Ultrafast spin dynamics of a ferrimagnet revealed by

Ultrafast spin dynamics of a ferrimagnet revealed by femtosecond soft X-ray and XUV radiationUltrafast spin dynamics of a ferrimagnet revealed by femtosecond soft X-ray and XUV radiation
vorgelegt von M. Sc.
an der Fakultät II - Mathematik und Naturwissenschaften der Technischen Universität Berlin
zur Erlangung des akademischen Grades
Doktor der Naturwissenschaften - Dr. rer. nat. -
genehmigte Dissertation
Vorsitzender: Prof. Dr. Mario Dähne Gutachter: Prof. Dr. Stefan Eisebitt Gutachter: Prof. Dr. Jan Lüning
Tag der wissenschaftlichen Aussprache: 13.08.2020
Berlin 2020
Die vorliegende Arbeit handelt von zeitaufgelösten experimentellen Untersuchungen ul- traschneller Spinphänomene in ferrimagnetischen metallischen Legierungen aus GdFeCo. Neuere Studien solcher ferrimagnetischen Systeme haben gezeigt, dass eine optische Anregung mit Femtosekundenpulsen nicht nur in der Lage ist, ein solches System auf einer Zeitskala von weniger als einer Picosekunde zu entmagnetisieren, sondern auch seine Magnetisierung dauerhaft umzuschalten, ohne dass dafür ein anderer externer Impuls wie ein Magnetfeld erforderlich wäre. Obwohl mehrere Theorien aufgestellt wurden, um die ultraschnelle Abnahme oder sogar Umkehrung der magnetischen Ordnung zu erklären, sind die tatsächlichen Mechanismen hinter diesen Phänomenen noch immer unklar. Eine der Schlüsselfragen ist z.B., wie der Spin- und Bahndrehimpuls der Elektronen, welche zusammen das magnetische Moment hervorrufen, auf einer so kurzen Zeitskala nach Anregung aus dem elektronischen System oder in dieses hinein übertragen werden. Eine weitere Frage betrifft die Art und Weise, auf die ein Lichtpuls während der Anregung mit dem magnetischen Medium interagiert. Dabei kann es sich im Allgemeinen entweder um einen thermischen Prozess handeln, der sich auf eine ultraschnelle optisch induzierte Erwärmung des elektronischen Systems stützt, oder um einen nichtthermischen, optomagnetischen Mechanismus wie den inversen Faraday-Effekt (IFE), der bei Anregung mit zirkular polarisiertem Licht eine helizitätsabhängige Magnetisierung oder einen effektiven optomagnetischen Feldpuls induziert. Die tatsächlichen Einflüsse der letztgenannten nichtthermischen Mechanismen auf einer Femtosekundenzeitskala sind in stark absorbierenden Materialien wie in Metallen, wo thermische Effekte normalerweise dominieren, jedoch stark umstritten. Die im Rahmen dieser Arbeit präsentierten Ergebnisse sollen Licht in die beiden zuvor genannten Fragen bringen.
Um die Drehimpulsübertragung während der ultraschnellen optisch induzierten Entma- gnetisierung einer ferrimagnetischen GdFeCo-Legierung zu untersuchen, verwenden wir zeit- und elementaufgelöste Messungen des zirkularen magnetischen Röntgendichroismus (XMCD) mittels weicher Röntgenpulse, die an der FemtoSpeX fs-Slicingquelle am Syn- chrotron BESSY II erzeugt werden. Die Anwendung magnetooptischer Summenregeln auf die fs-XMCD-Daten ermöglicht es, die Dynamik von Spin- und Bahnmomenten der Fe- und Gd-Atome individuell zu verfolgen. Anhand unserer experimentellen Daten lässt sich auf eine vollständige Übertragung sowohl des Spin- als auch des Bahndrehimpulses von Fe und Gd an das Atomgitter schließen, die während weniger hundert Femtosekunden nach Anregung stattfindet. Im Rahmen unserer experimentellen Zeitauflösung von ≈ 130 fs
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gibt es dabei keinen Hinweis auf einen interatomaren Drehimpulsaustausch zwischen Fe und Gd oder eine Ansammlung des Drehimpulses im Bahnmoment. Letzteres kann somit als Engpass für eine Drehimpulstransfer an das Gitter ausgeschlossen werden.
Um den Einfluss eines nichtthermischen, optomagnetischen Mechanismus wie des IFE in metallischen Ferrimagneten wie GdFeCo zu untersuchen, verwenden wir einen neuartigen Ansatz, um eine helizitätsabhängige ultraschnelle Entmagnetisierungsdynamik durch resonante Anregung von Elektronen aus den inneren 3p-Zuständen von Fe zu induzieren (resonant zur Fe M3,2-Absorptionskante). Dafür nutzen wir intensive Femtosekunden- pulse im XUV-Spektralbereich mit sowohl linearer als auch zirkularer Polarisation, die am Freie-Elektronen-Laser FERMI erzeugt werden, um den Prozess der ultraschnellen Entmagnetisierung als Funktion des Polarisationszustands und der Photonenenergie des XUV-Anregungspulses zu untersuchen. Die Motivation hinter diesem Ansatz ist die starke Spin-Bahn-Kopplung der inneren elektronischen Zustände. Da die Spin-Bahn-Kopplung der vermittelnde Mechanismus hinter jedem magnetooptischen oder optomagnetischen Ef- fekt ist, könnte dieser Ansatz Zugang zu einem Bereich bieten, in dem der nichtthermische IFE viel stärker ist im Vergleich zu sichtbaren Wellenlängen. Bislang liegen jedoch keine experimentellen Daten oder Theorien zur Existenz eines IFE im XUV-Spektralbereich vor. Unsere Messungen zeigen in der Tat einen starken dynamischen, helizitätsabhän- gigen Effekt, der sowohl für resonante als auch nichtresonante Anregung nahe der Fe M3,2-Absorptionskante existiert und der nicht durch dichroitische Absorption aufgrund des ebenfalls vorhandenen XMCD-Effekts erklärt werden kann. Unsere Ergebnisse ent- sprechen vielmehr den erwarteten Eigenschaften des IFE und deuten daher stark auf die erste Beobachtung eines IFE im bisher unerforschten XUV-Spektralbereich hin.
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Abstract
In this thesis, we will present time-resolved experimental investigations of ultrafast spin phenomena in ferrimagnetic metallic alloys of GdFeCo. Recent studies of such ferrimagnetic systems have revealed that a femtosecond optical excitation is not only able to demagnetize such a system on a subpicosecond timescale, but also to permanently reverse its magnetization without any other external stimulus like a magnetic field. Although several theoretical approaches were made to explain the ultrafast loss or even reversal of the magnetic order, the actual mechanisms behind such spin phenomena still remain unclear. One of the key issues is, e.g., how the spin and orbital angular momentum of the electrons, which gives rise to the magnetic moment, is transferred out of, or into the electronic system on such a short timescale after excitation. Another issue concerns the way a light pulse can interact with the magnetic medium during the excitation process. In general, this can either be a thermal mechanism relying on ultrafast light-induced heating of the electronic system or a non-thermal, opto-magnetic mechanism like the Inverse Faraday Effect (IFE) generating a helicity-dependent induced magnetization or an effective opto-magnetic field pulse upon excitation with circularly polarized light. However, the actual role of the latter non-thermal mechanisms on a femtosecond timescale in highly absorbing materials like metals, where thermal effects usually dominate, is highly debated. The scope of this thesis is to shed light upon both of the aforementioned issues.
To reveal the path of angular momentum flow during ultrafast laser-induced demagnetization of a ferrimagnetic GdFeCo alloy, we employ time- and element-resolved soft x-ray magnetic circular dichroism (XMCD) measurements at the FemtoSpeX fs-slicing facility of the BESSY II synchrotron light source. A magneto-optical sum rules analysis of the fs-XMCD data allows us to disentangle and monitor the dynamics of both spin and orbital moments individually, at Fe and Gd sites. Our experimental data enable us to conclude on a full transfer of angular momentum from both spin and orbital moments of Fe and Gd to the atomic lattice during the first hundreds of femtoseconds after excitation. Within our experimental time resolution of ≈ 130 fs, there is also no indication for an interatomic exchange of angular momentum between Fe and Gd, as well as for an accumulation in the orbital moment. Thus, the latter can be ruled out as a bottleneck for the angular momentum transfer to the lattice. In order to reveal the influence of a non-thermal, opto-magnetic mechanism like the
IFE in metallic ferrimagnets like GdFeCo, we use a novel approach of inducing helicity-
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dependent ultrafast demagnetization dynamics by resonantly exciting electrons from the 3p core levels of Fe (corresponding to the Fe M3,2 resonance). Therefore we employ highly intense, femtosecond XUV pulses with both linear and circular polarization generated at the free electron laser FERMI to study the ultrafast demagnetization process as a function of polarization state and photon energy of the XUV excitation pulse. The motivation behind this approach is the strong spin-orbit coupling of the core levels. While the spin- orbit coupling is the mediating mechanism behind any magneto-optical or opto-magnetic effect, this could provide access to a regime where the non-thermal IFE is much stronger compared to the visible wavelength regime. However, no experimental data or theory is available so far on the existence of an IFE in the XUV spectral range. Our results reveal a strong dynamic helicity-dependent effect present for both off- and on-resonant excitation around the Fe M3,2 resonance that can not be explained by dichroic absorption due to the XMCD effect, which is present as well. Our findings rather resemble the expected IFE fingerprints and strongly indicate that we have made the very first observation of an IFE in the so far unexplored XUV spectral range.
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Acknowledgments
First of all I would like to thank Stefan Eisebitt, who gave me the opportunity to join his division at the Max Born Institute and to become a PhD student in such a capable, collaborative and friendly team. Besides profiting from his experience and scientific advice, I was given great freedom to realize and work on my research projects and to extend my qualification by attending international conferences and summer schools, where I had the chance to present my work and connect with scientists from all over the world.
Special thanks go to my supervisor Ilie Radu, who introduced me to the field of ultrafast spin dynamics and whose extensive knowledge and experience gave me the opportunity to learn a lot about the underlying physics and scientific methods. During the last three and a half years of my PhD, he not only actively supported and encouraged me during our numerous beam times, at conferences and in the lab, but was also a very patient and committed supervisor, who always had an open ear for questions and discussions.
Of course the latter was also the case for many other members of our team. In particular I would like to thank Clemens von Korff Schmising, Daniel Schick, Dieter Engel, Christian Strüber, Bastian Pfau and Michael Schneider for always being ready to help in case I needed scientific or experimental advice and feedback on my talks, work and latest results. I would also like to thank Dieter Engel and Sascha Petz for spending so much time in the sputtering lab to prepare and optimize samples for me, as well as Marc Zieglarski for his software development and support in all Labview-related questions.
Thanks also go to my fellow PhD students Felix Willems, David Weder, Piet Hessing and the later joined Kelvin Yao and Martin Borchert, with whom I have shared the office for the last years. Discussing and solving scientific questions together, helping us out at beam times and in the lab as well as talking about the latest news and share prices made my PhD time much more productive and motivating.
I would also like to thank all my colleagues and the involved researchers mentioned in the Preface of this thesis, who also contributed greatly to the completion of this work, either by their assistance in preparing and conducting the experiments, or by providing the theory and contributing to the interpretation of the experimental data. Without their support and expertise, the experiments and results presented in this thesis could not have been achieved. Last but not least I would like to thank Ilie Radu, Felix Willems, Karsten Holldack,
Flavio Capotondi and Peter Oppeneer for proofreading various parts of my thesis, which helped me to increase the quality of the manuscript.
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Contents
Zusammenfassung . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v List of Acronyms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii
1 Introduction 1
2 Fundamentals and experimental techniques 5 2.1 Magnetic properties of rare earth and 3d transition metal systems . . . . 5
2.1.1 Magnetic interactions . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.1.2 Magnetic order in RE and 3d-TM elements . . . . . . . . . . . . . 8
2.2 Ultrafast laser-induced magnetization dynamics in RE and 3d-TM systems 12 2.2.1 Mechanisms behind ultrafast magnetization dynamics . . . . . . . 12 2.2.2 Local spin-flip scattering processes . . . . . . . . . . . . . . . . . . 13 2.2.3 Non-local spin transport processes . . . . . . . . . . . . . . . . . . 15 2.2.4 All-optical magnetization switching in RE and 3d-TM systems . . 17
2.3 Magneto-optical effects (probing magnetization with light) . . . . . . . . . 18 2.3.1 Magneto-optical Faraday and Kerr effect (MOFE/MOKE) . . . . . 19 2.3.2 X-ray/XUV magnetic circular dichroism (XMCD) . . . . . . . . . 21 2.3.3 Magneto-optical sum rules analysis . . . . . . . . . . . . . . . . . . 22
2.4 Opto-magnetic effects (inducing magnetization by light) . . . . . . . . . . 25 2.4.1 Inverse Faraday Effect (IFE) . . . . . . . . . . . . . . . . . . . . . 26
2.5 Soft x-ray and XUV radiation sources . . . . . . . . . . . . . . . . . . . . 29 2.5.1 FemtoSpeX fs-slicing facility at BESSY II . . . . . . . . . . . . . . 29 2.5.2 Free electron laser FERMI . . . . . . . . . . . . . . . . . . . . . . . 33 2.5.3 Static spectroscopy setup at BESSY II . . . . . . . . . . . . . . . . 35
3 Angular momentum flow during ultrafast demagnetization of GdFeCo 37 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.2 Results of static soft x-ray spectroscopy . . . . . . . . . . . . . . . . . . . 38
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3.3 Time-resolved optical pump – x-ray probe experiment . . . . . . . . . . . 40 3.3.1 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 3.3.2 Data acquisition and data treatment . . . . . . . . . . . . . . . . . 41 3.3.3 Applying sum rules to the time-resolved data . . . . . . . . . . . . 43
3.4 Time-resolved demagnetization of GdFeCo . . . . . . . . . . . . . . . . . . 46 3.4.1 Time-resolved XMCD measurements . . . . . . . . . . . . . . . . . 46 3.4.2 Spin and orbital moments dynamics during demagnetization . . . 49
3.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4 X-ray driven ultrafast demagnetization of GdFeCo 55 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 4.2 Results of static XUV spectroscopy . . . . . . . . . . . . . . . . . . . . . . 58
4.2.1 Absorbed fluence and penetration depth . . . . . . . . . . . . . . . 61 4.3 Time-resolved XUV pump – optical probe experiment . . . . . . . . . . . 63
4.3.1 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 4.3.2 Data sorting and data treatment . . . . . . . . . . . . . . . . . . . 67
4.4 Results of the time-resolved measurements . . . . . . . . . . . . . . . . . . 67 4.4.1 Pump-probe delay scans . . . . . . . . . . . . . . . . . . . . . . . . 68 4.4.2 Fluence-dependence . . . . . . . . . . . . . . . . . . . . . . . . . . 71 4.4.3 Comparison to the XMCD . . . . . . . . . . . . . . . . . . . . . . . 75
4.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 4.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5 Conclusions and outlook 83
Bibliography 87
A Appendix 101 A.1 Magnetic hysteresis loops . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 A.2 Faraday vs. Kerr probing . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 A.3 Pump-probe delay scans . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
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2TM two-temperature model 2D two-dimensional 3D three-dimensional 3TM three-temperature model AO-HDS all-optical helicity-dependent
switching APD avalanche photo diode bw. bandwidth DFT density functional theory FEL free electron laser fs femtosecond FWHM full width at half maximum FZP Fresnel zone plate GMD gas monitor detector HHG high harmonic generation HGHG high-gain harmonic generation IFE Inverse Faraday Effect lin.hor. linear horizontal MAE magnetic anisotropy energy M3TM microscopic three-temperature
model MCD magnetic circular dichroism MOFE magneto-optical Faraday effect MOKE magneto-optical Kerr effect nm nanometer ns nanosecond OISTR optical inter-site spin transfer PGM plane grating monochromator ps picosecond RE rare earth
RKKY Ruderman-Kittel-Kasuya-Yosida RZP reflection zone plate SASE self-amplified spontaneous emission SHG second harmonic generation SOC spin-orbit coupling THG third harmonic generation TM transition metal VIS visible XAS x-ray absorption spectroscopy XMCD x-ray magnetic circular dichroism XUV extreme ultra violet ZPM zone plate monochromator
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List of Figures
2.1 Temperature-dependence of the sublattice magnetizations in GdFe . . . . 10 2.2 Illustration of experiments employing the magneto-optical Faraday effect . 20 2.3 Illustration of the XMCD effect at the L edges of a 3d ferromagnet . . . . 23 2.4 Schematic illustration of the quantities needed to apply the sum rules . . 25 2.5 Schematic illustration and mechanism of the Inverse Faraday Effect . . . . 27 2.6 Static ab-initio calculations of the IFE in GdFe2 . . . . . . . . . . . . . . 28 2.7 Schematic top view on the FemtoSpeX fs-slicing facility at BESSY II . . . 30 2.8 Femtoslicing technique as implemented at BESSY II . . . . . . . . . . . . 32 2.9 Schematic illustration of the external seeding at FERMI . . . . . . . . . . 34
3.1 Static soft x-ray absorption (XAS) and XMCD spectra of GdFeCo . . . . 39 3.2 Schematic illustration of the pump-probe experiment at FemtoSpeX . . . 40 3.3 Time-resolved pumped and unpumped XMCD at Fe L3,2 . . . . . . . . . . 42 3.4 Comparison of the XMCD spectra measured at FemtoSpeX and PM3 . . 44 3.5 Time-resolved XMCD at Fe L3,2 and Gd M5,4 . . . . . . . . . . . . . . . . 47 3.6 Two-temperature model (2TM) simulation of GdFeCo . . . . . . . . . . . 48 3.7 Time-resolved XMCD spectra of GdFeCo measured at FemtoSpeX . . . . 50 3.8 Time-resolved evolution of spin and orbital moment at Fe and Gd sites . . 51
4.1 Static XUV absorption (XAS) and XMCD spectra measured at Fe M3,2 . 60 4.2 Static XUV absorption (XAS) and XMCD spectra measured at Gd N5,4 . 61 4.3 Selecting the XUV photon energies used for excitation . . . . . . . . . . . 62 4.4 Estimated XUV excitation and VIS depth profiles in the sample . . . . . 63 4.5 Schematic illustration of the pump-probe experiment at FERMI . . . . . 64 4.6 Analysis of the shot-resolved FEL pulse energies from the I0 GMD . . . . 67 4.7 Time-resolved normalized Faraday rotation . . . . . . . . . . . . . . . . . 69 4.8 Demagnetization amplitudes upon σ−, σ+ and lin. polarized excitation . . 72 4.9 Fluence-dependence of the difference σ = σ− − σ+ . . . . . . . . . . . . 73 4.10 Demagnetization for lin. polarized XUV excitation vs. absorbed fluence . 74 4.11 Estimation of asymmetry needed for the observed hel.-dependent effect . . 76 4.12 Comparison of the XMCD to the estimated asymmetries . . . . . . . . . . 77 4.13 Static ab-initio calculations of the IFE in the XUV spectral range . . . . . 80
A.1 Magnetic hysteresis loops of the studied GdFeCo samples . . . . . . . . . 103
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List of Figures
A.2 Fluence diagrams (Faraday vs. Kerr probing) at 51.0 eV . . . . . . . . . . 104 A.3 Fluence diagrams (Faraday vs. Kerr probing) at 54.1 eV . . . . . . . . . . 105 A.4 Fluence diagrams (Faraday vs. Kerr probing) at 56.1 eV . . . . . . . . . . 106 A.5 Fluence diagrams (Faraday vs. Kerr probing) at 64.0 eV . . . . . . . . . . 107 A.6 Demagnetization vs. lin. pol. absorbed XUV fluence (Faraday vs. Kerr) . 108 A.7 Pump-probe delay scans obtained from Faraday data (1/7) . . . . . . . . 109 A.8 Pump-probe delay scans obtained from Faraday data (2/7) . . . . . . . . 110 A.9 Pump-probe delay scans obtained from Faraday data (3/7) . . . . . . . . 111 A.10 Pump-probe delay scans obtained from Faraday data (4/7) . . . . . . . . 112 A.11 Pump-probe delay scans obtained from Faraday data (5/7) . . . . . . . . 113 A.12 Pump-probe delay scans obtained from Faraday data (6/7) . . . . . . . . 114 A.13 Pump-probe delay scans obtained from Faraday data (7/7) . . . . . . . . 115 A.14 Pump-probe delay scans obtained from Kerr data (1/7) . . . . . . . . . . 116 A.15 Pump-probe delay scans obtained from Kerr data (2/7) . . . . . . . . . . 117 A.16 Pump-probe delay scans obtained from Kerr data (3/7) . . . . . . . . . . 118 A.17 Pump-probe delay scans obtained from Kerr data (4/7) . . . . . . . . . . 119 A.18 Pump-probe delay scans obtained from Kerr data (5/7) . . . . . . . . . . 120 A.19 Pump-probe delay scans obtained from Kerr data (6/7) . . . . . . . . . . 121 A.20 Pump-probe delay scans obtained from Kerr data (7/7) . . . . . . . . . . 122
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List of Tables
4.1 Spin-orbit coupling constants of Fe, Co and Ni at 3d, 3p and 2p states . . 57 4.2 XUV photon energies and wavelengths used for excitation . . . . . . . . . 65 4.3 Demagnetization amplitudes upon σ+, σ− and lin. polarized excitation . . 70
A.1 Demagnetization time constants (Faraday vs. Kerr probing) . . . . . . . . 108
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Preface
Some parts of this thesis have already been published as an article in a peer reviewed journal. This concerns the experiment and results presented in Chapter 3. For this reason, several text passages and figures from this publication, including the supplemental material that was published alongside the article, also appear in this thesis in an identical or slightly modified version. The corresponding paragraphs and figure captions are marked by the following symbols:
† M. Hennecke, I. Radu, R. Abrudan, T. Kachel, K. Holldack, R. Mitzner, A. Tsukamoto, and S. Eisebitt. “Angular Momentum Flow During Ultrafast De- magnetization of a Ferrimagnet”. In: Phys. Rev. Lett. 122, 157202 (15 Apr. 2019) (cited as Ref. [1] in the bibliography)
‡ Supplemental Material belonging to Ref. [1].
Adapted with permission and copyright (2019) by the American Physical Society.
The author of this thesis (M. Hennecke) is also the principal author of the aforementioned article and supplemental material. The experiment was primarily conceived by I. Radu and M. Hennecke. It was conducted by M. Hennecke and I. Radu with the support of R. Abrudan, T. Kachel, K. Holldack and R. Mitzner. The sample was prepared by A. Tsukamoto. The data treatment and evaluation was done by M. Hennecke, with I. Radu and S. Eisebitt contributing to the interpretation of the experimental data. The experimental results presented in Chapter 4 have not yet been published in an
article. The corresponding experiment was primarily conceived and conducted by M. Hennecke and I. Radu. Several co-workers contributed to the successful conduction of the experiment: C. von Korff Schmising, K. Yao (Berlin, Germany), E. Jal, B. Vodungbo, V. Chardonnet (Paris, France), K. Légaré (Varennes, Canada), F. Capotondi, D. Naumenko and E. Pedersoli (Trieste, Italy). The sample was prepared by D. Engel (Berlin, Germany). The data treatment and evaluation was done by M. Hennecke. The ab-initio calculations of the Inverse Faraday Effect were carried out and contributed by L. Salemi, M. Berritta and P. M. Oppeneer (Uppsala, Sweden).
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1 Introduction
The fundamental interactions between light and matter provide the foundation for a variety of versatile techniques for non-invasive investigations of static and dynamic properties of matter. Commonly employed experimental techniques involve spectroscopic measurements as well as scattering and imaging techniques in order to gain microscopic insights into electronic, structural and magnetic properties of a material. The use of ultrashort light pulses with durations down to the femto- or even attosecond regime makes it possible to obtain information on the elementary processes (electron-electron, electron-magnon, phonon-magnon scattering etc.) and interactions (spin-orbit, exchange etc.) in solids on their intrinsic/characteristic time and length scales. In this thesis, we will present such time-resolved studies on the interaction of light and magnetic moments. In magnetically ordered materials, it is well established that such an interaction allows to probe the magnetization of the system via so called magneto-optical effects, which influence either the polarization state or intensity of a light wave while it is transmitted through or reflected by the magnetic material. A rather novel approach, however, is to pursue the opposite direction and use femtosecond light pulses to influence the magnetization and to optically excite ultrafast spin phenomena.
Over the last years, the use of such ultrashort light pulses to manipulate and control the magnetic order in a material on fundamentally limiting time and length scales has become an important quest in modern magnetism [2–4]. In a pioneering work in 1996, it was discovered that ferromagnetic nickel can be demagnetized on a subpicosecond timescale solely due to an optical excitation with a femtosecond laser pulse [5]. At that time, the impact of a laser excitation on the magnetic moments was understood as a sudden heating of the atomic lattice due to absorption of the laser pulse, followed by the formation of a new equilibrium magnetization state via spin-lattice relaxation, a process which typically happens on timescales of hundreds of picoseconds [6, 7]. Thus, the intriguing observation of such an ultrafast demagnetization process approaching the characteristic timescales of fundamental spin-orbit and exchange interactions (≈ 0.01–1 ps [2]) was extremely surprising and became the foundation for a new research area in condensed matter, the “Ultrafast Magnetism” or “Femtomagnetism” field. A few years later, it was shown that it is not only possible to demagnetize, but also fully and deterministically switch the magnetization of a ferrimagnet (i.e., rotate the direction of the magnetic moments by 180 ) by means of single femtosecond laser pulses without applying an external magnetic field [8]. This kind of all-optical magnetization switching was first observed
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1 Introduction
in ferrimagnetic GdFeCo systems using circularly polarized optical/visible laser pulses. The outcome of the process, i.e., the final magnetization direction, was thereby found to depend on the helicity of the light used for excitation, which is why the process was called all-optical helicity-dependent switching (AO-HDS). These findings were not only of large interest for fundamental science, but also for possible applications, as the optically induced demagnetization and magnetization reversal processes were several orders of magnitude faster than the typical times needed to demagnetize a material or reverse its magnetization by externally applied magnetic fields commonly available in a laboratory (≈ 1 ns [2]). As such, a process that allows such an ultrafast and deterministic control over magnetization could potentially be a large step forward in the further development of, e.g., spintronic devices and magnetic data storage technologies, which require manipulating the magnetization state of a system as fast and energy-efficient as possible [9].
The action of a femtosecond laser pulse on a magnetic sample, i.e., how such a pulse can interact with the magnetic moments and ultimately cause an optically induced demagnetization and even magnetization switching, could thereby be related to both thermal and non-thermal effects [2]: The first type relies on the absorption of the fs laser pulse leading to an ultrafast heating of the electronic system close to or above the Curie temperature, triggering secondary processes which quench the local magnetic moment. The second type is usually related to opto-magnetic effects like the Inverse Faraday Effect (IFE) [10–12], which does not involve the absorption of photons but describes a coherent interaction of the angular momentum of the circularly polarized light with the electron spins, inducing a helicity-dependent magnetization or effective magnetic field pulse in the material. Similar to other magneto-optical effects, such an interaction between light and electron spins is mediated by the spin-orbit coupling (SOC), suggesting a large induced magnetization in case of the involved electronic states possessing a strong SOC [13]. Relying on a coherent and dissipationless light-matter interaction, the IFE could thereby provide a path to ultrafast manipulation of magnetization (that avoids heating up the magnetic material) on very short timescales predicted to be fundamentally limited only by the pulse length of the excitation [14–16]. From a technological point of view, this would be of particular interest, as the repetition rate of the all-optical switching process is highly limited by the necessity of the system to cool down between subsequent laser shots [17]. Thus, a non-thermal control of the magnetic order could provide a way of achieving a significantly faster magnetization reversal and much higher switching rates.
While the IFE was originally discovered in transparent paramagnetic materials and found to be strong in nearly non-absorbing systems which exhibit a large spin-orbit coupling like garnets [14] and orthoferrites [17, 18], it was also proposed to explain the helicity-dependent sign reversal of the magnetization during the switching phenomena observed in metallic ferrimagnets like GdFeCo [8]. However, in case of garnets and orthoferrites, the photon energy of the visible light which was used to trigger the IFE is typically below the band gap of these systems, inhibiting electronic excitation and
2
heating due to the absorption of photons. Therefore, very high fluences can be used to generate a strong IFE-induced magnetization in such systems without heat-induced effects quenching the magnetic order. In contrast, the electronic and phononic heating is much more significant in highly absorbing materials like metals, leading to strong thermal effects which overlay any IFE-induced magnetization, making the observation of a non-thermal effect like the IFE in metallic systems particularly difficult [19]. Because of this reason, no experimental reports on time-resolved studies are available so far, by which one can systematically distinguish between the influence of thermal (ultrafast heating) vs. non-thermal (IFE) effects in metals on the femtosecond timescale of ultrafast demagnetization. Furthermore, it was later shown that also a purely thermal excitation with linearly polarized light can lead to all-optical switching in ferrimagnets, relying solely on the intrinsic ferrimagnetic properties like, e.g., antiferromagnetically coupled sublattices and the existence of a magnetization compensation temperature [20–24]. Thus, the influence of a non-thermal process like the IFE on the observed demagnetization and switching phenomena remained unclear so far.
The aforementioned effects are related to the excitation stage of the magnetization dynamics while the laser pulse is interacting with the material. Another very important issue in ultrafast magnetism concerns the microscopic mechanisms leading to a loss or reversal of the magnetic order, which has to involve an angular momentum transfer on a subpicosecond timescale [4, 25]. As the magnetic moment is fundamentally connected to the angular momentum of the electrons, which is a conserved quantity contained in both their spin and orbital moments, any change in magnetization requires a transfer of angular momentum out of, or into the electronic system. This transfer can either be a local angular momentum transfer from electron spins to another reservoir (e.g., orbital moment, atomic lattice or electrons of other atoms) [26–29] or a selective transport of spin-polarized electrons [30–32]. However, despite the existence of various theoretical models trying to explain the angular momentum transfer, the actual process is still highly debated and the experimental studies available so far do not provide definitive answers on the path of ultrafast angular momentum transfer during demagnetization and switching events [4].
The scope of this thesis is to shed light upon both of the aforementioned issues, i.e., the path of angular momentum transfer after femtosecond optical excitation, as well as the influence of an opto-magnetic effect like the IFE on timescales of ultrafast demagnetization in a metallic ferrimagnet. Therefore we will employ different pump-probe techniques which allow us to monitor the transient behavior of the magnetic moments in the studied sample systems of ferrimagnetic GdFeCo after excitation. For probing the magnetization state, we will utilize magneto-optical effects like the Faraday and Kerr effect (MOFE, MOKE) [33, 34] in the visible light regime as well as the x-ray magnetic circular dichroism (XMCD) [35] for element-selective studies. An introduction to the intrinsic magnetic properties of the studied ferrimagnetic GdFeCo alloys and to the ultrafast magnetization
3
1 Introduction
phenomena that can be observed in such systems will be given in Chapter 2, which also explains the magneto-optical and opto-magnetic effects employed for probing and excitation. Furthermore, in this chapter the femtosecond soft x-ray and XUV radiation sources at which the experiments presented in this thesis were carried out are described.
Chapter 3 will present element-selective and time-resolved XMCD studies at the L3,2
and M5,4 absorption edges of Fe and Gd, respectively, in a ferrimagnetic GdFeCo alloy. Employing a pump-probe technique allows us to monitor the transient changes of the element-specific magnetic moments of Fe and Gd after excitation with laser pulses of 800 nm wavelength and linear polarization. A magneto-optical sum rules analysis [36, 37] of the time-resolved XMCD data is employed to disentangle the individual contributions of spin and orbital moments at each atomic site during the ultrafast demagnetization process; an analysis which will enable us to draw conclusions on the path of angular momentum transfer in such systems. The experiments presented in this chapter were carried out at the FemtoSpeX fs-slicing facility at the BESSY II synchrotron light source, providing 100 fs short, circularly polarized soft x-ray pulses needed for time-resolved and element-specific XMCD studies [38]. In Chapter 4, the influence of an opto-magnetic effect like the IFE in ferrimagnetic
GdFeCo is studied by using a novel approach of inducing helicity-dependent ultrafast demagnetization dynamics by resonantly exciting electrons from the 3p core level states of Fe, corresponding to the Fe M3,2 resonance. This approach employs highly intense, 90 fs XUV pulses with both linear and circular polarization for excitation, which were generated at the free electron laser FERMI [39]. In contrast to previous studies on the IFE excited by visible light, the resonant XUV excitation could provide access to a regime where the opto-magnetic effect potentially gets larger due to the much stronger spin-orbit coupling of the core levels, allowing the influence of a non-thermal IFE to be distinguished from the thermally induced demagnetization. To quantify the magnitude of a helicity-dependent effect on the magnetization, the ultrafast demagnetization process is studied as a function of polarization state and photon energy of the XUV excitation pulse. The wavelength- and helicity-dependent dynamics are probed by light pulses in the visible wavelength regime, utilizing the magneto-optical Faraday and Kerr effects. As no theoretical and experimental studies are available so far regarding the existence of an IFE in the XUV spectral range, the experiment presented in this thesis is the first study aiming at the observation of an IFE in this wavelength regime.
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2 Fundamentals and experimental techniques
This chapter serves as an introduction to the fundamentals and experimental techniques employed in the time-resolved studies presented in the subsequent parts of this thesis. As all experiments were carried out on ferrimagnetic GdFeCo alloys, the first two sections will give an overview over their intrinsic magnetic properties and the ultrafast magnetization dynamics that can be observed in such systems. Afterwards, the physical principles behind the magneto-optical and opto-magnetic effects used for probing and inducing magnetization by light will be explained. Finally, the instrumentation used for generating femtosecond soft x-ray and XUV pulses at large-scale facilities will be described.
2.1 Magnetic properties of rare earth and 3d transition metal systems
The magnetic samples studied in this work are ferrimagnetic alloys of GdFeCo, consisting of the rare-earth (RE) element Gd and the 3d transition metals (TMs) Fe and Co. In their elemental form, both types of materials (RE and 3d-TM) undergo ferromagnetic ordering, but due to different origin. While the RE element Gd is a classical Heisenberg-ferromagnet due to its well-localized 4f magnetic moments (binding energy ≈ 8 eV below the Fermi level [40]), Fe and Co belong to the group of itinerant band-ferromagnets described by the Stoner model. In an alloy, they couple antiferromagnetically to each other and exhibit ferrimagnetic properties like a magnetization compensation temperature. Furthermore, thin films of GdFeCo can possess perpendicular magnetic anisotropy, leading to an out- of-plane orientation of the magnetic moments. Such properties can thereby be tuned by the composition and stoichiometry of the layer [41, 42]. In the first section of this chapter, we will thus briefly explain the underlying interactions leading to ferro- or antiferromagnetic ordering and magnetic anisotropy. In the second section, the individual magnetic properties and interactions in RE and 3d-TM elements and the studied GdFeCo alloys will be described. As a thorough description of the underlying physics and theories can be found in Ref. [40, 43, 44], this chapter will focus more on a qualitative description of the physical principles which are referred to in the later chapters. Unless mentioned otherwise, all formulas and values are taken from Ref. [40].
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2.1.1 Magnetic interactions
Exchange interaction
The mechanism responsible for the long-range magnetic ordering in solids is the microscopic exchange interaction. In general, there exist different types of exchange mechanisms, which can be divided into direct and indirect interactions. While the first describe a direct coupling between the electronic spins of two neighboring atoms due to a spatial overlap of their electronic wave functions, the latter describe indirect mechanisms involving an intermediary site (e.g., double-exchange, superexchange, Dzyaloshinskii–Moriya interaction) or between strongly localized states mediated by conduction band electrons (RKKY interaction) [40]. Regarding the materials studied in this thesis, i.e., ferrimagnetic GdFeCo alloys, the only relevant mechanisms are the direct exchange interaction (see below) and an RKKY-type coupling present in the RE element Gd (see Chapter 2.1.2). The direct exchange is thereby based on an interplay of Coulomb repulsion forces between the electrons and the Pauli exclusion principle which states that the total electronic wave function has to be antisymmetric, i.e., electrons with the same spin state have to be in different orbitals [40]. When the valence orbitals of adjacent atoms overlap, the electrons try to minimize their ground state energy which can in a simple Hubbard-like picture be seen as an interplay of Coulomb forces (repulsion of electrons in the same orbital) and their orbital degrees of freedom (inter-atomic hopping). In the classical Heisenberg model of fully localized spins, the direct exchange interaction can be described by an effective Hamiltonian, coupling the electronic spins Si,j of neighboring atoms (i,j):
Heff = − ∑ i,j
JijSi · Sj , (2.1)
where Jij is the exchange coupling constant. Depending on the electronic occupation of the overlapping orbitals and the bonding between different ligands, this can lead to the electrons either favoring a parallel (Jij > 0) or antiparallel (Jij < 0) spin alignment in the ground state, which gives rise to ferro- and antiferromagnetism. The exchange energy is thereby defined as the energetic difference between the states with different spin alignment.
Spin-orbit coupling
The spin-orbit coupling (SOC) is a relativistic microscopic interaction that couples the spin and orbital parts of the electronic wave functions. It can be understood as an interaction between the spin of an electron and its orbital motion within the electrostatic Coulomb potential Φ(r) = Ze/4πε0r of the positively charged nucleus (q = +Ze). The SOC thereby describes the coupling between spin (s) and orbital (l) angular momentum vectors to a total angular momentum j = l + s. In a semi-classical picture, it can be understood by treating the orbital motion around the nucleus as a current loop with
6
radius r, generating a magnetic field that acts on the spin moment of the electron. In a quantum-mechanical description, the SOC couples electronic states with spin and orbital quantum numbers s and l to new eigenstates with total quantum numbers j = l ± s and lifts the degeneracy of the corresponding energy levels. For a single electron (j = l± 1/2), the SOC energy can be described by the following Hamiltonian, scaling with the radial gradient ∇Φ = (r/r) dΦ(r)/dr of the nuclear Coulomb potential:
Hso = − e~2
8πε0m2 ec
2r3 (2.2)
where the expectation value ζnl = ξnl(r) is the so called SOC constant, corresponding to the energetic splitting of the two j states in an orbital with quantum numbers n,l, which also scales with the atomic number and thus gets larger for heavy elements with large Z values. The total magnetic moment mj of the electron is thereby given by both spin and orbital angular momentum:
mj = µB ~
(gels + l), (2.3)
where gel ≈ 2 is the electronic g-factor. For light atoms (Z ≤ 30) consisting of multiple electrons i, the same formalism can be applied to the total spin and orbital moments S =
∑ si and L =
∑ li of the atom (L-S or Russel-Saunders coupling, respectively).
The SOC gives rise to many different types of effects as it mediates the interaction of electronic spins with the atomic lattice and the angular momentum of light. Exemplary consequences are the magneto-crystalline anisotropy and the existence of magneto-optical and opto-magnetic effects (see Chapters 2.3 and 2.4).
Magnetic anisotropy
The magnetic anisotropy (MA) describes the tendency of the total magnetic moment to align along a certain crystallographic axis of a magnetically ordered system, which is then called the “easy axis”. A correlated quantity is the magnetic anisotropy energy (MAE), which is the energy that has to be spent in order to tilt the magnetic moment from the easy axis to the perpendicularly oriented hard axis. In magnetic materials, there is usually a competition between shape, magneto-crystalline and surface/interface anisotropy [40, 45]. The latter becomes especially relevant in magnetic thin films and multilayer structures consisting of them, where surface or interface effects can dominate over the 3D bulk properties of a magnetic crystal. Depending on the strength of each term, the magnetic layer can exhibit an overall in-plane or out-of-plane magnetic anisotropy. The shape anisotropy is an externally imprinted property given by the macroscopic
shape of the magnetic material and describes the urge of the system to lower its ground state energy by reducing the magnetic stray field. This can easily be understood in terms of a long rod magnet which always wants to magnetize along its longitudinal axis because a perpendicular alignment would lead to much higher stray fields and is thus the
7
energetically less favorable configuration. In thin films, the shape anisotropy therefore tends to align the magnetic moments parallel with respect to the surface.
The magneto-crystalline anisotropy, on the other hand, is of microscopic and quantum- mechanical origin. Given its complexity, only a qualitative description based on the Bruno model will be presented here [46, 47]. Due to the crystal field potential of the neighboring atoms in an atomic lattice, certain directions of the orbital motion of the electrons can be effectively suppressed. In conjunction with the spin-orbit coupling, which aligns the spins parallel or antiparallel with respect to the orbital moment, a preferential direction of the total magnetic moment can arise. The magneto-crystalline anisotropy thereby scales with the spin-orbit coupling strength and its direction depends on the individual composition and orbitals of the involved atoms in the lattice.
The surface or interface anisotropy arises due to the symmetry breaking of the crystallographic structure at the surface of a magnetic layer or at the interface between different layers. While in the plane of a magnetic thin film, the environment of each atom and thus the overlap of the orbitals of neighboring atoms is similar to a 3D bulk crystal, it is very different in out-of-plane direction at a surface or interface, where there are either no neighboring atoms on one side or they are of different elements with differing electronic structures. Thus, the surface or interface anisotropy can prefer an orientation of the magnetic moments which is different compared to the bulk material. With decreasing layer thicknesses, the surface/interface contributions get larger compared to the bulk term. Well established systems where the surface/interface anisotropy dominates are Co/Pt or Co/Pd multilayers that forms perpendicular magnetic anisotropy when the Co layers deceed a certain thickness, typically on the order of ≈ 1.2 nm or less [45].
2.1.2 Magnetic order in RE and 3d-TM elements
Heisenberg magnetism and intra-atomic 4f5d-exchange in RE elements
In case of the rare-earth elements (e.g., Gd, Dy, Tb, Ho), the magnetic moment is mainly given by the partially filled and strongly localized 4f electrons, while the valence electrons in the outer more band-like 5d, 6s and 6p states only yield a minor contribution [40]. Therefore, the magnetic exchange interaction can be treated in the classical Heisenberg- model by the effective Hamiltonian shown in Eq. 2.1. All RE elements are paramagnetic at room temperature and above, and show either antiferromagnetic or ferromagnetic ordering below a certain temperature. Gd (Z = 64) is a special case since it is the only RE element that has a ferromagnetic phase up to TC ≈ 289 K (close to room temperature) and an electronic configuration of [Xe]4f75d16s2, i.e., a half-filled 4f shell. Following Hund’s rules, the ground state is thus given by the spin and orbital quantum numbers S = 7/2 and L = 0, thus its local 4f magnetic moment is exactlymJ = 7µB/atom and arises completely due to spin angular momentum, while the orbital moment is zero. An additional yet small contribution arises from the itinerant magnetism of the 5d valence band (see below),
8
which for Gd is on the order of ≈ 0.6µB, thus less than 10 % of the total magnetic moment. An important consequence of the strong localization of the 4f orbitals is their vanishing overlap with neighboring atoms. Thus, the direct exchange interaction between the 4f electrons is very small, leading to strong, atomic-like local moments but cannot explain the long-range ferromagnetic ordering. The reason why Gd still enters a ferromagnetically ordered phase is an indirect exchange mechanism based on a RKKY-type coupling [40, 48]. A very strong intra-atomic direct exchange between the spatially overlapping 4f and 5d orbitals (J4f5d ≈ 100–130 meV [4, 49]) leads to a spin polarization of the delocalized 5d electrons. The latter then mediates an inter-atomic exchange between the neighboring atoms. The strong 4f-5d coupling also plays an important role in studies of ultrafast laser-induced demagnetization and switching phenomena as light in the visible wavelength regime can only excite electrons within the 5d band and not directly from the tightly bound 4f states which carry the largest part of the magnetic moment. However, it was shown experimentally in Gd and other RE elements that an optically excited quenching of the 5d magnetic moment leads to a respective change in the 4f magnetic moment, matching both relative demagnetization magnitudes and times [50, 51]. The intra-atomic coupling was thus shown to be quasi-instantaneous, on timescales much faster than the experimental time resolution and predicted to be as fast as given by the uncertainty relation (~/J4f5d ≤ 10 fs).
Itinerant (delocalized) ferromagnetism in 3d-TMs
In case of the 3d transition metals Fe, Co and Ni, the more than half-filled 3d shell leads to the formation of a strong ferromagnetic coupling (TC ≈ 600–1400 K) due to a spin polarization of the partially delocalized valence electrons of the 3d band [40]. The partial delocalization thereby leads to a strong overlap and exchange interaction with the 3d orbitals of the neighboring atoms. For that reason, Fe, Co and Ni are called itinerant or delocalized band-ferromagnets. As the Heisenberg model of localized spins cannot describe the itinerant magnetism anymore, the Stoner model of metallic ferromagnetism has been introduced. In this model, the ferromagnetic ordering leads to a spin polarization of the 3d valence band, shifting the density of states for spin up and down electrons with respect to the Fermi level. Thus, the relative occupation of spin up vs. down states is different, leading to the formation of a majority and minority spin band. The magnitude of the magnetic moment m and the Stoner splitting energy is thereby given by the difference between the occupation number of electrons in the majority (Nmaj
e ) and minority (Nmin e )
spin band, which in case of the band model can have non-integer values:
|m| = µB(Nmaj e −Nmin
e ), = 2mHex, (2.4)
where Hex is an effective field describing the exchange interaction. In case of Fe, the resulting total magnetic moment is on the order ≈ 2.2µB/atom (bcc Fe), given mainly by its spin moment with an orbital contribution of only ≈ 0.1µB.
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Gd
Fe
TC0
|M|
TTcomp
0
Figure 2.1: Illustration of the typical temperature-dependence of Gd and Fe sublattice magnetizations (red and blue curves) in ferrimagnetic GdFe leading to the formation of a magnetization compensation temperature Tcomp. For temperatures below Tcomp, the magnetic moment of the Gd sublattice (red arrows) dominates and determines the direction of the net magnetization (green arrows). Exactly at Tcomp, both sublattice magnetizations are equal and cancel each other out (zero net magnetization). Above Tcomp, the magnetic moment of the Fe sublattice becomes dominant, thus the net magnetization reverses its sign. When the Curie temperature TC is approached, the magnetic order disappears and both sublattices enter a paramagnetic phase.
Coupling between RE elements and 3d-TMs
Alloys of RE elements and 3d-TMs can be treated as two magnetic sublattices of the corresponding elements exhibiting either ferro- or antiferromagnetic coupling between their total magnetic moments. As described in Ref. [52], the coupling of the spin system is thereby determined by the density of states around the Fermi level and the hybridization of the 5d and 3d valence bands of the RE and TM, respectively. Due to the strong exchange shift of the ferromagnetically polarized 3d band, the 5d band of the RE element energetically overlaps mainly with the minority spin band of the TM, which results in a much stronger hybridization of 5d electrons with the 3d minority spin electrons compared to their majority spin counterparts. As a result, the 5d electrons will always polarize according to the minority spin of the TM and thus show an antiferromagnetic spin polarization. Due to the strong intra-atomic exchange with the 4f electrons, the latter will polarize accordingly. The type of coupling between the total magnetic moments is then determined by the polarity of the spin-orbit coupling in the RE element:
In alloys with light RE elements (less than half-filled 4f shell), the spin-orbit coupling of the RE is negative (L−S) and its orbital moment exceeds the spin moment. Thus, the total magnetic moments of RE and TM exhibit a ferromagnetic coupling. In alloys with heavy RE elements (half- or further filled 4f shell), the spin-orbit coupling of the RE is positive (L+S). Thus, the total magnetic moments will couple antiferromagnetically. Due to their different amount of magnetic moment per atom, an antiferromagnetic coupling between the sublattices usually does not lead to a compensation of their magnetic moments, which means the alloy is a ferrimagnet and possesses a non-zero net magnetization.
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The exchange between RE element and 3d-TM further leads to a common Curie temperature TC, which was theoretically derived and experimentally confirmed by the authors of Ref. [41] and shown to depend on the RE concentration in the alloy. However, due to the different exchange interactions in the RE and 3d-TM sublattices, their magnetic order and thus magnetization scales differently with the temperature. In particular, the power law describing the M(T ) behavior up to the Curie temperature TC where the magnetic order disappears is not the same for both sublattices [41]. As illustrated in Fig. 2.1 for the case of ferrimagnetic GdFe, this can lead to the existence of a magnetization compensation temperature Tcomp, where both sublattice magnetizations are equal and the net magnetization vanishes. Below and above Tcomp, either the Gd or Fe sublattice dominates and determines the direction of the net magnetization. Thus, static heating across Tcomp leads to a reversal of the net magnetization. If the heating is done under an applied magnetic field, the net magnetization will always align along the field direction, so the sublattice magnetizations will reverse. As shown in the next chapter, the ferrimagnetic compensation point was found to play a significant role with respect to ultrafast magnetization dynamics, when excitation by a laser pulse leads to ultrafast heating across the compensation point.
Ferrimagnetic GdxFeCo1-x alloys
The amorphous GdFeCo alloys studied in this thesis consist of the RE sublattice Gd coupled ferrimagnetically to a 3d-TM sublattice of Fe and Co. As the latter two exhibit a strong ferromagnetic exchange coupling to each other and show the same temperature dependent behavior up to TC, they can be treated as a single sublattice of FeCo [41]. The total magnetic moment of the Gd sublattice is thereby provided mostly by the spin moment of the 4f electrons (≈ 7µB/atom) due to the half-filled 4f shell which has zero orbital angular momentum. In case of FeCo, the total magnetic moment is provided by both the spin and orbital angular momentum of the 3d electrons, although its main contribution (≈ 2µB/atom) is given by the spin moment, as the orbital moment is much smaller and quenched by the crystal field potential of the lattice. The critical temperatures (TC, Tcomp) and the magnetic anisotropy of thin GdFeCo films can be tuned by varying the composition and thickness of the magnetic layer [45]. Systematic studies on the Gd concentration influencing the Curie and compensation temperatures of 30 nm thin Gdx(FeCo)1−x layers can be found in Ref. [41], leading to a common Curie temperature of TC ≈ 550 K and a ferrimagnetic compensation point of Tcomp ≈ 60–350 K for Gd contents of x = 23.4–29%. Respective studies on the magnetic anisotropy, which is also temperature dependent and leads to the layer magnetizing either in- or out-of-plane, were carried out in Ref. [42]. The latter showed out-of-plane magnetic anisotropy at room temperature in the low Gd contents regime of x = 20–34 % (close to an existing compensation point) and also for higher Gd concentrations between 52–59 %, where the Gd magnetic moments dominate over the whole temperature range.
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2.2 Ultrafast laser-induced magnetization dynamics in RE and 3d-TM systems
†Since it was discovered in 1996 that ferromagnetic Ni can be demagnetized on a subpicosecond timescale by a femtosecond laser pulse excitation [5], the investigation of ultrafast magnetization dynamics has become an intense field of research.† At that time, this was a very surprising result, as the laser-induced demagnetization was so far understood in terms of a sudden lattice temperature increase due to the laser absorption, followed by a spin-lattice relaxation until a new equilibrium magnetization is reached; a process which usually happens on timescales of ≈ 100 ps in case of Fe and Gd [6, 7]. This led to the question, how the spin moment of an electron can be reduced so fast and which microscopic mechanisms allow a transfer of angular momentum out of the spin system on a femtosecond timescale. More recent studies on ferrimagnetic rare earth and 3d transition metal systems like, e.g., GdFe alloys have shown that it is even possible to permanently switch magnetization (i.e., rotation/reversal of the magnetization vector by 180 ) on ultrashort timescales by a single optical laser pulse without any other external stimulus [8, 22, 23]. This type of all-optical magnetization switching was first discovered in ferrimagnetic GdFeCo alloys and could be related to the intrinsic properties of the ferrimagnetically coupled RE and 3d-TM elements described in the previous section, and how they react to a femtosecond laser excitation. Therefore, revealing the microscopic processes leading to the distinct dynamics observed in RE-TM alloys and multilayers gained large amount of interest in the last years and is the motivation behind the choice of ferrimagnetic GdFeCo for the studies presented in this thesis. In the following, we will thus describe the so far proposed mechanisms which allow an optical laser pulse to influence the magnetization state of a system on femtosecond timescales. At the end of this section, we will also give an overview over the all-optical magnetization switching dynamics that could be observed in RE-TM systems.
2.2.1 Mechanisms behind ultrafast magnetization dynamics
As the total magnetic moment is given by the spin and orbital moments of the electrons, any change in magnetization is fundamentally connected to an ultrafast transfer of angular momentum out of or into these moments; a process which has to be induced by the femtosecond laser excitation. It is thereby important to distinguish between different types of mechanisms: Local processes describe an actual change of the local magnetic moment, which due
to the conservation of angular momentum is connected to its transfer between different reservoirs like the spin and orbital moments, electrons of different atoms or the atomic lattice. Such processes are the underlying mechanisms of most ultrafast magnetization phenomena, including the laser-induced switching observed in ferrimagnetic RE-TM
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systems [2]. Typical processes leading to such a local dissipation of angular momentum are Elliot-Yafet type spin-flip scattering events (see Chapter 2.2.2). Non-local processes, on the other hand, describe a non-local change of magnetic moment
where the laser-excitation of the electronic system leads to the generation of spin-polarized currents which transport the magnetic moment out of the probed volume or to another atomic site. Typical mechanisms leading to such a non-local transport of magnetic moment are super-diffusive spin transport [30, 31] and the recently discovered optical inter-site spin transfer [32, 53, 54] (see Chapter 2.2.3). The ultrafast demagnetization phenomena studied in the Chapters 3 and 4 are local
processes of both thermal and non-thermal origin. While opto-magnetic effects leading to a non-thermal change of magnetization will be discussed in more detail in Chapter 2.4, the following sections will give an overview over the different local spin-flip scattering and non- local transport mechanisms that were proposed to explain the ultrafast demagnetization process after thermal excitation.
2.2.2 Local spin-flip scattering processes
Local effects describe a change of magnetization due to a local dissipation of angular momentum following the excitation of electrons via the absorption of a femtosecond laser pulse. As optical dipole transitions are forbidden to directly change the spin state of an electron due to the dipole selection rules, the ultrafast demagnetization can be understood in terms of the excited electrons undergoing spin-flip scattering events which ultimately lead to a loss of magnetic order. The underlying mechanisms behind such scattering events which are accompanied by a certain spin-flip probability include Elliott-Yafet type electron-phonon and electron-impurity/defects scattering [55, 56] as well as scattering of an excited electron with other electrons or quasi-particles like magnons. This can be understood as follows: In presence of spin-orbit coupling, the spin itself is not a good quantum number anymore, thus an electron does not have a pure spin eigenstate |Ψ↑,↓, but a mixed spin state with majority (a↑,↓) and minority (b↑,↓) spin components [4]:
|Ψ↑ = a↑|↑+ b↑|↓
|Ψ↓ = a↓|↓+ b↓|↑ (2.5)
Such mixed spin states, the so called “spin hotspots”, were predicted to appear as an avoided crossing between spin up and down bands in the band structure of a ferromagnet and have been indeed observed in photoemission studies (see, e.g., Ref. [57]). The spin- mixing was shown to open up a channel for transitions into states with a changed dominant (majority) spin component, allowing a scattering event to effectively flip the spin of an electron. The spin-flip probability thereby depends on the minority spin coefficient, corresponding to the strength of spin mixing.
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Electron-phonon scattering
The first microscopic model explaining the ultrafast demagnetization on the basis of an Elliott-Yafet type mechanism included phonon-mediated spin-flip scattering events [26]. The theory is based on a Hamiltonian describing the interactions between the three subsystems of electrons, spins and phonons, and is the basis for the microscopic three- temperature model (M3TM) as explained later. Despite the classical electron-electron and electron-phonon equilibration terms, a further term is added which accounts for the Elliott-Yafet spin-flip probability during electron-phonon scattering events, leading to a transfer of angular momentum from the electrons to the lattice. It was shown that this model allows to obtain demagnetization times which are much faster than the electron-phonon thermalization processes. However, ab-initio calculations carried out by the authors of Ref. [58–60] showed that, although there is a significant contribution from phonon-mediated spin-flips, the induced demagnetization rate is too small in order to explain the observed dynamics, thus further mechanisms have to be taken into account.
Electron-electron scattering
The contribution of an electron-electron interaction was proposed in Ref. [28] by describing an inelastic Coulomb scattering process involving the optically excited majority and minority electrons of a band-ferromagnet. In presence of spin-orbit coupling, interband scattering events change the spin-mixture and lead to a redistribution of electrons from majority to minority bands, which consequently reduces the magnetization. It was shown that simulations carried out using this model lead to a good agreement with the ultrafast demagnetization effects observed in ferromagnetic Co and Ni.
In an extended model developed by the authors of Ref. [61], the influence of electron- electron vs. Elliott-Yafet type electron-phonon scattering was studied. It was proposed that a combination of both mechanisms needs to be considered in order to fully describe the ultrafast dynamics in Ni, as they act differently on demagnetization and remag- netization timescales, while the phonon-mediated scattering also leads to an increased demagnetization efficiency.
Electron-magnon scattering
Another proposed mechanism is electron-magnon scattering. In this model, excited electrons undergo electron-electron interactions leading to the excitation of collective spin modes and thus emission of a magnon [27]. This is mediated by the spin-orbit coupling, which allows the corresponding transfer of angular momentum out of the electronic spin system into the orbital moment and eventually to the lattice that acts as a final sink of angular momentum. However, experiments have shown that there is no indication for an increase of orbital angular momentum on the so far experimentally accessible timescales (see, e.g., Ref. [25, 62] and also Chapter 3). Therefore, a second and much faster process
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was assumed, leading to a rapid quench of the orbital moment by the crystal field, which efficiently transfers the angular momentum to the lattice. While the latter would be in line with another recent theory, proposing a dissipation of angular momentum to the lattice within just ≈ 1 fs [29], calculations carried out by the authors of Ref. [63] have shown that the spin-flips caused by electron-magnon scattering do not lead to sufficient demagnetization rates and only play a minor role. Instead, a combined mechanism was proposed, taking also electron-phonon scattering into account [60, 63].
Three-temperature model (3TM)
The three-temperature model (3TM) was originally proposed in 1996 [5] and is a phenomenological model describing the demagnetization process by assigning temperatures to the three subsystems of electrons, spins and lattice. The excitation by the laser is regarded as an ultrafast increase of the electronic temperature, which subsequently thermalizes with the other baths coupled via rate equations. The 3TM thereby allows only a phenomenological description of the process by fitting the transfer rates between the heat baths to the experimentally obtained data. As such, no insights into the microscopic mechanisms or angular momentum transfer can be provided. A simplified version of the 3TM is the two-temperature model (2TM), which treats only the electronic and phononic bath independently and is used in Chapter 3 to estimate the electron-lattice thermalization time.
The model was later extended to the microscopic three-temperature model (M3TM) by including Elliott-Yafet type phonon-mediated spin flips, considering also angular momentum conservation by allowing its transfer from the electrons to the lattice [64]. Although the M3TM can be used to successfully reproduce experimental data, it usually fails to predict the actual dynamics [4]. Reasons are that, as mentioned before, phonon-mediated spin flip scattering was found to be not sufficient to fully explain the demagnetization process, and that it assumes a full internal equilibrium of each heat bath by assigning it a certain temperature. It was shown, however, that the largest spin-flip rate arises from nonequilibrium electrons before they are thermalized [58].
2.2.3 Non-local spin transport processes
In contrast to the local effects described in the previous section, non-local effects do not rely on a process changing the spin state of an electron but on a transport mechanism leading to a reduced net magnetic moment due to laser-excited spin-polarized currents which transport mainly the majority spin electrons out of the probed volume or atomic site [31, 32]. Such effects were thus proposed to explain ultrafast demagnetization and switching phenomena without requiring the existence of a local (on-site) angular momentum dissipation channel and are briefly introduced in the following.
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Super-diffusive spin transport
Super-diffusive spin transport describes a non-local change of magnetic moment in conductive materials due to a diffusive motion of mostly majority spin electrons out of the probed volume [31]. It was experimentally observed for the first time in ultrafast demagnetization studies of antiferromagnetically vs. ferromagnetically coupled Co/Pt multilayers which were separated by a spacer layer of either insulating NiO or metallic Ru [30]. It could be shown that using a conducting spacer layer leads to a faster and more efficient demagnetization of the antiferromagnetic phase of the Co/Pt multilayer, which was explained by a spin-polarized current leading to a transport of majority spin electrons from Co to Pt and vice versa. A semi-classical model describing such spin transport processes in a 3d band-ferromagnet was proposed by the authors of Ref. [31]. It relies on a spin-polarized diffusion of electrons due to different electronic scattering probabilities (which are treated as spin-conserving in this model) and thus mobility of the excited majority vs. minority spin electrons. The larger mean free path and higher velocity of the majority spin electrons thereby lead to a super-diffusive motion of majority carriers out of the probed volume, reducing the net magnetic moment in this region.
A specific type of super-diffusive spin transport has also been observed in amorphous alloys of ferrimagnetic GdFeCo, which can occur due to the amorphous state and thus not necessarily homogeneous elemental distribution in the sample. This ultrafast spin transport was shown to happen laterally (i.e., in the sample plane) between nanometer scale regions with different Gd and Fe concentrations (e.g., from Gd-rich towards Fe- rich regions) [65]. However, such non-local spin transport or its observation is usually suppressed when the magnetic layer is grown on an insulating substrate and probed over its whole thickness and a sufficiently large area, preventing spin-polarized currents between different layers and suppressing the observation of both longitudinal (i.e., along the sample normal) and lateral spin diffusion which averages out due to the macroscopic probing volume. This was the case in the experiments presented in Chapters 3 and 4.
Optical inter-site spin transfer (OISTR)
Another recently discovered mechanism is optical inter-site spin transfer (OISTR), which describes an optically induced spin-selective charge flow between different sublattices (A,B) of multi-component magnetic systems [32, 53, 54]. Although it is a short ranged interaction involving a charge transfer between neighboring atoms, it is referred to as a non-local process in this overview as the electronic spin state is not changed during this process and it does not generate local (on-site) spin flips. Instead, the process relies on an optical spin-conserving excitation of electrons from occupied states of an atom in sublattice A to unoccupied states of an adjacent atom in sublattice B. Being an electronically coherent effect, it is expected to act only during the presence of the laser excitation pulse and to occur on timescales shorter than the intrinsic electronic lifetimes
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(given by inelastic electron-electron scattering times). As it was shown exemplary for antiferromagnetically coupled Mn atoms by the authors of Ref. [32], the OISTR process can lead to a direct excitation of majority spin electrons from Mn site A to empty minority spin states of Mn site B, leading to an extremely fast demagnetization on timescales corresponding to the pulse duration of the laser. Very recent theoretical and experimental studies have shown that the OISTR process is also present in ferromagnetically coupled CoPt alloys, playing a decisive role in the ultrafast demagnetization dynamics observed in such systems [54]. However, the presence of OISTR highly depends on the density of states around the Fermi level and so far it was neither predicted nor observed to happen in ferrimagnetic RE-TM systems.
2.2.4 All-optical magnetization switching in RE and 3d-TM systems
Laser-induced all-optical magnetization switching was first observed in amorphous ferrimagnetic GdFeCo alloys [8], employing circularly polarized light pulses to permanently switch the magnetization. The direction of switching, i.e., the final magnetization state, was thereby found to be dependent on the helicity of the light, with no external magnetic field required. This type of switching was initially explained by a combination of both thermal and non-thermal mechanisms: In a first step, the laser pulse excites the electronic temperature up to slightly below TC, leading to an ultrafast demagnetization. In a second step, the circularly polarized light acts as a helicity-dependent effective magnetic field due to the Inverse Faraday Effect (see also Chapter 2.4.1), which is antiparallel or parallel to the small remaining magnetization and thus determines the direction of the subsequent relaxation. A different and purely thermal mechanism was proposed to be based on ultrafast
heating of the system across its ferrimagnetic compensation point (Tcomp) in presence of an external magnetic field [20, 21]. Time-resolved XMCD studies showed that this type of thermally induced switching is mediated by a transient ferromagneticlike state, where the magnetic moment of the usually antiferromagnetically coupled Gd and FeCo sublattices is aligned parallel [22]. It was later shown that the external field is not required and that a thermal excitation alone is sufficient to switch the magnetization forth and back (so called “toggle switching”) [23]. The magnetization reversal could be related to the different demagnetization times of the two sublattices, depending on their amount of magnetic moment per atom [22, 24]. A multi-sublattice model was used to give a phenomenological explanation for the switching process in terms of two thermal regimes [66]: Directly after excitation, the electrons are heated far beyond the Curie temperature (T TC), leading to a temperature-dominated regime with negligible exchange coupling between the sublattices. Consequently, they will demagnetize independently on their intrinsically different timescales, with Gd still demagnetizing when the Fe sublattice magnetization approaches zero. In the mean time, the electronic temperature thermalizes with its
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environment, approaching a second regime of T < TC, where the angular momentum exchange between the two sublattices dominates. Any further spin-flip in Gd will then oppositely flip an Fe spin due to their antiferromagnetic coupling. Subsequently, the magnetization of the FeCo and later the Gd sublattices reverse sign. It was shown in Ref. [67], that the vicinity to the compensation temperature is thereby crucial for an efficient magnetization reversal process, as it leads to an increased domain wall mobility that favors the relaxation to a state with reversed magnetization.
While all-optical magnetization switching was first discovered in GdFeCo, such phenomena can also be observed in other ferrimagnetic RE-TM alloys and multilayers like, e.g., TbFeCo, DyCo and HoFeCo, exhibiting similar properties regarding antiferromagnetically coupled sublattices and compensation temperatures [68, 69]. Although several theoretical approaches and phenomenological models tried to give
explanations for the microscopic mechanism behind the ultrafast demagnetization and magnetization switching phenomena [66, 70, 71], the actual path of angular momentum transfer mediating both processes remains elusive so far [4]. X-ray scattering experiments on thin films of GdFeCo alloy have revealed that there is also a non-local contribution due to an angular momentum transfer mediated by lateral spin currents on the nanometer length scale, which further complicates the microscopic picture of all-optical switching processes [65]. Furthermore, the influence of a non-thermal effect like the Inverse Faraday Effect on the magnetization dynamics is unclear, as the authors of Ref. [72] were able to explain the helicity-dependent all-optical switching process originally observed in Ref. [8] by a purely thermal effect, relying on magnetic circular dichroism leading to a helicity-dependent threshold fluence. Thus, further studies are required to shed light upon the path of angular momentum transfer during ultrafast demagnetization and switching events, as well as to disentangle thermal from non-thermal contributions. Such studies will be presented in the subsequent chapters, investigating the angular momentum flow in GdFeCo during ultrafast demagnetization (see Chapter 3) as well as non-thermal contributions due to an opto-magnetic effect (see Chapter 4), respectively.
2.3 Magneto-optical effects (probing magnetization with light)
One possibility to probe the magnetization of a system is its interaction with light via magneto-optical effects that influence either the polarization state or the magnitude (i.e., intensity) of a light wave while it is being transmitted through or reflected by a magnetic medium. In this thesis, both light from the visible (≈ 380–780 nm [73]) and soft x-ray spectral range (≈ 250 eV up so several keV [74]) was used to perform time-resolved measurements of magnetization on a femtosecond timescale. Chapter 4 will employ the magneto-optical Faraday and Kerr effect to probe the magnetization of a ferrimagnetic GdFeCo system using linearly polarized visible light pulses. While an advantage of using visible light for probing is the flexibility and feasibility of the
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detection scheme as well as the high stability of femtosecond optical laser systems, it lacks element-selectivity by probing only the valence bands of the FeCo and Gd sublattices due to its low photon energy. Therefore, Chapter 3 makes use of circularly polarized soft x-ray pulses to probe element-specific magnetic moments of Fe and Gd by doing core level spectroscopy, utilizing the x-ray magnetic circular dichroism (XMCD). The latter technique also allows to extract information about the elemental spin and orbital angular momentum of the electrons by applying magneto-optical sum rules [36, 37]. While the XMCD is mainly used as a probing technique, it can also affect the magnetization when employing highly intense and circularly polarized x-ray pulses; such short and intense pulses could potentially trigger fast helicity-dependent magnetization dynamics via the dichroic (i.e., x-ray helicity dependent) absorption of the magnetic sample. One such example is described in Chapter 4 where resonant circularly polarized XUV excitation is studied and thus the XMCD in the XUV spectral range has to be taken into account.
In this section, we will briefly introduce both types of magneto-optical effects employed for static characterization and time-resolved experiments. As the underlying physics of these effects are well known and understood, we will focus mainly on the aspects which are important regarding their application in our experiments and the ferrimagnetic GdFeCo alloys under investigation.
2.3.1 Magneto-optical Faraday and Kerr effect (MOFE/MOKE)
The magneto-optical Faraday and Kerr effects (MOFE/MOKE), originally discovered in 1845 [33] and 1877 [34], describe the influence of magnetization on the polarization of linearly polarized light when it is transmitted through (Faraday) or reflected by (Kerr) a magnetized medium, leading to a rotation and ellipticity of the polarization plane of the light wave scaling linearly with the magnetization via magneto-optical constants. Qualitatively, both magneto-optical effects can be described in the following way [4]:
Due to linearly polarized light being a superposition of left- and right-circularly polarized waves of equal amplitudes, the rotation of the polarization can be understood in terms of a circular birefringence caused by the magnetization of the system, resulting in different refractive indices for left- and right-circularly polarized light. This leads to different phase velocities of the circularly polarized waves while traveling through the magnetic medium and thus an accumulated phase shift between both components. As a result, the polarization plane of the exit wave is rotated with respect to the incident wave by the so called Faraday or Kerr angle, while the magnitude and direction of rotation depends linearly on the magnetization vector. In addition, an ellipticity can be introduced due to different absorption of the left- and right-circularly polarized components in the magnetized medium. The underlying microscopic mechanism is of quantum mechanical origin, due to the interaction of the two helicities of circularly polarized light with the spin-orbit coupled and exchange split states [75, 76].
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VIS
D+
D-
Θ
F
L
B
magnetic layer
Wollaston prism
Figure 2.2: Illustration of an experiment employing the magneto-optical Faraday effect as a contrast mechanism to probe the magnetization state of a sample. When a linearly polarized, visible light pulse (VIS) is transmitted through the magnetic layer, the polarization plane of the pulse gets rotated by the Faraday angle ΘF, depending on the direction of the applied magnetic field B and the thickness L of the sample. A Wollaston prism splits the transmitted wave into two linearly polarized components with orthogonal polarization axes. Their difference and sum intensities are then measured using a balanced detector consisting of two photodiodes D+,−.
A quantitative description of the Faraday and Kerr effect can be derived macroscopically via Maxwell’s and Fresnel equations, based on the magnetization inducing antisymmetric off-diagonal components in the dielectric tensor. This allows to derive expressions for the complex Faraday and Kerr angles depending on the geometry between the magnetization vector M and the propagation direction k of the light [77]. In case of the Faraday effect in polar geometry (M k along the z direction), this leads to the following complex relation:
ΘF + iεF ≈ iπL λv
, (2.6)
where εxx, εxy are the diagonal and off-diagonal components of the dielectric tensor, λv is the wavelength of the light in vacuum and L the distance the light travels inside of the material, leading to a rotation ΘF and ellipticity εF of the polarization. While the latter definition is typically used for the magneto-optical Faraday effect in ferromagnetic materials, a more general definition of the Faraday effect in transparent materials subjected to an external magnetic field B expresses the rotation via a material-specific Verdet constant VF [78]:
ΘF + iεF = VFLB ≈ iπL λv
εBxy√ εxx
, (2.7)
where εBxy is now the perturbation of the off-diagonal term in the dielectric tensor due to the magnetic field B. In time-resolved experiments, the Faraday and Kerr effect can be used to probe the
magnetization state of a magnetic layer by using linearly polarized visible light pulses
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generated by a femtosecond laser system. Fig. 2.2 shows a schematic illustration of an experiment probing the Faraday rotation of a light pulse after transmission through a sample by employing a polarization-sensitive detection scheme, consisting of a Wollaston prism and a balanced photodetection. The prism separates the transmitted wave into two linearly polarized components with orthogonal polarization axes. Their difference and sum intensities are then measured using a balanced detector consisting of two photodiodes. Any change of magnetization and thus rotation of the polarization plane can then be detected by a change of the difference signal. Normalizing to the sum provides a quantity which is proportional to the Faraday rotation and thus magnetization of the magnetic layer, averaged over the magnetic moments of all constituent elements.
2.3.2 X-ray/XUV magnetic circular dichroism (XMCD)
The magnetic circular dichroism in the (soft) x-ray or XUV spectral range (XMCD) describes a helicity- and magnetization-dependent absorption of circularly polarized x-rays or XUV radiation while being transmitted through a magnetic medium. If the magnetic moment is oriented (anti-)parallel to the k vector of the light wave, this leads to a different absorption cross section of left- (σ−) and right-circularly (σ+) polarized light. The existence of the XMCD effect was theoretically predicted in 1975 [79] and experimentally demonstrated for the first time in 1987 by hard x-ray spectroscopy at the K absorption edge of iron [35]. In contrast to the magneto-optical Faraday and Kerr effect in the visible light regime as presented in the previous section, doing core-level spectroscopy provides much larger dichroic effects and high element-selectivity due to resonant excitation of well separated absorption edges of the different elements [74]. Because a full description of the XMCD effect can be found in Ref. [40, 80], the following paragraph will only give a brief summary.
As the absorption of a photon requires the excitation of an electron from an occupied state below the Fermi energy to an empty state above, the absorption probability of the photon depends both on the density of available states above the Fermi level and the possible dipole transitions between initial and final states allowed by the selection rules. As the latter forbid spin-flips during optical transitions, the secondary spin quantum number ms of an electron cannot be changed when it is promoted from initial to final states, i.e., ms = 0. Additionally, the magnetic quantum number ml of the orbital has to change depending on the helicity, i.e., ml = ±1 for left- or right-circularly polarized radiation, respectively. Due to the spin-orbit coupling of initial and final states, this leads to an imbalance in the number of allowed transitions from spin up or down states comparing left- and right-circularly polarized excitation. Thus, one helicity compared to the other possesses a larger probability of exciting spin up vs. spin down electrons and vice-versa, resulting in a helicity-dependent, spin-polarized excitation. In a non-magnetic or fully demagnetized medium, where the number of available states above the Fermi
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level is equal for both spin up and down electrons, this does not

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Ultrafast spin dynamics of a ferrimagnet revealed by