delay (ps)

Cha

nge

in R

ota

tio

n (m

deg

)

2kOe

a)

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2Pum p-Probe Delay (ps)

Ch

ang

e in

Elli

pti

city

(m

deg

2kOe

b)

Figure 4.8: Dynamic hysteresis loops obtained by sweeping the magnetic field at a fixed

time delay are shown. The two panels show measurements of (a) the rotation and (b) the

ellipticity signal. The field scale is indicated by the arrow bars. The dynamic loops are

plotted offset in time so that their centres correspond to the time delays on the horizontal

axis. Time-dependent measurements made in a static external field of ±860 Oe are also

shown.


pump beam rather than the magnetisation itself. It is measured using the same

phase-sensitive detection scheme as that used for the time-resolved measurements.

But here the time delay is kept fixed and the external field is swept. In addition

to the dynamic loops, time-resolved scans for an external field of ± 860 Oe are

displayed as well. Despite the strange loop shapes the signal at saturation agrees

well with that observed in the time scans. The possible origin of the loop shape is

discussed in the next section.

4.3 Discussion

Most existing models of the demagnetisation process have assigned different temper-

atures to the lattice and various electronic sub-systems, and then described the heat

flow between the sub-systems with rate equations as described in the background

chapter. Reflectivity changes in noble metals have been modelled by taking account

of non-thermal electrons and allowing for heat transport into the interior of the film.

This model is not easily extended to Ni due to the overlap of the sp and d bands at

the Fermi level. However, the reflectivity curve in figure 4.4 is of similar shape to

others reported previously e.g. in (36).

Figure 4.9 provides a direct comparison of time-dependent rotation and ellipticity

signals after accounting for reflectivity breakthrough. The ellipticity and rotation

time scans both rise within a time of about 300 fs. Contrary to earlier reports (7; 8)

there does not seem to be any significant difference in the time dependence of the

rotation and ellipticity scans. This suggests that the thermalisation time of 300 fs


-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

-1 0 1 2 3 4 5

Pum p-Probe D elay (ps )

Nor

mal

ised

Sig

nal (

arb.

uni

ts)

Figure 4.9: Comparison of the time-dependent demagnetisation signals in Ni (average

differences) obtained from the magneto-optical rotation (solid) and ellipticity (dashed). In

order to compare the shapes the backgrounds were subtracted and the curves were nor-

malised.

can be still considered as an upper limit for the demagnetisation time.

The strange shape of the dynamic loops in figure 4.8 (a) and (b) might result

from a number of mechanisms. These include the ultrafast demagnetisation, nano-

or picosecond magnetic reorientation due to precession or domain wall motion, or

a slower reorientation of the magnetisation associated with the increase in average

temperature when the chopper blade is open. The ultrafast demagnetisation is

not expected to depend upon the small applied field since in these experiments

the system is never close to a phase transition to the paramagnetic state. This

is clear since we observeed that the static MOKE loop is hardly affected by the

presence of the pump beam. The dynamic loops at negative delay are at a positive


time delay of about 12 ns relative to the previous pump pulse. Any precessional

motion will be damped out on time scales much shorter than 12 ns. Since the loop

shape does not depend upon the position of the focused spots upon the sample,

a domain wall process seems unlikely. Therefore it is suggested that the inverted

loops seen at negative time delay result from a reorientation of the macroscopic

magnetisation associated with sample heating on time scales comparable to the

period of the chopper. This heating also causes the 1% background demagnetisation

observed in the saturated state at negative delays. The dynamic hysteresis loops

show that the reduction of the spontaneous magnetisation associated with ultrafast

demagnetisation can only be reliably measured when the sample is saturated.

4.4 Summary

In this chapter measurements of optically induced ultrafast electron dynamics and

the ultrafast demagnetisation effect in a ferromagnetic Nickel sample were presented.

They show that the experiment was set up successfully. The electron and magneti-

sation dynamics measured appear to be similar to those reported in the literature.

For the magnetisation dynamics, both the rotation and the ellipticity component

of the magneto-optical Kerr signal were measured. Both signals show the same be-

haviour on sub-ps times within the resolution of the experiment, and therefore our

results do not confirm the findings of Koopmans and co-workers who reported a dif-

ference between rotation and ellipticity. Dynamic hysteresis loops were measured at

fixed time delays. Their shape most likely results from a reorientation of the macro-


scopic magnetisation due to sample heating. They also showed the importance of

measuring the demagnetisation effect at saturation.

Chapter 5

Time-Resolved Circular Pump

Measurements in GaAs, Ni and Al

5.1 Introduction

After the successful measurements of the demagnetisation of the Ni sample the

question arose as to whether it would be possible to create a spin orientation in a

non-magnetic metal by pumping with circularly polarised light and then measure the

relaxation of those spins. As described in the background chapter, optical pumping

with circularly polarized light can selectively excite spin-polarized electrons in semi-

conductors and optical pump-probe experiments with fs lasers have already been

successfully performed in semiconductor samples. Al seems to be a good candidate

for optical orientation experiments. Its band structure features a direct interband

transition between parallel bands on the square face of the Brillouin zone which

90

CHAPTER 5. CIRCULAR PUMP IN GAAS, NI AND AL 91

leads to a strong optical absorption at a wavelength of about 800 nm, that is well

matched to the peak output of a mode-locked Ti:sapphire laser. Also the value of the

longitudinal spin relaxation time T1 for Al was calculated (55) to be of the order of

100 ps at room temperature in good agreement with room temperature CESR data

(56). In previous measurements made on metals such as Au (58), only intraband

transitions were excited, and so no comparison could be made with the interband

pumping mechanism that is used to optically orient spins in GaAs. A further conse-

quence of the interband transition in Al is a strong piezo-optic response at 800 nm

wavelength (32). Recently it was shown that both thermal and elastic transients

must be considered in order to understand the reflectivity response of Al observed

in picosecond pump-probe experiments (26). In addition, a rapid surface melting

was observed for very large pump fluences and explained in terms of an ultrafast

collapse of the band structure (11).

In this chapter pump-probe studies will be presented that were performed with

an elliptically polarised pump beam. The aim was to create a possible spin orien-

tation by selective spin pumping and then measure its subsequent decay. At first

studies were made on intrinsic GaAs in order to check the set-up and compare with

the literature. Also additional polarisation and power dependent measurements were

made. Then the Ni sample was examined with an elliptical pump in order to check

whether the demagnetisation signal would be affected by an additional spin orienta-

tion. Finally an Al thin film was examined. For all three series, sets of time-resolved

sum (reflectivity) and difference (rotation) data were taken. The degree of elliptical


polarisation of the pump beam was varied by rotating a quarter wave plate placed

in the pump beam. An initial peak is observed in the transient rotation signal for all

three materials. The dependence of the peak height upon the ellipticity of the pump

is found to be qualitatively different for the three materials, indicating different con-

tributions from the specular inverse Faraday effect (SIFE) and specular optical Kerr

effect (SOKE) in each case. For ferromagnetic Ni the peak is superimposed upon a

longer-lived ultrafast demagnetisation signal. For GaAs and Al a rotation signal is

observed that decays on time scales of several picoseconds.

5.2 Experiment

The measurements were made upon an intrinsic GaAs(100) wafer (Hall mobility

7000-8000 cm2V −1s−1, carrier density 1.5 − 6.5× 107cm−3), a 500A thick polycrys-

talline Ni film (the same one as used in the previous chapter) and a 500A thick

polycrystalling Al film, both grown on Si(100) wafers by DC magnetron sputtering.

The optical set-up was largely the same as in the previous experiments and as shown

in figure 3.1 in the experimental section. An additional quarter wave plate was in-

troduced into the pump beam in order to continuously vary the pump polarisation

from linear p, through elliptical, to circular polarisation. Also a second lock-in am-

plifier was acquired to measure reflectivity (sum signal from the bridge detector) and

rotation (difference) signals simultaneously and so ensure that the same assignment

of the zero delay position was used in all scans.

Some care must be taken in setting the plane of polarisation of the incident


probe beam. The probe beam must be linearly polarised in the plane of incidence.

If the sample normal is not exactly horizontal then the plane of incidence will not

be parallel to the optical table. A reflectivity component may then be detected

in the magneto-optical data if the probe is horizontally polarised, leading to an

asymmetry in the difference scans upon reversing the magnetic field or reversing the

pump beam helicity. Such an asymmetry was found in the Ni measurements in the

previous chapter. During the measurements performed with the GaAs and the Al

sample an alignment method was developed that allowed the plane of polarisation

to be adjusted when no magnetic background signal was apparent. This led to

symmetrical scans upon reversal of the pump helicity. This method was already

described in the experimental chapter. For a magnetic sample a strong rotation

signal is expected when the pump beam is linearly polarized due to the ultrafast

demagnetisation effect. It is then more difficult to set the probe beam polarization

correctly as this technique cannot be applied. In this case the method applied in

the previous chapter is used again to identify the true magnetisation signal: the half

difference of pairs of measurements made with magnetic fields of opposite sign is

taken.


-1 0 1 2 3 4 5 6-250

-200

-150

-100

-50

0

50

100

150

200

250

0 2 4 6

30

40

50

right circular

left circular

∆θ (

arb.

uni

ts)


∆ R (

arb

. uni

ts)

Figure 5.1: Pump-induced MOKE rotation in GaAs for linear and circular pump. The

inset shows the time-dependent reflectivity change.

5.3 Results

5.3.1 Gallium Arsenide

At first measurements were taken on the GaAs wafer with different pump polari-

sations in order to characterise the experimental set-up. At that time the study of

Kimel et al. (10) had not yet been published. The time dependent Kerr rotation θ(t)

obtained for linearly and circularly polarized pump beams is shown in Figure 5.1.

Three components can be distinguished in the response obtained with a circularly

polarized pump. Firstly there is a sharp peak, centered at zero delay, with a full

width half maximum of 160fs. Secondly there is a contribution visible at the right


hand flank of the peak where the signal changes sign and which decays exponentially

with a short time constant. Thirdly there is a contribution that decays exponentially

but with a longer time constant. The rotation scans can be fitted with equation 2.19

introduced in the background chapter. It describes a δ-function and two exponen-

tial decays folded with the pump and probe pulse shapes. The fits are in excellent

agreement with the data. Scans were recorded for four different cw equivalent pump

powers in the range of 10 to 200 mW. The obtained rotation and reflectivity scans

are shown in figure 5.2. The variation of the fitted parameter values using equation

2.19 is shown in figure 5.3. The Kerr rotation was also measured for intermediate

elliptical pump polarization states by rotating the quarter wave-plate in the pump

beam. The dependence of the height of the peak at zero delay upon φ is shown in

figure 5.4, where φ is the angle that the fast axis of the quarter wave plate describes

with the plane of polarization of the incident light. For settings of 0, 90, 180

and 270 the pump is p-polarized and no magneto optical signal is observed. At

45, 135, 225 and 315 the light is circularly polarized and the peak has maximum

amplitude.


-5 0 5 10 15 20 25

0

10

20

30

40

50

60

100mW

10mW

50mW

200mW

Ref

lect

ivity

Cha

nge

(arb

. uni

ts)


a)

-10 -5 0 5 10 15 20-20

0

20

40

60

80

100

120

140

160

180

200

10mW

50mW

Rot

atio

n Si

gnal

(arb

. uni

ts)


200mW

100mW

Figure 5.2: (a) Reflectivity change and (b) rotation from the GaAs sample for circular

pump light of varying intensity. The reflectivity data was plotted as measured to show the

linear dependence of the background on the pump power. The rotation data was offset for

clarity on both horizontal and vertical scales. Here the background was almost zero in each

case.


0 50 100 150 200-20

0

20

40

60

80

A B C

Am

plitu

des

(arb

. uni

ts)

Average Pump Power (mW)

(b)

0.0

0.1

0.2

0.3

2

4

6

w τ

1

τ2

Tim

e C

onst

ants

(ps

)(a)

Figure 5.3: Dependence of the fitted parameter values upon the pump intensity. The

rotation data was fitted to equation 2.19.


0 30 60 90 120 150 180 210 240 270 300 330 360-200

-100

0

100

200

Pea

k H

eig

ht a

t Ze

ro D

ela

y (a

rb. u

nits

)

Pump Waveplate Angle φ (degrees)

right rightleft left

Figure 5.4: Dependence of the height of the peak observed in the time-resolved rotation

from GaAs upon the pump wave plate angle φ The pump beam polarisation is sketched

above the figure.

5.3.2 Nickel

In the previous chapter measurements made on a thin film Ni sample with a lin-

early polarized pump beam were presented. An ultrafast demagnetisation of ap-

proximately 7% was observed to occur within a time delay of less than 300fs, in

agreement with previous reports (1; 2). Figure 5.5 shows the time dependence of

the pump-induced reflectivity and Kerr rotation changes obtained with both lin-

early and circularly polarized pump beams. The measurements were made in the

presence of large positive and negative magnetic fields of ±960 Oe which were suf-


-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1

-0.5 0.0 0.5 1.0 1.5 2.0-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

-18

-16

-14

-12

-10

-8

-6

-4

-2

0

2

Average Difference

-960 Oe

+960 Oe

Rot

atio

n C

hang

e (m

deg)

left circular

right circular

Rot

atio

n C

hang

e (m

deg)


b)

c)

a)

Ref

lect

ivity

Cha

nge

(arb

. uni

ts)

Figure 5.5: The figure shows time-dependent reflectivity and rotation scans obtained

from Ni. The top panel (a) shows the change in reflectivity for a p-polarised pump. In

the middle panel (b) the rotation signals obtained for a p-polarised pump are shown for

saturating external fields of ±960 Oe. The open circles represent the average difference of

the two traces. In the bottom panel (c) the rotation signals for p-polarised as well as right

and left circularly polarised pump obtained in an external field of +960 Oe are shown.


-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

-4

-2

0

2

4

MO

KE R

otat

ion

(mde

g)

Applied Field (kOe)

Figure 5.6: The figure shows the static hysteresis loop of Ni (MOKE rotation).

ficient to saturate the sample as can be seen from the hysteresis loop in figure 5.6.

The total loop height is about 7.6 mdeg. This value is in good agreement with the

value calculated in the previous chapter. The shape of the reflectivity curve does

not seem to be affected by the pump beam polarization. However for the rotation

measurements, when the pump is circularly polarized a peak is observed at zero

delay in addition to the ultrafast demagnetisation signal. The peak width is about

160 fs and is similar to that observed in GaAs. There is an asymmetry in the two

traces for opposite magnetisation due to some residual misalignment of the probe

polarisation. The true ultrafast demagnetisation signal is obtained by taking the

average difference of the two traces. The peak demagnetisation signal is obtained

at a time delay of approximately 200 fs. The demagnetisation was found to be 9%

in good agreement with the 7% measured with similar pump power in the previous


chapter.

The two curves in positive and negative field appear to rise at slightly different

times. This is due to a small residual zero delay peak that does not change sign as

the magnetic field is reversed. Indeed the sum of the two curves shows a zero delay

peak with width identical to that of the zero delay peak obtained with a circular

pump. Although the pump beam is linearly polarized after the quarter waveplate,

birefringence in the focusing optics may cause it to have a small ellipticity at the

sample. It is essential that there is no experimental uncertainty in the zero time

delay position if the curves obtained with a linear pump are to be correctly compared,

i.e. for taking the average difference. Therefore the second lock-in amplifier is used

to measure the rotation signal simultaneously with the reflectivity. The reflectivity

scans can be overlaid to confirm the integrity of the zero delay position in scans

where no zero delay peak is observed. The data measured in the previous chapter

lacked this zero delay check. There is therefore some uncertainty about the correct

relative timings of different measurements which could possibly affect the rise times

and shapes of the average difference signals.

On longer time scales there seems to be no effect of the pump polarisation upon

the demagnetisation signal. However, it is difficult to observe this potentially small

effect on top of the large demagnetisation effect. This background may be removed

by rotating the orientation of the static magnetic field through 90 to the transverse

Kerr configuration. The set-up is insensitive to transverse MOKE contributions

and only the pump-induced rotation effect should then be seen. Figure 5.7 shows


-0.5 0.0 0.5 1.0 1.5 2.0

-60

-40

-20

0

20

40

60

p-polarised

left circular

right circular

Rot

atio

n Si

gnal

(arb

. uni

ts)


Figure 5.7: Rotation signal from the Ni sample for linear and circular pump in a trans-

verse magnetic field.

measurements obtained in a transverse field with linear and circular pump polarisa-

tion. As in the longitudinal geometry, no pump-helicity dependent effect could be

observed on long time scales.

The rise and decay times of the zero delay peak are much faster than the rise time

of the demagnetisation signal. The zero delay peak does not seem to be affected by

the orientation of the magnetization of the sample but is observed in addition to the

normal demagnetisation signal. Again the height of the zero delay peak depends

upon the pump polarization and has opposite sign for pump beams of opposite

helicity. This is shown in figure 5.8. The dependence of the peak height upon the

degree of circular polarization of the pump (or equivalently the waveplate angle φ)

is somewhat different to that in GaAs.


0 30 60 90 120 150 180

-150

-100

-50

0

50

100

150

Pe

ak h

eigh

t at Z

ero

Del

ay (

arb.

uni

ts)


right left

Figure 5.8: The dependence of the height of the peak in the time-resolved rotation signal

obtained from Ni upon the pump wave plate angle φ is shown. The pump polarisation is

sketched on the top.


0 2 4 6 8 10

-80

-60

-40

-20

0

20

40

60

left elliptical (-22°)

right elliptical (+22°)

∆θ

(ar

b. u

nits

)


35

40

45

50

55

60

65

(b)

∆R (

arb.

un

its)

(a)

Figure 5.9: (a) Reflectivity and (b) Kerr rotation scans from the Al sample close to zero

delay are shown for an elliptical pump polarisation at a wave plate setting of ±22.5.

5.3.3 Aluminum

Finally the Al sample was examined. Both GaAs and Al are non-magnetic and so a

p-polarized pump leads to a flat rotation signal as observed in GaAs. As shown in

figures 5.9 and 5.10, a rotation signal was generally observed when the sample was

pumped with elliptically polarized light. The pump-induced change in reflectivity is

also shown. The reflectivity signal in figure 5.9(a) shows a sharp peak at zero delay

and then a slower increase in the signal with a maximum at about 6 ps. Then the

signal decays exponentially with a longer decay constant. Some oscillations are seen


-10 0 10 20 30 40 50 60 70 80

-8

-6

-4

∆θ

(ar

b. u

nits

)


40

50

60

70

(b)

∆R

(ar

b. u

nits

)(a)

Figure 5.10: (a) Reflectivity scan from the Al sample for time delays up to 80 ps. (b)

Average difference of the Kerr rotation scans for elliptical pump polarisation at wave plate

settings of ±22.5.

to be superimposed on the signal as shown in figure 5.10(a). The rotation signal

contains both a peak at zero delay, again with a FWHM of 160fs, and a longer lived

signal. Again the average difference of the curves in figure 5.9(b) is taken as the

best representation of the rotation signal obtained from the sample. This is shown

in figure 5.10(b). Equation 2.19 was then used to fit the data shown in this figure. It

was found that only one exponential term, analogous to the third term used in fitting

the GaAs data, was required. Unlike in GaAs, the rotation signal does not change

its sign. The time constant for the exponential decay was found to have a value of

6 ps. The dependence of the height of the zero delay peak and the amplitude of


right left

-200

-100

0

100

200

0 30 60 90 120 150 180

-10

0

10

Pe

ak H

eig

ht

at

Ze

ro D

ela

y (a

rb.

un

its)


Am

plit

ude

of

Ta

il (a

rb.

un

its)

Figure 5.11: The dependence of following quantities upon the pump wave plate angle φ

is shown for tha Al sample: the height of the zero delay peak in the rotation signal (top

panel); the amplitude of the long lived tail (bottom panel).

the longer lived contribution to the rotation signal upon the orientation of the wave

plate are shown in figure 5.11. The trend is completely different to that observed

for GaAs (see figure 5.4). The rotation signal is seen to vanish when the pump is

circularly polarized whereas a maximum was observed for GaAs. The data in figure

5.11 has a period of only 90 and the signal has maximum amplitude for a wave

plate orientation of φ = ±22.5 at which the pump beam has elliptical polarization.

The amplitude of the exponentially decaying component was found to have a similar

angular dependence to that of the zero delay peak as can be seen at the bottom of

the figure.


5.4 Discussion

The first measurements made on GaAs (figure 5.1) demonstrate that high quality

optical orientation and spin relaxation data can be obtained with this measurement

technique. They also establish a basis for comparison with measurements made

upon metals. The results are qualitatively similar to those reported by Kimel et al.

(10). In this study the measurements were made at a wavelength of 800 nm which

is in the center of the range used in reference (10). It corresponds to an energy

of 1.55 eV, well above the 1.42 eV room temperature band gap of intrinsic GaAs.

However the pump fluence used here is one to two orders of magnitude greater.

Three separate contributions to the rotation signal have been clearly identified. The

three amplitudes A, B, and C in figure 5.3 show a monotonic non-linear dependence

upon pump power. This is unsurprising given that interactions between excited

carriers and renormalization of the band structure are likely to play an important

role. The width of the Gaussian peak at zero delay appears to be constant while the

time constants for the two exponential terms both increase with pump power. The

measured values of τ1 are longer than that of 30 fs reported in reference (10) while

the values of τ2 never reach that of 10 ps reported by the same authors. The reason

for these differences is presently unclear but it is likely that the detailed form of the

rotation response may be highly sample dependent. Since the exponential term with

the short time constant has been attributed to population effects, one might expect

to see a component with similar time constant in the reflectivity data. However, no

such component could be found when a form similar to equation 2.19 was fitted to


the reflectivity data.

The ultrafast demagnetisation observed in Ni when the pump is linearly polar-

ized is in good agreement with previous reports by ourselves (72) and others (1; 2).

A circularly polarised pump leads to a peak at zero delay in addition to the ultrafast

demagnetisation signal. No effect of the pump helicity upon the demagnetisation

signal on longer timescales could be seen. Also the measurements in the transverse

geometry without the demagnetisation background did not reveal any pump-induced

effect on longer time scales. This is not surprising if an interband transition is re-

quired for optical orientation of electrons after thermalization. The magneto-optical

response of Ni should be more complicated than that of GaAs because there are two

different quantisation axes to be considered. Firstly, the spontaneous magnetisation

lies in the plane of the sample and is sensed by means of longitudinal MOKE. Sec-

ondly, since the angle of incidence of the pump beam is 25, any optically oriented

spins should be aligned close to the sample normal and be sensed by polar MOKE.

However, the optically oriented spins would be expected to precess in the exchange

field associated with the spontaneously magnetised electron population and may

rapidly dephase. Therefore the effect of the pump helicity upon the ultrafast de-

magnetisation should be studied in samples magnetised perpendicular to the plane

and pumped at normal incidence. For that purpose the shape anisotropy of the thin

film must be overcome which requires a strong magnetic field while maintaining a

wide field optical access. This was not technically possible within the present study.

The reflectivity signal observed in the Al film rises on a time scale much longer


than that observed for Ni and GaAs. A time resolved photoemission study (28)

showed that single electron states in Al have lifetimes of less than 200 fs at energies

of greater than 0.5 eV above the Fermi level. It seems unlikely then that the re-

flectivity signal results purely from heating of the electron system since the electron

system thermalises on sub-picosecond time scales. Similarly long rise times were

recently observed and explained by Richardson and Spicer (26). In their model the

optical pump initially heats the electron system, and heat is transferred to the lattice

through electron-phonon scattering, so that the electron and phonon systems reach

equilibrium within about 0.6 ps (73). However heating of the electron system also

creates a thermal stress that causes an acoustic pulse (coherent phonon) to propa-

gate from the surface into the interior of the film. The rise time of the reflectivity

signal is therefore related to the time taken for the acoustic pulse to move out of

the region sensed by the probe beam (about one optical skin depth). Echoes are

expected as the acoustic pulse is reflected from the film-substrate interface back into

the optically probed region. This is the origin of the small dip in the data of figure

5.10, between 10 and 20 ps. A similar feature was observed for a 50 nm film studied

in reference (26).

The dependence of the Al rotation signal upon the pump helicity is one of the

most surprising aspects within this chapter. Since the pump beam is incident upon

the sample at an angle of 25, one might expect the polarization of the electric field

within the surface of the sample to be somewhat different to that outside the sample.

However, by calculating the Fresnel transmission coefficients ts and tp it was found


that ts is approximately equal to tp in each case so that this cannot explain the

strange angular behaviour. Peaks at zero delay were observed in all three samples

so their behavior may be compared. In each case the FWHM of 160 fs corresponds

to the expected width of the cross-correlation of two laser pulses of 120 fs pulse

width. If the peak is assumed to arise from the orientation of hot electron spins

then one can deduce that the relaxation time of the hot electron spin is much

shorter than our pulse width. The dependence of the peak height upon the pump

helicity is completely different for GaAs and Al while exhibiting an intermediate

behavior for Ni. A simple sinusoidal variation with period of 180 was observed

for GaAs in figure 5.4. It is easily shown that the difference in number of photons

of left and right circular polarization present in the pump beam is proportional

to sinφ, the sine of the angle of orientation of the quarter wave plate. Therefore

the angular dependence observed for GaAs is consistent with a model in which the

rotation signal arises due to optical orientation. Equation 2.28 in the background

chapter describes the incoherent contribution to the rotation of the probe beam due

to cubic non-linearity, for the case that both pump and probe beams are at normal

incidence. This is a reasonable approximation to the present situation since the

pump and probe beams within the sample are strongly refracted towards the film

normal. The first and second terms in this equation that vary with the wave plate

angle φ as sin(4φ) and sin(2φ) are identified with the Specular Optical Kerr Effect

(SOKE) (optically induced linear birefringence) and the Specular Inverse Faraday

Effect (SIFE) (optically induced circular birefringence) respectively. From figures


5.4, 5.8 and 5.11 one might therefore conclude that the SIFE is dominant in GaAs

(10), the SOKE is dominant in Al, while the more complicated dependence in Ni

is the result of competition between the SIFE and the SOKE. No comprehensive

microscopic theory of the cubic non-linearity giving rise to the peak has yet been

advanced, and there seems to be no reason why a similar behavior should be observed

in GaAs, Ni and Al given their very different electronic structures.

Figure 5.11 shows that the slowly decaying tail and the zero delay peak obtained

in the Al rotation signal both exhibit the same dependence upon the pump polari-

sation that is characteristic of linear birefringence. A purely electronic mechanism

would require a redistribution of electronic charge that would be screened on fem-

tosecond time scales, or else a redistribution of electronic momentum states that

would be destroyed by momentum scattering on similarly short time scales. There-

fore an alternative mechanism is required to explain the presence of the tail. One

possibility is that the apparent rotation (difference) signal results from misalignment

of the probe beam polarisation. However, the alignment was carefully checked as

described above. Also a signal resulting from changes in the optical constants of the

sample would be expected to appear with the same sign in both the curves shown

in figure 5.9(b). A second possibility is that the thermal electrons become spin-

polarised. However, the observed relaxation time of 6 ps is an order of magnitude

smaller than the T1 values obtained by calculation (55) and from CESR data (56).

Also the dependence upon the pump beam polarisation would require a completely

different mechanism for optical orientation to that which is well established in GaAs.


So this possibility seems rather unlikely.

Finally, the long-lived birefringence could result from a distortion of the lattice.

The coherent phonon in reference (26) was generated by an isotropic thermal stress

that would not be expected to produce birefringence. By fitting equation 2.19 to

the reflectivity data in figures 5.9(a) and 5.10(a) it was found that the rise of the

reflectivity between 0.2 and 6 ps has a time constant of 2 ps that is somewhat shorter

than the value of 6 ps obtained from the rotation data. Therefore if the slow rise of

the reflectivity curve is due to propagation of the thermoelastic wave, an additional

mechanism is still required to explain the rotation data. Since the tail within the

rotation signal rises instantaneously, it would be necessary for either the optical field

to act directly upon the ion cores within the lattice, or for the lattice to respond

to the short-lived redistribution of conduction electron momentum states induced

by the optical field. The recent observation of ultrafast surface melting in Al lends

some support to this idea (11), and so it seems that a lattice excitation provides the

most likely mechanism for the long-lived linear birefringence.

5.5 Summary

We have investigated how optical pump-probe measurements may be used to study

transient linear and circular birefringence at room temperature in semiconductors

and both magnetic and non-magnetic metals, and whether a spin orientation could

be created and measured in the non-magnetic metals Ni and Al. Measurements

made upon GaAs are consistent with optical orientation and relaxation of spin.


However the measured relaxation times depend upon the pump fluence and suggest

that interactions between excited carriers and renormalisation of the band structure

play an important role when the pump fluence is large. In the case of Ni, no effect

of the pump helicity upon the picosecond demagnetisation signal could be detected.

This is unsurprising if excitation of an interband transition is essential for optical

orientation of thermalised electron spins. While all three materials exhibit a peak

in the transient rotation signal at zero delay, the dependence of the peak height

upon the helicity of the pump is markedly different in each case. The behavior

observed in GaAs is characteristic of circular birefringence (SIFE), that observed

in Al is characteristic of linear birefringence (SOKE), while that in Ni has mixed

character. Al also exhibits a longer-lived transient rotation signal that has the same

dependence upon the pump helicity as the zero delay peak. This signal appears to

rise instantaneously and relaxes with a time constant of 6 ps. It is suggested that

this transient is associated with an ultrafast lattice distortion rather than optical

orientation of spin. The development of a realistic microscopic model for the cubic

optical non-linearity in Al is now required so that the origin of the transient rotation

signal may be more clearly understood.

Chapter 6

Al SIFE and SOKE Measurements

6.1 Introduction

The time-resolved measurements on Al in the previous chapter showed some unex-

pected behaviour. From the dependence of the peak height on the degree of circular

polarisation one would expect the SOKE to be the dominant non-linearity. However,

the long-lived tail of the signal shows exactly the same polarisation dependence as

the peak. The microscopic origin of the long lifetime of the birefringence effect that

is visible in the tail is still unclear. There is also a possibility that there is a SIFE

effect present but that it is not visible in the rotation signal. In this chapter four sets

of time-resolved optical-pump measurements are shown in order to fully characterise

the dependence of the probe signal upon the pump polarisation. In two cases the

pump polarisation is elliptical as in the previous chapter. In the other two cases

the pump polarisation is linear and the polarisation axis is rotated with respect to

114

CHAPTER 6. AL SIFE AND SOKE MEASUREMENTS 115

the probe polarisation. In each case the rotation and the ellipticity response of the

reflected probe beam are measured. From these four sets of measurements it will

be determined whether SIFE or SOKE contribute to the time-resolved signal. The

corresponding elements of the local cubic nonlinearity tensor χxxyy and χxyyx will

be calculated.

6.2 Experiment

The experimental set-up was largely the same as used in the previous experiments

and the same Al sample was used. For the elliptical pump measurements the linear

polariser (set to p) is followed by a rotatable quarter wave plate. The degree of

elliptical polarisation (between linear and circular) is set by rotating the wave plate.

For the linear pump measurements the quarter wave plate is placed in front of the

polariser. It is set to make the pump beam circularly polarised. Then by rotating

the linear polariser the polarisation axis may be changed while leaving the intensity

constant. The pump intensity for the linear pump experiments is only half that

for the elliptical pump experiments. Most of the measurements presented in this

chapter were performed with the full average pump power of ∼200 mW, except the

linear pump polarisation series that were measured at ∼100 mW.

As before, either the rotation or the ellipticity of the reflected probe beam are

measured simultaneously with the reflectivity signal using the optical bridge detec-

tor. Inserting a quarter wave plate in front of the detector allows ellipticity to be

measured instead of rotation. Finally a few additional measurements were made


with the probe beam set to s-polarisation in order to investigate the behaviour of a

peak at zero delay in the reflectivity scans.

The alignment of the quarter wave plate seemed to be somewhat inaccurate. It

was noticed that for the linear scans, when the linear polariser was rotated, the

height of the reflectivity curves stayed essentially constant. For the case of an ellip-

tical pump, when the wave plate was rotated the heights changed considerably with

the wave plate angle. It is likely that the rotation of the wave plate slightly changes

the orientation of the pump beam so that the critical overlap of pump and probe

on the sample is affected. This would change the effective intensity of the pump

beam within the probed area. In order to account for this, the time-resolved scans

were normalised to the height of the reflectivity signals at large positive delay. This

method seems appropriate since the reflectivity signal at long time delays should

only depend upon the pump intensity and not upon the polarisation. If the change

in reflectivity was due to a difference in the rss and rpp reflection coefficients then

even bigger changes should have been observed in case of the linear pump polarisa-

tion, especially when comparing purely p- and s-polarised scans. This was not the

case. The normalisation of the rotation/ellipticity signals to the reflectivity height

improved the quality of the sinusoidal fits that will be presented later in this chapter.

Also when normalised, the different reflectivity scans that will be discussed below

were found to perfectly overlap apart from a small peak at zero delay.


6.3 Results

Figure 6.1 shows the dependence of the reflectivity change and the rotation signal

upon the pump power. Scans were taken with an elliptically polarised pump at

pump wave plate angles of ±22.5 for pump powers from 10 to 200 mW. In the

case of the reflectivity signal, the average sum of both angles was taken for each

pump power. The signal levels at negative delay and at a positive delay of 1 ps are

plotted in figure 6.1a. The rotation data was fitted with equation 2.19 with only

one exponential decay term. The fit parameters offs, A and B are shown in figure

6.1b. Both signals, reflectivity and rotation are seen to depend linearly on the pump

power.

6.3.1 Reflectivity Data

Figures 6.2 to 6.5 show how the reflectivity and rotation/ellipticity signals vary

in the vicinity of zero delay as the pump polarisation is varied. Typical transient

reflectivity signals are a few tenths of percent in size. When comparing the signal

size for linear pump with that for an elliptical pump one has to keep in mind that,

owing to the different order of the optics, the pump intensity in the first case is

only about half that in the second case. The reflectivity signals all follow the same

general shape of an initial rise and exponential decay with some extra features due

to thermo-elastic contributions. This can be seen in more detail in the reflectivity

scan up to 180 ps time delay that is shown in figure 6.6. The data was taken

with a linearly p-polarised pump. It shows a sharp peak at zero delay, then a few


0 50 100 150 200

0

5

10

15

20

250

5

10

15

Rot

atio

n Si

gnal

(arb

. uni

ts)

Average Pump Power (mW)

offset A B

(a)

(b)

Ref

lect

ivity

Cha

nge

(arb

. uni

ts)

negative delay signal at 1ps

Figure 6.1: Dependence of (a) the reflectivity signal and (b) the rotation signal upon the

pump power. The signal levels at negative delay and at 1 ps were used to characterise the

reflectivity signal. The rotation signals were fitted with equation 2.19 and the offset, A

and B are shown. Both, reflectivity and rotation are seen to depend linearly on the pump

power. The lines are straight line fits through the origin.


-10 -5 0 5-2

0

2

4

6

8

10

12

(b) polariserangle: -90o

-75o

-60o

-45o

-30o

-22.5o

-15o

0o

+15o

+22.5o

+30o

+45o

+60o

+75o

+90o

Prob

e R

otat

ion

(mde

g)


0.00

0.05

0.10

0.15

0.20 (a)

Ref

lect

ivity

Cha

nge

(%)

polariserangle:-90o

-75o

-60o

-45o

-30o

-22.5o

-15o

0o

+15o

+22.5o

+30o

+45o

+60o

+75o

+90o

Figure 6.2: Time-resolved pump-induced reflectivity change (a) and rotation signal (b)

obtained from the Al sample for linear pump polarisation. The orientation of the pump

beam polariser is shown within the figure. The curves are offset for clarity.


-10 -5 0 5

-2

0

2

4

6(b)

Prob

e El

liptic

ity (m

deg)


polariserangle:-90o

-75o

-45o

-22.5o

0o

+22.5o

+45o

+75o

+90o

0.00

0.05

0.10

0.15

(a)

Ref

lect

ivity

Cha

nge

(%)

polariserangle:-90o

-75o

-45o

-22.5o

0o

+22.5o

+45o

+75o

+90o

Figure 6.3: Time-resolved pump-induced reflectivity change (a) and ellipticity signal (b)

obtained from the Al sample for linear pump polarisation. The orientation of the pump

beam polariser is shown within the figure. The curves are offset for clarity.


0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35 (a)

Ref

lect

ivity

Cha

nge

(%)

wave plateangle:-90o

-75o

-67.5o

-60o

-45o

-30o

-22.5o

-15o

0o

+15o

+22.5o

+30o

+45o

+60o

+67.5o

+75o

+90o

-10 -5 0 5

-5

0

5

10

15

(b)

Prob

e R

otat

ion

(mde

g)



-75o

-67.5o

-60o

-45o

-30o

-22.5o

-15o

0o

+15o

+22.5o

+30o

+45o

+60o

+67.5o

+75o

+90o

Figure 6.4: Time-resolved pump-induced reflectivity change (a) and rotation signal (b)

obtained from the Al sample for elliptical pump polarisation. The orientation of the pump

wave plate is shown within the figure. The curves are offset for clarity.


0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

Ref

lect

ivity

Cha

nge

(%)


-67.5o

-45o

-22.5o

0o

+22.5o

+45o

+67.5o

+90o

-10 -5 0 5-1

0

1

2

3

4

5

6

7

(a)

(b)

Prob

e El

liptic

ity (m

deg)



-67.5o

-45o

-22.5o

0o

+22.5o

+45o

+67.5o

+90o

Figure 6.5: Time-resolved pump-induced reflectivity change (a) and ellipticity signal (b)

obtained from the Al sample for elliptical pump polarisation. The orientation of the pump

wave plate is shown within the figure. The curves are offset for clarity.


0 20 40 60 80 100 120 140 160 180 20010

20

30

40

50

60

70

80

90

0 5 10 1510

20

30

40

50

60

70

80

90

Ref

lect

ivity

Cha

nge

(arb

. uni

ts)


Figure 6.6: Exponential decay of the Al reflectivity signal fitted for long time delays with

τ=132 ps. The data clearly shows the oscillations caused by strain induced ultrasonic

waves up to a delay of 30 ps. The inset shows the reflectivity signal at zero delay together

with the same exponential fit.

oscillations up to a time delay of ∼30 ps with a first maximum at about 6-7 ps.

Afterwards the signal decays exponentially with a time constant of 132 ps. The

figure also shows that the initial oscillations seem to be superimposed on top of the

exponentially decaying signal. The distance in between the first two peaks is about

12.5 ps. Other measurements on the same sample showed values up to 15 ps.

While the shapes of the reflectivity signals at time delays greater than 200 fs

do not depend on the pump polarisation, the signals differ in the vicinity of zero


-90 -60 -30 0 30 60 900.00

0.05

0.10

0.15

0.20

0.25

linear pump, rotation linear pump, ellipticity elliptical pump, rotation elliptical pump, ellipticity

Ref

lect

ivity

Pea

k H

eigh

t (%

)

Angle Setting (degrees)

Figure 6.7: Dependence of the peak value of the Al reflectivity signal at zero delay upon the

pump polariser angle (linear pump) and pump quarter wave-plate angle (elliptical pump).

The fitted curves are sinusoidal fits with periodicities of 90 and 180 respectively.

delay. Generally a sharp peak can be observed. The width of the peak is similar

to the peak in the magneto-optical signal. The height of this peak depends on the

pump polarisation. In the case of a linear pump polarsiation in combination with

a p-polarised probe beam (figures 6.2a and 6.3a) the peak height is maximal when

the pump is p-polarised (0). The peak completely disappears for s-polarisation

(±90). In the case of an elliptical pump polarisation (figures 6.4a and 6.5a) and a p-

polarised probe, the peak height is again maximal for a linearly p-polarised pump (0

and ±90) and minimal, but non-vanishing, for circular pump polarisation (±45).

Plots of the peak height are shown in figure 6.7. The underlying background was

not subtracted from the signal so that the peak values are offset from zero. Some

additional reflectivity measurements for linear pump polarisation in combination


-5 0 5

5

10

15

20

25

Ref

lect

ivity

Cha

nge

(arb

. uni

ts)


top to bottom: -90o

-45o

0o

+45o

+90o

Figure 6.8: Time-resolved pump-induced reflectivity change of the Al sample for linear

pump polarisation and s-polarised probe beam. The angles denote the pump polariser

setting with 0 for p- and 90 for s-polarisation. The curves are offset for clarity.

with an s-polarised probe beam are shown in figure 6.8. Here the dependence of

the zero delay peak height on the pump polarsiation is reversed, i.e. the peak

disappears for p-polarisation at 0 and is maximal for s-polarisation at ±90. Hence

we deduce that the peak depends only on the relative orientation of pump and

probe polarisation and not on the absolute orientation of pump or probe polarisation

relative to the sample.

6.3.2 Rotation and Ellipticity Data

The rotation and ellipticity data for a linearly polarised pump beam in the vicinity

of zero delay are shown in figures 6.2b and 6.3b. A sharp peak with Gaussian

shape at zero delay is followed by a long-lived tail as was observed with an elliptical


0 10 20 30 40 50 600

2

4

6

8

10

Rot

atio

n Si

gnal

(mde

g)


Figure 6.9: Time-resolved pump-induced rotation signal from the Al sample for linear

pump polarisation. The average difference of the ±45 signals is shown.

0 10 20 30 40 50 60

-3

-2

-1

0

Ellip

ticity

Sig

nal (

mde

g)


Figure 6.10: Time-resolved pump-induced ellipticity signal from the Al sample for linear

pump polarisation. The average difference of the ±45 signals is shown.


pump in the previous chapter. The peak and tail show the same dependence on the

pump polarisation. The signal vanishes for p- and s-polarised pump at 0 and ±90

respectively, and the magnitude of both peak and tail are a maximum when the plane

of polarisation of pump and probe lie 45 apart. In the rotation measurements the

peaks and tails show the same sign whereas they have opposite signs in the ellipticity

measurements. The average difference of the signals obtained for longer time delays

at ±45 pump polarisations are shown in figures 6.9 and 6.10. Fitting these data sets

with equation 2.19 one obtains relaxation times τ2=8 ps and τ2=5 ps for rotation

and ellipticity respectively.

The rotation data for the elliptically polarised pump has been already discussed

in the previous chapter. As shown in figure 6.4b a sharp peak at zero delay and a

long-lived tail are observed. They exhibit the same dependence upon the orientation

of the quarter wave plate. Peak and tail both vanish for linear pump (0 and ±90)

and for circular pump polarisation (±45). The peak has a maximum positive value

for +22.5 and −67.5 and a maximal negative value for −22.5 and +67.5. The

periodicity of the complete signal (offset at negative delay, peak height and tail

amplitude) upon the pump wave plate angle is therefore 90. In figure 6.11 the

average difference of the signals measured at ±22.5 pump wave plate orientation is

shown. The decay time was fitted to be τ2=3 ps.

Finally, the ellipticity data for the elliptically polarised pump is shown in figure

6.5b. Here the shape of the curves is somewhat more complicated. Some background

due to misalignment of the optics causes a small peak at zero delay and a step


0 10 20 30 40 50 60-1

0

1

2

3

4

5

6

7

8

Rot

atio

n Si

gnal

(mde

g)


Figure 6.11: Time-resolved pump-induced rotation signal from the Al sample for elliptical

pump polarisation. The average difference of the ±22.5 signals is shown.

at positive delay that is overlapped with the signal. This background signal was

observed to change during the series of scans so that it cannot simply be subtracted.

Again for a linear pump (wave plate angles of 0 and ±90) the signal vanishes. For a

circular pump (±45) a sharp peak is observed and the sign changes with the helicity.

This is different from the rotation data where the signal is zero. For intermediate

elliptical polarisation at ±67.5 an even bigger peak is observed whereas at ±22.5

a smaller peak with different shape is observed. This peak does not have a gaussian

shape but rather looks like its first derivative (see figure 6.12). No tails can be

reliably identified. The average difference of the signals at ±45 pump wave plate

orientation (circular pump) is shown in figure 6.13. The decay cannot be fitted very

well and time constants of 2-5 ps were obtained. Overall, the data in figure 6.5(b)

look as if they are formed from a superposition of two sets of data with 90 and 180


-0.5 0.0 0.50

2

4

6

8

10

12

Ellip

ticity

Sig

nal (

mde

g)


+/- 22.5O

+/- 45O

+/- 67.5O

Figure 6.12: Shapes of the time-resolved pump-induced ellipticity signal at zero delay for

different elliptical pump polarisations. Plotted are the average differences of the signals of

opposite helicity. For clarity the 45 and the 67.5 curves were shifted vertically upwards

by 2 mdeg and 4 mdeg respectively.

periodicity.

In order to quantify the dependence of the signals upon the polariser angle (linear

pump) and wave plate angle (elliptical pump), the individual scans were all fitted

with a simplified version of equation 2.19. For the analysis of the present data sets

only the offset at negative delay (offs), the peak height at zero delay (A) and the

height of the tail at short positive delays (B) are needed. Therefore the exponential

decay constants are set to infinity, C is set to be zero and the equation simplifies to:

∆θ,∆η = offs + A exp

(

− t2

4w2

)

+B

2

(

1 − erf

(

− t

2w

))

. (6.1)

In case of the last data set (ellipticity measurement with elliptical pump) the equa-

tion does not reflect the proper shape of the data for angles close to ±22.5 but


0 10 20 30 40 50 60

2

3

4

5

6

7

Ellip

ticity

Sig

nal (

mde

g)


Figure 6.13: Time-resolved pump-induced ellipticity signal from the Al sample for ellip-

tical pump polarisation. The average difference of the ±45 signals is shown.

nevertheless the formula was used for the sake of consistency. The values of offs, A

and B are plotted in figures 6.14-6.17.

Now the contributions from the SIFE and SOKE will be identified. Consider the

dependence of the linear pump data upon the pump polariser angle Θ1. According

to equation 2.25 the SOKE contributions should have a period of 180. In the case of

the elliptical pump data, the SOKE signals should vary with the pump wave plate

angle φ (sin 4φ term in equation 2.28) with a period of 90. SIFE contributions

should vary with a period of 180 (sin 2φ). Therefore the angular dependence of the

fitted parameters offs, A and B in figures 6.14 and 6.15 are fitted with one sinusoid

and in figures 6.16 and 6.17 with two sinusoids:


-90 -60 -30 0 30 60 90

-10

-5

0

5

10

-1.0

-0.5

0.0

0.5

1.0 zero delay peak height (A)

Zero

Del

ay P

eak

Hei

ght (

mde

g)

Pump Polariser Angle Q (degrees)

offset at negative delay (offs) tail height at positive delay (B)

Neg

ativ

e O

ffset

, Tai

l Hei

ght (

mde

g)

Figure 6.14: Fitted values for the parameters off, A and B in equation 6.1 are shown

for the case that the probe rotation is measured with a linear pump polarisation of variable

orientation. The pump polarisation is shown schematically above the figure.

-90 -60 -30 0 30 60 90-4

-3

-2

-1

0

1

2

3

4


-0.2

-0.1

0.0

0.1

0.2

Zero

Del

ay P

eak

Hei

ght (

mde

g)

Pump Polariser Angle Q (degrees)

zero delay peak height (A)N

egat

ive

Offs

et, T

ail H

eigh

t (m

deg)

Figure 6.15: Fitted values for the parameters off, A and B in equation 6.1 are shown for

the case that the probe ellipticity is measured with a linear pump polarisation of variable

orientation. The pump polarisation is shown schematically above the figure.


-90 -60 -30 0 30 60 90-10

-8

-6

-4

-2

0

2

4

6

8

10

-2

-1

0

1

2

Zero

Del

ay p

eak

Hei

ght (

mde

g)

Pump Wave Plate Angle f (degrees)

zero delay peak height (A)

Neg

ativ

e O

ffset

, Tai

l Hei

ght (

mde

g)


Figure 6.16: Fitted values for the parameters off, A and B in equation 6.1 are shown for

the case that the probe rotation is measured with an elliptical pump polarisation of variable

wave plate orientation. The pump polarisation is shown schematically above the figure.

-90 -60 -30 0 30 60 90-10

-5

0

5

10

-2

-1

0

1

2

Zero

Del

ay p

eak

Hei

ght (

mde

g)


zero delay peak height (A)


Neg

ativ

e O

ffset

, Tai

l Hei

ght (

mde

g)

Figure 6.17: Fitted values for the parameters off, A and B in equation 6.1 are shown

for the case that the probe ellipticity is measured with an elliptical pump polarisation of

variable wave plate orientation. The pump polarisation is shown schematically above the

figure.


linear pump:

(

ΘR2

ηR2

)

= sin 2Θ1

(ℜℑ

)

E (6.2)

elliptical pump:

(

ΘR2

ηR2

)

= sin 4φ

(ℜℑ

)

F + sin 2φ

(−ℑℜ

)

G (6.3)

where:

E = −32π2I ′pump

c |1 − n|2

χxxyy + χxyyx

n (1 − n2)

(6.4)

F = −1

2· 32π2Ipump

c |1 − n|2

χxxyy + χxyyx

n (1 − n2)

(6.5)

G = −32π2Ipump

c |1 − n|2

χxxyy − χxyyx

n (1 − n2)

(6.6)

Two sets of fits were performed. In one set the amplitudes as well as an amlitude

offset and phase offset of the sinosoids were used as fit parameters. In the second

set the amplitude offset and the phase offset were set to zero. Figures 6.14-6.17

show only the first fit that reproduces the data more closely. However, the fitted

amplitudes are not much affected by the inclusion of the offsets as shown in table

6.1. All zero delay peak fits are in excellent agreement with the data as are most

of the offset and tail fits. Only the tail of the ellipticity scans for an alliptically

polarised pump cannot be fitted properly.

Since I ′pump is only half as large in the linear case as it is in the elliptical case,

the fitted values of E and F should have the same values, offering a check between

the two measurements. From the table the second set of fits of the peak height is


pump linear linear elliptcal elliptical

probe rotation ellipticity rotation ellipticity

2Θ 2Θ 2φ 4φ 2φ 4φ

component ℜE ℑE −ℑG ℜF ℜG ℑF

offset1) 0.772 0.161 -0.629 0.765 2.126 0.132

peak1) 8.028 -2.935 -0.572 7.082 4.511 -2.834

tail1) 0.317 0.139 0.005 0.229 0.156 -0.079

offset2) 0.771 0.143 -0.655 0.763 2.108 0.136

peak2) 8.028 -2.955 -0.704 7.044 4.507 -2.829

tail2) 0.316 0.139 0.028 0.229 0.086 0.091

Table 6.1: The table shows the parameters fitted from figures 6.14-6.17 using equations

2.25 and 2.28. All values are in mdeg. 1) denotes data fitted with variable amplitude offset

and phase offset, 2) denotes data fitted with zero amplitude offset and phase offset.

taken to calculate χxxyy and χxyyx:

E = (8.028 − 2.955i) mdeg = (14.01 − 5.157i) × 10−5 rad (6.7)

F = (7.044 − 2.829i) mdeg = (12.29 − 4.937i) × 10−5 rad (6.8)

G = (4.507 + 0.704i) mdeg = (7.866 + 1.229i) × 10−5 rad (6.9)

For these values and for the values in table 6.1 four digits have been retained for

further calculations. This does not reflect the accuracy. Due to uncertainties in ex-

perimental parameters such as the exact pump intensity only one digit is significant.

The fitted values of E and F are in good agreement. The tensor components will


be calculated in cgs units. The pump intensity for the elliptical case is estimated to

be Ipump = 9 × 109 W cm−2 = 9 × 1016 erg s−1 cm−2 by assuming an average pump

power of 200 mW at a repetition rate of 82 MHz, a square pulse width of 120 fs and

a square spot profile of 15 × 15 µm2. The speed of light is c = 2.998 × 1010 cm s−1

and an index of refraction n = 2.685 + 8.453i was calculated from (69). Convering

F and G to radians the tensor values are:

χxxyy = −(1 + 0.4i) × 10−8 rad cm3 erg−1

χxyyx = −(0.6 + 0.04i) × 10−8 rad cm3 erg−1

These values are similar in magnitude to the value of |χxxyy−χxyyx| ≃ 1.5×10−8 esu

observed for Au by Zheludev et al. (58).

Finally a method to separate SIFE and SOKE effects in the elliptical pump

measurements will be illustrated. From equation 2.28 it can be seen that SIFE

and SOKE both show sinusoidal behaviour with respect to the wave plate angle

φ but with different periods. If they are both present as in the ellipticity data,

they should add up to yield more complex curve shapes as already seen in figure

6.12. The angular behaviour is simulated in figure 6.18 assuming equal amplitudes

for SIFE and SOKE. It can be seen that only the SIFE is present at an angular

setting of -45. At angles of -22.5 and -67.5 the SIFE has the same sign and

magnitude whereas the SOKE has the same magnitude but opposite sign. If these

two scans are added together the SOKE will cancel leaving only the SIFE. If instead

the difference of the scans is taken the SIFE will cancel and the SOKE will remain.

This procedure was performed as shown in figure 6.19. The plot contains the original


-90 -60 -30 0 30 60 90-2

-1

0

1

2

Sign

al (a

rb. u

nits

)


SIFE SOKE sum signal

Figure 6.18: Simulated ellipticity signal for elliptical pump polarisation containing the

SIFE and SOKE. A method for separating the two effects is described in the text.

data at 45 (containing only SIFE), half the sum of the ±22.5 and ±67.5 data

(SIFE) and also half their difference (SOKE). Also half the sum multiplied by√

2 is

plotted. It perfectly matches the scan for 45 as one would expect from figure 6.18.

The difference data in the inset looks very similar to the ellipticity data obtained

with linear pump polarisation shown in 6.10 and corresponds to SOKE. The rather

complicated behaviour of the peaks in the ellipticity measurements (6.5b and 6.12)

can therefore be understood as a simple superposition of the SIFE and SOKE effects

due to a different dependence upon the wave plate angle.


-1.0 -0.5 0.0 0.5 1.0-3

-2

-1

0

1

2

3

4

5

6

7

0 10 20 30-3

-2

-1

0

Ellip

ticity

Sig

nal (

mde

g)


45O (SIFE) 0.5*(22.5O+ 67.5O)(SIFE) 0.5*(22.5O+ 67.5O)*1.41 0.5*(22.5O- 67.5O)(SOKE)

Figure 6.19: Separation of the SIFE and SOKE contributions from the MOKE ellipticity

scans obtained with elliptical pump polarisation. The curves in the graph were obtained

in the following way: First the average differences of the ellipticity scans at the angles of

±22.5, ±45 and ±67.5 were calculated. These average differences are in the following

referred to as “data” and were already plotted in figure 6.12. The 45 data containins only

the SIFE and is plotted unchanged. Also half the sum of the 22.5 and 67.5 data (SIFE)

and half their difference (SOKE) are plotted. The sum multiplied by√

2 matches the 45

data. The inset shows the long-time behaviour of the difference which looks similar to the

linear pump ellipticity data shown in figure 6.10.


6.4 Discussion

6.4.1 Reflectivity Data

The peak around zero delay in the reflectivity signal is somewhat curious. The

height of the peak seems to depend on the relative orientation of the polarisation

of pump and probe beam. No such effect was observed in the measurements made

upon GaAs. For GaAs there is no peak and the reflectivity curves for different

linear polarsiations have the same shape. The width of the peak corresponds to the

laser cross-correlation width suggesting that it is an effect that takes place while

the pulses overlap in time. This effect may be understood as a linear dichroism

induced by the pump pulse similar to the linear birefringence that leads to the

SOKE. The laser pulse changes the refractive index of the medium. Let us first

consider a linear pump. If the pump pulse changes the complex refractive index

along its polarisation axis, then the reflectivity of the probe is changed depending

on the orientation of the probe polarisation relative to the pump polarisation. The

probe can be split into components polarised parallel and perpendicular to the pump.

Only the absorption of the parallel component will be affected, leading to a change

in the total reflectivity. A probe polarised parallel to the pump (Θ=0 for p-probe,

Θ = ±90 for s-probe) will therefore experience the maximum effect whereas a probe

polarised perpendicular to the pump (Θ = ±90 for p-probe, Θ = 0 for s-probe) will

experience no change. An elliptically polarised pump can be split in an s- and a p-

polarised component. In the specific configuration of the experiment the polarisation


was varied between p-polarisation (φ = 0,±90) and circular polarisation (φ =

±45) by rotating the quarter wave plate. When the pump is linear the dichroic

effect upon the probe is at its maximum. When rotating the wave plate the relative

amount of p-polarised pump decreases and the s-component increases. For circular

pump polarisation the amplitudes of the s and p components are equal and the

p-component reaches its minimum value. Hence the effect upon the probe beam

reflectivity should be at a minimum but not disappear as there is still p-polarised

pump light present. In the case of a linear pump the effect should show a 180

period compared to a 90 period for an elliptically polarised pump. This is indeed

observed as can be seen in figure 6.7.

Following the initial peak the reflectivity signal shows a few oscillations before

following a simple exponential decay. As already discussed in the previous chapter

these oscillations and the rather long rise time originate from thermoelastic effects.

From the period of the oscillations the speed of sound can be calculated. Assuming

the second peak to be an echo of the first peak reflected from the Al/Si interface,

the time delay between the peaks is the time needed for the pulse to travel to the

interface and back. For a nominally 500A thick film and time delays of 12.5-15 ps

one obtains values of 6.7-8 nm ps−1. Given the uncertainty in the film thickness,

these values agree quite well with the accepted longitudinal sound velocity in Al of

vl=6.15 nm ps−1 (73).


6.4.2 Rotation and Ellipticity Data

The linear pump measurements show only the SOKE. It is somewhat surprising to

see not only the short lived peak but also a long lived tail in those signals. The

relaxation time of a few ps is of the same order of magnitude as in the elliptical

pump data. This seems to confirm that the tail seen in the elliptical pump data in

the previous chapter is indeed due to the SOKE. Also in the rotation data obtained

with the elliptical pump only SOKE contributions are visible. However, the ellip-

ticity measurements give evidence of some SIFE contribution (2φ-component of the

signal). The shapes and sizes of the peaks are a superposition of SIFE and SOKE

contributions, constructive or destructive depending on the angle of the wave plate.

The 2φ-component attributed to SIFE has a similar amplitude to the 4φ-component

attributed to SOKE. However, in this case there is no clear tail visible. Therefore

there seems to be no clear evidence for a long-lived spin polarisation induced by the

pump. However it is not clear why the SOKE tail is not visible when the probe ellip-

ticity is measured with an elliptical pump, since it is clearly present in all the other

sets of data. A potential cancellation of the SOKE tail by a SIFE tail is possible

but perhaps unlikely because the angular dependence of the peaks is different, and

a SIFE tail should follow the periodicity of the SIFE peak. Therefore a cancellation

would only be expected for certain orientations of the pump wave plate. We note

that a small tail is in fact present in the ellipticity measurement when the pump is

circularly polarised although the signal to noise ratio is poor.

From the peak heights the tensor elements χxxyy and χxyyx were calculated. As


a check χxxyy +χxyyx determined from the linear and the elliptical data sets are seen

to be in excellent agreement. The values of the components of the susceptibility

tensor are of the order of 1× 10−8 esu and are of similar magnitude to the value for

Au (|χxxyy + χxyyx| ≈ 1.5 × 10−8 esu) published by Zheludev and co-workers (58).

6.5 Summary

Measurements of the reflectivity, rotation and ellipticity of the Al sample were

performed using linearly and elliptically polarised pump light. The polarisation

orientation of the pump beam was systematically changed and the corresponding

time-resolved curves were recorded. The reflectivity is independent of the pump po-

larisation except for a peak at zero delay that depends upon the relative orientation

of pump and probe polarisation. This dependence can qualitatively be explained

with a transient linear dichroism induced by the pump beam. The initial oscillations

in the reflectivity signal are due to a thermoelastic excitation of ultrasonic waves

in the sample. The speed of sound determined from the oscillation period is in

agreement with the literature value.

For both the rotation and ellipticity signals the dependence of the peak height

and a long-lived tail upon the pump polarisation was determined. The data was

fitted with a formula introduced by Kimel et al. The fitted parameters were plot-

ted against the polariser/wave plate angles and then their dependence upon the

polariser/wave plate orientation was fitted. In the case of the linear pump the

variation of the peak heights was consistent with the SOKE mechanism. For an


elliptical pump the rotation signal again shows a SOKE peak as predicted by the

theory. The ellipticity signal shows contributions from both SIFE and SOKE to

the peak. Both contributions were successfully extracted from the signal. From

the four data sets the components χxxyy = −(1 + 0.4i) × 10−8 rad cm3 erg−1 and

χxyyx = −(0.6 + 0.04i)× 10−8 rad cm3 erg−1 of the third order susceptibility tensor

were calculated.

Also tails with a relaxation time of the order of a few ps were found to exist for

both a linear and an elliptical pump. This seems to support the conclusion drawn in

the previous chapter that a long-lived linear birefringence effect is responsible for the

existence of the tail. The microscopic origin of this birefringence effect still remains

unclear. The weak tail observed in the ellipticity after pumping with circularly

polarised light suggests that there may be a small optically induced spin polarisation.

Although parallel bands may favour optical orientation of hot electrons, the slope

of the bands implies that rapid depolarisation may occur during the cascade of hot

electrons to the Fermi level. Consequently the spin polarisation of the thermalised

electron population may be significantly weaker than in GaAs.

Chapter 7

Summary

In this thesis a time-resolved pump-probe experiment for the study of sub-picosecond

electron and spin dynamics such as those discussed in chapter 2 was successfully set

up. Different detection schemes for the measurement of the pump-induced effects

were tried and a method for focusing and aligning the pump and probe spots to

a diameter of 15 µm was developed. A fringe-resoved autocorrelator was built to

measure the laser pulse width at different positions in the set-up. The chirp in

the pump and probe pulses introduced by group velocity dispersion in the optics

was largely compensated by a set-up with Brewster prisms. Full details of the

experimental apparatus were given in chapter 3.

In chapter 4 first measurements were made upon a Ni sample. The pump-

induced reflectivity change and the magnetisation dynamics were recorded using a

p-polarised pump. A demagnetisation was found to take place within less than 300 fs,

in agreement with previous studies by others. The rotation and the reflectivity part

143

CHAPTER 7. SUMMARY 144

of the magneto-optical response were measured and compared. Both components

show the same behaviour on short time scales. This behaviour is different to the

results reported by Koopmans et al. Dynamic hysteresis loop were measured for

different fixed pump-probe time delays while scanning the external magnetic field.

Rather strange loop shapes were found. The shape of these loops are most likely the

result of a reorientation of the macroscopic magnetisation due to sample heating.

At magnetic saturation there is a good agreement between the magnetic signal in

the loops and the time-dependent scans. We conclude that the demagnetisation is

best studied in saturation.

After successfully measuring the ultrafast demagnetisation effect in the Ni sample

the question arose as to whether the experiment could be used to create a spin

orientation in a nonmagnetic metal so that the subsequent spin dynamics could

be measured. Such studies have been successfully carried out for semiconductor

samples. In chapter 5 the experiment was slightly modified to allow samples to be

excited with an elliptically polarised pump. By rotating a quarter wave plate the

pump polarisation could be continuously varied between p-polarisation and circular

polarisation. A further improvement was made by using a second lock-in amplifier

to measure the reflectivity signal simultaneously with the magneto-optical response

to ensure a consistent calibration of the zero delay positions for different scans.

Also an alignment procedure was established for non-magnetic samples that allowed

the probe polarisation to be correctly adjusted to p-polarisation, compensating for

sample misalingments. As a result the reflectivity breakthrough previously observed


in the Ni measurements and leading to asymmetric signals could be eliminated.

The spin orientation and relaxation dynamics of an intrinsic GaAs wafer were

examined as a first test. Three separate contributions have been clearly identified

in the magneto-optical signal: a sharp peak at zero delay followed by a slower signal

containing two different exponential decay components. The shape is similar to that

in a study conducted by Kimel et al. Measurements were made for a varying pump

power in the range of 10 to 200 mW and the amplitudes of three components in the

signal were fitted. They all show a monotonic non-linear dependence upon pump

power. The width of the Gaussian peak at zero delay appears to be constant while

the time constants for the two exponential terms both increase with pump power.

The pump polarisation was varied between p-polarisation and circular polarisation.

The amplitude of peak and tail were found to change with pump polarisation with

a maximum at circular polarisation and a zero effect for linear polarisation. The

sign of the signal changed with the pump helicity. This behaviour is consistent with

optical orientation and relaxation of spin and the angular dependence is simply

related to the relative amplitudes ofthe two circular components of the elliptically

polarised pump.

After successfully measuring the GaAs sample the Ni sample was examined to de-

termine whether a circular pump could modify the ultrafast demagnetisation signal.

The measurements showed a sharp peak at zero delay similar to the one observed

for GaAs. This peak was simply superimposed upon the demagnetisation signal and

was not affected by the magnetisation of the sample. The magnetic signal at long


time delays was found to be unaffected by the polarisation of the pump. Again the

dependence of the amplitude of the peak upon the pump polarisation was measured

and a slightly more complicated behaviour was found than in GaAs.

Finally Al was chosen as a nonmagnetic metallic sample because of its band

structure, with a direct interband transition between parallel bands that can be

excited at the laser wave length of 800 nm. The reflectivity signal showed a sharp

peak at zero delay followed by a rather slow rise to a peak at about 6 ps. Up to

a time delay of about 20-30 ps some oscillations could be observed superimposed

on an exponential decay of the signal. Both the slow rise and the oscillations are

the result of thermoelastic contributions to the reflectivity signal. The laser pulse

creates an isotropic stress at the surface that causes an acoustic pulse to travel into

the bulk leading to the slowly rising contribution to the reflectivity signal. When the

pulse is reflected at the film/substrate interface it travels back to the surface where

it gives rise to reflectivity oscillations. The dependence of the rotation signal upon

the pump polarisation was measured. Again a sharp peak at zero delay was found

followed by a slowly decaying tail with a time constant of 6 ps. The dependence of

the peak and tail amplitude upon the wave plate angle was completely different to

GaAs. No signal was found for linear and circular polarisation and maxima were

observed for intermediate elliptical polarisations. The peak and tail showed the

same angular dependence.

In each sample the FWHM of the zero delay peaks of 160 fs corresponds to the

expected width of the cross-correlation of two laser pulses of 120 fs pulse width. If


the peak is assumed to arise partially from orientation of hot electron spins then

one can deduce that the relaxation time of the hot electron spin is much shorter

than our pulse width. The angular dependence of the amplitude of the peak and

tail in the rotation signals was compared. The behaviour of the GaAs signal is

characteristic of circular birefringence (SIFE), that observed in Al is characteristic

of linear birefringence (SOKE), while that in Ni has mixed character. The tail

in GaAs is a result of the deacying spin orientation in the sample. No long lived

signal could be observed in Ni which is unsurprising if an interband transition is

required for optical orientation of electrons after thermalization. The magneto-

optical response of Ni should also be more complicated than that of GaAs because

there are two different quantisation axes to be considered. Optically oriented spins

would be expected to precess in the exchange field associated with the spontaneously

magnetised electron population and may rapidly dephase. Therefore the effect of

the pump helicity upon the ultrafast demagnetisation should be studied in samples

magnetised perpendicular to the plane and pumped at normal incidence. Al exhibits

a longer-lived transient rotation signal that has the same dependence upon the pump

helicity as the zero delay peak. This signal appears to rise instantaneously and

relaxes with a time constant of 6 ps. It is suggested that this transient is associated

with an ultrafast lattice distortion rather than optical orientation of spin.

Since the origin of the long-lived tail in Al could not be reliably explained some

further measurements of the magneto-optical response were performed in chapter 6.

We wanted to know if there is only a SOKE contribution to the cubic nonlinearity


or whether a SIFE component could also be observed. In order to fully characterise

the effect measurements with a linearly polarised pump of varying polarisation an-

gle were performed in addition to the measurements with elliptically polarised light.

For both pump configurations the reflectivity as well as the rotation and the ellip-

ticity contribution to the magneto-optical signal were measured. The sharp peak

in the reflectivity signal depends on the relative orientation of the pump and probe

polarisation and it can be explained as an ultrafast linear dichroism created by the

pump. From the period of the oscillations found in the reflectivity signal the speed

of sound in Al was calculated and found to be in agreement with the literature

value. In the measurements made with linear pump only SOKE contributions to

the magneto-optical signal were found as expected from the theory. The elliptical

pump measurements measured in rotation showed only the SOKE as in the earlier

study. In all cases long lived tails were observed in the signal with life times of a

few ps. The elliptical pump measurements for ellipticity however showed a SIFE

and a SOKE contribution of about equal size. No tail could be reliably measured.

From the dependence of the zero delay peak upon the wave plate angle two com-

ponents χxxyy and χxyyx of the susceptibility tensor χ were determined. The values

are of the order of 1 × 10−8 esu and are of similar magnitude to the value for Au

(|χxxyy+χxyyx| ≈ 1.5×10−8 esu) published by Zheludev et al. These additional mea-

surements reveal that there is a SIFE component present in the nonlinear response

of Al. There is also a weak indication of a longer lived SIFE tail. Although paral-

lel bands may favour optical orientation, the slope of the bands implies that rapid


depolarisation may occur during the cascade to the Fermi level. A more prominent

long lived tail was attributed to a long-lived birefringence effect. Its microscopic

origin is still unclear and the development of a realistic microscopic model for the

cubic optical non-linearity in Al is now required so that the origin of the transient

rotation signal may be more clearly understood.

In conclusion the study of metals by optical pump-probe experiments is a very

rich area for future research. Measurable nonlinear effects seem generally to be

present in metals. Magnetisation dynamics can be studied and a variety of informa-

tion can be obtained about linear and circular birefringence and dichroism effects

when measuring the reflectivity and magneto-optical signals. It would be inter-

esting to study the noble metals using lasers with shorter wave lengths to access

interband transitions of higher energy. Furthermore it is worth looking at the Ni

sample again. Measurements with polar magnetisation and a pump beam at normal

incidence would allow the quantisation axes of the magnetisation and the circular

pump to be aligned. It would then be interesting to examine whether the mag-

netic signal can be affected on longer time scales by the helicity of the pump beam.

Finally, with a demagnetisation effect of 7-9% the Ni sample was only partially de-

magnetised. It would be interesting to use a stronger pump or ultrathin samples

with reduced Curie temperature to fully demagnetise the sample and then examine

the response induced by a second circularly polarised pump beam.

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