University of Groningen A terahertz view on magnetization dynamics Awari, Nilesh

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University of Groningen

A terahertz view on magnetization dynamics

Awari, Nilesh

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A Terahertz View On Magnetization

Dynamics

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Zernike Institute PhD thesis series 2019-03 ISSN: 1570-1530

ISBN: 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 Condensed Matter Physics group at the Zernike Institute for Advanced Materials of the University of Groningen, The Netherlands and at Helmholtz Zentrum Dres-den Rossendorf, DresDres-den, Germany.

Cover design by Nilesh Awari Printed by Gildeprint

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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

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Supervisor Prof. T. Banerjee Co-supervisors Dr. M. Gensch Dr. R. I. Tobey Assessment committee Prof. B. Koopmans Prof. M. M¨unzenberg Prof. L.J.A. Koster

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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 magnetic materials. . . 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 repetition rate, 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 geometry employed 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 laser irradiation . . . 49

4.5 Analysis of the THz emission measurements . . . 51

4.6 The 180◦ _{phase shift of FMR mode observed in Mn} 3-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 thin films . . . 53

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

4.10 Schematic of the THz emission spectroscopy set-up and sample geometry employed 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

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List of Figures LIST OF FIGURES 4.13 Thickness dependence of the emitted THz emission from Mn3-XGa thin

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

source. . . 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 THz

induced 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 pump

as 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 1

THz pump . . . 74 5.9 Ultra-fast demagnetization observed in CoFeB thin films as a function of

the THz pump frequency . . . 75 5.10 Comparison of ultra-fast demagnetization observed in CoFeB thin films

at 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 spin

modes in NiO. . . 96

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List of Tables

4.1 Ms from VSM [6, 8] and inferred values of 10Hkfrom dynamic THz

emis-sion measurements. THz emisemis-sion measurements have been performed in the presence of an external magnetic field of 400 mT and at a temperature of 19.5◦C. THz driven Faraday rotation measurements were performed with an external magnetic field of 200 mT. . . 53 5.1 A summary of the THz frequencies used in the THz pump Polar MOKE

experiments along with their peak electric field values. . . 71

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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.

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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 based GMR heads. (b) The rate of telecommunication as a function of time. The rate at

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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.

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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. ˇZuti´c, 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.

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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. Kl¨aui, 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. N¨otzold, S. M¨ahrlein,

V. Zbarsky, F. Freimuth, Y. Mokrousov, S. Bl¨ugel, 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. M¨ahrlein, 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.

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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. F¨orst, 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.

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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 magnetizadescrip-tion 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.

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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 = _2me~ 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 =P

isi is the total angular spin momentum of the electron system and L =

P

ili 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.

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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 = −

∞

X

i6=j

JijSi.Sj (2.5)

here Jijis 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.

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Figure 2.1: Different types of magnetic ordering present in materials. Black arrows indicate 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= Ku2sin2θ (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

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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;

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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) Hysteresis loop 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 N´eel temperature (TN), but at and above TN the antiferromangetic order is lost.

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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, ferromagnet and antiferromagnet is shown, adapted from [4]

.

χm= CP/(T − TC) (2.10)

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

ferromag-netic material. For antiferromagferromag-netic 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 Hef f of the material, where Hef f is defined as

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where Haniis 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 × Hef f (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

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dm

dt = −γm × Hef f (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 × Hef f + α Ms m ×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) with damping.

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

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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 demagnedemagne-tization 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 scatterscatter-ing [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]:

Cel

dTel

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

Clat

dTlat

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

Csp

dTsp

dt = −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

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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 magnetic materials over 1 ps time scale. The thermalization processes between electrons and spins 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 non-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

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Figure 2.6: Effect of femtosecond laser excitation in the near infrared regime on magnetic materials. The excited hot carriers undergo local and non local physical pro-cesses which determine the magnetization dynamics of the material. The local effects includes; hot carriers populating empty electronic states and the spin flip scattering. In the non-local effects, inhomogeneous distribution of hot carriers enable spin-polarized super-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

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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

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[9] B. Koopmans, G. Malinowski, F. Dalla Longa, D. Steiauf, M. F¨ahnle, 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. M¨unzenberg, “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. B¨urstel, D. Diesing, M. M¨unzenberg, 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. G¨unther, 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. D¨urr, “Thz-driven ultrafast spin-lattice scattering in amorphous metallic ferromagnets,” Physical review letters, vol. 117, no. 8, p. 087205, 2016.

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[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. D¨urr, 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. Kl¨aui, and D. Turchinovich, “Accessing the fundamentals of magne-totransport in metals with terahertz probes,” Nature Physics, vol. 11, no. 9, p. 761, 2015.

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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.

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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 = −δA δt ∼ δ[m × ˆn] δt (3.1)

where m is the magnetic dipole moment, A is vector potential and ˆn 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.

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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) = 2πLn

3 0r

λ E(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

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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 800 nm NIR laser pulses (shown in green) are collinear with the THz pulses. The THz field induces birefringence in the electro-optic crystal, the differences in the orthogonal polarization is detected using a quarter-wave plate (λ

4), 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(ωT Hz) =

πc

ωT Hz|nopt(ω0) − nTHz(ωT Hz)|

(3.4)

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

<110> direction and nT Hz 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:

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3.2. Magneto-optic effect 27 = xx 0 0 0 yy 0 0 0 zz ! (3.5)

When an external magnetic field is applied parallel to the direction of propagation of incident light, for example along ˆz, considering time reversal symmetry and energy conservation, we can write,

= xx xy(B) 0 −xy(B) yy 0 0 0 zz ! (3.6)

The normalized eignemodes of 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 xx± ixy(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 popo-larized after interacting with the material having the above permitivity tensor. Refractive indices for circularly polarized light would be n+=p(xx+ ixy) and n− =p(xx− ixy). 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 introintro-duce 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

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28 3. Experimental Techniques THz delay 2 WP PD 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. 100 femtosecond 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 polarization rotation of the 800 nm NIR laser pulse passing through the material. λ

2, WP, and

PD 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=

xy

√

xx(xx− 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

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3.3. Light sources 29

Figure 3.3: Different configurations for measurement of Kerr effect [18]. Longitudinal and 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

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30 3. Experimental Techniques THz delay BS 800 nm WP PD PD 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. 100 femtosecond 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 of the 800 nm NIR laser pulse reflected back from the material. λ

2, WP, and PD stand for

the 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

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motion of charge carriers emits electromagnetic radiation which has a bandwidth of ∼

1

τ, 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(E ) = − 4π c2 δ2_P δt2 (3.10)

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

nvis_gr = nT Hz_ph (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

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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 THz radiation using LN as a THz source. (a) time domain trace of the electric field of generated 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

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accelerated electron bunches is based on the principle of 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 an electron bunch. (a) when the electron bunch width is larger than the wavelength of emitted radiation, incoherent radiation is observed (b) when the electron bunch width becomes 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-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

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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 repetition rate, for a given THz frequency. Adapted from [47] (a) Maximum pulse energy at TELBE as a function of repetition rate. With 100 pC electron bunches, TELBE pulse energy is 2 orders of magnitude higher than from intense table top THz sources at the same repetition rate of 100 kHz. (b) maximum pulse energy at TELBE as a function of 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.

3.4 Bibliography

[1] X.-C. Zhang, B. Hu, J. Darrow, and D. Auston, “Generation of femtosecond elec-tromagnetic pulses from semiconductor surfaces,” Applied Physics Letters, vol. 56,

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Figure 3.9: Frequency tunability of TELBE source. (a) Electric field wave-forms for different THz frequencies (b) normalized intensity spectrum for the THz frequencies

shown in (a).

no. 11, pp. 1011–1013, 1990.

[2] E. Beaurepaire, G. Turner, S. Harrel, M. Beard, J.-Y. Bigot, and C. Schmuttenmaer, “Coherent terahertz emission from ferromagnetic films excited by femtosecond laser pulses,” Applied Physics Letters, vol. 84, no. 18, pp. 3465–3467, 2004.

[3] D. J. Hilton, R. Averitt, C. Meserole, G. L. Fisher, D. J. Funk, J. D. Thompson, and A. J. Taylor, “Terahertz emission via ultrashort-pulse excitation of magnetic metal films,” Optics letters, vol. 29, no. 15, pp. 1805–1807, 2004.

[4] T. Kampfrath, K. Tanaka, and K. A. Nelson, “Resonant and nonresonant control over matter and light by intense terahertz transients,” Nature Photonics, vol. 7, no. 9, p. 680, 2013.

[5] T. H. Kim, S. Y. Hamh, J. W. Han, C. Kang, C.-S. Kee, S. Jung, J. Park, Y. Toku-naga, Y. Tokura, and J. S. Lee, “Coherently controlled spin precession in canted antiferromagnetic YFeO3 using terahertz magnetic field,” Applied Physics Express, vol. 7, no. 9, p. 093007, 2014.

[6] 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.

[7] 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.

University of Groningen A terahertz view on magnetization dynamics Awari, Nilesh