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A Terahertz View On MagnetizationDynamics

Nilesh Awari

Zernike Institute PhD thesis series 2019-03ISSN: 1570-1530ISBN: 978-94-034-1301-3 (printed version)ISBN: 978-94-034-1300-6 (electronic version)

The work presented in this thesis was performed in the Optical CondensedMatter Physics group at the Zernike Institute for Advanced Materials of theUniversity of Groningen, The Netherlands and at Helmholtz Zentrum Dres-den Rossendorf, Dresden, Germany.

Cover design by Nilesh AwariPrinted by GildeprintNilesh Awari, 2019

A Terahertz View On Magnetization

Dynamics

PhD thesis

to obtain the degree of PhD at the

University of Groningen

on the authority of the

Rector Magnificus Prof. E. Sterken

and in accordance with

the decision by the College of Deans.

This thesis will be defended in public on

Friday 18 January 2019 at 14.30 hours

by

Nilesh Awari

born on 28 September 1987

in Sangamner, India

Supervisor

Prof. T. Banerjee

Co-supervisors

Dr. M. Gensch

Dr. R. I. Tobey

Assessment committee

Prof. B. Koopmans

Prof. M. Munzenberg

Prof. L.J.A. Koster

Dedicated to my Father

Contents

List of Figures vii

List of Tables ix

1 Introduction 1

1.1 Outline of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2 Introduction to Magnetism 7

2.1 Origin of magnetism and magnetic properties . . . . . . . . . . . . . . . . 8

2.2 Magnetic properties of materials . . . . . . . . . . . . . . . . . . . . . . . 10

2.3 Ultra-fast magnetization dynamics . . . . . . . . . . . . . . . . . . . . . . 13

2.4 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3 Experimental Techniques 23

3.1 THz emission spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.1.1 Electro-Optic Sampling . . . . . . . . . . . . . . . . . . . . . . . . 25

3.2 Magneto-optic effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.2.1 Faraday effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.2.2 Magneto-optical Kerr effect (MOKE) . . . . . . . . . . . . . . . . . 28

3.3 Light sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.3.1 Near infra-red (NIR) femtosecond laser sources . . . . . . . . . . . 29

3.3.2 Laser-based THz light sources . . . . . . . . . . . . . . . . . . . . . 30

3.3.3 TELBE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.4 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

4 Narrow-band Tunable THz Emission from Ferrimagnetic Mn3-XGaThin Films 41

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4.2 Experimental details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

4.3 Results & Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

4.3.1 Effect of Mn content on THz emission from Mn3-XGa . . . . . . . 50

4.3.2 Effect of laser power on THz emission from Mn3-XGa . . . . . . . . 52

4.3.3 Effect of temperature on THz emission from Mn3-XGa . . . . . . . 54

4.3.4 Field dispersion for Mn3-XGa . . . . . . . . . . . . . . . . . . . . . 55

4.3.5 Thickness dependence of THz emission from Mn3-XGa . . . . . . . 57

4.4 Conclusion & Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

v

Contents CONTENTS

4.5 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

5 THz-Induced Demagnetization: Case of CoFeB 65

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66




5.5 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

6 THz-Driven Spin Excitation in High Magnetic Fields: Case of NiO 83

6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84



6.3.1 Temperature dependence of AFM mode . . . . . . . . . . . . . . . 89

6.3.2 Field dependence of AFM mode . . . . . . . . . . . . . . . . . . . 91


6.5 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

Summary 99

Samenvatting 101

Acknowledgements 103

Publications 107

Curriculum Vitae 111

vi

List of Figures

1.1 Areal density growth of HDD devices as a function of time. . . . . . . . . 2

2.1 Different types of magnetic ordering present in materials. . . . . . . . . . 10

2.2 Properties of a typical ferromagnet. . . . . . . . . . . . . . . . . . . . . . . 12

2.3 Susceptibility as a function of temperature for different magnetic ordering. 13

2.4 Schematic of the magnetic precession. . . . . . . . . . . . . . . . . . . . . 15

2.5 Schematic of time scales involved in laser driven excitation of magneticmaterials. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.6 Effect of femtosecond laser excitation on magnetic materials. . . . . . . . 18

3.1 Schematic of the electro-optic set-up. . . . . . . . . . . . . . . . . . . . . . 26

3.2 Schematic of the Faraday set-up. . . . . . . . . . . . . . . . . . . . . . . . 28

3.3 Geometries for measurement of Kerr effect. . . . . . . . . . . . . . . . . . 29

3.4 Schematic of the polar MOKE set-up. . . . . . . . . . . . . . . . . . . . . 30

3.5 Schematic of the optical rectification process for THz generation. . . . . . 31

3.6 Electric field and power spectrum of LiNbO3 as a THz source. . . . . . . . 32

3.7 Schematic representing the principle of superradiant process. . . . . . . . 33

3.8 Maximum pulse energy observed at TELBE as a function of repetitionrate, for a given THz frequency . . . . . . . . . . . . . . . . . . . . . . . . 34

3.9 Frequency tunability of TELBE source. . . . . . . . . . . . . . . . . . . . 35

4.1 Schematic of the THz emission spectroscopy set-up and sample geometryemployed for the Mn3-XGa samples. . . . . . . . . . . . . . . . . . . . . . 44

4.2 Schematic of the idealized crystal structure of Mn3Ga . . . . . . . . . . . 44

4.3 Schematic of the bilayer system in Mn3-XGa thin films . . . . . . . . . . . 46

4.4 Emitted THz wave-forms from Mn3-XGa thin films because of NIR laserirradiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

4.5 Analysis of the THz emission measurements . . . . . . . . . . . . . . . . . 51

4.6 The 180◦ phase shift of FMR mode observed in Mn3-XGa thin film. . . . . 51

4.7 Resonant THz excitation of the FMR mode in Mn3Ga thin film . . . . . . 52

4.8 Laser power dependence of the emitted THz emission from Mn3-XGa thinfilms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

4.9 Temperature dependence of the emitted THz emission from Mn3-XGa thinfilms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

4.10 Schematic of the THz emission spectroscopy set-up and sample geometryemployed with 10 T split coil magnet . . . . . . . . . . . . . . . . . . . . . 56

4.11 Field dispersion relation for ferromagnetic mode in Mn3-XGa thin films . . 56

4.12 THz emission from the films with island morphology . . . . . . . . . . . . 57

vii

List of Figures LIST OF FIGURES

4.13 Thickness dependence of the emitted THz emission from Mn3-XGa thinfilms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

4.14 Characterization of Mn3-XGa thin films for tunable, narrow band THzsource. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

5.1 Experimental set-up used for narrow band THz pump MOKE probe mea-surements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

5.2 Experimental geometry used in the experiments . . . . . . . . . . . . . . . 69

5.3 The electric field waveform of 0.5 THz used in the experiment . . . . . . . 70

5.4 Example showcasing the coherent and incoherent contributions of THzinduced magnetization dynamics in CoFeB . . . . . . . . . . . . . . . . . 70

5.5 Ultra-fast demagnetization observed in CoFeB at 0.5 THz pump . . . . . 71

5.6 Ultra-fast demagnetization observed in CoFeB thin films with THz pumpas a function of pump power . . . . . . . . . . . . . . . . . . . . . . . . . 73

5.7 Excitation of the FMR mode in CoFeB using THz as a pump. . . . . . . . 73

5.8 Ultra-fast demagnetization observed in CoFeB thin films at 0.7 THz 1THz pump . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

5.9 Ultra-fast demagnetization observed in CoFeB thin films as a function ofthe THz pump frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

5.10 Comparison of ultra-fast demagnetization observed in CoFeB thin filmsat 0.7 THz pump, taken 6 months apart . . . . . . . . . . . . . . . . . . . 75

5.11 Effect of implantation on THz induced ultra-fast demagnetization ob-served in CoFeB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

6.1 Illustration of the crystallographic and magnetic structure of NiO. . . . . 86

6.2 Sketch of the THz pump Faraday rotation probe technique used for NiO. 87

6.3 Electric field and power spectrum of the utilized THz radiation. . . . . . 87

6.4 Illustration of the two distinct magnetic modes in antiferromangetic res-onance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

6.5 Typical transient Faraday measurement for NiO obtained at 280 K. . . . 90

6.6 Temperature dependence of the magnon mode in NiO. . . . . . . . . . . . 91

6.7 Field dispersion for magnon mode in NiO. . . . . . . . . . . . . . . . . . . 92

6.8 Theoretical calculation of Field dependence of the higher-energy spinmodes in NiO. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

viii

List of Tables

4.1 Ms from VSM [6, 8] and inferred values of 10Hk from dynamic THz emis-sion measurements. THz emission measurements have been performed inthe presence of an external magnetic field of 400 mT and at a temperatureof 19.5◦C. THz driven Faraday rotation measurements were performedwith an external magnetic field of 200 mT. . . . . . . . . . . . . . . . . . 53

5.1 A summary of the THz frequencies used in the THz pump Polar MOKEexperiments along with their peak electric field values. . . . . . . . . . . . 71

ix

CHAPTER 1

Introduction

Magnetism has been known to mankind for centuries, but its fundamental understanding

and the resultant technology started to take shape in the early 20th century. One of

the major applications of magnetic materials can be found in modern data storage

devices. Recent developments in information and communication (ICT) technology can

be subdivided into three major aspects; data processing at high speeds, data storage

using ensemble of spins in magnetic materials, and data transfer at fast speeds. The data

storage density and the speed of data processing has been increasing at a tremendous

rate, roughly 100% every 18 months, also known as Moore’s law [1]; see Figure 1.1. The

continuation of this trend in the future using conventional technologies is improbable

since there are limitations to miniaturizing the physical size of the devices beyond a

certain length regime. An alternative approach could involve spintronics, where spin

degree of freedom is used for transport, that would meet the requirements of future ICT

(such as low-power operation, nano-scale devices etc). In spintronics, spin polarized

current can be achieved without having an electronic transport which minimizes the

ohmic heating and enables green ICT applications. The effective manipulation, transport

and control of spin degrees of freedom forms the basis of spintronics. Spintronics [2]

emerged after the discovery of giant magneto-resistance (GMR) in 1988. GMR is defined

as a change in resistance depending on the relative orientation of the two magnetic

layers separated by a non-magnetic spacer. The implementation of GMR into hard disk

drives (HDD) increased the areal density of the HDD drastically (See Figure 1.1a) and

the impact of GMR on technology resulted in the Nobel prize for Physics in 2007 [3].

Besides GMR, recent works have also focused on developing spin based memories, such

as spin-RAM, racetrack memory, spin transfer torque-MRAM [2–5]. These devices have

already been incorporated into embedded systems.

1

2 1. Introduction

Figure 1.1: (a)Areal density growth of HDD devices as a function of time, taken from[6]. The slope of the curve has increased from the introduction of spintronics basedGMR heads. (b) The rate of telecommunication as a function of time. The rate at

which telecommunication takes places has doubled every 18 months [7].

1.1. Outline of the thesis 3

The new field of antiferromagnetic spintronics is driven by the need for high-density

storage devices operating at high frequencies. As shown in figure 1.1b, wireless data

rates are also continuously increasing over the last few decades [8]. Following this trend,

terabits per second (Tbps) rates can be realized very soon, provided that new spectral

bandwidth to support such high data rates are made available. In this context, Terahertz

(THz) bandwidth is envisioned as a key technology for wireless communication. THz

band spanning 0.1 THz to 10 THz can support the Tbps links, which requires functional

devices to operate at a THz frequency band [7].

An important question in the spintronics field is how to generate and detect spin current

efficiently. While research in spintronics is focused on the generation and detection of

spin current efficiently [9, 10], it is essential that developed devices can operate at THz

frequencies. Recently, the spin dependent Seebeck effect has been established which

converts heat in to spin current. This imposes a basic question - can spin generation

and detection be achieved at THz frequencies? Recent research has shown that several

spintronics concepts are valid in the THz frequency range. Linear THz spectroscopy has

been used to study the GMR effect [11]. The anomalous Hall effect has been observed

at THz frequencies [12]. Ultra-broad band THz generation has been achieved from

the hetero-structure of ferromagnetic metal and non-magnetic metal [13], based on the

principle of the inverse spin Hall effect. THz control of magnetic modes in the THz

frequency range has been shown [14–16]. THz emission spectroscopy has been used to

study the spin dynamics of magnetic modes [17, 18]. Advanced fields such as off resonant

coupling of the spin to phonons/magnons [19] allows non-linear physical processes to be

understood [20].

Despite significant progress in the science related to THz range spintronics, there are

several interesting questions yet to be tackled. Can we use THz resonances in mag-

netic materials for advanced spintronics applications? How do fundamental scattering

processes taking place at sub-picosecond timescales, affect the efficiency of spintronics

processes? The work presented in this thesis aims to provide deeper understanding of

THz control of magnetic resonances in magnetic materials. The thesis aims to exploit

new materials systems for their characterization in the THz frequency range.

1.1 Outline of the thesis

In this thesis, different techniques are used to study and understand magnetization

dynamics at THz frequency. In chapter 2, an overview of basic properties of magnetic

materials and an outline of light-driven magnetization dynamics are provided. In chapter

3, the experimental techniques used in this thesis are discussed.

4 1. Introduction

In chapter 4 of the thesis, the high frequency ferrimagnetic Mn-based Heusler alloys

are studied for their future application as spin transfer torque oscillator in the sub-THz

frequency range. These materials have high spin polarization and ferromagnetic modes

from 0.15 to 0.35 THz. THz emission spectroscopy is employed to observe ferromagnetic

modes and to characterize it further with temperature and external magnetic fields up

to 10 T.

Then in chapter 5, the focus shifts to THz control of non-resonant magnetization dynam-

ics in ferromagnetic CoFeB. Here, the THz pump Magneto-Optical Kerr effect is used

to study the magnetic properties of CoFeB. The effect of THz excitation on ultra-fast

demagnetization is studied and explained using the Eliot-Yafet scattering mechanism.

Finally, the spin dependent scattering of conduction electrons is discussed to provide a

microscopic understanding of the magnetization dynamics.

In the final chapter, THz radiation is used to excite the antiferromagnetic mode in

NiO. The antiferromagnetic resonance mode is studied with the transient Faraday probe

technique in the temperature range 3-290K, with an external magnetic field up to 10

T. Such THz control of antiferromagnetic mode helps in the understanding of the spin

dynamics at sub-picosecond timescales for high frequency spintronics memory devices.

1.2 Bibliography

[1] R. R. Schaller, “Moore’s law: past, present and future,” IEEE spectrum, vol. 34,

no. 6, pp. 52–59, 1997.

[2] S. Wolf, D. Awschalom, R. Buhrman, J. Daughton, S. Von Molnar, M. Roukes,

A. Y. Chtchelkanova, and D. Treger, “Spintronics: a spin-based electronics vision

for the future,” Science, vol. 294, no. 5546, pp. 1488–1495, 2001.

[3] A. Fert, “Nobel lecture: Origin, development, and future of spintronics,” Reviews

of Modern Physics, vol. 80, no. 4, p. 1517, 2008.

[4] I. Zutic, J. Fabian, and S. D. Sarma, “Spintronics: Fundamentals and applications,”

Reviews of modern physics, vol. 76, no. 2, p. 323, 2004.

[5] A. D. Kent and D. C. Worledge, “A new spin on magnetic memories,” Nature

nanotechnology, vol. 10, no. 3, p. 187, 2015.

[6] J. R. Childress and R. E. Fontana Jr, “Magnetic recording read head sensor tech-

nology,” Comptes Rendus Physique, vol. 6, no. 9, pp. 997–1012, 2005.

1.2. Bibliography 5

[7] I. F. Akyildiz, J. M. Jornet, and C. Han, “Terahertz band: Next frontier for wireless

communications,” Physical Communication, vol. 12, pp. 16–32, 2014.

[8] S. Cherry, “Edholm’s law of bandwidth,” IEEE Spectrum, vol. 41, no. 7, pp. 58–60,

2004.

[9] Y. Ohno, D. Young, B. a. Beschoten, F. Matsukura, H. Ohno, and D. Awschalom,

“Electrical spin injection in a ferromagnetic semiconductor heterostructure,” Na-

ture, vol. 402, no. 6763, p. 790, 1999.

[10] A. Fert and H. Jaffres, “Conditions for efficient spin injection from a ferromagnetic

metal into a semiconductor,” Physical Review B, vol. 64, no. 18, p. 184420, 2001.

[11] Z. Jin, A. Tkach, F. Casper, V. Spetter, H. Grimm, A. Thomas, T. Kampfrath,

M. Bonn, M. Klaui, and D. Turchinovich, “Accessing the fundamentals of magne-

totransport in metals with terahertz probes,” Nature Physics, vol. 11, no. 9, p. 761,

2015.

[12] R. Shimano, Y. Ikebe, K. Takahashi, M. Kawasaki, N. Nagaosa, and Y. Tokura,

“Terahertz faraday rotation induced by an anomalous hall effect in the itinerant

ferromagnet SrRuO3,” EPL (Europhysics Letters), vol. 95, no. 1, p. 17002, 2011.

[13] T. Kampfrath, M. Battiato, P. Maldonado, G. Eilers, J. Notzold, S. Mahrlein,

V. Zbarsky, F. Freimuth, Y. Mokrousov, S. Blugel, et al., “Terahertz spin cur-

rent pulses controlled by magnetic heterostructures,” Nature nanotechnology, vol. 8,

no. 4, p. 256, 2013.

[14] T. Kampfrath, A. Sell, G. Klatt, A. Pashkin, S. Mahrlein, T. Dekorsy, M. Wolf,

M. Fiebig, A. Leitenstorfer, and R. Huber, “Coherent terahertz control of antifer-

romagnetic spin waves,” Nature Photonics, vol. 5, no. 1, p. 31, 2011.

[15] T. Moriyama, K. Oda, and T. Ono, “Spin torque control of antiferromagnetic mo-

ments in NiO,” arXiv preprint arXiv:1708.07682, 2017.

[16] Z. Jin, Z. Mics, G. Ma, Z. Cheng, M. Bonn, and D. Turchinovich, “Single-pulse

terahertz coherent control of spin resonance in the canted antiferromagnet YFeO3,

mediated by dielectric anisotropy,” Physical Review B, vol. 87, no. 9, p. 094422,

2013.

[17] R. Mikhaylovskiy, E. Hendry, V. Kruglyak, R. Pisarev, T. Rasing, and A. Kimel,

“Terahertz emission spectroscopy of laser-induced spin dynamics in TmFeO3 and

ErFeO3 orthoferrites,” Physical Review B, vol. 90, no. 18, p. 184405, 2014.

6 1. Introduction

[18] J. Nishitani, K. Kozuki, T. Nagashima, and M. Hangyo, “Terahertz radiation from

coherent antiferromagnetic magnons excited by femtosecond laser pulses,” Applied

Physics Letters, vol. 96, no. 22, p. 221906, 2010.

[19] T. F. Nova, A. Cartella, A. Cantaluppi, M. Forst, D. Bossini, R. Mikhaylovskiy,

A. Kimel, R. Merlin, and A. Cavalleri, “An effective magnetic field from optically

driven phonons,” Nature Physics, vol. 13, no. 2, p. 132, 2017.

[20] Z. Wang, S. Kovalev, N. Awari, M. Chen, S. Germanskiy, B. Green, J.-C. Deinert,

T. Kampfrath, J. Milano, and M. Gensch, “Magnetic field dependence of antiferro-

magnetic resonance in NiO,” Applied Physics Letters, vol. 112, no. 25, p. 252404,

2018.

CHAPTER 2

Introduction to Magnetism

This chapter introduces the basic concepts in magnetism and outlines the current state of

the art in light-driven ultra-fast magnetization dynamics. Firstly, an introduction to the

origin of magnetic moments in solid materials is provided, followed by a brief descrip-

tion of the properties of magnetic materials. Secondly, the magnetization dynamics of

magnetic materials is discussed. The interaction of the magnetization of material with

an externally applied field and with femtosecond laser excitation/THz excitation forms

the basis of the subject of ultra-fast magnetization dynamics.

7

8 2. Introduction to Magnetism

2.1 Origin of magnetism and magnetic properties

The spin of a single electron s is the microscopic source of magnetism (in materials).

The spin magnetic moment ms is defined as

ms =e

2mgs (2.1)

here e and m are the charge and mass of an electron, g is the gyro-magnetic ratio. s is

quantized and has values ± 1/2. Measurement of the spin magnetic moment yields,

ms,z = ±1

2gµB (2.2)

where µB = e~2m is known as the Bohr magneton, the basic unit of magnetism and

magnetic properties of materials are explained using this quantity. For an electron

circulating around its nucleus, the total magnetic moment of the electron is given by

the combination of its spin s and its orbital angular moment l, (where l is given by the

rotational motion of an electron). For material systems with several electrons, the total

magnetic moment of the electron system is given by

J = S + L (2.3)

where S =∑

i si is the total angular spin momentum of the electron system and L =∑i li is the total angular orbital momentum. The ground state energy of a single atom

is defined by Pauli’s exclusion principle and Hund’s rule [1].

• The state with highest S has the lowest energy, consistent with Pauli’s principle

• For a given S, the state with the highest L will have the lowest energy

• For a sub-shell which is not more than half filled, J = |S − L| will have lower

energy; for sub-shells more than half filled, J = |S + L| will have lower energy.

The total magnetic moment of such systems is given by,

m = −γJ (2.4)

where γ is the gyro-magnetic ratio. The above discussed Hund’s rule explains the mag-

netic properties of 3d and 4f shell materials where unpaired electrons are localized and

shielded by filled electronic states.

2.1. Origin of magnetism and magnetic properties 9

For more complex systems where electron wave functions of neighbouring atoms start

to overlap, Hund’s rule does not give a satisfactory explanation of magnetization. For

such cases one needs to consider the contributions from kinetic energy, potential energy,

and Pauli’s principle to explain parallel or anti-parallel alignment of spin moments. The

Hamiltonian of such a system is given by,

H = −∞∑i 6=j

JijSi.Sj (2.5)

here Jij is the exchange constant for the Hamiltonian describing the coupling strength of

two different spins. The sign of the exchange constant decides parallel (ferromagnetic)

or anti parallel (antiferromagnetic) alignment of the spins in the ground state.

Magnetization is defined by, M = m/V , with V being the volume of the material under

consideration. Magnetic materials are categorized based on the response of the mag-

netization to the externally applied magnetic field. For materials where no unpaired

electrons are present, all spin moments cancel each other resulting in no net magneti-

zation. Such materials show weak magnetization in an external magnetic field which

is opposite to the applied magnetic field and are known as diamagnetic materials. On

the other hand, materials with unpaired electron spin will react to an external magnetic

field and their response can be categorized in five different ways, as indicated in figure

2.1.

Paramagnetic ordering occurs when materials have unpaired electrons resulting in a net

magnetic moment. These magnetic moments are randomly aligned as the coupling be-

tween different spin moments is weak (� kT ). In the presence of an applied magnetic

field, these spin moments are aligned in the same direction as the external magnetic

field giving rise to a change in net magnetization. For a system where spin moments are

coupled with each other, ferromagnetic ordering (all spins are aligned parallel to each

other) or antiferromagnetic ordering (adjacent spins are anti parallel to each other) is ob-

served. The parallel alignment of spins in ferromagnetic materials results in an intrinsic

net magnetization even in the absence of an external magnetic field. For ferrimagnetic

materials, adjacent spins are of different values. For a canted antiferromagnet, adjacent

spins are tilted by a small angle giving rise to a small net magnetization. The canting

of spins is explained based on the competition between two processes; namely isotropic

exchange and spin-orbit coupling.

Ferromagnetic, antiferromagnetic, and ferrimagnetic materials have a critical tempera-

ture above which thermal energy causes randomized ordering of spin moments, resulting

in no net magnetization or long range ordering of the spin moments.


Figure 2.1: Different types of magnetic ordering present in materials. Black arrowsindicate the direction of magnetic moment, modified from reference [2]

2.2 Magnetic properties of materials

In magnetic materials, magnetic moments have a preferred direction because of the mag-

netic anisotropy of the materials. The direction along which spontaneous magnetization

is directed is known as the easy axis of magnetization. The magnetic anisotropy energy

(Ha) can be defined by the following equation,

Ha = K2u sin2 θ (2.6)

where Ku is the anisotropy constant and θ is the angle between the direction of magne-

tization (M ) and the easy axis.

One form of magnetic anisotropy is magneto-crystalline anisotropy, also known as in-

trinsic anisotropy, which is a result of the crystal field present inside the material. This

is the only source of anisotropic energy present for infinite-sized crystals, apart from

negligible contributions from the moments generated due to non-cubic symmetry. The

2.2. Magnetic properties of materials 11

crystal field is the static electrical field present because of surrounding charges. When

an electron moves at high speed through such an electric field, in its own frame of ref-

erence this electric field is perceived as a magnetic field. This magnetic field interacts

with the spin of a moving electron, which is known as spin-orbit coupling. Magneto-

crystalline anisotropy can also be generated because of an anisotropic growth of the

materials and/or the presence of interfaces.

Another form of magnetic anisotropy occurs because of the shape of the material. The

shape anisotropic energy is generally defined as the demagnetizing field as it acts in an

antagonistic way to the magnetization which creates it. For a thin rod, the demagne-

tizing field is smaller if all the magnetic moments lie along the axis of the rod. As the

thickness of the rod increases, it is not necessary to have magnetic moments lying along

the axis of the rod. For a spherical object, there is no shape magnetic anisotropy as all

the directions are equally preferred.

When an external field (B0) is applied to a magnetic material, the magnetization of

the material aligns itself parallel to the applied magnetic field. The magnetic potential

energy HZeeman is given by,

HZeeman = −m ·B0 (2.7)

If one considers only the magnetic anisotropy and exchange interactions between the

spin moments, then there is degeneracy for the spin direction with lowest energy state.

The applied magnetic field can lift this degeneracy and split the electronic states into

equally spaced states, which is known as Zeeman splitting. In the Zeeman effect, the

external magnetic field is too low to break the coupling between spin magnetic moment

and orbital magnetic moment. When higher magnetic fields are applied where this

coupling is broken, then splitting is explained using the Paschen-Back effect.

In the presence of an externally applied field, the total magnetic field (B) inside the

material is given by

B = B0 + µ0M (2.8)

where µ0 is magnetic permeability of free space. The magnetic strength arising from

magnetization of the material is H = B0/µ0, which when applied to equation 2.8, gives

the relation between B, H, and M as;

B = µ0(M + H) (2.9)


For a ferromagnetic material kept in an external magnetic field, the magnetization of the

material as a function of applied field is shown in figure 2.2(a). Ferromagnetic materials

show saturation magnetization (Ms). This is the maximum magnetization shown by

ferromagnetic materials in an applied external field. If one increases the external field

further, magnetization of the ferromagnet does not increase. Saturation magnetization

is an intrinsic property, independent of particle size but dependent on temperature.

Another property of a ferromagnet is that they can retain the memory of an applied

magnetic field which is known as the hysteresis effect. The remanent magnetization (Mr)

is the magnetization remaining in the ferromagnet when the applied field is restored to

zero. In order to reduce the magnetization of a ferromagnet below Mr, a reverse magnetic

field needs to be applied, with the magnetization reducing to zero at the coercivity field

(Hc).

Figure 2.2: Properties of a typical ferromagnet, Nickel, taken from [3]. (a) Hysteresisloop observed in Nickel. (b) Temperature dependence of the saturation magnetization

for Nickel.

The saturation magnetization of a ferromagnet decreases with increasing temperature

and at the critical temperature, known as the Curie temperature (TC), it goes to 0,

see figure 2.2(b). Below TC, a ferromagnet is magnetically ordered and above TC it is

disordered.

In ferrimagnetic materials, two sub-lattices have different magnetic momenta which gives

rise to a net magnetic moment which is equivalent to ferromagnetic materials. Therefore,

a ferrimagnetic material shows all the characteristic properties of a ferromagnet such

as: spontaneous magnetization, Curie temperatures, hysteresis, and remanence. In an

antiferromagnet, the two sub-lattices are equal in magnitude but oriented in opposite

directions. The antiferromagnetic order exists at temperatures lower than the Neel

temperature (TN), but at and above TN the antiferromangetic order is lost.

2.3. Ultra-fast magnetization dynamics 13

Magnetic susceptibility is the property of magnetic materials which defines how much a

magnetic material can be magnetized in the presence of an applied magnetic field. The

magnetic susceptibility of a material is calculated from the ratio of the magnetization

M within the material to the applied magnetic field strength H, or χ = M/H. For

paramagnetic materials, χ diverges as temperatures approach 0 K (figure 2.3(a)). For

ferromagnetic/ferrimagnetic materials χ diverges as the temperature approaches the

Curie temperature, as explained by the Curie-Weiss law,

Figure 2.3: Susceptibility as a function of temperature for paramagnet, ferromagnetand antiferromagnet is shown, adapted from [4]

.

χm = CP /(T − TC) (2.10)

Here, CP is the Curie-Weiss constant and TC is the Curie temperature of the ferromag-

netic material. For antiferromagnetic materials (see figure 2.3(c)), χ follows a behavior

similar to ferromagnetic materials until the Neel temperature (TN), below (TN) it de-

creases again.

2.3 Ultra-fast magnetization dynamics

The static magnetic properties of a material depend on the time-independent effective

magnetization Heff of the material, where Heff is defined as

Heff = Hani + Hext + Hdemag (2.11)


where Hani is the magnetic anisotropy, Hext is the externally applied magnetic field, and

Hdemag is the demagnetizing field present inside the material. When this equilibrium

state is perturbed, the magnitude and/or direction of Heff changes, which causes the

magnetization (M) of the material to change and relax back to its equilibrium state.

Magnetization dynamics can be seen as the collective excitation of the magnetic ground

state of the system. For magnetic materials, the elementary excitations, such as electron,

spin, and lattice degrees of freedom, become spin-dependent which contributes further

to magnetization dynamics [5]. The interaction/coupling of these elementary excitations

with magnetic ordering is studied under the scope of magnetization dynamics. With the

advancements in femtosecond laser systems, it is now possible to study these interactions

on the femtosecond timescale, which has enabled ultra-fast control of magnetization

required for spintronics applications. Magnetization dynamics can be categorized into

two categories: coherent precessional dynamics and incoherent dynamics.

The coherent precessional dynamics can be explained by the Zeeman interaction of the

magnetization of a material with an externally applied field. The magnetic moment

undergoes precessional motion when kept in an external magnetic field. Assuming there

is no damping involved, the precessional motion of the magnetic moment under consid-

eration is given by the torque (T) acting on the magnetic moment,

T = m×Heff (2.12)

Torque is the rate of change of the angular momentum (L),

T =d

dtL (2.13)

The magnetic moment of an electron is directly proportional to its angular momentum

through γ (gyro-magnetic ratio with the value of 28.02 GHz/T for a free electron).

m = −γL (2.14)

The time derivative of the above equation yields,

dm

dt= −γ dL

dt= −γT (2.15)

Including the classical expression of torque in the above equation and considering the

magnetic anisotropy, and the demagnetizing field present in the system, the above equa-

tion can be modified to


dm

dt= −γm×Heff (2.16)

Equation 2.16 is the Landau-Lifschitz (LL) equation for magnetization dynamics. This

equation only considers the precessional motion of the magnetization. In order to ac-

count for motion of the magnetization toward alignment with the field, a dissipative

term is introduced by Gilbert. A new equation including a dissipative term is known as

the Landau-Lifschitz-Gilbert (LLG) equation and is as below;

dm

dt= −γm×Heff +

α

Msm× dm

dt(2.17)

Heff

m

m x dm/dt

dm/dt

a) b)

Heff

m

Figure 2.4: Schematic of the magnetic precession (a) without damping and (b) withdamping.

where α is the dimensionless Gilbert damping constant. The LLG equation can also be

used in the atomistic limit to calculate the evolution of the spin system using Langevin

dynamics to model ultra-fast magnetization processes [6]. The frequency of the preces-

sion is normally in the GHz range and the time required to reach the equilibrium state

can be as high as nanoseconds, depending on the damping mechanism.

Another way to disturb the static magnetic properties of a material is by irradiating

it with femtosecond near infra-red (NIR) optical pulses. In this case, the electron ab-

sorbs part of the laser energy and achieves a non-equilibrium state. The thermal energy

provided by the ultra-fast laser perturbs the spin ordering resulting in demagnetization


of the magnetic system. The demagnetization takes place during the first few 100 fs

after laser excitation. This timescale is orders of magnitude shorter than the timescale

involved in coherent precessional dynamics. The first observation of ultra-fast demagne-

tization of Ni [7] by ultra-short laser pulses has shown a demagnetization time of less than

1 ps. Laser induced magnetization dynamics can be divided into coherent interactions

[8] and incoherent demagnetization. In order to explain the incoherent demagnetization

process, the Elliot-Yafet (EY) type spin flip mechanism has been used. The EY scatter-

ing based on electron-phonon scattering [9, 10] has been most widely used. In the EY

mechanism, electron spins relax via momentum scattering events because of spin-orbit

coupling (SOC). In the presence of SOC, electronic states are admixtures of spin up and

spin down states because of which, at every scattering event of electrons, there is a small

but finite probability of spin-flip.

In order to interpret ultra-fast demagnetization, the 3-temperature model (3TM) [7, 9]

based on electron-phonon scattering was developed. In this model, the interactions

between 3 thermal baths which are in internal thermal equilibrium is explained. The

electron bath temperature Tel, spin bath temperature Tsp, and lattice temperature Tlat

are coupled to each other via thermal coupling constants as shown in the equations

below [7]:

CeldTeldt

= −Gel,lat(Tel − Tlat)−Gel,sp(Tel − Tsp) + P (t) (2.18)

ClatdTlatdt

= −Glat,sp(Tlat − Tsp)−Gel,lat(Tel − Tlat) (2.19)

CspdTspdt

= −Gel,sp(Tsp − Tel)−Glat,sp(Tsp − Tlat) (2.20)

Here, P(t) is the excitation laser pulse, C is the heat capacities of the three systems and

G is the coupling constant between the three systems. The thermalization process of

these three thermal baths upon laser excitation is summarized as follows (also see figure

2.5):

1. The laser beam hits the sample and creates electron-hole pairs on a time scale of

∼ 1 fs, which results in heating of the electron system (ultra-fast process)

2. Electron-electron interaction reduces the electronic temperature (Tel) within the

first few 100 fs, depending on the material under investigation


3. Electron-phonon interaction relaxes the electronic excitation in 0.1 to 10 ps which

increases the temperature of the lattice (Tlat)

4. The electron-spin interactions or lattice-spin interactions are responsible for the

demagnetization of the magnetic materials.

In order to gain a deeper understanding of ultra-fast demagnetization, one needs to

understand how angular momentum conservation takes place.

Figure 2.5: Schematic of time scales involved in laser driven excitation of magneticmaterials over 1 ps time scale. The thermalization processes between electrons andspins are shown after 50-100 fs. Thermalization process for the lattice is taking place

on the timescale 1 ps and higher. Taken from [11].

Figure 2.5 shows the various processes occurring after irradiation of ferromagnetic ma-

terials with femtosecond NIR pulses. The coherent excitation of charge and spin occurs

in the first few femtosecond after irradiation with NIR pulses, which leads to a non-

thermalized distribution. The thermalized distribution is reached on a 50 femtosecond

timescale, whereas the thermalization process involving phonons takes place on the time

scale of 1 picosecond and higher. Upon laser excitation, non equilibrium hot carriers are

generated. These hot carriers result in spin-dependent transport and their distribution

in the magnetic materials is spatially inhomogeneous, which affects the optical response

of the material. The excited hot carrier dynamics can be categorized into local and

non-local physical processes.

One of the important local effects of excited hot carriers is spin-flip scattering, which

is considered to be an important factor in explaining ultra-fast laser-induced demagne-

tization observed in magnetic systems. Spin-flip scattering is the process in which the

angular momentum of the local spin is transferred to the lattice or to impurity sites


Figure 2.6: Effect of femtosecond laser excitation in the near infrared regime onmagnetic materials. The excited hot carriers undergo local and non local physical pro-cesses which determine the magnetization dynamics of the material. The local effectsincludes; hot carriers populating empty electronic states and the spin flip scattering. Inthe non-local effects, inhomogeneous distribution of hot carriers enable spin-polarizedsuper-diffusive spin transport. The magneto-optical response of the material is a com-bination of both local and no-local effects taking place upon laser excitation. Figure

adapted from [12].

[7, 9, 10], thus changing the effective magnetization of the system locally. The timescale

of demagnetization is predicted under the assumption that the speed of demagnetization

is defined by the speed of spin-flip under the Elliot-Yafet mechanism [11, 13]. Apart from

the demagnetization, excited hot carriers also contribute to state-filling effects because

of the strong non-equilibrium distribution of hot carriers. The state filling effects are

also spin-dependent in nature and results in a transient magneto-optical signal. This

could also excite spin waves/magnon modes in a magnetic materials with the frequency

of magnetic modes present in the material.

The excited hot carriers exhibit spin-dependent transport across the magnetic material

because of the inhomogeneous distribution of hot carriers. This transport can be mod-

elled with a two-channel model [14, 15] with separate channels for transport of spin up

and spin down electrons. This enables spin-polarized super-diffusive current in magnetic

materials [16–18]. A thermally driven spin-polarized current originates from different

Seebeck coefficients in the two spin channels. The super-diffusive transport changes the

spin distribution in a magnetic material which changes the magnetization of the mate-

rial. The super-diffusive transport is considered as spin conserving, which means that

there is no spin flip taking place during the transport of a spin from one place to an

other. There have been multiple experiments showing the existence of both the pro-

cesses but their relative contribution is still under debate. Despite the intense research

2.4. Bibliography 19

in the field of ultra-fast demagnetization, the mechanism responsible for dissipation of

angular momentum on sub-picosecond timescale is not clear. In order to explain the

experimental results, a variety of theoretical models have been proposed that aimed to

model the large complexity of NIR femtosecond laser-induced highly non-equilibrium

state. Recently, intense THz radiation has been used to induced demagnetization in

ferromagnetic materials [19–22]. With THz excitation, the electronic temperature is

slightly increased whereas with NIR excitation the electronic temperature is higher than

1000 K [23]. Because of a lower electronic temperature, individual electron scattering

becomes dominant over electronic cooling [22]. In this experimental approach, THz

pulses drive spin current in ferromagnetic systems [19, 24] and it has been shown that

the inelastic spin scattering is of the order of ∼ 30 fs [19].

This thesis discusses the experimental studies where low energy THz radiation is used to

excite, control, and manipulate the magnetization of materials on ultra-fast timescales.

2.4 Bibliography

[1] D. J. Griffiths, Introduction to quantum mechanics. Cambridge University Press,

2016.

[2] J. S. Miller, “Organic-and molecule-based magnets,” Materials Today, vol. 17, no. 5,

pp. 224–235, 2014.

[3] J. M. Coey, Magnetism and magnetic materials. Cambridge University Press, 2010.

[4] Z.-F. Guo, K. Pan, and X.-J. Wang, “Electrochromic & magnetic properties of

electrode materials for lithium ion batteries,” Chinese Physics B, vol. 25, no. 1,

p. 017801, 2015.

[5] A. Eschenlohr, U. Bovensiepen, et al., “Special issue on ultrafast magnetism,” Jour-

nal of Physics: Condensed Matter, vol. 30, no. 3, p. 030301, 2017.

[6] R. F. Evans, W. J. Fan, P. Chureemart, T. A. Ostler, M. O. Ellis, and R. W.

Chantrell, “Atomistic spin model simulations of magnetic nanomaterials,” Journal

of Physics: Condensed Matter, vol. 26, no. 10, p. 103202, 2014.

[7] E. Beaurepaire, J.-C. Merle, A. Daunois, and J.-Y. Bigot, “Ultrafast spin dynamics

in ferromagnetic nickel,” Physical review letters, vol. 76, no. 22, p. 4250, 1996.

[8] J.-Y. Bigot, M. Vomir, and E. Beaurepaire, “Coherent ultrafast magnetism induced

by femtosecond laser pulses,” Nature Physics, vol. 5, no. 7, p. 515, 2009.


[9] B. Koopmans, G. Malinowski, F. Dalla Longa, D. Steiauf, M. Fahnle, T. Roth,

M. Cinchetti, and M. Aeschlimann, “Explaining the paradoxical diversity of ultra-

fast laser-induced demagnetization,” Nature materials, vol. 9, no. 3, p. 259, 2010.

[10] B. Koopmans, J. Ruigrok, F. Dalla Longa, and W. De Jonge, “Unifying ultrafast

magnetization dynamics,” Physical review letters, vol. 95, no. 26, p. 267207, 2005.

[11] J. Walowski and M. Munzenberg, “Perspective: Ultrafast magnetism and thz spin-

tronics,” Journal of applied Physics, vol. 120, no. 14, p. 140901, 2016.

[12] I. Razdolski, A. Alekhin, U. Martens, D. Burstel, D. Diesing, M. Munzenberg,

U. Bovensiepen, and A. Melnikov, “Analysis of the time-resolved magneto-optical

kerr effect for ultrafast magnetization dynamics in ferromagnetic thin films,” Jour-

nal of Physics: Condensed Matter, vol. 29, no. 17, p. 174002, 2017.

[13] S. Gunther, C. Spezzani, R. Ciprian, C. Grazioli, B. Ressel, M. Coreno, L. Poletto,

P. Miotti, M. Sacchi, G. Panaccione, et al., “Testing spin-flip scattering as a pos-

sible mechanism of ultrafast demagnetization in ordered magnetic alloys,” Physical

Review B, vol. 90, no. 18, p. 180407, 2014.

[14] A. Slachter, F. L. Bakker, and B. J. van Wees, “Modeling of thermal spin transport

and spin-orbit effects in ferromagnetic/nonmagnetic mesoscopic devices,” Physical

Review B, vol. 84, no. 17, p. 174408, 2011.

[15] T. Valet and A. Fert, “Theory of the perpendicular magnetoresistance in magnetic

multilayers,” Physical Review B, vol. 48, no. 10, p. 7099, 1993.

[16] M. Battiato, K. Carva, and P. M. Oppeneer, “Superdiffusive spin transport as a

mechanism of ultrafast demagnetization,” Physical review letters, vol. 105, no. 2,

p. 027203, 2010.

[17] K. Carva, M. Battiato, D. Legut, and P. M. Oppeneer, “Ab initio theory of

electron-phonon mediated ultrafast spin relaxation of laser-excited hot electrons

in transition-metal ferromagnets,” Physical Review B, vol. 87, no. 18, p. 184425,

2013.

[18] E. Turgut, J. M. Shaw, P. Grychtol, H. T. Nembach, D. Rudolf, R. Adam,

M. Aeschlimann, C. M. Schneider, T. J. Silva, M. M. Murnane, et al., “Control-

ling the competition between optically induced ultrafast spin-flip scattering and

spin transport in magnetic multilayers,” Physical review letters, vol. 110, no. 19,

p. 197201, 2013.

[19] S. Bonetti, M. Hoffmann, M.-J. Sher, Z. Chen, S.-H. Yang, M. Samant, S. Parkin,

and H. Durr, “Thz-driven ultrafast spin-lattice scattering in amorphous metallic

ferromagnets,” Physical review letters, vol. 117, no. 8, p. 087205, 2016.


[20] M. Shalaby, C. Vicario, and C. P. Hauri, “Low frequency terahertz-induced de-

magnetization in ferromagnetic nickel,” Applied Physics Letters, vol. 108, no. 18,

p. 182903, 2016.

[21] M. Shalaby, C. Vicario, and C. P. Hauri, “Simultaneous electronic and the magnetic

excitation of a ferromagnet by intense THz pulses,” New Journal of Physics, vol. 18,

no. 1, p. 013019, 2016.

[22] D. Polley, M. Pancaldi, M. Hudl, P. Vavassori, S. Urazhdin, and S. Bonetti, “Thz-

driven demagnetization with perpendicular magnetic anisotropy: Towards ultrafast

ballistic switching,” Journal of Physics D: Applied Physics, vol. 51, no. 8, p. 084001.

[23] H.-S. Rhie, H. Durr, and W. Eberhardt, “Femtosecond electron and spin dynamics

in Ni/W (110) films,” Physical review letters, vol. 90, no. 24, p. 247201, 2003.




2015.

CHAPTER 3

Experimental Techniques

This thesis focuses on questions related to magnetization dynamics involving THz pulses

either for excitation or as a sensitive probe. Here, the experimental techniques and

instruments employed to address the questions in the following chapters are discussed as

follows:

• THz emission spectroscopy (TES) is a technique used to measure the magnetic

properties of ultra-thin films (Chapter 4). The ferromagnetic resonance (FM) for

Mn3-XGa thin films is in the range of 0.1 - 0.4 THz, which are studied using TES.

In this frequency range, TES proved to be a more sensitive technique as compared

to all optical ultra-fast magneto-optical techniques.

• Chapter 5 of the thesis deals with THz induced demagnetization of amorphous

CoFeB thin films. Here we use the ability of THz radiation to generate spin-

polarized current in ferromagnetic thin films and its effect on ultra-fast demagne-

tization is studied using the polar magneto-optical Kerr effect.

• Chapter 6 of the thesis discusses the THz coherent control of antiferromagnetic

(AFM) mode of the single crystalline NiO. The AFM mode of the NiO is selectively

excited using a narrow band THz pump and it is probed using the Faraday effect.

23

24 3. Experimental Techniques

3.1 THz emission spectroscopy

Terahertz (THz) emission spectroscopy is a technique based on the coherent detection

of flashes of THz light emitted when intense ultra-short photon pulses interact with

matter. The first demonstration of radiation emitted in this way was in 1990 when it

was observed as a result of free carrier excitation and optical rectification in semicon-

ductors [1]. The emitted pulses were broadband, and carried information on carrier

relaxation time, phonon absorption, and/or the electro-optical coefficients. Since then,

this technique has been used to study a multitude of materials for their different ultra-

fast dynamics. In 2004, it was discovered that laser-driven demagnetization processes

can give rise to broadband, single-cycle THz pulse emission [2, 3]. In that case, the spec-

trum of the emitted burst carries information on the time-scale of the demagnetization

process, making THz emission spectroscopy a powerful diagnostic technique for study-

ing laser-driven ultra-fast non-equilibrium dynamics in matter. In 2013, the method was

successfully applied to determine the duration of ultra-fast laser-driven spin currents [4].

Most recently, researchers have succeeded in detecting narrow-band emission from spin

waves in ferrimagnetic bulk insulators [5, 6] and antiferromagnetic insulators [7].

In this study TES is emplyed to study the FM modes in Mn3-XGa. The THz emission

from these materials is based on magnetic dipole emission. The electromagnetic radiation

is emitted when a magnetic dipole oscillates in time. Using vector potentials for a

circulating current loop one can find the electric field (Et) emitted from such a loop [8]

as:

Et =−δAδt∼ δ[m× n]

δt(3.1)

where m is the magnetic dipole moment, A is vector potential and n is the radial unit

vector for circulating motion. In the case of Mn3-XGa, the emission is from multiple

magnetic dipoles which are oscillating in a coherent fashion at the frequency of the

ferromagnetic resonance (FMR) upon excitation by ultra-fast laser pulses with a pulse

duration shorter than the magnetization oscillation, as discussed in chapter 4. For such

cases, the far-field radiation is diffraction limited and given by the following equation

[9],

Et ∼ sinc(πd(sinθ)/λ)2 (3.2)

where d is the laser spot size on the sample, λ is the wavelength of the emitted radiation

and θ is the angle between the surface normal and the observation angle.

3.1. THz emission spectroscopy 25

3.1.1 Electro-Optic Sampling

The detection technique for freely propagating THz radiation used in this work is based

on electro-optic (EO) sampling [10–12]. The linear EO effect, also known as the Pockels

effect, describes birefringence induced in electro-optic material in response to an applied

electric field. This effect is observed in materials with broken inversion symmetry. EO

detection allows simultaneous detection of phase and amplitude of the THz electric field.

In the presence of the THz electric field, EO material becomes birefringence. This bire-

fringence is proportional to the THz electric field and can be probed with collinearly

propagating short near infrared 800 nm probe pulses. The probe pulse experience the

transient birefringence and changes its polarization state which can be detected using a

balanced detection scheme. A balanced detection scheme consists of a λ4 wave-plate for

probe wavelength, a Wollaston prism (WP) and, a pair of balanced photo-diodes (PD),

see Figure 3.1. In the absence of a THz electric field, a linear probe beam becomes circu-

larly polarized because of the λ4 wave-plate. WP separates two orthogonal polarizations

from the circularly polarized probe beam and they are balanced on the photo-diodes.

When the THz electric field is present, ellipticity in probe beam is induced in the EO

material, which unbalances the photo-diode signal. This unbalanced photo-diode signal

is a measure of the THz electric field.

For collinear EO sampling in a material of thickness L, the differential phase retardation,

which is a measure of the THz electric field, is given by [13],

δφ(t) =2πLn3

0r

λE(t) (3.3)

Here r is the EO coefficient of the detector material, E is the electric field of the THz

radiation, and n0 is the unperturbed refractive index. The complete mapping of the

THz electric field transient can be done by delaying the probe beam with respect to the

THz beam. This equation assumes perfect phase matching between the group velocity

of the 800 nm probe beam and the phase velocity of the THz beam.

In this thesis, a ZnTe crystal cut along the <110> crystallographic direction is used for

THz detection. ZnTe is an isotropic crystal having a zincblende structure with non-zero

EO coefficients along the r41, r52, and r63 directions.

The THz detection efficiency decreases as the velocity mismatch between two beams

increases. Therefore it is important to optimize the thickness of the ZnTe crystal for the

efficient detection of the THz frequency under consideration. The minimum distance


Figure 3.1: Schematic of the electro-optic set-up used in this thesis. The THz ra-diation pulses (shown in red) are focused on the electro-optic crystal (ZnTe) and 800nm NIR laser pulses (shown in green) are collinear with the THz pulses. The THzfield induces birefringence in the electro-optic crystal, the differences in the orthogonalpolarization is detected using a quarter-wave plate (λ4 ), a Wollaston prism (WP) and

a pair of photo-diodes (PD).

over which velocity mismatch can be tolerated for THz detection is called the coherence

length, defined as

lc(ωTHz) =πc

ωTHz|nopt(ω0)− nTHz(ωTHz)|(3.4)

where, nopt is the refractive index of the probe pulse inside the ZnTe crystal along the

<110> direction and nTHz is the refractive index of THz radiation in ZnTe crystal along

the same crystallographic axis.

3.2 Magneto-optic effect

Magneto-optical effects are the result of the interaction of light and matter when the

latter is subject to a magnetic field. For some magnetically ordered materials, such as

ferromagnets, ferrimagnets etc, magneto-optical effects are present even in the absence

of an externally applied magnetic field. In magneto-optical effects, the polarization of

the incident light rotates after interacting with magnetization of the materials [14, 15].

For the analysis of the magneto-optic Kerr effect [16] and other phenomena in detail,

consider the isotropic media having a permittivity tensor as written below:

3.2. Magneto-optic effect 27

ε =

( εxx 0 0

0 εyy 0

0 0 εzz

)(3.5)

When an external magnetic field is applied parallel to the direction of propagation of

incident light, for example along z, considering time reversal symmetry and energy

conservation, we can write,

ε =

( εxx εxy(B) 0

−εxy(B) εyy 0

0 0 εzz

)(3.6)

The normalized eignemodes of ε are given by

(Ex

Ey

)±

=1√2

(1

±i

)(3.7)

Here Ex and Ey are the electric fields along x and y direction. The eigen values of the

above matrix are εxx ± iεxy(B) with eigen vectors [1, i] and [1, -i]. These eigen vectors

correspond to right and left circularly polarized light, which shows that circularly po-

larized light will remain circularly polarized after interacting with the material having

the above permitivity tensor. Refractive indices for circularly polarized light would be

n+ =√

(εxx + iεxy) and n− =√

(εxx − iεxy). This implies that for circularly polarized

light, different helicities will experience different speed in the material which will intro-

duce a phase delay. For linearly polarized light, it will introduce polarization rotation,

but light at the exit of the media will remain linearly polarized.

3.2.1 Faraday effect

In the Faraday effect [14, 17], the polarization of light which is transmitted through

magnetic materials is rotated. Following the analysis discussed for the case of isotropic

media with permittivity tensor given by equation 3.6, the Faraday rotation (θF ) of light

propagating through magnetic media is given by [15]

θF =ω

2c(n+ − n−)L (3.8)

where ω is the angular frequency of the light, L is the length travelled by the light in the

magnetic medium and n+ and n− are refractive indices for right handed and left handed


THz

delay

2 WPPD

PD

polarizer

800 nm

Figure 3.2: Schematic of the Faraday set-up used in this thesis. The THz pump(shown in red) is incident on the material under investigation at normal incidence. 100femtosecond 800 nm NIR laser pulses (shown in green) are collinear with the THz pump.The transient change in magnetization of the materials is probed with the polarizationrotation of the 800 nm NIR laser pulse passing through the material. λ

2 , WP, andPD stand for the half-wave plate for 800 nm wavelength, a Wollaston prism and the

photo-diodes, respectively.

circular polarization of light. If the light propagates through a magnetic medium with

non zero absorption coefficient, i.e., the absorption is different for right handed and left

handed circular polarization then polarization is changed from linear to elliptical. The

schematic of THz pump NIR Faraday probe is shown in the figure 3.2.

3.2.2 Magneto-optical Kerr effect (MOKE)

In the Kerr effect [15] the polarization of the reflected light from the sample surface

changes. This change is proportional to the internal magnetization of the sample. The

Kerr effect can be measured in three different geometries as shown in the figure 3.3.

In the polar MOKE configuration, the magnetization of the medium is pointing out of

the plane. The NIR probe pulses can be perpendicular to the sample surface and one

observes the change in out-of-plane magnetization by measuring the changes of probe

pulse polarization state. For normal incidence, the analytical expression for the Kerr-

rotation angle is given by [19],

θpol =εxy√

εxx(εxx − 1)(3.9)

In longitudinal and transverse MOKE, the magnetization of sample lies in the plane

of the sample. For longitudinal MOKE, the magnetization of the sample is parallel to

the plane of incidence while for transverse MOKE it is perpendicular to the plane of

3.3. Light sources 29

Figure 3.3: Different configurations for measurement of Kerr effect [18]. Longitudinaland transverse MOKE geometry allows to probe the magnetization which is in plane,whereas polar MOKE geometry allows to probe magnetization which is out of plane.

incidence. For polar and longitudinal MOKE, there is always a non-zero component of

magnetization on the wave vector of the probe pulses, which results in the rotation of

polarization.

The magnitude of the Kerr effect depends on the geometry and the angle of incidence.

The largest effect is observed with polar MOKE geometry with probe pulses being

perpendicular to the sample surface. The schematic of the polar MOKE geometry used

is shown in figure 3.4.

3.3 Light sources

3.3.1 Near infra-red (NIR) femtosecond laser sources

The femtosecond laser systems used in the laboratory consist of a Ti-sapphire Vitara-T

oscillator, a regenerative amplifier (RegA) system and a Legend Elite amplifier system

from Coherent. The oscillator laser system is pumped by Verdi18 solid state continuous

laser system. The VitaraT oscillator [20] produces short laser pulses centered around

800 nm with a bandwidth of 30-120 nm and repetition rate of 78 MHz with average

power > 450 mW.

The oscillator pulses are then used to seed RegA and Legend amplifiers. The purpose of

the amplifier is to enhance the energy per pulse by few orders of magnitude. The RegA

[21] has an output of 5 µJ at 200 KHz with a repetition rate that can be varied from 100


THz

delay

BS

800 nm

WP

PDPD

2

Figure 3.4: Schematic of the polar MOKE set-up used in this thesis. The THz pump(shown in red) is incident on the material under investigation at normal incidence. 100femtosecond 800 nm NIR laser pulses (shown in green) are collinear with the THz pump.The transient change in magnetization is probed with the change in the polarization ofthe 800 nm NIR laser pulse reflected back from the material. λ

2 , WP, and PD stand forthe half-wave plate for 800 nm wavelength, a Wollaston prism and the photo-diodes,

respectively.

KHz to 250 KHz with a 100 fs pulse duration. On the other hand, the Legend Elite[22]

has a 1 mJ pulse energy at repetition rate of 1 KHz with a 100 fs pulse duration.

3.3.2 Laser-based THz light sources

The readily available table-top laser-based THz sources and their detection schemes [23–

25] have helped to gain understanding of the physics in the THz frequency regime. THz

time domain spectroscopy has been extensively used to probe low energy excitations in

materials, liquids and gases [26–30]. Recent advancements in high electric field amplitude

THz sources have opened up a new branch of fundamental science where high-field THz

sources have been used to excite and control the low-energy excitations in a coherent

fashion [4, 23, 31–38].

The typical laser-based THz sources used in laboratories are based on the optical rectifi-

cation process using intense near infra-red (NIR) fs laser systems, see figure 3.5. Optical

rectification is based on a second order nonlinear process which can be seen as difference

frequency generation. When a fs laser pulse is incident on a material, electrons move

back and forth following the electric field of the laser pulse. In case of materials with

broken symmetry, excited electrons and ions undergo additional displacement caused by

polarization (Pr(t)) which follows the intensity envelope of the laser pulse. This rectified


motion of charge carriers emits electromagnetic radiation which has a bandwidth of ∼1τ , where τ is the laser pulse duration in femtoseconds, corresponding to frequencies in

the few THz regime.

According to Maxwells equations, the polarization P acts as a source term, radiating

off a single cycle electro-magnetic pulse in the far field.

∆×∆×E +1

c2

δ2

δt2(εE) = −4π

c2

δ2P

δt2(3.10)

Figure 3.5: Schematic of the optical rectification process for THz generation, adaptedfrom [4]. An intense femtosecond pulse is incident on a non-inversion symmetric crystal.This femtosecond pulse induces a charge displacement, which follows the envelope ofthe femtosecond pulse. This charge displacement acts as a source of THz generation

from the non-inversion symmetric crystal.

In order to have a high efficiency of THz generation, the laser pulse and generated THz

should travel at the same speed in the crystal. In such a situation, THz waves can add

up coherently throughout the length of the crystal. This is known as the phase matching

condition, which requires a crystal where the group refractive index for the femtosecond

laser pulse is equal to the phase refractive index for the THz:

nvisgr = nTHzph (3.11)

The most commonly used materials for THz generation are ZnTe, GaP, LiNbO3, DAST.

The phase matching of optical group velocity and THz phase velocity is essential for

efficient THz generation. Such phase matching can be achieved in collinear fashion with


materials such as ZnTe, GaP. To further increase the efficiency of THz generation one

needs materials with higher dielectric constants, such as LiNbO3, that offers a higher

elector-optic coefficient. In such materials, collinear phase matching cannot be achieved

collinearly [39]. For such cases, tilted pulse-front schemes for LiNbO3 using gratings

can be used as demonstrated [40]. The advantage of this technique over collinear phase

matching THz emission is the scalabilty of emitted THz power with pump power and

spot size of the pump [41].

In this thesis, a 800 nm NIR laser pump at 1 KHz repetition rate has been used for THz

generation using a tilted wave-front. The average laser pump power used was ∼ 1W and

emitted THz power is of the order of a few mW. Thus, the conversion efficiency for tilted

pulse-front THz generation is roughly 10−3. The typical waveform of the THz emission

using tilted pulse-front generation and its Fourier spectrum is shown in the figure 3.6.

Figure 3.6: Typical time trace along with its frequency spectrum of generated THzradiation using LN as a THz source. (a) time domain trace of the electric field ofgenerated THz radiation, (b) shows the frequency spectrum of the recorded time scan.

3.3.3 TELBE

In the experiments where multi-cycle, narrow-band and spectrally dense THz pulses

are required, the TELBE facility is used. The TELBE facility has two different THz

sources: i) tunable THz radiation based on a magnetic undulator and ii) broadband

coherent diffraction radiation. The THz radiation is generated from electron bunches

accelerated in superconducting radio frequency (SRF) cavities. The emission from the


accelerated electron bunches is based on the principle of super-radiance. The super-

radiance radiation is emitted when the area of emitters become significantly smaller

than the wavelength of radiation. For the electron bunch duration (τ), the frequency

of superradiant emission is given by the inverse of τ . Figure 3.7 shows the schematic

of the superradiant process. When the electron bunch has a width larger than the

wavelength of the radiation then one gets the incoherent radiation, where the intensity

of the radiation is proportional to the number of electrons. In contrast, when the

electron bunch has a width smaller or comparable to the wavelength of the radiation

then a superradiant process is observed. For a superradiant process, the intensity of the

emission is proportional to the square of the electron number N.

Figure 3.7: Schematic representing the concept of superradiant emission from anelectron bunch. (a) when the electron bunch width is larger than the wavelength ofemitted radiation, incoherent radiation is observed (b) when the electron bunch widthbecomes comparable to the wavelength of the radiation then superradiant emission with

square law is observed.

TELBE has an advantage over conventional laser-based table top THz sources because

of its high spectral density and frequency tunability. Figure 3.8a shows the maximum

pulse energy for the TELBE source. Figure 3.8a shows the comparison between laser-

based sources (black dots) and the TELBE source. Laser-based sources operating higher

than 10 kHz repetition rate are limited to pulse energies less than 10 nJ [42, 43], whereas

for repetition rates above 250 kHz it can produce 0.25 nJ pulse energies [44, 45]. TELBE

currently exceeds these values by more than 2 orders of magnitude (blue shaded) with

100 pC electron bunches. Electron bunches with 1 nC result in pulse energies of 100 µJ

(light-blue-shaded). A high repetition rate also provides an exceptional dynamic range

required for better detection statistics. Figure 3.8b shows the maximum observed pulse


energy as a function of frequency at TELBE (red dots) with 100 kHz repetition rate

and 100 pC electron bunches. The pulse energies exceed the currently most intense

high-repetition rate laser-based sources (shaded) by up to 2 orders of magnitude. It

should be noted that, the laser-based sources are broadband and have a distribution of

spectral weight over many frequencies as indicated by the color tone in the respective

shaded areas in figure 3.8b. Experiments aimed at driving a narrow-band low frequency

excitation resonantly thereby benefit additionally from the considerably higher spectral

density. A novel pulse-resolved data acquisition system facilitates a timing accuracy

between TELBE and NIR laser systems of 12 fs (rms) and an exceptional dynamic

range of 106 or better in experiments [46].

Figure 3.8: Maximum pulse energy observed at TELBE as a function of repetitionrate, for a given THz frequency. Adapted from [47] (a) Maximum pulse energy atTELBE as a function of repetition rate. With 100 pC electron bunches, TELBE pulseenergy is 2 orders of magnitude higher than from intense table top THz sources at thesame repetition rate of 100 kHz. (b) maximum pulse energy at TELBE as a functionof THz frequency, observed at 100 KHz repetition rate and 100 pC electron bunches.

TELBE currently operates at 100 KHz repetition rate with the THz frequencies that

can be tuned from 0.1 THz to 2 THz with a 20 % bandwidth [47], see figure 3.9. The

pulse energy of the THz pulses is up to 2 µJ. Figure 3.9 shows the wave-forms and the

spectra of the undulator-based THz emission for the TELBE facility. The polarization

of the THz radiation is linear but can be controlled between circular and elliptical by

means of appropriate wave plates. All the experiments using TELBE, included in this

thesis, were done with 800 nm probe pulses from RegA.

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shown in (a).

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CHAPTER 4

Narrow-band Tunable THz Emission from Ferrimagnetic

Mn3-XGa Thin Films

This chapter deals with laser-driven narrow band THz emission from ferrimagnetic

Mn3-XGa nano-films, which have recently attracted considerable attention due to their

unique combination of low saturation magnetization, and high spin polarization near

Fermi level which makes them promising candidates for high frequency spintronic de-

vices. The THz emission originates from coherently excited spin precession. The central

frequency of the emitted radiation is determined by the anisotropy field, while the band-

width relates to Gilbert damping. The central frequency of the emission can be tuned by

the Mn content in Mn3-XGa. Varying the Mn content from 2 to 3 results in a change

of emission frequency from 0.15 THz to 0.35 THz. Another way to tune the emission

frequency of laser-driven THz emission is by changing the temperature of the sample,

laser power and the externally applied magnetic field. Recent experiments in external

magnetic fields of up to 10 T allowed the observation of laser-driven THz emission be-

yond 0.5 THz. The ferromagnetic nature of the magnetic resonance mode is confirmed

by field dispersion curves. It is shown how THz emission can be used for the characteri-

zation of dynamical properties of ultra-thin magnetic films. The comparison between this

technique and the conventional one; such as SQUID and VSM; shows good agreement.

This chapter is based on the publications:

Awari, N., et al. ”Narrow-band tunable terahertz emission from ferrimagnetic Mn3-xGa thin

films.” Applied Physics Letters 109, 3 (2016)

and Awari, N., et al. ”Continuously Tunable Spintronic Emission in the sub-THz Range”, in

preparation

41

42 4. Narrow-band Tunable THz Emission from Ferrimagnetic Mn3-XGa Thin Films

4.1 Introduction

Current spintronics devices are capable of operating at frequencies of up to 65 GHz [1]

and are compatible with current C-MOS technology [2]. In order to meet the current

and future societal demands of transferring very big data at speeds in sub-THz regime,

research is focusing on finding new magnetic materials which operate at the THz fre-

quency range and are compatible with today’s C-MOS technology. The properties of

ferromagnetic materials which are important for spintronic applications are ferromag-

netic resonance mode (FMR) [3] and spin polarization. One of the important materials

system to emerge from the extensive research to find materials with high FMR modes

and high spin polarization are Mn-based Heusler alloys. These materials have been

shown to exhibit ferrimagnetic resonance of between 0.15 THz to 0.3 THz with high

spin polarization. These materials are envisioned for spin transfer torque oscillator [4]

devices operating at sub-THz frequency range.

The family of Heusler alloys [5] includes metals, semiconductors, and half metals. Heusler

alloys are ternary inter-metallic compounds with X2YZ stoichiometry for full Heusler

compounds and XYZ for semi-Heusler compounds. The unit cell consists of four inter-

penetrating FCC sub-lattices with the positions (0, 0, 0) and (1/2, 1/2, 1/2) for X, (1/4,

1/4, 1/4) for Y and (3/4, 3/4, 3/4) for Z elements. In semi-Heusler compounds, the (1/2,

1/2, 1/2) position is vacant. The full Heusler compound crystallizes in L21 structure

whereas semi-Heusler one crystallizes in C1b structure. There is a wide range of fer-

romagnetic, antiferromagnetic, superconducting, and topologically insulating materials

in this family. In particular, the Heusler alloys family shows a vast variety of magnetic

properties ranging from localized and itinerant magnetism, antiferromagnetism, ferri-

magnetism, helimagnetism, and Pauli magnetism by mere change of stoichiometry of

the family.

The samples used in this experiment belong to the D022 class of tetragonal Mn-rich

Heusler alloys Mn3-XGa [6–8], which have recently attracted considerable attention due

to their unique combination of low saturation magnetization, high spin polarization, high

magneto-crystalline anisotropy, and low magnetic damping [9–11]. The D022 tetragonal

structure is variation of a L21 structure where the c-axis is stretched by roughly 27%. In

Mn3-XGa, these properties are easily tuned by varying the Mn content, which modifies

the FMR via sublattice magnetization and anisotropies. These materials show high

magnetic anisotropy and high Fermi-level spin polarization. Because of this it is possible

to drive the magnetic resonance mode in resonance with spin polarized currents. These

materials have been envisioned for high frequency THz chip-based spintronics oscillators,

4.2. Experimental details 43

which will enable ultra-fast short range wireless data transfer. These materials offers

CMOS compatibility, size advantages, and ambient temperature operation.

In this chapter we show how these alloys can be used as a laser-driven tunable narrow-

band spintronics THz source, as a function of the stoichiometry of the alloy used. The

emitted THz radiation frequency is determined by the FMR. Along with the observation

of the FMR, THz emission spectroscopy also enables the study of their magnetic prop-

erties beyond a current static measurements system. We further characterize the THz

emission from these alloys as the function of laser power used for excitation, externally

applied magnetic field, and temperature of the alloys. We discuss the THz emission

from these alloys by a considering magnetic dipole radiation model and characterize it

further as laser-like, near Gaussian beam.

4.2 Experimental details

The experimental set-up used is shown in Figure 4.1. The samples are irradiated at

normal incidence with unfocused pulses from a laser-amplifier system with a wavelength

of 800 nm and a repetition rate of 1 kHz. The laser pulse duration of 100 fs is much

shorter than the period of the emitted THz bursts, which is few ps, enabling fully

coherent emission. The emitted radiation can be detected in the backward or forward

direction. Our detection principle for the emitted light pulses is based on electro-optic

sampling in a 2 mm thick ZnTe crystal [12]. A small portion of the excitation pulses

is split-off by a dichroic mirror (DM) acting as a 1:1000 beam splitter. Electro-optical

detection enables the removal of any thermal background from the measurement and

hence allows extremely weak signals to be observed. Our frequency range is limited

to below 2 THz by phase matching between the THz and near infrared (NIR) laser

wavelengths in the ZnTe crystal. All measurements were done under ambient conditions,

if not otherwise specified.

All the thin film samples used in this chapter were grown by our collaborators at Trin-

ity College Dublin. Thin films of three different alloy compositions Mn2Ga, Mn2.5Ga,

and Mn3Ga were grown by magnetron sputtering on heated MgO substrates in a fully

automated Shamrock deposition tool with a base pressure of 1×10−8 Torr. The optimal

deposition temperature of the substrate was found to be 350◦C. Mn3Ga and Mn2Ga

samples were grown from stoichiometric targets at a power of 30 W for 40 min, Mn2.5Ga

was grown by co-sputtering from the Mn3Ga and the Mn2Ga targets at equal power of

20 W for 30 min [6, 8]. All the films had crystallographic c-axis along the surface normal.

The crystal structure was determined by X-ray diffraction. All three films crystallize in

the tetragonal D022 structure (space group 139) illustrated in Figure 4.2.


MnxGa

ZnTe

DM

N

S

Delay

λ/4

Si

Figure 4.1: Schematic of the THz emission spectroscopy set-up and sample geometryemployed for the Mn3-XGa samples. 800 nm NIR laser pulses are split into beams inthe ratio of 90-10 % (shown in red). The stronger beam is used as a pump to irradiatethe Mn3-XGa thin films. The thin films are kept in the in-plane magnetic field of 400mT (shown as North (N) and south (S) poles). The emitted THz radiation is collectedon parabolic mirror in reflection geometry (shown in solid gray). THz radiation andprobe NIR pulses are focused on ZnTe crystal for electro-optic sampling. λ

4 is quarterwave plate for 800 nm wavelength and WP is Wollaston prism and PD is photo-diodes.

Figure 4.2: Idealized crystal structure of Mn3Ga. The arrows represent the magneticmoment on each Mn site. The crystallographic c-axis is perpendicular to the sample

surface and parallel to the net magnetic moment.


Mn in the 4d positions, couples ferromagnetically to each other, while the 4d and 2b

magnetic sub-lattices are strongly antiferromagnetically coupled, resulting in ferrimag-

netic order. For the stoichiometric compound (X = 0), the net moment per formula

unit is 2|m4d | - |m2b |. The local symmetry, especially the Ga coordination of the two

Mn-sites is quite different, leading to different magnetic properties for the Mn on the two

different sites. Mn in 2b positions possesses a larger magnetic moment of 3.3 µB with

weak easy-c-plane anisotropy (Ku = 0.09 MJm3) [13], while the Mn in 4d positions has

a smaller moment of 2.1 µB and strong easy-c-axis anisotropy (Ku = 2.26 MJ m3). As

the composition of the films is varied from X = 0 to 1 (from Mn3Ga to Mn2Ga), Mn is

primarily lost from the 2b position. Hence, the net magnetization increases with increas-

ing X, and there is no compensation composition. Simultaneously, ions with in-plane

anisotropy are replaced by vacancies, so that the net magneto-crystalline anisotropy

increases.

Saturation magnetization (Ms) and coercivity (µ0Hc) were determined by vibrating sam-

ple magnetometry (VSM). However, the magnetic anisotropy field, µ0Hk, exceeds the

field available in our magnetometer, so it was not possible to saturate the magnetization

in the plane of the films. µ0Hk is usually determined by extrapolation [14], but other

techniques such as anomalous Hall effect [15], electron spin resonance (ESR) [16], or

dynamic all-optical MOKE/Faraday [9] measurements can also be used. The two latter

methods relate the resonance frequency to the magnetic properties via the Kittel formula

[17].

In ferrimagnetic materials, where the two sub-lattices have different magnetizations and

anisotropies but are strongly coupled to each other by exchange, one expects two funda-

mental modes: one where the two sub-lattices precess out-of-phase and one where they

remain in-phase. Due to the antiferromagnetic exchange coupling, we expect the out-of

phase mode to have lower energy and frequency. One can describe the ferrimagnet as

a system of two exchange-coupled ferromagnetic layers as shown in Figure 4.3. As can

be seen in the Figure, the upper (bottom) one a (b) has saturation magnetization Mas

(M bs) and magneto-crystalline anisotropy µ0 M

ak(µ0 M

bk). Because the external field

is applied along the Z -axis, it is assumed that the magnetizations are in the Z-Y plane,

in such a way that the azimuthal angle ϕ, which is measured from the Z -axis (see Figure

4.3), can be considered zero for both layers. Thus, only the polar angle φ will change

when external field H is applied. The energy density of the system can be written as

Efull = Ea + Eb + Eint (4.1)


Figure 4.3: Bilayer system of Mn3-XGa showing the ferrimagnetic alignment of mag-netic moments.

where Ea and Ea include Zeeman and magneto-crystalline anisotropies. Also the inter-

action term is given by

Eint = −JMa ·M b

MasM

bs

+µ0

2

∑i

Nii

[(M a + M b) · i

](4.2)

where the first term is a bi-linear exchange interaction [18] and the second term repre-

sents the demagnetizing energy of the structure. Because the system is a thin film, the

demagnetizing factors associated with orthogonal axes are Nxx = Nzz ≈ 0 and Nyy ≈1. Furthermore, we concentrate on the J < 0 case, corresponding to antiferromagnetic

coupling between the layers, and under zero applied field so that the Zeeman energy is

zero. In addition, the system satisfies the condition µ0Hak � µ0H

as and therefore the

equilibrium polar angles can be assumed as φa = π/2 and φa = −π/2.

Local coordinates (Xi,Yi,Zi) are used for each sub-lattice, with i = a, b, and under

the linear approach, the magnetization can be written as M i = M isZ

i + miXiX

i +

miY i Y

i. Here, Zi represents the equilibrium orientation of the layer i and miXi, Yi are

the dynamic components of the magnetization. Using the Landau-Lifshitz equation

dM i/dt = −γiM i ×H ieff (4.3)

the frequency modes can be obtained from


iω

γaMas−ΓMa

s0 −ΓMs

ΓMas

iωγaMa

s−ΓMs 0

0 −ΓMsiω

γbMbs−ΓMb

s

−ΓMs 0 ΓMbs

iωγbMb

s

maXa

maY a

mbXb

mbY b

= 0 (4.4)

where ω = 2πf and

ΓMas

= 1Ma

s

[µ0H

ak − µ0(Ma

s −M bs )− J

Mas

],

ΓMbs

= 1Mb

s

[µ0H

bk − µ0(Ma

s −M bs )− J

Mbs

],

ΓMs = JMa

sMbs

The roots of the determinant of the 4×4 matrix [equation 4.4] give the dispersion relation

of the exchange-coupled system, where the two meaningful solutions are

f± =1

2π

√1

2(B ±

√B2 − 4C) (4.5)

with

B = (γbMbsΓMb

s)2 − γaMa

s (2γbMbsΓ2

Ms− γaMa

s Γ2Ma

s)

and

C =[γaγbM

asM

bs (Γ2

Ms− ΓMa

sΓMb

s)]2

From equation 4.5, it is clear that the resonance frequency exhibits two modes f+ and

f− corresponding to the upper and lower frequency one, respectively. One can show

that for a strong coupling constant J, the lower frequency mode does not significantly

depend on the coupling, since in this case the precession of both magnetizations occurs

in an anti-parallel (J < 0) or parallel (J > 0) state. On the contrary, the upper mode

strongly depends on J and appears at very high frequencies. We are interested in the

mode occurring within our experimental range (f) and give an approximate expression

of equation 4.5, derived under the condition µ0Hik � |J/M i

s|:

f− = fres ≈ (γeff/2π)[2( Ka + kb

Mas −M b

s

)− µ0(Ma

s −M bs )]] (4.6)

where µ0Hik = 2Ki/M i

s

with [19]


γeff = γaγb(Mas−Mb

s )γbMa

s−γaMbs

Now with defining net magnetization as Ms = Mas −M b

s and µ0Hbk = 0 the resonance

frequency is

f res = (γeff/2π)(µ0Hk − µ0M s) (4.7)

where γeff is an effective value of the gyro-magnetic ratio, µoHk is an effective perpendic-

ular anisotropy field, which depends on the sub-lattice anisotropy and magnetizations

of both sub-lattices. Ms is the net saturation magnetization (M4d-M2b). These values

and hence the resonance frequency can be controlled via the films stoichiometry. Using

previously obtained data from neutron scattering measurements on bulk Mn3Ga [13]

samples, the frequency of the out-phase mode in Mn3Ga is predicted from Eq. (4.7), to

lie in the region of 0.35 THz. This is at the same time the highest frequency expected

in Mn3-XGa thin films. Due to the loss of Mn from the 2b sites when X = 1, the lowest

frequency should be observed for Mn2Ga. Assuming that the Mn on the 2b sites is

completely lost, the low frequency limit is estimated to be 0.12 THz. The frequency

tunability is limited in both directions by the eventual loss of the tetragonal D022 struc-

tural phase. Note that the in-phase mode, due to the extremely large exchange fields

in the system, should exhibit higher frequencies which could reach values in excess of 4

THz in Mn3Ga.

4.3 Results & Discussion

The process of THz emission from coherent spin precession can be understood as fol-

lows: The 100 fs NIR laser pulse leads to both ultra-fast demagnetization and a sudden

change of the easy axis of the magnetic system [20]. This in turn produces a coherent

precessional motion of the net magnetization M around the easy axis with a frequency

fres,exc that converges towards the frequency fres given in equation 4.7 for low excitation

fluences. In the case of strong, easy-c-axis, magneto-crystalline anisotropy, the tip of the

magnetization vector oscillates around the crystallographic c-axis, corresponding to the

X-Y plane in our experimental geometry shown in Figure 4.1. A small external field is

applied in the X -direction in order to synchronize the precession of the spins after the

ultra-fast perturbation allowing for the emission of a coherent wave. The emitted electric

field due to both demagnetization and spin precession can be expressed as [21–23]

E ∼ d2/dt2(µ0M) (4.8)

4.3. Results & Discussion 49

As can be seen from equation (4.8), it is proportional to the second derivative of M. This

implies the following: the electric field vector of the wave originating from the precession

of the out-of-phase mode is oriented perpendicular to M and lies in the (X-Y ) plane.

This wave therefore propagates in the Z direction, normal to the film surface, and the

electric field component along the Y -axis is

Ex,y ∼ A0e(−αt) sin(2πfres,dynt) (4.9)

where A0 is the initial deflection of M caused by the laser excitation and α is the damping

of the precessional motion. As discussed in chapter 3 (section 3.1), the THz emission

from Mn3-XGa films is based on magnetic dipole emission. It is interesting to note that

THz emission spectroscopy probes the in-plane components, making it complementary to

Faraday effect measurements (see chapter 3), which probe the out-of plane component.

Figure 4.4: Left column shows the detected electric field component of the emittedTHz radiation from Mn2Ga, Mn2.5Ga and Mn3Ga films. The right column is a Fouriertransform of the same data which highlights any predominant frequencies in the spectra.It is clearly seen that Mn3-XGa films can emit THz radiation between 0.21 THz and

0.35 THz based on the relative content of manganese and gallium.


4.3.1 Effect of Mn content on THz emission from Mn3-XGa

THz emission measurements for the three different compositions are shown in Figure 4.4.

The laser excitation fluence in all measurements was 0.1 mJ cm−2 with an average laser

power of 30 mW. The observed center frequency depends on composition and shifts from

0.205 THz for Mn2Ga to 0.352 THz for Mn3Ga. The time plots for all three thin films

shows the raw data recorded in the experimental section, plotted in arbitrary units. The

normalized FFT of these time domain traces is plotted. The frequency resolution in the

intensity spectra shown in Figure 4.4 is defined by the time-window in the time-domain

measurements and does not represent the natural bandwidth of the emission. The center

frequencies are determined by fitting a damped sine function to the measurements. The

THz emission measurements are based on the coherent detection of the emitted THz

bursts utilizing the set-up described in Figure 1. The intensity spectrum is derived

from the time-domain measurement via Fourier transformation. The thereby achievable

frequency resolution is directly related to the time window evaluated in the time-domain

measurements δν = 1/δt. In the measurement, one observes a replica of the THz pulse

at a few 10 ps after time zero which originates from a part of the THz pulse reflected

on the back surface of the 2 mm thick electro-optic crystal (ZnTe). This second pulse

is interfering with the remnants of the decaying initial pulse which complicates the

analysis. For this reason we choose to only evaluate the time window of 50 ps after time

zero where the initial THz pulse is exclusively sampled (see Figure 4.5), which leads to

a frequency resolution of nominal 0.02 THz. The THz transient in this window is then

fitted by a damped sine function (according to equation 4.9), see Figure 4.5a. Under

this assumption values for the center frequency can be derived. Fourier transformation

of a sine damped fit can be used to obtain a better approximation of the real natural

bandwidth as can be seen in Figure 4.5b.

The phase of the emitted coherent THz transient can be reversed by the sign of an

in-plane external magnetic field (∼ 200 mT) proving that the emission is of magnetic

origin, see Figure 4.6.

Another approach that allows direct measurement of the quasi-equilibrium frequency is

THz-driven transient Faraday probe measurements, where the magnetic field of the THz

pulse couples directly to the spins via the Zeeman-torque [24]. We were able to drive the

same mode in the Mn3Ga film selectively by resonant THz excitation, see Figure 4.7.

The spectral densities of the TELBE source [25] are orders of magnitude higher than

those available from tabletop sources, making it possible to detect the minute Faraday

rotation signal. The absorbed energy goes predominantly into excitation of the coherent

spin precession, so that heating and off-resonant excitation is minimal. The derived

frequencies should therefore correspond better to the equilibrium value. We find that


Figure 4.5: Analysis of the THz emission measurements a) example: sequentialelectro-optic sampling of an emitted THz transient from Mn2Ga taken with time stepsof 130 fs (bullets). A damped sin function is fitted to derive the center frequency (redsolid). b) Fourier transformation of the fits to the electro-optic sampling measurementsyields an approximation of the natural line-width. Shown in the plot are the thereby

derived spectra for Mn2Ga (red), Mn2.5Ga (black), and Mn3Ga (blue).

Figure 4.6: The time-domain wave-forms for an applied field of 100 mT, directedalong +x and -x, respectively. The phase shift between the two is 180◦, which confirms

the magnetic origin of the observed modes.


the frequency derived from THz-driven transient Faraday rotation is slightly higher (∼7 GHz), when compared to the peak value obtained from FFT, than the value inferred

from linear extrapolation of the emission measurements.

Figure 4.7: Faraday measurement of the resonance of Mn3-XGa driven by direct THzexcitation with an intense quasi-cw narrow-band THz source, TELBE (green solid line).Blue shaded peak shows the THz emission from Mn3-XGa by NIR laser irradiation.The resonance mode observed with Faraday measurements is higher ( by ∼ 7 GHz) andnarrower than the one observed from the laser-driven THz emission mode because theFaraday measurement is a resonant excitation technique with minimal heating induced

in the films whereas THz emission spectroscopy is heat driven.

These observed FMR frequencies can be used to calculate saturation magnetization and

in turn Hkeff using Kittels formalism [26]. The FMR mode observed in these films

scales with their Mn content. A similar trend is followed by effective magnetization of

these alloys. The saturation magnetization and magnetic anisotropy energy decreases

as the Mn content is increased in Mn3-XGa alloys. Table 4.1 summarizes the magnetic

properties calculated using THz emission spectroscopy for all 3 films considered here.

These values are in close agreement with the values reported in [6, 8, 9].

4.3.2 Effect of laser power on THz emission from Mn3-XGa

The magnetization of a ferromagnet decreases when it is heated and above Curie tem-

perature all long range ordering is lost. In our experiment, upon irradiation with NIR

laser pulses, the sample temperature will increase. In order to characterize the Mn3-XGa

thin films as a tunable, narrow band THz source, we studied the frequency of emission

and power of radiated THz radiation as a function of laser power. Figure 4.8a shows the

normalized THz power emitted from thin films of Mn3-XGa as a function of laser power.


Mn2Ga Mn2.5Ga Mn3Ga

Magnetometry data

VSM µ0Ms (T) 0.401 0.263 0.163

NIR-driven THz emission

observed fres (THz) 0.205 0.259 0.352

bandwidth ∆ fres (THz) 0.012 0.018 0.029

µ0Hk (T) 7.98 9.95 13.17

THz pump Faraday rotationprobe

observed fres (THz) - - 0.359

µ0Hk (T) - - 13.43

Table 4.1: Ms from VSM [6, 8] and inferred values of 10Hk from dynamic THz emis-sion measurements. THz emission measurements have been performed in the presenceof an external magnetic field of 400 mT and at a temperature of 19.5◦C. THz drivenFaraday rotation measurements were performed with an external magnetic field of 200

mT.

As the laser power is increased from 30 mW to 700 mW, emitted THz power increases

linearly, showing saturation around 500 mW of laser power. It is important to note that

irrespective of the Mn content in Mn3-XGa, all three films show similar dependence on

laser power.

Figure 4.8: Laser power dependence for Mn2Ga (red), Mn2.5Ga (green) and Mn3Ga(blue). (a) The THz power increases linearly with incident laser power for lower powersand seems to saturate at higher powers. (b) The THz frequency scales down linearly

with incident laser power.

The dependence of emitted THz power on the incident laser power can be explained as

follows: as the laser power is increased, the magnetization (M ) is suppressed more which


deflects the magnetization away from equilibrium. This results in a larger precession

angle and thus results in a larger electric field as measured in experimentally. The

larger electric field implies larger power in FFT. At higher fluences, one can saturate the

initial angle of magnetization resulting in saturation in the power spectrum. When laser

fluence was increased further, we observed the ablation of thin films from the substrate,

so complete quenching of the THz amplitude/power is not observed.

The FMR frequency decreases linearly as laser power is increased (see Figure 4.8b).

This decrease in FMR is consistent with the temperature dependence of FMR, which

is in agreement with increasing sample temperature with NIR laser irradiation. As the

temperature of the films is increased, its Ms decreases; which should result in a lowering

of frequency as expected from the Kittel equation. The extrapolated frequency at zero

excitation power will be used as an approximation for fres at equilibrium (see Table 4.1).

The detailed description of the observed temperature dependence of FMR for Mn3-XGa

is discussed in the following section.

4.3.3 Effect of temperature on THz emission from Mn3-XGa

The temperature dependence of FMR modes for Mn3-XGa are studied using TES. Figure

4.9 shows the dependence of FMR mode observed in Mn3-XGa thin films as a function

of temperature. As the temperature is increased, the frequency of FMR mode decreases

for all three samples.

As the temperature approaches the Curie temperature of the system, the FM mode

softens. The saturation magnetization of the system as a function of temperature is

given by following equation (based on mean field theory) [27],

M = Nm tanh (mλM/kBT ) (4.10)

with m being the magnetic moment of an electron, N being the number of electrons, λ

is the mean field constant and kBT is the thermal energy. The above equation has a

non-zero solution in the temperature range 0 K to TC . The temperature dependence

of magnetic anisotropy follows the Mn relation ( n = 3 for uniaxial magnets) [28–30],

which implies with increasing temperature, magnetic anisotropy reduces rapidly.

In Figure 4.9, the fitting of mean field theory for magnetization to temperature depen-

dence FMR mode obtained from THz emission spectroscopy measurements is shown.

From this fitting, we estimate the compensation/Curie temperature (TC) of the thin

film under consideration between 650 K - 730 K. These estimated values are in quali-

tative agreement with the values reported in ref. [31–33] for Mn3Ga. These references


Figure 4.9: Temperature dependence for Mn2Ga (red), Mn2.5Ga (green) and Mn3Ga(blue). The mean field fit is used to estimate the Curie temperatures (TC) of thethin films under consideration. The estimated TC values of Mn3Ga are compared with

reported values, see Table 4.2.

have predicted the TC in the range of 700 K - 770 K. To the best of our knowledge, there

are no reported values of TC for Mn2Ga and Mn2.5Ga.

4.3.4 Field dispersion for Mn3-XGa

In order to study the sublattice anisotropies, magnetization, and inter-layer exchange

field, the field dependence of THz emission is carried out in an externally applied field

of 2-10 T. The external field was applied out of plane (∼ 5◦ with respect to c-axis

of the films) to Mn3-XGa films. This slight angle with respect to the surface normal

tilts the magnetization slightly in-plane, allowing for detection of coherent precession.

The experimental set-up used for these measurements is shown in Figure 4.10. Geo-

metrical constraints of the split-coil magnet, such as small size optical windows, and

comparatively large distances between these windows and the sample, lead to consid-

erable transport losses of the emitted THz pulses, reducing the achievable sensitivity

in these measurements. The power of emitted THz radiation in these films scales with

saturation magnetization (Ms). From Mn3-XGa, Mn3Ga has lowest Ms. Likely for this

reason, THz emission from the Mn3Ga sample, which has earlier been determined to be

the weakest of the three samples, could not be observed. The experimental study was

hence performed on the Mn2Ga and Mn2.5Ga thin films.


Figure 4.10: Schematic of the THz emission spectroscopy set-up and sample geometryemployed with 10 T split coil magnet. The experimental setup is very similar to theone shown in Figure 4.1 with the exception that thin films are placed inside the 10 Tsplit-coil magnet with an external field applied along the magnetization of the films,

which is normal to the surface of the thin film.

Figure 4.11 shows the derived results. Considering equation 4.7, as an externally applied

field is increased, the total effective magnetization of the samples increases resulting in

increased resonance frequency of FMR. As the out of plane field increases, the resonant

frequency increases linearly with the slope of 28.2 GHz/T for Mn2Ga and 27.8 GHz/T

for Mn2.5Ga. The linear slope corresponds to what is expected from a material with

uniaxial anisotropy with the external field applied along the easy axis [34], and shows

that we are clearly probing the low-frequency ferromagnetic-like mode.

Figure 4.11: Magnetic field dependence for Mn2Ga (red) and Mn2.5Ga (green). (a)The THz power increases nonlinearly with the magnetic field. (b) The THz frequency

scales up linearly with the magnetic field.

The power of emitted THz radiation scales with externally applied field. This can be

understood as follows; as the external field is increased, the precession angle increases


which results in larger electric field amplitudes.

4.3.5 Thickness dependence of THz emission from Mn3-XGa

In order to realize the spin transfer torque devices which makes use of Mn3-XGa as a free

layer, we need to grow films with sub-10 nm thicknesses [35]. THz emission spectroscopy

turned out to be much more sensitive than transient-MOKE/Faraday and absorption

techniques and hence was employed to study the films with sub-10 nm thickness. During

this project we observed that the efficiency of THz emission has varied for films fabricated

at different times. On closer inspection of these films, we observed that THz emission

efficiency depends on the surface morphology of the film under consideration. Thin films

with uniform surface morphology gives very inefficient THz emission whereas films with

island structures gives highly efficient THz emission.

A new set of discontinuous films of Mn2Ga, Mn2.5Ga and Mn3Ga were prepared with

thicknesses between 2.5 and 40 nm and measured with THz emission spectroscopy for

FMR modes and magnetometry. These new island films (see Figure 4.12) exhibited a

vastly improved THz emission efficiency, in the similar range of the films used earlier.

The island size for these newly prepared thin films are of the order of few 100 nm (see

Figure 4.12b).

Figure 4.12: THz emission from the newly grown films with island morphology. (a)Example measurement of the THz emission from a 40 nm Mn2Ga island film (b) AFM

image of the same film showing the average island size, described in the text.

We measured these deliberately prepared island films in THz emission set-up and the

results are shown in Figure 4.13. We observed that the peak power observed FMR

mode decreases as the thickness of the film goes down. It should be noted that we do

not observe any THz emission from the films below 10 nm thickness. We expect the


thickness dependence to follow quadratic behavior because of the superradiant process

of THz emission but instead we see a clear deviation from expected quadratic behavior

(see Figure 4.13a and figure 4.13c), except for Mn2.5Ga which shows quadratic behavior

(see Figure 4.13b). The deviation could suggest that the magnetic properties of the films

are also changing as the thickness of the film is changed. Although expected quadratic

behavior with respect to thickness was not observed for all of the films, the laser-driven

THz emission spectroscopy shows that the FMR mode frequency is independent of the

thickness of the films, see Figure 4.13 (g,h,i).

In order to confirm this claim we did complimentary magnetometry measurements with

the external field applied along the easy axis of magnetization. Magnetometry measure-

ments on Mn3-XGa films with varying thickness shows that the saturation magnetization

Ms and the coercivity Hc change with film thickness. This could be due either to changes

in the film structure or canting of the magnetic moment as the layer thickness is reduced.

Figure 4.13 (d,e,f) shows how saturation magnetization (Ms) is changing drastically as

film thickness is reduced. Hard-axis measurements could not be performed, given the

high saturation fields of the films.

As shown in Figure 4.13, we could not observe the THz emission from films with thick-

nesses below 10 nm. This should not impose any serious limitations on the realization

of a spin transfer torque device as, according to theory, antiferromagnetic or ferrimag-

netic films of such film thicknesses (∼ 10nm) are probably already suitable to act as

active layers. Unlike ferromagnets, where only the first nano-meter absorbs the spin-

momentum transfer [35], in ferri/antiferromagnets this is done by the entire layer [36].

This relates to the onset currents for precession, which in ferromagnetic layers scale as

the volume of the layer, which would consequently not be the case for ferrimagnetic

films.

4.4 Conclusion & Outlook

We have demonstrated narrow-band laser-driven THz emission from an ultra-thin, fer-

rimagnetic metallic film. The observed bandwidth of the emission is between 6 % and

9 %. The emission frequency can be tuned via the Mn-content, temperature of the films,

and NIR laser power used. Figure 4.14 shows the continuously tunabality of the FMR

mode from Mn3-XGa thin films as a function of Mn content and the temperature of the

films, and laser power used for the measurements. From Figure 4.14b, it is evident that

the frequency of THz emission from these thin films can be varied from continuously

0.15 THz to 0.5 THz which makes these alloys technologically interesting for tunable,

narrow band THz sources.

4.4. Conclusion & Outlook 59

Figure 4.13: Results of THz emission measurements (a,b,c) and magnetometry mea-surements (d,e,f). Both techniques indicate that the magnetic properties of the filmschange for different thicknesses. The earlier used films were also measured in same runand are shown in black dots. The FMR mode of the films are constant with respect to

thickness of the film (g,e,f).

Figure 4.14: Characterization of Mn3-XGa thin films for tunable, narrow band THzsource. a) Frequency of THz emission as a function of Mn content in the stoichiometryof the thin films b) tunability of emitted THz frequency as a function of laser power

and temperature.


The efficiency of this type of spintronic emission is, within the narrow emission band-

width, comparable or even up to an order of magnitude greater than that of classical

ZnTe emitters based on optical rectification. This makes Mn3-xGa thin films interest-

ing candidates for narrow-band, on-chip, spintronics emitters in the sub-THz frequency

range. Heusler type alloys may furthermore be integrated as free layers in spin-transfer-

torque driven oscillators. This could propel such devices into the terahertz regime,

combining the high tunabilty and output power of spin-torque oscillators with the ultra-

high frequency intrinsic to the materials analyzed here. Further increase in the resonance

frequencies may be achieved by alloying different tetragonal Heuslers or by atomic sub-

stitution. Another extremely interesting result of this study is that film morphology

can be used to improve the THz emission efficiency. One way to study the effect of

morphology on the THz emission could be to do optical/electron-beam lithography on

the continuous films and study the dependency of THz emission on the island size.

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CHAPTER 5

THz-Induced Demagnetization: Case of CoFeB

Narrow band, tunable THz radiation is used to induce ultra-fast demagnetization in

amorphous ferromagnetic thin films of CoFeB. The ultra-fast demagnetization is probed

using the time resolved magneto-optical Kerr effect. We observe the non-monotonic fre-

quency dependence of the ultra-fast demagnetization with a peak at ∼ 0.5 THz. This

non-monotonic dependence is discussed using the Drude conductivity model and the

Eliot-Yafet type scattering mechanism.

This chapter is based on a manuscript which is being prepared for a publication.

Awari N., et al. ”Speed limits of ultra-fast demagnetization” in preparation

65

66 5. THz-Induced Demagnetization: Case of CoFeB

5.1 Introduction

The observation of ultra-fast demagnetization of nickel upon irradiation with near infra-

red (NIR) femtosecond (fs) laser pulses on sub-picosecond (sub-ps) timescale [1] initiated

extensive research in the field of ultra-fast magnetization dynamics [2–8]. In laser in-

duced ultra-fast magnetization dynamics, laser pulses heat electronic temperature above

the Curie temperature on an ultra-fast timescale which results in loss of macroscopic

spin order [9, 10]. The spin excitation in such experiments is an indirect process and

it takes place by exchange of heat and angular momentum between the driving laser

pulses, electrons, spins and lattice [11, 12]. The underlying physical mechanism explain-

ing dissipation of the spin angular momentum on sub-ps timescale is still not clear.

There have been many different experimental and theoretical contributions to explain the

dissipation of spin angular momentum on sub-ps timescale. Two major spin dissipation

channels have been suggested:

1. The 3-temperature model (see chapter 2), based on the Elliot-Yaffet (EY) scat-

tering mechanism, has been used to explain the ultra-fast demagnetization on the

basis of spin-flip scattering. In this model ultra-fast demagnetization has been

shown to be a thermal process, driven by the difference in the electronic, spin,

and, lattice temperatures.

2. Alternatively, non-local spin transport, super-diffusive spin current[13–15], has

been considered for spin dissipation. In this case, the energy and spin dependent

lifetimes of optically excited hot electrons results in spin currents inside the ma-

terial under investigation and that results in ultra-fast magnetization dynamics.

There have been theoretical predictions suggesting super-diffusive spin current as

the sole source of ultra-fast demagnetization[13, 16].

Reference [9] has shown that both spin-flip scattering and super-diffusive spin current

plays an important role in ultra-fast magnetization. To date, the relative contributions

of these two processes to the ultra-fast demagnetization is under debate.

Recently, THz radiation has been used to study ultra-fast magnetization dynamics in

ferromagnetic systems [17–19]. As compared to NIR femtosecond driven ultra-fast de-

magnetization experiments, the use of the THz radiation allows the coupling of the spin

system directly via the magnetic field component of the THz radiation. The THz pulses

have been used to drive spin currents in magnetic metals [20]. When spin currents

are generated, they undergo scattering events that changes the material magnetization.

The THz pulse duration, being of the same order as elementary scattering rates, allows

5.1. Introduction 67

to accurately model the influence of scattering events on material magnetization [17].

When compared with the optical excitation, in THz excitation of ferromagnetic mate-

rials, individual scattering events are more dominant than the relaxation of the highly

non-equilibrium electronic system [17]. Bonetti et al. [17] have shown that ultra-fast

demagnetization is detectable for amorphous CoFeB but not for crystalline Fe thin films.

This hints towards defect mediated spin-lattice scattering. THz conductivity measure-

ments on these thin films allowed the interpretation of these observations as Elliot-Yaffet

[21, 17] type scattering processes. All of these experiments have made use of broadband

THz radiation to study the ultra-fast demagnetization of the samples.

When strong THz pulses hit the ferromagnetic sample, spin-polarized current flows inside

the sample which has two responses;

1. The coherent response can be explained using the Landau-Lifshitz equation. The

magnetic field of the THz pump couples with the initial magnetization of the

sample and results in precession. This magnetization dynamics can be explained

using,

dM

dt= −γ(M ×H ) (5.1)

where γ is the gyro-magnetic ration with the value 28.02 GHz/T, M is the mag-

netization of the sample and H is the effective applied magnetic field. In the

absence of a THz pulse, the sample magnetization is along the effective magnetic

field comprising of anisotropy and demagnetizing fields. When a THz pulse passes

through the sample, the magnetic field of the THz pulse (BTHz) applies a torque

on the sample magnetization which results in precession of the magnetization. For

small angle precession, the magnetization can be given by [17],

M(t) = γ sin θ

∫BTHz(t)dt (5.2)

where θ is an angle between M and H. This effect is odd in the magnetic field of

the THz pulse. As we change the polarity of the BTHz by π, the sense of precession

also reverses.

2. The incoherent response is a result of the spin-polarized current flowing through

the sample because of the THz pulse inside the material. This effect is odd with

respect to the magnetic field of the THz pulse [17]. The incoherent response can

be modelled as a cumulative integral of the THz energy deposited in the sample

[17],∫B2THz(t)dt.


In this chapter, tunable THz radiation is used as a non-resonant pump to excite the

amorphous ferromagnetic thin films of CoFeB. This allows one to disentangle the spin

to charge conversion processes at the THz frequencies with timescales which are similar

to fundamental scattering rates.


The experimental set-up used in the experiment is shown in Figure 5.1. We used

the narrow-band, tunable accelerator-based superradiant THz source, TELBE, to drive

ultra-fast spin-polarized currents in an amorphous CoFeB thin film. The thin films were

grown with sputtering with 5 nm thickness with a stack of Al2O3(2nm)/CoFeB(5nm)

on silicon substrate. The peak electric field of the tunable THz radiation used were up

to ∼ 100 kV/cm. The static magnetization of the sample was aligned in plane (M0)

using a 100 mT permanent magnet, which is larger than the coercive field of CoFeB (∼ 5

mT). Then we applied an external field of 100 mT perpendicular to the sample plane to

bring the component of static magnetization out of the plane (M). The magnetic field

component of THz (BTHz) was aligned orthogonal to the magnetization of the sample

(see Figure 5.2). The magnetization dynamics of the sample because of the THz-induced

spin-polarized current was probed using THz pump 800 nm polar MOKE geometry. The

ultra-fast magnetization response of the sample was recorded by taking the sum of the

data taken at opposite polarities of the incident THz pump. In order to study the pump

frequency dependence of the ultra-fast magnetization we made use of the tunability of

the TELBE source.

The terahertz fields generated by TELBE are multicycle electromagnetic pulses with a

center frequency tunable between 0.1 and 1.3 THz and with a bandwidth of approxi-

mately 20% (8 cycles) [22]. The electric field of these pulses can be measured through

electro-optical (EO) sampling in a birifringent crystal such as ZnTe. An example of

such a measurement is shown in Figure 5.3, where the EO sampling trace for two tera-

hertz pulses with a center frequency of 0.5 THz and with opposite polarity is presented.

Precise control of the phase of the terahertz radiation is achieved with suitable λ/2

wave-plates. In this experiment, we used the tunability of the TELBE source to study

the incoherent response of magnetization as a function of THz pump frequency. Table

5.1 summarizes different THz pump frequencies used along-with its maximum electric

field values.

At first we wanted to separate the coherent and incoherent responses of magnetization in

CoFeB. In order to achieve that, we recorded the THz induced magnetization dynamics

with opposite polarity of the THz pulse. As discussed earlier, the coherent response of


Figure 5.1: Experimental set-up used for narrow band THz pump MOKE probe mea-surements. A frequency tunable, narrow-band THz radiation (shown in light red band)is focused on the sample using a parabolic mirror. The NIR laser pulses (shown in red),which are synchronized to THz radiation, is incident colinearly on the samples. Thetransient change in sample magnetization is probed using the rotation of polarizationof the NIR laser pulses using λ

2 (a half wave-plate for 800 nm), Wollaston prism (WP),and balanced photo-diodes (PD). A reference PD is used to monitor and normalize the

reflected signal from the sample.

Figure 5.2: Experimental geometry used in the experiments. Initial magnetization ofthe sample (M0) is along the y axis and (BTHz) is orthogonal to the initial magnetiza-

tion.


Figure 5.3: Time traces of the THz pump used in the experiment at 0.5 THz. (a)0.5 THz time domain traces measured using electro-optic sampling in a 100 µm GaPdetector at orthogonal half-wave plate angles (b) FFT of time trace for one of the HWP

angles.

Figure 5.4: (a)THz pump time resolved MOKE signal observed in amorphous CoFeBthin films which includes the coherent and incoherent responses observed for oppositepolarity of the THz electric/magnetic field. The frequency of the THz radiation usedfor this measurement was 1 THz with a focused spot size of 700 µm. (b) The incoherentresponse of the sample is obtained by taking the sum of the two curves shown in (a).(c)The coherent precession signal is separated from the incoherent one by taking the

difference of the two curves shown in (a).


the magnetization is odd with respect to the magnetic field of the THz pulse, so it can

easily be separated by subtracting the measurements done with opposite polarity of the

THz pump. In contrast, addition of the measurements done with opposite polarity of

the THz pump will only give the incoherent response of the magnetization. Figure 5.4

shows an example of the measured THz pump-MOKE signal for opposite THz pump

polarity. It also shows how coherent and incoherent responses can be separated from

each other.

Frequency (THz) Electric field (kV/cm)

0.3 24

0.4 47

0.5 28

0.6 35

0.7 42

0.7 54.6

1 89

1 53

Table 5.1: A summary of the THz frequencies used in the THz pump Polar MOKEexperiments along with their peak electric field values.

Figure 5.5: Ultra-fast demagnetization observed in CoFeB thin films with 0.5 THzpump is plotted in blue. The experimental data shows the second step in demagneti-zation around 10 picoseconds (ps). The integral of BTHz is plotted and shown in red.The cumulative integral does not follow the experimental data above 10 ps because

reflections are not considered in the cumulative integral.



Figure 5.5 shows the incoherent response of the CoFeB thin film sample following the

arrival of the terahertz pulse, as measured by the time-resolved MOKE with 0.5 THz as

a pump and showing that the sample demagnetizes while the THz pulse is present in the

sample. This is consistent with the results of Refs.[17, 18], with the important difference

that in those works the excitation was a broadband terahertz pulse, while here we use

narrow-band radiation. However, the magnetization dynamics is based on the very same

mechanism: the coherent response can be modeled as the integral of BTHz, showing it

obeys the Landau Lifshitz Gilbert (LLG) equation; the incoherent response is modelled

by the cumulative integral of B2THz, i.e. by the energy deposited by the terahertz field

in the material.

In Figure 5.5, we also observe two steps in the demagnetization data. The observed

second step is believed to be because of the reflection of the THz pulse from the back

surface of the substrate. The time delay between the two steps (approximately 10 ps) is

consistent with the optical path traveled in a 500 µm thick silicon substrate (n ≈ 3.41).

In order to compare the demagnetization step as a function of the THz pump, we consider

the first step, as it is not influenced by the reflected THz pulse from the back surface of

the substrate. The modelled cumulative integral does not follow the experimental data

after 10 ps because we do not consider reflections in the cumulative integral.

In Figure 5.6 the demagnetization step as a function of THz pump power is plotted.

We observe the linear relation between the demagnetization step and THz pump power

which is expected for the energy dissipation because of the scattering in THz induced

spin current [17].

In order to probe the complete coherent response initiated by the THz pump, one needs

to scan longer as the ferromagnetic resonance (FMR) of CoFeB can be seen on nanosec-

ond timescales. In TELBE, one can probe the dynamics on longer timescales by delaying

the phase between the probe laser and the accelerator master-clock by electronic means.

Figure 5.7 shows the FMR observed for CoFeB, initiated after the initial demagnetiza-

tion.

Similar ultra-fast demagnetization scans were measured for different THz pump frequen-

cies, with electric field values summarized in Table 5.1. The tunable and narrow-band

excitation measurements allows one to study the ultra-fast demagnetization as a func-

tion of excitation frequency and allows us to measure the efficiency of the ultra-fast

demagnetization directly. In Figure 5.8, the demagnetization steps observed for two

different THz pump frequencies (0.7 THz and 1 THz) are plotted. In order to compare


Figure 5.6: Ultra-fast demagnetization observed in CoFeB thin films with THz pumpas a function of pump power.

Figure 5.7: The initiated incoherent demagnetization leads to the excitation of theferromagnetic resonance on nanosecond timescales in CoFeB thin films. (a) the time-domain scan of the FMR mode in CoFeB (b) Fourier transform of the time-domain

scan showing the FMR mode of roughly 7 GHz.


these two curves, we normalize these demagnetization curves with the square of the

electric field used as a pump. The normalization factor used here gives the amount of

energy deposited inside the material by the THz excitation. Upon normalization, we

observed that demagnetization step is frequency dependent and, at 0.7 THz pump, the

demagnetization step is larger than one at 1 THz. The 0.7 THz pump scan looks noisier

than the one at 1 THz because of the different normalization factors used.

Figure 5.8: Ultra-fast demagnetization observed in CoFeB thin films (a) with 0.7THz pump and (b) 1 THz pump. The demagnetization step is lower at 1 THz pumpas compared to demagnetization at 0.7 THz. The noise floor for the 1 THz scan looks

smaller than at 0.7 THz because of the normalization with respect to B2THz.

Figure 5.10 shows the normalized ultra-fast demagnetization observed in CoFeB thin

films over two different TELBE beam-times, taken 6 months apart. In this figure, we

see that demagnetization of CoFeB thin films shows non-monotonous dependence on

THz pump frequency with a peak observed at 0.5 THz. The error bar in the THz

frequency is taken as the bandwidth of the TELBE source (20%). The error in the

demagnetization step is calculated by taking the standard deviation of the measurement

points before time zero, within 1 σ interval. The data point at 0.7 and 0.4 THz has

a larger error bar. This larger error bar could be because of systematic errors in the

measurements. This systematic error could be because of having slightly different THz

pump frequency in different beam-times. The error in such cases is calculated using the

following equation;

δ(∆M) = (δ(∆M1)2 + δ(∆M2)2 + (δ(syst))2)1/2 (5.3)


Figure 5.9: Ultra-fast demagnetization observed in CoFeB thin films as a function ofthe THz pump frequency. The error bars are explained in the text. Modelling of thefrequency dependence of the THz induced demagnetization in CoFeB is done using twocompeting mechanisms; Eliot-Yafet type spin-flip scattering and Drude conductivity

model (black line).

Figure 5.10: Ultra-fast demagnetization observed in CoFeB thin films at 0.7 THzpump. Red data points were measured during March 2017 TELBE beam-time whereas

magenta data points were measured during September 2017 beam-time.


Here δ(∆M1) and δ(∆M2) is calculated by taking the standard deviation of the measure-

ments points before time zero and δ(syst) is the difference in demagnetization observed

in two different beam-times. In order to explain the non-monotonic dependence of de-

magnetization on THz pump frequency, we propose the following mechanisms.

The first mechanism is based on an assumption that defect-driver Eliot-Yafet spin flip

scattering events are the cause for demagnetization in the thin film [17]. Following the

Drude model for free electrons [23, 24], the average distance travelled by a conduction

electron when THz field is applied to the sample is;

x(t) = eE(t)/mω2 (5.4)

where E(t) is an applied electric field, e is the electronic charge and ω is the angular

frequency of the THz pulse, and m is the free electron mass. It corresponds to the

mean free path for electric field of infinite duration. When electron travels because of

the sinusoidal electric field, it gets scattered from the defect site. This scattering will

result in spin-flip and thus in demagnetization (∆M). The magnitude of ∆M can be

estimated from,

∆M = PsfN(εµB2e

) (5.5)

where Psf is spin-flip scattering probability and N is the number of scattering events

which will be proportional to distance travelled by an electron and the density of defects.

Factor εµB2e is spin to charge conversion factor with µB is Bohr magneton and ε is spin

polarization of the material.

The total number of scattering events during time t for which THz electric field is applied

to the sample can be estimated using;

N =

∫ t

0

x(t)

xdefectsI(ζ)dζ (5.6)

where x(t) is average distance travelled by conducting electrons because of the electric

field (E ), given by equation 5.4, xdefect is the average distance between the defects, and

integral gives the current flowing inside the material in the presence of the THz pulse.

Combining equation 5.5 and 5.6 one can write;

∆M ∼ ρdefectsE2(t)

ν2(5.7)


Here, ρdefects = 1/xdef is the density of the defects and ν = ω/2π. This equation shows

that the magnetization is dependent on the density of defects and the square of the

THz field, as observed in ref. [17] and as shown in Figure 5.6. Above equation shows

that the demagnetization of the material will increase as the the frequency of excitation

has decreased. This can be understood as the frequency of THz pump is decreased,

the time for which an electron is travelling is larger making it more susceptible for

spin-flip scattering. This will result in increased demagnetization as the THz pump

frequency is decreased. With this mechanism one can predict the high frequency response

demagnetization observed in CoFeB (above 0.5 THz), see Figure 5.9.

The decrease in demagnetization at lower frequencies is still debated and here two pos-

sible mechanisms are considered. At first the effect of frequency on the efficiency of EY

mechanism considered. In EY mechanism the spin scattering rate (Γs) is proportional

to momentum scattering rate (Γ) [25, 26];

Γs ∝ Γ (5.8)

The Fermi liquid theory, where interacting electrons are considered, predicts the mo-

mentum scattering rate to be [27];

Γ ∼ (E − EF )2 (5.9)

where (E − EF ) is the energy of the accelerated electrons because of the THz electric

field and EF is the Fermi energy. The above equation is valid for weakly interacting

electrons with energy of electrons being very close to the Fermi surface. The energy

provided by the THz excitation is few meV as compared to few eV for the Fermi energy

of the system considered here. Considering equations 5.8 and 5.9, one can predict that

the spin scattering rate (Γs) scales with the square of the energy of the free electron.

In this experiment, the spin scattering rate (Γs) is proportional to the demagnetization

observed in the material, which predicts the demagnetization to scale with the square

of the THz frequency used for excitation.

Psf ∼ ν2 (5.10)

Combining equations 5.7 and 5.10, one can predict the occurrence of the peak in the

frequency dependence of the demagnetization (see Figure 5.9). In Figure 5.9, two func-

tions are used to fit the high frequency data points and low frequency data points. The


exact relation and dependence of these two functions on each other is not yet clear and

would form the basis for future experiments.

Another approach to describe the peak behavior in the Figure 5.9 is based on attempts

to form universal spin-relaxation theory. Spin-relaxation is generally defined using two

different mechanisms with and without inversion symmetry of the system under con-

sideration. The Elliot-Yafet (EY) mechanism is applied for materials with inversion

symmetry where as Dyakonov-Perel mechanisms (DY) is applied for materials which

lacks inversion symmetry. Recently it has been shown that EY and DP are closely re-

lated and each mechanism can be derived in the framework of the other mechanism [28].

In this article authors have suggested a practical and simpler numerical way to calculate

the spin scattering rate. The universal function to calculate the spin scattering rate is

[28],

Γs(Γ) ∼ Γ/(1 + Γ2) (5.11)

here Γs and Γ are measured in the units of spin orbit energies. This equation correctly

predicts the peak in spin scattering rate as a function of momentum scattering rates but

only qualitatively for the experiment discussed in this chapter. One of the key features

of this function is smooth decay at higher frequencies whereas for the current experiment

we observe sharp decay at higher frequencies.

Another mechanism to understand the lowering of demagnetization at lower frequency

is based on the atomistic re-magnetization model [29]. A microscopic model, based on a

3 temperature model (3TM), has been proposed to explain the thermal recovery of the

magnetization. In this article, authors have shown a non-monotonic temporal evolution

of atomic moments and the macroscopic re-magnetization. The timescale involved in

such calculations are of the order of picosecond to nanosecond [2, 29]. In the current

experiment, as the frequency of THz pump is lowered, the amount of time for which spin-

polarized current flows inside the material increases. At sufficiently lower frequencies, the

time for which spin-polarized current flows may become longer than the timescale of the

re-magnetization process. But in the current experiment, the timescale involved is faster

than the one predicted for re-magnetization in ref.[29] and therefore this mechanism is

not considered to explain the non-monotonous dependence of demagnetization on the

THz frequency.

In order to support the claim on the effect of defects/scatterers on the ultra-fast demag-

netization of the sample, new thin films of CoFeB (20 nm) were grown and implanted

with platinum (Pt) and copper (Cu). The implantation of different elements in pristine


CoFeB increases the number of defects in it. The defects with stronger spin-orbit cou-

pling and spin-scattering probability will enhance the spin-flip scattering and may result

in higher demagnetization. Two different elements were chosen for implantation because

of their different spin-orbit strengths. Pt-implanted films are believed to be more ef-

fective for spin-flip scattering because of its higher spin-orbit coupling as compared to

Cu ones. Figure 5.11 shows the demagnetization observed at 1 THz pump for different

samples. One can clearly see that Pt implanted CoFeB shows higher demagnetization as

compared to pristine CoFeB and Cu implanted CoFeB for same the thicknesses. When

the demagnetization of 20 nm thin films were compared with 5 nm films (Figure 5.11,

red dot), one observes that demagnetization is roughly 4 times higher for 5 nm thin films

as compared to 20 nm films. We believe that the reason for smaller demagnetization in

thicker films is because of the lower conductivity of the films.

Figure 5.11: Comparison of normalized demagnetization efficiency at 1 THz for pris-tine CoFeB (5 nm, red dot), pristine CoFeB, Pt-CoFeB, and Cu-CoFeB. The THz spot

size was roughly 700 µm with electric field of 89 kV/cm.


THz induced ultra-fast demagnetization is studied for amorphous CoFeB thin films. We

observe the non-monotonic frequency dependence of ultra-fast demagnetization. To ex-

plain the non-monotonus frequency dependence we propose the mechanism which is a

competition between Eliot-Yafet type scattering spin-flip mechanism and scattering of

the conducting electrons in Drude model. In order to support the Drude conductivity


model for ultra-fast demagnetization, we implanted CoFeB thin films with different el-

ements to introduce the defects. The implanted samples with Pt implantation showed

higher demagnetization as compared with pristine, supports the claim of spin-flip scat-

tering because of higher spin-orbit coupling introduced by Pt implantation.

This study provides an experimental tool to understand the physics of fundamental scat-

tering rates as a function of THz frequency at sub-picosecond timescales. To understand

our experimental work better, a new theoretical framework is expected to be developed.

Our experimental findings will pave the way for new experimental work to develop a

microscopic understanding of ultra-fast magnetization dynamics. This will allow one to

design efficient data storage devices for technological applications.

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CHAPTER 6

THz-Driven Spin Excitation in High Magnetic Fields:

Case of NiO

In this chapter we focus on the study of the THz driven response of spin waves in an-

tiferromagnetic (AFM) NiO. The AFM mode of NiO is excited with high intensity THz

pulses which are resonant with the AFM mode, and probed with the Faraday rotation

technique involving femtosecond laser pulses. At the beginning of the chapter, we in-

troduce the importance of studying the dynamical properties of AFM mode for advance

high frequency spintronics applications. The implemented experimental scheme is then

discussed. The theory of AFM resonance is discussed in brief. In the later phase of the

chapter, the temperature and the field dependence of the observed AFM mode in NiO

in the vicinity of 1 THz are discussed. The measurements reveal two antiferromagnetic

resonance modes which can be distinguished by their characteristic magnetic field de-

pendencies. The observed field dependence of the AFM mode at different temperatures

is discussed on the basis of an eight-sublattice model. Our study indicates that a two-

sublattice model is insufficient for the description of spin dynamics in NiO, while the

magnetic-dipolar interactions and magneto-crystalline anisotropy play important roles.

This chapter is based on the publication:

Wang, Zhe, et al. ”Magnetic field dependence of antiferromagnetic resonance in NiO.” Applied

Physics Letters 112, 25 (2018)

83

84 6. THz-Driven Spin Excitation in High Magnetic Fields: Case of NiO

6.1 Introduction

The fundamental understanding of how fast the magnetic state of a material can be

manipulated for future data storage applications has driven the field of antiferromag-

netic (AFM) based spintronics devices [1, 2]. The absence of macroscopic magnetization

makes AFM-based devices preferred candidates for robust memory storage applications,

rapid switching and manipulation of spins [3–5]. Also as AFM response (magnon mode)

has higher resonant frequencies than ferromagnetic resonance (FMR), it makes them

prime candidates for high frequency spintronics devices. One of the most promising

AFM compounds for device fabrication is Nickel Oxide (NiO) as it is easy to grow in

the form of bulk single crystals as well as in nano-films [6–10]. The magnon mode in

NiO has been shown to be at 1 THz. Current research on NiO focuses on investigat-

ing interesting phenomena, such as the THz magnon dynamics [11] and the Spin Hall

magneto-resistance [12]. In a recent experiment on NiO, coherent control and manip-

ulation of magnon mode was demonstrated [5, 13]. For the development of spintronics

devices operating at higher frequencies, it is important to understand how to manipulate

and control the magnetization state at ultra-fast time scales (∼ 100 fs).

NiO has been studied extensively because of its simpler crystal structure as compared to

other antiferromagnetic materials. NiO is a prototype antiferromanget with a Neel tem-

perature of 523 K. Above the Neel temperature, NiO crystallizes in a centrosymmetric

cubic structure of NaCl while below the Neel temperature to rhombohedral structure by

contracting in one of the four <111> axes. This contraction, as shown in Ref.[14], takes

place due to exchange striction resulting in the formation of four equivalent crystallo-

graphic twin domains. Neutron diffraction experiments have shown that the easy axis

for Ni2+ spins lies in the {111} plane [14, 15] and the spin direction is shifted by 180◦ in

adjacent planes (Figure 6.1). The magnetic moments are ferromagnetically aligned on

the {111} plane and they antiferromagnetically couple with the magnetic moments in

neighboring {111} planes. The predominant spin interaction is an AFM exchange be-

tween the next nearest neighbor Ni2+ ions, which are linked by a super-exchange path of

the 180◦ Ni2+-O2−-Ni2+ configuration. Due to additional magnetic anisotropy, the spins

are oriented along one of the three <112> axes, which corresponds to three equivalent

spin domains in each crystallographic domain [16].

The low-energy dynamic properties of the NiO spin degrees of freedom are characterized

by antiferromagnetic spin-wave excitations as revealed by inelastic neutron scattering

[14]. They were explained based on a two-sublattice antiferromagnetic model [14, 15, 17].

Further experimental studies, especially based on Raman and Brillouin spectroscopy,

revealed five antiferromagnetic magnon modes close to zero wave vector [18, 19], thereby


suggesting the magnetic structure should to be more complex than a two-sublattice

antiferromagnet. These observations were satisfactorily explained by an eight-sublattice

model [18], which has been further extended to study the dependence of the three lowest-

lying modes (below 0.5 THz) on an external magnetic field by Brillouin spectroscopy

[20].

So far, however, it has remained unclear how the two highest-lying modes would evolve

in an external magnetic field. Experimentally, one high-energy mode at ∼ 1 THz has

recently been shown to be coherently controllable by intense THz electromagnetic pulses

at room temperature [13]. Here, taking advantage of a new type of narrow-band tunable

superradiant THz source [21], we selectively excite these resonances and measure their

frequency as a function of temperature and magnetic field. While at room temperature,

only one antiferromagnetic spin resonance mode with a nonlinear dependence on the ex-

ternal magnetic field is present, an additional mode appears below 250 K which exhibits

a much weaker field dependence. Calculations based on an eight-sublattice model of the

spin interactions in NiO were performed [18, 20], which can describe the observed field

dependencies of the two high-frequency antiferromagnetic spin resonance modes.


In order to selectively excite the AFM mode in NiO and to study its dynamics, the

narrow band THz pump Faraday rotation probe technique was employed. Narrow-band

THz pulses generated at the TELBE facility [21], centered at 1 THz, were used to

selectively excite the magnon mode. Probe pulses were generated from a Ti:sapphire

laser system with 100 fs pulse duration. The measurement of spin deflection is obtained

by recording the rotation of probe polarization utilizing Faraday effect. The schematic

of the experimental set up is shown in Figure 6.2. The electric field profile of the 1 THz

pump and its frequency spectrum is shown in Figure 6.3. The THz pump has a maximum

electric field of ∼ 60 kV/cm with 20 % bandwidth. 1 THz pump pulses were focused

on a 50 µm thick free standing NiO with collinear probe pulses. The change in probe

polarization was measured with a pair of balanced photo-diodes. By varying the time

delay between pump and probe pulses, we determined the dynamics of the AFM state.

The measurements were also done at varying temperatures from 3 K to 280 K along

with external fields up to 10 T in a commercial Oxford Instrument split coil magnet.

The magnetic field was applied parallel to the incident laser beam and perpendicular

to a (111) surface of a single crystalline NiO sample. For this field orientation, the

Ni moments within the different antiferromagnetic domains remain stabilized along the

< 112 > directions in finite fields.


Figure 6.1: Illustration of the crystallographic and magnetic structure of NiO, basedon an eight sub-lattice model. Antiferromagnetic structure consists of ferromagneticallyaligned spins along the (111) planes which are alternatively stacked along the perpen-dicular direction. Spins of the Ni2+ ions are along the <112> directions, as indicatedby the arrows. The dominant spin interaction is the super-exchange between the next-nearest-neighbor Ni2+ ions via the 180◦ Ni2+-O2−-Ni2+ configuration as denoted by

J.

The AFM mode in antiferromagnetic material can be explained in general, using the two

sub-lattice model, by the theory of Keffer and Kittel [22]. In typical antiferromagnetic

materials one has two sub-lattices with magnetization M 1 and M 2. The equation of

motion for the two magnetizations are given by the following equations,

dM 1

dt= −γ

[M 1 ×

(H 0 + HA − λH 2

)](6.1)

dM 2

dt= −γ

[M 2 ×

(H 0 −HA − λH 1

)](6.2)

here, H 0 is the static magnetic field, HA is the uniaxial anisotropy, and H exch 1,2 =

λM2,1 is the exchange field. The anisotropy field acts on two sub-lattices in the oppo-

site direction. If H 0 and HA are parallel and in the z direction, then the resonance


THz

delay

2 WPPD

PDsample

H

polarizer

magneto opticcryostat(3 K, 10 T)

800 nm

Figure 6.2: Sketch of the THz pump Faraday rotation probe technique equippedwith a cryomagnet up to 10 T field. The THz pulses (red) are focused on the sampleat normal incidence. 800 nm probe pulses (green) are collinear with THz pulses. Thetransient change in the magnetization of the sample is probed by the Faraday rotationof the probe polarization with a timing accuracy of 12 fs. λ

2 , WP and PD are thehalf-wave plate, the Wollaston prism and the photo-diodes respectively.

Figure 6.3: (a) Time domain signal of the 1 THz multi-cycle pump pulse. (b) Powerspectrum of the pump pulse obtained by Fourier transformation. Above 1.1 THz the

signal is strongly suppressed by water absorption.


frequencies are as given below [17],

ωres = ±γH0 ± γ[HA

(2HE +HA

)] 12

(6.3)

Equation 6.3 shows that even for zero external field, there is a finite frequency of AFM

mode, determined by the exchange and anisotropy fields. In the absence of an external

field, the motion of magnetization is governed by four frequency modes which can be

grouped into two distinct modes as depicted in Figure 6.4.

Figure 6.4: Illustration of the two distinct magnetic modes in antiferromangetic res-onance. H0 the is static magnetic field, M1,2 is the magnetization of the two sub-lattices of the antiferromagnetic material, HA is the uniaxial magnetic anisotropy. Fig-

ure adapted from [22]

Both of the magnetizations rotate around the effective magnetization, determined by

the axis of an uniaxial anisotropy field. Observing from the positive z direction, both

modes either rotate in clockwise or anti clockwise direction, as shown in Figure 6.4(a).

The same holds true for the other two modes as depicted in Figure 6.4(b). The only

difference between these two modes is the stiff cone angle η = θ2/θ1. For modes shown

in Figure 6.4(a), η is smaller than 1, whereas for modes shown in Figure 6.4(b) it is

larger than 1. The η is a material dependent property given by Ref. [22].

η =[HA +HE + (HA(2HE +HA))1/2

]/HE (6.4)


Here HA is the anisotropy field and HE is the exchange field. When the external field

H0 is applied, the resonance frequency of one mode increases by the factor γµ0H0,

while it decreases by same amount for the other mode. This model, based on two

sub-lattices, fails to explain the five distinct AFM modes observed in NiO [18, 19].

These observations were satisfactorily discussed in the context of an eight-sublattice

model [18], which has been further extended to study the field dependence of the three

lowest-lying modes (below 0.5 THz) observed by Brillouin spectroscopy in an external

magnetic field [20]. So far it remains unclear how the two highest-lying modes would

evolve in an external magnetic field, although experimentally one high-energy mode has

been proven to be coherently controllable by intense THz electromagnetic fields at room

temperature. Here, using the TELBE facility, one excites the AFM mode resonantly.

The THz magnetic field and electron spins interact via Zeeman torque and collectively

excite the magnon mode, as discussed in reference [23].

τ = γS ×BTHz (6.5)

Here, γ is the gyro-magnetic constant for electron spin S and BTHz denotes the magnetic

field component of the THz transient. The projection of the induced magnetization M(t)

along the propagation direction (ek) of the NIR probe causes circular birefringence and

rotates the probe polarization by an angle

θF(t) = V l < ek.M (t) > (6.6)

where V is the Verdet constant of the material and l is a distance travelled by the NIR

probe inside the material.


6.3.1 Temperature dependence of AFM mode

Figure 6.5a shows the recorded Faraday rotation time scan for NiO at 280 K without

external field and in the air. The FFT of the time scans (Figure 6.5b) shows the ∼1 THz mode which corresponds to the high frequency spin (AFM) mode in NiO. The

observed time trace of Faraday rotation is free from any background heating as usually

observed in all-optical pump probe techniques. In Figure 6.5a, we see the beating effect

which can be understood as the superposition of the 1 THz AFM mode and a water


absorption line present at around 1 THz, which lies within the bandwidth of the THz

pump.

Figure 6.5: Typical transient Faraday measurement for NiO obtained at 280 K. Thecoherent oscillation of the magnetization is probed by the determination of the polar-ization change. (a) Time domain trace of the Faraday rotation at room temperature.

(b) Power spectrum of the Faraday rotation signal.

The measurements of the temperature dependence at zero field have been performed

for various temperatures between 3.3 and 280 K [see Figure 6.6(a)]. At each temper-

ature, the amplitude spectrum derived from Fourier transformation of the transient

Faraday signal exhibits a single peak with a well-defined position. The peak positions

are shown in Figure 6.6(b) as a function of temperature with the error bars indicating

the full width at half maximum (FWHM) of the peaks. With decreasing temperature

from 280 K, the peak position shifts to higher frequencies monotonically. This harden-

ing of the peak frequency is consistent with previous measurements of the temperature

dependence [24], which reflects an increase in the spontaneous magnetization of each

sublattice with decreasing temperature [22]. It is worth noting that in our experiment,

the higher-frequency components are affected by water absorption lines. Thus, for the

low-temperature measurements, the obtained resonance frequencies have larger uncer-

tainty. The 1.29 THz mode, observed by Raman spectroscopy at low temperatures [19],

was not observed because this mode can not be resonantly pumped by the THz pump

at 1 THz with 20 % bandwidth.

The observed temperature dependence of the AFM mode in NiO can be explained by

equation [25, 26],

T

TN= F (σ)

[1 + 6S2σ2 j

J

](6.7)

where F (σ) = −3NkBSσ[(S + 1)(δS∗/δσ)T

]−1, N is the total amount of the spin,

kB is the Boltzmann constant, J is the exchange interaction constant, j/J defines the


Figure 6.6: Temperature dependence of the magnon mode in NiO. (a) Amplitudespectra obtained from Fourier transformation of the time-domain signals of Faradayrotation angle at various temperatures. The shaded area in the high-frequency limitindicates the spectral range where the THz radiation is strongly reduced by waterabsorption. (b) Temperature dependence of the peak frequencies in (a). Error bars

indicate the apparent full widths at the half maxima.

magnitude of the exchange interactions, S is the total spin angular momentum of the

system under consideration, S∗ is the spin entropy of the system under consideration

and σ is normalized magnetization M/M0 with M0 being magnetization at 0 K.

6.3.2 Field dependence of AFM mode

The THz-pump Faraday-rotation probe experiments have been extended to study the

effects of external magnetic fields at different temperatures. Figure 6.7 shows the field

dependence of zero field frequency mode at three different temperatures. The zero

field mode shifts to higher frequencies with increasing external field and decreasing

temperature. Figures 6.7a, 6,7b, and 6.7c show the obtained amplitude spectra in various

applied magnetic fields up to 10 T at 280 K, 253 K, and 200 K, respectively. At 280 K, the

peak position of the single peak continuously shifts to higher frequencies with increasing

magnetic fields. The frequencies at the peak positions are shown in Figure 6.7b, which

clearly exhibit a nonlinear increase with increasing external magnetic field. Such a

nonlinear field dependence has been predicted for antiferromagnets in which an in-plane

anisotropy is also important in addition to the uniaxial anisotropy. In contrast, at 253 K

and 200 K, a second peak appears for magnetic fields above 6 T. While the observed peak

position is plotted as a function of applied magnetic field [Figure 6.7 (b,d,f)], the higher

frequency mode exhibits non-linear dependence on applied filed where as the other mode

is almost field independent. It is worth noting that at zero field, Raman spectroscopy

has also revealed two modes at low temperatures, consistent with our observations.


Figure 6.7: Magnetic field dependence at (a,b) 280 K, (c,d) 253 K and (e,f) 200K. While only one mode is observed at 280 K, at the lower temperatures two modesare resolved. The qualitatively different field-dependencies of the two modes are inagreement with the predicted behaviors for mode A and mode B (see Figure 6.8 and

Eq.(6.8)). In (b,d,f), the solid lines are guides for the eyes.


To understand the field-dependent behavior, our collaborators performed calculations of

an eight-sublattice model, as described in Ref. [18, 20]. In contrast to the common two-

sublattice model [14, 15], which cannot explain our observations, we show that the eight-

sublattice model correctly predicts not only the two antiferromagnetic modes around 1

THz, but also their characteristic field dependencies. In the eight-sublattice model,

the magnetic interactions comprise the antiferromagnetic exchange interactions Eexch,

magnetic-dipole interactions Edip, magnetic anisotropy Eani, and a Zeeman interaction

with an external magnetic field EZeeman,

E = Edip + Eexch + Eani + EZeeman (6.8)

The exchange energy term is given by,

Eexch = J(m1 ·m2 + m3 ·m4 + m5 ·m6 + m7 ·m8

)(6.9)

with J being the antiferromagnetic coupling constant. The exchange energy term couples

only the sublattices 1 and 2, 3 and 4 , 5 and 6, and 7 and 8.

Edip can be written as,

Edip = D∑i

[∑j>i

m i.T ij.m j

](6.10)

The magnitude of D is exclusively determined by the magnetic moment of each Ni atom

and lattice constant, −4 × 104 erg/cm3. The dipole energy term defines the coupling

between four AF lattices in ferromagnetically aligned (111) planes, but it does not

account for alignment of spins in any preferred axis in this plane. In order to do so the

magneto-crystalline anisotropy term is introduced as follows,

Eani = K∑i

(mixmiymiz)2 (6.11)

The magneto-crystalline constant K < 0 favors spins aligning along the <111> direc-

tions. A compromise with the stronger dipolar interactions leads to the orientation of

spins close to the [112] direction. This anisotropy favors alignment along <111> di-

rections, which acts in the opposite sense to the dipolar term. In order to model the

experimentally observed frequencies, the magnitude of K necessarily is small and has a

small effect on the (111) easy planes [18].

In addition to this, the externally applied magnetic field interacts with each sublattice

with the Zeeman term as shown below.


EZeeman = −gµBH ·∑i

m i (6.12)

The equilibrium values corresponding to the eight sub-lattices are found by direct min-

imization of the free-energy density given in equation (6.9). The magnetization of each

sub-lattice is given by,

mi = ((sin θi cosφi), (sin θi sinφi), (cos θi)) (6.13)

Here polar coordinates are used to define the magnetization of the sub-lattice with

θi being the polar angle of the magnetization with respect to Z axis which is normal

to the surface of NiO, and φi is the azimuth angle in the surface plane. Following

references[27, 28], a matrix is constructed from the second derivatives of the energy

Eθ(φ)iφ(θ)j with respect to magnetization angles θi and φj , in which the matrix elements

Bn,m are given by [20],

B2i−1,2j−1 = Eθ(i)φ(j)/ sin θj (6.14)

B2i,2j−1 = Eφ(i)φ(j)/ sin θi sin θj (6.15)

B2i,2j = −Eφ(i)θ(j)/ sin θi (6.16)

B2i−1,2j = −Eφ(i)θ(j) (6.17)

By solving eigenvalues dk of the matrix, frequencies of the antiferromagnetic modes are

obtained as ωk = iγdk/M ,

where γ is the gyro-magnetic ratio (98 cm−1/Oe for Ni) [29] and M is the saturation

magnetization of each sublattice M = µB/a3 = 128G.

This model, essentially focusing on the zero-temperature spin dynamics, has successfully

described the experimentally observed modes by Raman and Brillouin spectroscopy at

the lowest temperatures [20], and the field dependencies of the three lower-lying modes

[18]. According to this model, application of a high external magnetic field (H > 2

T) can lead to the instability of the spin domains in most situations. For example, if

the external magnetic field is applied along the spin orientation of one spin domain, i.e.

H ‖ [112] , the zero-field magnetic structure becomes unstable above ∼ 1 T. A quite

stable configuration is found for the external field applied along the [111] direction,

which is exactly the orientation of a crystallographic domain that is perpendicular to

the sample surface [23]. In this case, the spins are stabilized to be oriented along the


<112> directions, meaning that the zero-field spin configuration remains stable at high

fields. Thus, our theoretical results are intrinsic to a single spin domain, which are

presented in Figure 6.8 for the two higher-lying modes (i.e. 1.29 THz and 1.15 THz),

where J = 8.36 ×108 erg/cm3, D = −4.4 × 104 erg/cm3, K = 9 × 104 erg/cm3, and

the value of Lande g-factor for the spin Ni2+ ions is taken as 2 [14, 20]. While the 1.15

THz mode is almost field-independent up to 10 T, because the oscillating sub-lattice

magnetizations of this mode have larger components along the <110> directions which

is perpendicular to the applied field. In contrast, the 1.29 THz mode evidently shifts to

higher frequencies with increasing magnetic field.

Upon Comparison with the experimental observations, there is agreement on the field

dependencies of the two resonance modes. Naturally we assume that the thermal exci-

tations [15] do not qualitatively alter the dependencies on an external magnetic field.

Thus, we can assign the mode with nonlinear field dependence as the mode A of 1.29

THz obtained from the model calculation (see Figure 6.8), while the other mode, ob-

served at 253 and 200 K and almost field-independent up to 10 T (see Figure 6.7 and

Figure 6.8), should correspond to the mode B of 1.15 THz. It should be noted that

the agreement between eight sub-lattice model calculations and the experimental ob-

servations is a qualitative one. In order to have quantitative agreement between them,

one needs to do the theoretical calculations at finite temperatures. With the current

0 K calculations it is possible to adjust the free parameter and overlay calculations on

the experimental observations but it does not give any additional information about the

calculations.


The coherent THz control of the AFM spin mode in NiO has been studied using superra-

diant THz radiation as a function of temperature and magnetic field. In high magnetic

fields (H > 6 T) and at lower temperatures (T ≤ 253 K), two different spin modes have

been resolved with distinguished field dependencies. By performing calculations of an

eight-sublattice model, the two modes are identified by their characteristic dependencies

on the external magnetic fields. Thus, besides the antiferromagnetic exchange interac-

tions of the Ni spins, our work has established that magnetic dipolar interactions and

magneto-crystalline anisotropy are crucial for a proper description of the spin dynamics

in the canonical antiferromagnet NiO. From an applied viewpoint, the existence of two

modes with tunable frequency difference could open up new possibilities for control over

antiferromagnetic order through individual or combined resonant pumping of the two

modes. This work paves the way for studying non-equilibrium phenomenon driven by


Figure 6.8: Field dependence of the higher-energy spin modes mode A at 1.29 THz(red) and mode B at 1.15 THz (blue) obtained from the eight-sublattice model [Eq.

6.8], for the external magnetic field applied along the [111] direction

intense THz fields at low temperatures and high magnetic fields based on high repetition

rate superradiant sources.

6.5 Bibliography

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[22] F. Keffer and C. Kittel, “Theory of antiferromagnetic resonance,” Physical Review,

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[23] T. Kampfrath, “T. kampfrath, a. sell, g. klatt, a. pashkin, s. mahrlein, t. dekorsy,

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the Seventh Conference on Magnetism and Magnetic Materials, pp. 1248–1253,

Springer, 1962.

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magnetic resonance in exchange-coupled Co/Ru/Co trilayer structures,” Physical

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lands, 1980.

Summary

The advances in spintronics have seen a great revolution in technology in the last few

decades. In order to develop spintronics further into high-frequency regime (at sub-

picosecond timescale or at THz frequencies), it is important to study spin-dependent

physical properties of magnetic materials at such high-frequency regime. The work

described in this thesis is a contribution towards the understanding of the physics behind

the high-speed ultra-fast spintronics.

Laser-driven tunable, narrow-band THz emission from ferrimagnetic Heusler

alloys. First, we study Mn3-XGa ferrimagnetic thin films for laser-driven THz emission.

We observe the tunable, narrow -band in the range of 0.15 THz - 0.5 THz as a function of

Mn content, temperature, and applied magnetic field. In this work we emphasis on the

THz emission spectroscopy technique for characterization of magnetization dynamics

in the sub-THz frequency regime. We observed that THz emission spectroscopy is an

efficient technique to study ferromagnetic modes as compared to time-resolved magneto-

optical probe techniques in the sub-THz frequency range. This project also resulted in

THz emission spectroscopy end-station which allowed us to do interesting scientific and

technologically relevant experiments.

This work shows that Mn3-XGa thin films can be used as a free layer in spin transfer

torque devices which will allow using these devices in the THz frequency range. The

frequency of such devices can be further increased by changing the magnetic properties

of these films or with atomic substitutions. One can also use these materials for making

an on-chip narrow-band, tunable THz source.

THz induced ultra-fast demagnetization in amorphous CoFeB. This experi-

ment allows us to study the frequency dependence of ultra-fast demagnetization in THz

regime. The time scales involved in this experiment are very similar to fundamen-

tal timescales of scattering processes, which allows to study spin-dependent scattering

events and its effect on magnetization dynamics in sub-picosecond timescale. The non-

monotonic dependence of ultra-fast demagnetization on the THz pump frequency is

99

100 Summary

explained using the Elliot-Yafet type spin-flip scattering mechanism and Drude conduc-

tivity model. This type of experiments allows one to study the fundamental physics at

very short timescales.

Such experiments will allow us to study electron, spin, and phonon dynamics at sub-

picosecond timescale which is very important to understand spin transport at such ultra-

short timescales. Another importance of this experiment would be to study the effect

of spin-orbit coupling on spin transport at a sub-picosecond timescale to design efficient

data storage devices.

THz control of antiferromangetic mode in NiO. In this experiment, we use an

intense THz pump to resonantly excite the antiferromagnetic (AFM) mode in NiO. The

resonant excitation allows us to study the AFM mode as a function of temperature

and externally applied magnetic field. A new magnetic mode was observed and it was

shown that the two sub-lattice model is not enough to explain the observed results. We

used more detailed eight sub-lattice model to explain our results. We also established

that dipolar-interactions and magneto-crystalline anisotropy are of great importance to

describe spin dynamics accurately.

Experiments of these kinds are essential to gain control over the magnetic order of the

material. The ultra-fast switching of magnetic order at THz frequencies will be helpful

for spintronics memory devices.

To summarize, this work discusses the magnetization dynamics at THz frequency range

which will enable to understand fundamental physics at play at sub-picosecond timescales.

This work may provide a pathway to deepen our knowledge of spin dynamics at speeds

which are technologically relevant for efficient spintronics devices.

Samenvatting

De vooruitgang in de spintronica heeft de afgelopen decennia een grote revolutie in

de technologie laten zien. Om spintronica verder te ontwikkelen naar hogere frequenties

(sub-picoseconde tijdschaal ofwel THz frequenties) is het belangrijk om spin-afhankelijke

fysische eigenschappen van magnetische materialen te bestuderen op deze hoge frequen-

ties. Het werk dat in dit proefschrift is beschreven, is een bijdrage aan het begrijpen

van de fysica achter ultra-snelle spintronica.

Door laser aangedreven afstembare, nauwbandige THz emissie van ferrimag-

netische Heusler legeringen. Eerst bestuderen we Mn3-xGa ferrimagnetische dunne

films voor laser aangedreven THz emissie. We bekijken de afstembare, nauwbandige

emissie in het bereik van 0.15-0.5 THz als functie van het Mn-gehalte, de temperatuur

en het toegepaste magnetische veld. In dit werk leggen we de nadruk op de THz emissie

spectroscopie techniek voor de karakterisatie van de magnetische dynamica in het sub-

THz frequentie bereik. We zagen dat THz emissie spectroscopie een efficinte techniek

is om ferromagnetisches modes te bestuderen, dit in vergelijking met tijds-opgeloste

magneto-optische probe technieken in het sub-THz frequentie bereik. Dit project re-

sulteerde ook in een THz emissie spectroscopie eindstation, wat ons in staat stelde om

wetenschappelijk interessante en technologisch relevante experimenten te doen.

Dit werk laat zien dat Mn3-xGa dunne films gebruikt kunnen worden als een vrije laag

in spinoverdracht torsie devices, waarmee deze devices in het THz frequentie bereik

gebruikt kunnen worden. De frequentie van zulke devices kan verder worden verhoogd

door het veranderen van de magnetische eigenschappen van deze films of met atomaire

substituties. Men kan deze materialen ook gebruiken voor een on-chip, nauwbandige,

afstembare THz bron.

Door THz genduceerde, ultrasnelle demagnetisatie in amorf CoFeB. Met dit

experiment kunnen we de frequentie afhankelijkheid van de ultra-snelle demagnetisatie in

het THz regime bestuderen. De tijdschalen in dit experiment zijn van dezelfde grootte als

de fundamentele tijdschalen van verstrooiingsprocessen, wat het mogelijk maakt om spin-

afhankelijke verstrooiing en het effect ervan op sub-picoseconde magnetisatie dynamica

101

102 Samenvatting

te bestuderen. De niet-monotone afhankelijkheid van de ultrasnelle demagnetisatie op de

THz pomp frequentie wordt uitgelegd met het Elliot-Yafet type spin-flip verstrooiing en

het Drude geleidingsmodel. Met dit type experimenten kan men de fundamentele fysica

bestuderen op zeer korte tijdschalen. Door dit soort experimenten kunnen we elektron,

spin en foton dynamica bestuderen op een sub-picoseconde tijdschaal, wat zeer belangrijk

is om spintransport op zulke ultrasnelle tijdschalen te begrijpen. Een ander belangrijk

aspect van dit experiment is het bestuderen van het effect van spinbaankoppeling op

spintransport in het sub-picoseconde regime, om efficinte dataopslag devices te kunnen

ontwerpen.

THz controle van de antiferromagnetische mode in NiO. In dit experiment

gebruiken we een intense THz pomp om de antiferromagnetisch (AFM) mode in NiO

resonant te exciteren. Door de resonante excitatie kunnen we de AFM mode bestud-

eren als functie van temperatuur en extern toegepast magnetisch veld. We vonden een

nieuwe magnetische mode en we toonden aan dat het tweevoudige sub-rooster model niet

genoeg is om de waargenomen resultaten te verklaren. We gebruikten een meer gede-

tailleerd achtvoudig sub-rooster model, om de resultaten te verklaren. We hebben ook

vastgesteld dat dipolaire interacties en magneto- kristallijne anisotropie van groot be-

lang zijn om spin dynamica nauwkeurig te kunnen beschrijven. Dit soort experimenten

zijn essentieel om controle te krijgen over de magnetische ordening van het materiaal.

Het ultrasnel schakelen van de magnetische ordening op THz frequenties zal nuttig zijn

voor spintronica geheugendevices.

Samenvattend, dit werk behandelt de magnetisatie dynamica op THz frequenties, wat

het mogelijk zal maken de fundamentele fysica te begrijpen, die optreedt op sub-picoseconde

tijdschalen. Dit werk kan een pad bieden om onze kennis van spindynamiek te verdiepen

met snelheden die technologisch relevant zijn voor efficinte spintronics-apparaten.

Acknowledgements

This thesis concludes my Ph.D. life, spanning over last 4 years. This journey would have

not been possible without contributions from several people and organizations. I would

like to thank the number of people who have contributed to this journey and made it a

memorable one.

First and foremost, I would like to thank my supervisors Prof. Tamalika Banerjee, Dr.

Micheal Gensch and Dr. Ra’anan Tobey.

Prof. Tamalika Banerjee, thank you for accepting to be my supervisor. Even though our

field of scientific research is different, you always helped me to stay on schedule with my

work. I thank you for all the administrative help and suggestions regarding my thesis.

Next, I would like to thank Dr, Micheal Gensch for giving me an opportunity to explore

the possibilities with working with high field THz sources at large scale facilities. I

very much appreciated the open door access to your office to discuss scientific and

administrative questions. I am still intrigued by your capabilities to work longer hours

during our TELBE beam-time.

I would also like to express my great appreciation to Dr. Ra’anan Tobey. It was

inspiring to see your dedication to scientific research and the ability to come up with

smart experimental ideas in an optics lab. I will always remember the ”Make your own

Laser” practicum and ”the fearsome” competition we had to get higher TEM modes.

Sergey, I am very grateful for all the experimental skills you taught me and your willing-

ness to discuss scientific questions at lengths. My Ph.D. work would have not been the

same without your support and encouragement. I wish I would have contributed more

to your collection of the coins.

I would like to thank prof. Maxim Pchenitchnikov for his inputs about spectroscopic

techniques and ever enthusiastic nature. I appreciate your great teaching ability. Your

talk on ”how to give a presentation” has helped me a lot.

103

104 Acknowledgements

I thank all my fellow lab mates in High field THz driven phenomenon group; Bert, Jan,

Zhe, Thales, Min, Medo, Frederik for all our scientific, and ”not so scientific” discussions.

I enjoyed working with you all on different projects during our long, sleepless TELBE

shifts. I would also like to thank all my Optical Condensed Matter group colleagues;

Julius, Chia-Lin, Qi, Bjrn, Oleg, Evgenia, Arthur. Thank you for the great working

atmosphere and outings we had.

The scientific work would not be possible without continuous support from technicians

and group secretaries. I would like to offer my special thanks to Foppe for always being

there to solve all technical issues, especially providing me with Dutch translation of the

summary for my thesis. I would also like to express my gratitude to Petra and Katrin

for their strong support with administrative work. I would also like to thank Jeannette

and Henriet for their valuable support to make my work life easier.

Dr. Alina Deac helped me to learn magnetism. I thank you for reminding me that

there is a need for researchers with great Humor. I appreciate your kind-hearted nature.

Thank you for letting me participate in your group meetings. I thank Ciaran, Alexandra,

and Serhii for their fruitful collaboration on TRANSPIRE project. Anna, thanks for all

the help during our collaboration. I would also like to thank Dr. Stefano Bonetti for

introducing me to the field of magnetization dynamics. You are a very good person and

a researcher. I hope to continue our collaboration in the future. Prof. J. M. D. Coey,

Prof. Plamen Stamenov, and Prof. Arne Brataas are thanked for their valuable inputs

during our collaboration.

Fasil, I appreciate your kind and hardworking nature. You encouraged me to plan my

work properly and helped me to understand the importance of time management. I

thank you for your guidance and for being patient during my master’s thesis. Sid babu,

thanks for all the coffee and late night Ghazals. I enjoyed our scientific discussions a

lot. I wish you all the best with the future. Mallik, Ivan, Jing, Sander, Subir, Saurabh,

Gaurav, Juan, Martijn, Juliana, Jasper, Paul, Joost; thank you for your help during my

masters in FND group.

I have been fortunate to be part of the top masters cohort 2012-2014. My classmates,

who became close friends very soon, helped me to get started with life in Groningen.

They helped to overcome all sorts of cultural and social difficulties, which I faced in the

first few months. Musty, I thank you for introducing me to the rich culture of Africa and

for your unfailing presence and willingness to talk about life. Thank you for teaching me

how to ask for a candid response. Jamo, I thank you for all the educational time we had

during our masters. Learning quantum mechanics and crystal symmetries were lot more

fun with you. I appreciate your kind and modest nature. I also want to thank Alessio

for introducing me to Italian culture and warmly including me as part of his family.

Acknowledgements 105

Machteld, thank you for teaching me Dutch culture. The ”nieuwjaarsduik” was amazing,

thanks for the experience. I wish you and Tom a lot of success in future life. Koen, thank

you for your help during our study sessions, especially during the mathematics course,

which we took together. I will always cherish our small dutch lunches with pindakass

and bananas. Sampson, Kumar, Bert, Maria, Safdar, Jos, Gerjan, and Kostya; thank

you for all the fun and memories of our master studies.

Alok, you have been the director of my social and interpersonal life. You have helped

me through tough times and provided me with a piece of advice whenever required. I

thank you for all your help and support. Mayuri, thanks for being the Annapurna devi

of my life in the Netherlands. You are a gem of a person. I wish you a lot of success

with ”Talent Transmitter”.

Marcos, you have been the go-to-guy to discuss science, music, and life in general. Thank

you for the adventurous and fun time we had. I wish to continue our collaboration on

science and life. Marloes, you are a great person. Thank you for all the fun activities

and support during my last phase of thesis writing. I wish you and Marcos a lot of

success in the future.

Ankur, I cannot thank you enough for everything that you have done for me. You have

taken care of me in my worst times. You always tried to keep me sane, whether it is

about career or about personal life. Because of you, I met awesome people on the 8th

floor of Kornoeljestraat, the group we named as ”a family away from home”. Mirka,

Alex (the French one), Yvette, Romain, Ana, Anna, Elisa, Qais, Mihaela, Alex; thank

you guys for taking care of me. I had a wonderful time with you all.

Garima, I am fortunate to have met you in Groningen. I do not have enough words

to thank you for always being there for me. You have been the best partner to go to

parties/events. I still can not understand how we two managed to be (in)sane.

Shayera, I still can not believe that you are not with us anymore. I miss you a lot. I will

always remember you as a friend with whom I felt most secure. Rest in peace, Shayera.

I express my gratitude towards my friends from Groningen. Lara, Bruno, Marta, Ana,

Agnes thank you for all music festivals and social gatherings. Agnes, I remember meeting

you in one of the ESN parties and then we became housemates. I had a lot of fun

with you in Groningen, Marseilles, and Vienna. I hope to increase this list further,

maybe to include India. I thank my ”mango group”, Balaji and Ajinkya. Thank you

guys for lazy weekends and for endlessly binge-watching Shaktiman together. I thank

Sarrvesh, Aarti, Simone, Dipayan, Nikki, and Systze for amazing dinners and dancing

evenings. RP, Tarun, Arijit, Pulkesh, Millon, Ketan, Ali, Ashish, Gabriele; thank you

for all the fun that we had together. Tarun, I cannot forget your capabilities to beat

106 Acknowledgements

Wikipedia. I would like to thank all my friends whom I met through different students

organizations in Groningen. Especially I would like to thank Mary (we have to conquer

the 6th country soon!), Rosa-Lin, Kaisa, Mike, Ekta, Felipe, Elise, Lievin, Silvana,

Manu, Andres, Angelica, Diana, Amina, Turhan, Navid. You guys made my student

life much more fun and memorable. Manasi, Abhishek, Renuka, Uttara, Sandesh, Amit,

Padmnabh, Yogita, Aparajeeta, Swaresh; thank you for your support.

In Dresden, I became part of the RCD group and met a lot of amazing people. Ani,

Rahul A, Rahul, Uddi, Siva, Raghav thanks for all the cricketing actions and fun

evenings. Nandu, Prbs thanks for introducing me to football, #YNWA. Akanksha,

Manasi, Lokesh, Atul, Tohid, Guru, Vignesh, Vaibhav, Sami thanks for all the inter-

actions in Dresden and all the best for future. The journey to HZDR is not possible

without bus line 261 and friends you make on that journey. Kritee, Tanmaya, Swati,

Cem, Garima; I thank you for all the fun activities we have done together. You guys

made my HZDR life easier.

Prabhu Sir, thank you for teaching me how to be a researcher. Thank you for all the

motivation that you have given me to pursue my Ph.D. I wish you and FOTON lab a

lot of success.

At last, I would like to thank most special people in my life. Mom, I cannot thank you

enough for your support and patience you have shown to fulfill my dreams. After dad

passed away, you tried to stay strong so that I can complete my Ph.D. abroad. Tai,

Anil, Kirti; thank you all for taking care of mom in my absence. I am happy to see you

all grown mature and taking care of each other in the absence of dad and uncle. Uncle,

you have been my favorite person. I still cannot believe that I lost you and Dad in 3

months time. I wish you both were with us to see me graduate. I miss you both.

Dad, You always gave me the freedom to choose my career. You taught me how to be

nice with people, I think I have tried my best to do that. I miss you a lot. I dedicate

this thesis to you.

It is not possible to mention all the people who have helped in some way or other to

fulfill my dream to get a Ph.D. I thank you all for your support and belief in me.

List of publications

Publications described in this thesis

1. “Magnetic field dependence of antiferromagnetic resonance in NiO”,

Zhe Wang, S. Kovalev, N. Awari, Min Chen, S. Germanskiy, B. Green, J.-C. Dein-

ert, T. Kampfrath, J. Milano, and M. Gensch

Applied Physics Letters, 112, 25 (2018)

2. “Narrow-band tunable terahertz emission from ferrimagnetic Mn3-xGa thin films”,

N. Awari, S. Kovalev, C. Fowley, K. Rode, R. A. Gallardo, Y.-C. Lau, D. Betto,

N. Thiyagarajah, B. Green, O. Yildirim, J. Lindner, J. Fassbender, J. M. D. Coey,

A. M. Deac, and M. Gensch

Applied Physics Letters, 109, 3 (2016)

3. “Speed limits of ultrafast demagnetization”,

N. Awari, S. Kovalev, D. Polley, K. Neeraj, M. Hudl, A. Semisalova, B. Green, P.

Arekapudi, S.-H. Yang, M. Samant, S.S.P. Parkin, O. Hellwig, M. Gensch, and S.

Bonetti

In preparation

4. “Continuously Tunable Spintronic Emission in the sub-THz Range”,

N. Awari, A. Titova, S. Kovalev, C. Fowley, J. Lindner, M. Gensch, A. Deac

In preparation

Other publication(s) during Ph.D. work

5. “Extremely efficient terahertz high-harmonic generation in graphene by hot Dirac

fermions”,

Hassan A. Hafez, Sergey Kovalev, Jan-Christoph Deinert, Zoltan Mics, Bertram

107

108 List of publications

Green, Nilesh Awari, Min Chen, Semyon Germanskiy, Ulf Lehnert, Jochen Te-

ichert, Zhe Wang, Klaas-Jan Tielrooij, Zhaoyang Liu, Zongping Chen, Akimitsu

Narita, Klaus Mullen, Mischa Bonn, Michael Gensch and Dmitry Turchinovich

Nature , (2018).

6. “On-chip THz spectrometer for bunch compression fingerprinting at fourth-generation

light sources”,

M. Laabs, N. Neumann, B. Green, N. Awari, J. Deinert, S. Kovalev, D. Plette-

meier, M. Gensch

Journal of Synchrotron Radiation 25, 1509-1513 (2018).

7. “Towards femtosecond-level intrinsic laser synchronization at fourth generation

light sources”,

M. Chen, S. Kovalev, N. Awari, Z. Wang, S. Germanskiy, B. Green, J-C Deinert,

M. Gensch

Optics letters 43 (9), 2213-2216 (2018).

8. “Selective THz control of magnetic order: new opportunities from superradiant

undulator sources”,

S. Kovalev, Zhe Wang, J-C Deinert, N. Awari, M. Chen, B. Green, S. Germanskiy,

TVAG de Oliveira, J.S. Lee, A. Deac, Dmitry Turchinovich, N. Stojanovic, S.

Eisebitt, I. Radu, Stefano Bonetti, Tobias Kampfrath, M. Gensch

Journal of Physics D: Applied Physics 51, 11 (2018).

9. “High-field high-repetition-rate sources for the coherent THz control of matter”,

B. Green, S. Kovalev, V. Asgekar, G. Geloni, U. Lehnert, T. Golz, M. Kuntzsch,

C. Bauer, J. Hauser, J. Voigtlaender, B. Wustmann, I. Koesterke, M. Schwarz, M.

Freitag, A. Arnold, J. Teichert, M. Justus, W. Seidel, C. Ilgner, N. Awari, Daniele

Nicoletti, Stefan Kaiser, Yannis Laplace, Srivats Rajasekaran, Lijian Zhang, S.

Winnerl, H. Schneider, G. Schay, I. Lorincz, A.A. Rauscher, I. Radu, Sebastian

Mahrlein, T.H. Kim, J.S. Lee, Tobias Kampfrath, S. Wall, J. Heberle, A. Malnasi-

Csizmadia, A. Steiger, A.S. Muller, M. Helm, U. Schramm, T. Cowan, P. Michel,

Andrea Cavalleri, A.S. Fisher, N. Stojanovic, M. Gensch

Scientific reports 6, 22256 (2016).

List of publications 109

Publication(s) prior to Ph.D. work

10. “Multilayer broadband absorbing structures for terahertz region”,

A. Dubey, A. Jain, C.G. Jayalakshmi, T.C. Shami, N. Awari, S.S. Prabhu

Microwave and Optical Technology Letters 55 (2), 393-395 (2013).

11. “Charge-density wave condensate in charge-ordered manganites: impact of ferro-

magnetic order and spin-glass disorder”,

R. Rana, N. Awari, P. Pandey, A. Singh, S.S. Prabhu, D.S. Rana

Journal of Physics: Condensed Matter 25 (10), 106004 (2013).

12. “Charge density waves condensate as measure of charge order and disorder in

Eu1-xSrxMnO3 (x=0.50, 0.58) manganites”,

P. Pandey, N. Awari, R. Rana, A. Singh, S.S. Prabhu, D.S. Rana

Applied Physics Letters 100 (6), 062408 (2012).

Curriculum Vitae

Nilesh Awari

28th September 1987 Born in Sangamner, India.

Education

09/2014 - 09/2018 Ubbo Emimus Phd Program

Optical Condensed Matter Physics, University of

Groningen and

High Field THz-driven Phenomenon Group,

Helmholtz Zentrum Dresden Rossendorf

Supervisors: Prof. dr. T. Banerjee, dr. M. Gensch

09/2012 - 07/2014 Top masters Nanoscience Program

Masters in sciences, University of Groningen

Thesis: Towards the understanding of 3-terminal

metallic spintronics devices

Supervisors: Prof. B.J. van Wess

06/2008 - 05/2010 Masters of Science with emphasis on Solid State

Physics, University of Mumbai, India

06/2005 - 05/2008 Bachelors of Science with emphasis on Physics,

University of Mumbai, India

111

112 Curriculum Vitae

Work Experience

07/2010 - 07/2012 Junior Research Fellow

Tata Institute of Fundamental Research

Mumbai, India

Project: THz time domain spectroscopy of man-

ganites

Supervisors:Dr. S.S. Prabhu

university of groningen a terahertz view on magnetization ... · nilesh awari, 2019. a terahertz...

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