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A terahertz view on magnetization dynamicsAwari, Nilesh
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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
5.2 Experimental details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
5.3 Results & Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
5.4 Conclusion & Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
5.5 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
6 THz-Driven Spin Excitation in High Magnetic Fields: Case of NiO 83
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
6.2 Experimental details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
6.3 Results & Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
6.3.1 Temperature dependence of AFM mode . . . . . . . . . . . . . . . 89
6.3.2 Field dependence of AFM mode . . . . . . . . . . . . . . . . . . . 91
6.4 Conclusion & Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
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.
10 2. Introduction to Magnetism
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)
12 2. Introduction to Magnetism
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)
14 2. Introduction to Magnetism
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
2.3. Ultra-fast magnetization dynamics 15
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
16 2. Introduction to Magnetism
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
2.3. Ultra-fast magnetization dynamics 17
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
18 2. Introduction to Magnetism
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.
20 2. Introduction to Magnetism
[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.
2.4. Bibliography 21
[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.
[24] 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.
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
26 3. Experimental Techniques
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
28 3. Experimental Techniques
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
30 3. Experimental Techniques
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
3.3. Light sources 31
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
32 3. Experimental Techniques
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
3.3. Light sources 33
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
34 3. Experimental Techniques
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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Figure 3.9: Frequency tunability of TELBE source. (a) Electric field wave-forms fordifferent THz frequencies (b) normalized intensity spectrum for the THz frequencies
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.
44 4. Narrow-band Tunable THz Emission from Ferrimagnetic Mn3-XGa Thin Films
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.
4.2. Experimental details 45
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)
46 4. Narrow-band Tunable THz Emission from Ferrimagnetic Mn3-XGa Thin Films
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
4.2. Experimental details 47
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]
48 4. Narrow-band Tunable THz Emission from Ferrimagnetic Mn3-XGa Thin Films
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.
50 4. Narrow-band Tunable THz Emission from Ferrimagnetic Mn3-XGa Thin Films
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
4.3. Results & Discussion 51
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.
52 4. Narrow-band Tunable THz Emission from Ferrimagnetic Mn3-XGa Thin Films
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.
4.3. Results & Discussion 53
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
54 4. Narrow-band Tunable THz Emission from Ferrimagnetic Mn3-XGa Thin Films
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
4.3. Results & Discussion 55
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.
56 4. Narrow-band Tunable THz Emission from Ferrimagnetic Mn3-XGa 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
4.3. Results & Discussion 57
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
58 4. Narrow-band Tunable THz Emission from Ferrimagnetic Mn3-XGa Thin Films
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.
60 4. Narrow-band Tunable THz Emission from Ferrimagnetic Mn3-XGa Thin Films
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.
68 5. THz-Induced Demagnetization: Case of CoFeB
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.
5.2 Experimental details
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
5.2. Experimental details 69
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.
70 5. THz-Induced Demagnetization: Case of CoFeB
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).
5.2. Experimental details 71
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.
72 5. THz-Induced Demagnetization: Case of CoFeB
5.3 Results & Discussion
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
5.3. Results & Discussion 73
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.
74 5. THz-Induced Demagnetization: Case of CoFeB
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)
5.3. Results & Discussion 75
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.
76 5. THz-Induced Demagnetization: Case of CoFeB
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)
5.3. Results & Discussion 77
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
78 5. THz-Induced Demagnetization: Case of CoFeB
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
5.4. Conclusion & Outlook 79
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.
5.4 Conclusion & Outlook
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
80 5. THz-Induced Demagnetization: Case of CoFeB
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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82 5. THz-Induced Demagnetization: Case of CoFeB
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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
6.2. Experimental details 85
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.
6.2 Experimental details
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.
86 6. THz-Driven Spin Excitation in High Magnetic Fields: Case of NiO
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
6.2. Experimental details 87
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.
88 6. THz-Driven Spin Excitation in High Magnetic Fields: Case of NiO
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)
6.3. Results & Discussion 89
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 Results & Discussion
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
90 6. THz-Driven Spin Excitation in High Magnetic Fields: Case of NiO
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
6.3. Results & Discussion 91
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.
92 6. THz-Driven Spin Excitation in High Magnetic Fields: Case of NiO
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.
6.3. Results & Discussion 93
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.
94 6. THz-Driven Spin Excitation in High Magnetic Fields: Case of NiO
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
6.4. Conclusion & Outlook 95
<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.
6.4 Conclusion & Outlook
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
96 6. THz-Driven Spin Excitation in High Magnetic Fields: Case of NiO
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.
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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