Dynamics of lattice vibrations, molecular rotations and spins studied by terahertz spectroscopy

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Dynamics of lattice vibrations, molecular rotations and spins studied by terahertz spectroscopy

by Jian Lu

B.Eng., Tianjin University (2011) Submitted to the Department of Chemistry

in partial fulfillment of the requirements for the degree of

Doctor of Philosophy at the

MASSACHUSETTS INSTITUTE OF TECHNOLOGY

MASSACHUSETTS INSTITUTE OF TECHNOLOGY

JUL 0

6 2017

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June 2017

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Department of Chemistry May 18, 2017

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Keith A. Nelson Professor Thesis Supervisor

Accepted by...

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Robert W. Field Chairman, Department Committee on Graduate Students

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This doctoral thesis has been examined by a committee of the Department of Chemistry as

follows:

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Professor Jianshu Cao... ...

Chairperson, Thesis Committee Professor of Chemistry

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Professor Keith A. Nelson....

Professor Sylvia T. Ceyer...

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Thesis Supervisor Haslam and Dewey Professor of Chemistry

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Mimber, Thesis Committee John C. Sheehan Professor of Chemistry

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Dynamics of molecular rotations, spins and lattice vibrations

studied by terahertz spectroscopy

by

Jian Lu

Submitted to the Department of Chemistry on May 18, 2017, in partial fulfillment of the

'requirements for the degree of Doctor of Philosophy

Abstract

In this thesis, I describe generation of strong THz electromagnetic pulses with broad bandwidths or tailored waveforms using organic nonlinear optical crystals and spectroscopy experiments utilizing THz pulses to study the linear and nonlinear responses of molecular dipole, spin, and lattice degrees of freedom in molecular and condensed-matter systems. We have developed several THz spectroscopy methods suitable for interrogating different material systems including THz pump-optical probe spectroscopy, THz time-domain electron paramagnetic resonance (EPR) spectroscopy, and

two-dimensional (2D) THz spectroscopy using either the THz electric or magnetic field. Using the electric fields of two time-delayed strong THz pulses, we have demonstrated

2D THz rotational spectroscopy. In the time domain, we have directly observed THz

photon echoes and other nonlinear dynamics originating from the rotating permanent dipoles of a thermal ensemble of gas-phase molecules. Multiple pathways that lead to the nonlinear responses are mapped out in the 2D THz rotational spectrum, which allows the detailed study of the nonlinear THz field-dipole interactions with resolution of each rotational level.

We have demonstrated a new THz EPR technique that allows rapid and precise determination of the THz-frequency spin energy level structures characteristic of molecular complexes including molecular magnets and metalloproteins which contain high-spin transition-metal ions. The linear THz spectra of several molecular complexes both in the absence of and as a function of an external static magnetic field show the absorption features and their magnetic field-dependence as expected from quantum mechanical simulations, which allow precise determination of the spin energy level structures. We have demonstrated 2D THz magnetic resonance spectroscopy and its application to directly reveal the nonlinear dynamics of collective spin waves in a magnetic material. The 2D THz

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spectra reveal spin echoes that have the highest frequency ever observed, and correlations between the spins.

In a bulk quantum paraelectric material, we have observed temperature-dependent lattice dynamics and fluctuating polar domain dynamics, both associated with the incipient ferroelectric structural phase transition, through time-resolved optical second harmonic generation. We have observed that THz fields break lattice centrosymmetry in a paraelectric material, which results in THz activity in originally only Raman-active vibrational modes. The THz pulse can provide a second interaction that leads to the excitation of coherent Raman-active vibrations, which are detected by Raman scattering through optical birefringence.

Thesis Supervisor: Keith A. Nelson

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Acknowledgements

My six-year time at MIT has been one of the most wonderful periods in my life. I am

indebted to many people without whom none of this would have been possible.

The first person I would like to thank is my advisor Prof. Keith Nelson. Keith is always enthusiastic about science and about our research. He cares about all of us in every aspect.

I have learnt a great deal from him not only about knowledge and research, but also about

culture and life wisdom. Whenever I told him that experiments did not work out, he would think of many ways to tackle the problems that I thought impossible and convey them to me in a way that made me think the problems could be readily solvable, and he would constantly encourage me to keep trying. Whenever I had problems thinking about something, he would explain them to in his way that was the most easily understood. Whenever I need his help in revising any writings or in preparing for a presentation for conferences or interviews, he would spend his time and efforts to go through every word and talk about every possible suggestion with me in his office, even if it was after midnight on a Friday, and even if it was about the iteration of revising the same paper for several times. Work is not the only circumstance that we interact with Keith. The fun times of our group hiking, group barbeque, apple picking, parties at Keith's house, parties at school, as well as group socials and beer drinking, were all very enjoyable.

In addition, I would like to thank Prof. Jianshu Cao and Prof. Sylvia Ceyer for being my thesis committee. Jianshu's courses on Thermodynamics and Statistical Mechanics which

I took in my first year were very helpful to me. Annual meetings with Jianshu provided a

constructive perspective on my work. I feel grateful that Sylvia read and commented on my oral paper and thesis within three days, and she cared about my work.

Next, I would like to thank the Nelson group members who have taught me everything about our THz lab, and have made the lab awesome. I overlapped with many people in the THz project. When I joined our THz lab in my first year, I had the luck to work with Xibin Zhou, Sharly Fleischer, and Brad Perkins, who had a great deal of experience and knowledge. I worked with Xibin for a semester. Xibin taught me how to do ultrafast experiments with the KMLabs oscillator from the beginning. After trial and error, we both

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became experts on Z-scan measurements, which were my first experiments in our lab. Xibin also taught me how to align my first THz setup and taught me how to do my first THz (TFISH) experiment. Sharly is a humorous person, and working with him was enjoyable. When things did not work out, Sharly was always ready to help. I remember when the THz was misaligned the first time, I was very worried and did not know how to deal with it. Sharly came in and taught me how to realign the THz. He made me think that generating THz was not as hard as I thought. I learnt a lot about gas phase molecules and orientation and alignment from him. He offered me very helpful and detailed suggestions on writing the draft for the 2D THz rotational spectroscopy paper. Brad taught me about superconductors as well as working the KMLabs oscillator. I felt grateful for their guidance for me as a first year student.

I overlapped with senior graduate students Harold Hwang and Nate Brandt for the

longest time. They were both like big brothers to me, and taught me the little secrets about THz and the lasers. Harold has extensive knowledge about everything with THz. I often asked him about his ideas and input of the experiments that we should try. Many of the ideas and samples were attributed to his efforts. He has also got a great taste for Scotch whisky and Asian (and Mexican) food. Nate is a patient teacher with extensive experience in lasers, parabolic mirrors, machining, as well as plumbing. Nate taught me how to align parabolic mirrors well. The parabolic mirrors we aligned had nearly no aberrations for the He-Ne laser after hours and hours of aligning. When I encountered any problems in the lab, Nate was ready to help. Whenever the Mantis oscillator lost mode-lock, Nate would set aside his own work and help get it back in shape in less than half an hour. He also taught me how to fix the laser oscillator and amplifiers and how to fix the plumbing for the chillers, from which I benefitted quite a lot. During our visit to the LCLS for two back-to-back beamline experiments which lasted for three weeks, Harold, Nate and I had learnt a great deal, and also had a lot of fun together. The photos of us "playing" in the experimental hutch, boozes, and Monster drinks are still in Nate's Instagram and keep reminding me of the fun time. Working with them made the lab a fun place.

The contemporary Team THz consists of Brandt Pein, Andreas Steinbacher, Yaqing Zhang, Xian Li, and Jiaojian Shi. Brandt has extensive knowledge and experience about lasers and about Raman spectroscopy. He is always ready to offer me constructive

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suggestions when I discuss with him about any problems. Though he found a job recently, he still comes back to our lab and office once in a while. Yaqing and Xian are the senior graduate students in the THz project. They were also from the optoelectronics departments at Nankai and Tianjin Universities. Each of them has played a major role in the simulation work in the 2D THz work. They have been instrumental in getting the lab to the current state. Andreas is relatively new to the project. He has always been curious about THz and been keen on THz driving chiral molecules which is going to be a cool experiment. He is always ready to provide constructive ideas in our conversations. Jiaojian is a second-year graduate student. He takes on the project from Brandt very quickly. Apparently, Andreas, Yaqing, Xian, and Jiaojian have completely taken over the THz project. And I am excited to see the new and interesting directions that they will take the project.

I would also like to thank Ben Ofori-Okai, Steph Teo and Prasahnt Sivarajah of the Team

Polaritonics. The LabView programs using the data acquisition card and differential chopping were mostly from Ben. Ben and Steph were always patient to help me when the LabView code encounters bugs. I had a lot of stimulating discussions about cavities, strong couplings, and magnons and ideas that could be worth a try with Prasahnt, which led to my better understanding about light-matter interactions. I am indebted to other past Nelson group members including Kit Werley, Johanna Wolfson, Dylan Arias, Patrick Wen, Kara Manke, Felix Hofmann, Jeff Eliason, Sam Teitelbaum, Colby Steiner, Yongbao Sun, Alejandro Flick, Keiichi Nakagawa and Longfang Ye; and present Nelson group members including David Vesset, Alex Maznev, Jake Siegel, Doug Shin, Joseph Yoon, Leora Cooper, Ryan Duncan, Ronny Huang. Yu-Hsiang Cheng, Dimitro Martynowych, Frank Gao and Blake Dastrup. All of them have been an important scientific resource, have made the office an enjoyable place, and have maintained the great group dynamic. I would like to thank Li Miao and Julian Burnett for their help in dealing with the processes related to financial stuff. I need to thank Susan Brighton, Melinda Cerny, Jennifer Weisman, Lynn Marie Guthrie-Libby, Rebecca Teixeira, Jay Matthews, and others in the Chemistry Education Office for their constant help for us graduate students.

Much of the work would be impossible without the strong collaborators we have had the opportunity to work with. The molecular complexes samples in Chapter 5 were synthesized or prepared by Grigorii Skorupskii, Lei Sun from Prof. Mircea Dinca's group in our

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department. The THz measurements under a magnetic field were done using the setup in Prof. Nuh Gedik's lab in the Physics Department at MIT. Ozge Ozel and Carina Belvin from Nuh's group had helped a great deal in taking these measurements. Without their help in sample preparation and THz experiments, none of this would have been possible. In addition, I would like to thank Rose Hadley and Emily Zygiel from Prof. Liz Nolan's group for the protein sample and stimulating discussions on the experiment. Though it did not work out this time, we will try again next time. The YFeO3 crystal used in Chapter 6 was from Takayuki Kurihara from Prof. Tohru Suemoto's lab at the University of Tokyo. The

TSCC sample used in Chapter 7 was provided by Dr. Stanislav Kamba, Dr. Jan Petzelt,

and Petr Ondrejkovic from the Czech Academy of Sciences. We also received other samples from them. We look forward to trying them out. The organic nonlinear optical crystals used in Chapter 8 were grown by Seung-Heon Lee from Prof. O-Pil Kwon's lab at Ajou University. I greatly appreciate their hard work in growing these crystals and their generosity in sending us the crystals for tests. I would also like to thank the groups of Prof. Aaron Lindenberg and Prof. Hermann Duerr, and other collaborators involved in the two

LCLS experiments. I would also like to thank the rest of the collaborators including Dr.

Yuanmu Yang, Dr. Igal Brener, and Dr. Rohit Prasankumar at Sandia National Lab for experimental ideas, samples, metamaterial fabrication, and electromagnetic simulations; Dr. Hari Nari and Prof. Darrel Schlom at Cornell University for the MBE thin-film samples; Dr. Jungwoo Lee and Prof. Chang-Beom Eom at University of Wisconsin for the superlattice samples; and Tom Mahony and Prof. Vladimir Bulovic at MIT for metamaterial fabrication.

The first year in graduate school was about the craziest time in the past six years. I would like to thank my fellow incoming classmates including Hang Chen, Qing Liu, Jingjing Ling, Mike Mavros, Kurt Cox, Igor Coropceanu, Wankyu Lee, Jenny Liu, Dave Song, Matt Welborn, Thomas Avila, Phoom Chairatana, Stephanie Cheung, Jess McCombs and others, who have made me feel welcome from the beginning.

I am grateful for my professors at Tianjin University, including Minglie Hu, Bo Liu,

Shengjiang Chang, Xiaocong Yuan, Xing Zhao, Xiaoying Li, and others, who helped me broaden my horizon and stimulated my desire of pursuing my graduate study abroad.

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Most of all, I would like to thank my family for their love. I am grateful for my wife Maopin Yan for her love and support over the past years. I am grateful for my parents Bo Lu and Baoju Hu, and my grandfather Yicheng Lu and other family members for their lifelong love of me. Without them, I would not have been who I am today.

Jian Lu May 30, 2017

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List of Figures

Figure 2.1 Schematic structures of PCAs with different electrode designs. The semiconductor substrates are

shown in grey. Electrode structures including (a) stripline electrodes, (b) inter-digitated electrodes, (c) dipole electrodes, are in gold. The structures are not drawn on the same scale in (a), (b) and (c). ... 42 Figure 2.2 THz time-domain spectroscopy system based on PCAs. Red lines indicate optical paths and black

lines indicate electrical connections. The blue shaded areas indicate THz beam paths...44

Figure 2.3 THz pulse generated and detected by the setup based on PCAs. (a) THz time-domain trace

showing a single-cycle THz waveform. (b) FT amplitude spectrum resulting from FFT of the time-domain tra c e in (a )...4 5

Figure 2.4 Schematic illustration of THz generation by OR. (a) A Gaussian pulse with an intensity duration

of 100 fs (full width at half maximum). The red curve is the carrier and the blue curve the envelope of the light electric field. (b) A single-cycle THz waveform (black) resulting from the second-order time derivative of the intensity envelope (blue) of the pulse in (a). ... 47

Figure 2.5 Schematic illustration of the optical setup for THz electric field profile characterization via EOS.

The phase retardation A0 of the gate pulse experienced in the EO crystal is converted to an intensity difference Iv and IH in the vertical and horizontal polarization components of the depolarized gate pulse by the phase-sensitive optics including a quarter wave-plate and a Wollaston prism. The intensity difference is m easured by the balanced photodetectors. ... 49

Figure 2.6 A typical THz time-domain spectroscopy system with ZnTe as the THz generation and detection

crystals. THz pulses are generated by OR of the 800 nm laser pulses in a 2-mm ZnTe crystal, and are detected

by EOS with another 2-mm ZnTe crystal. A Teflon sheet is used to block the residual 800 nm pump light

that exits the ZnTe TH z generation crystal... 51

Figure 2.7 (a) THz time-domain trace from ZnTe. (b) FT amplitude spectrum resulting from FFT of the THz

trace sh o w n in (a). ... 5 2 Figure 2.8 (a) Schematic geometry of THz generation with a Cherenkov radiation pattern. Optical intensity

front of the pump pulse is depicted by the red circle, with the propagation direction indicated by the red arrow. Optical phase front is depicted by red dashed circles. THz phase front is depicted by the black lines that form a cone. The direction of THz propagation is indicated by the black lines. (b) Schematic geometry of the TPF method. The red solid arrows indicate the propagation direction of the optical pulses. The optical intensity front shown by the red solid line is tilted such that it is parallel to the THz wave front shown by the black solid line and the propagation direction of the THz field shown by the black arrow. ... 53 Figure 2.9 Schematic illustration of the experimental implementation of the TPF method. Laser pulses with

a flat intensity front and horizontal polarization are incident onto the grating. The first-order diffraction is collected and imaged into the LiNbO3 prism (the crystal c-axis is vertical), with the polarization rotated to

vertical by the half wave-plate (HWP). The tilt angle is increased by the demagnification of the imaging lens and further increased when the pump pulse enters the LiNbQ3 prism. When velocity matching is optimized,

the maximum THz fields are generated and coupled out of the LiNbO3 prism. The cut angle of the LiNbO3

prism is show n in the dashed box...55

Figure 2.10 An example of the experimental setup based on LiNbO₃. THz pulses are generated in LiNbQ₃

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Figure 2.11 (a) THz time-domain trace from LiNbO3. (b) FT amplitude spectrum resulting from FFT of the

T H z trace show n in (a)...56

Figure 2.12 Molecular structures of OHI (a) and DSTMS (b). Intra-molecular charge transfer between

electron donor and acceptor is through the 7r-conjugation bridge consisting of alternating single and double b o n d s. ... 5 8 Figure 2.13 Experimental implementation of THz generation by OR with organic nonlinear optical crystals.

The laser system used is also indicated. A Ti:Sapphire oscillator is used to seed a Ti:Sapphire amplifier system, which is used to pump a high-energy OPA that delivers the pump pulses to the organic crystals. A weak portion of the 800 nm amplifier pulses is split, time-delayed and incident onto the GaP crystal for EOS.

... 5 8 Figure 2.14 THz time-domain trace (a) and FT amplitude spectrum (b) generated by a 0.5-mm OHI crystal

pumped at 1450 nm. THz time-domain trace (c)and FT amplitude spectrum (d) generated by a 0.55-mm

D ST M S crystal pum ped at 1400 nm . ... 59 Figure 3.1 A THz transmission spectroscopy setup. A generic THz source and a generic THz detection unit

are used. AD denotes analog-to-digital signal converter, which generates the raw THz time-domain signals fo r an aly sis. ... 6 4

Figure 3.2 Propagation of THz fields through a sample whose refractive index is denoted as n2. The sample is assumed to be in air whose refractive index is denoted as n1. The input THz fields denoted as Ei, go through reflection and transmission at the sample-air interfaces obeying Fresnel equations. The reflection and transmission coefficients from a medium with a refractive index ni to that with a refractive index nj are denoted as rij and tij respectively. The output fields are denoted as Eout...65

Figure 3.3 THz pump-optical SHG probe setup. Laser pulses are split into two paths by a beamsplitter (BS).

The strong laser pulses are used to generate THz pulses in the LiNbO3 crystal. The generated THz pulses are

collimated and focused onto the sample. The weak laser pulses are time delayed, attenuated and focused onto the sample. Optical SHG at 400 nm propagates in two directions collinear with the fundamental pulses at 800 nm as phase matching is fulfilled. Here, the SHG reflection is collected by a dichroic mirror (DM) and detected by a photomultiplier tube (PMT). A pair of wiregrid polarizers is used to vary the THz field strength w ithout affecting the w aveform ... 69 Figure 3.4 THz pump-optical birefringence probe setup. (a) Experimental geometry. (b) Polarizations of the

THz and probe fields. THz pulses are generated in the LiNbO3 crystal and focused onto the sample. The THz field strength is controlled by the wiregrid polarizers. The THz field is polarized along the optical axis of the sample. The probe field is polarized at 45 degrees with respect to the THz field. Probe pulses are time delayed, attenuated and focused onto the sample. The birefringence of the +45* and -45* polarization components of the probe pulse is detected by phase-sensitive detection using a quarter wave-plate, a Wollaston prism, and photodetectors PD I and PD 2...70

Figure 3.6 Pulse sequences of 2D THz spectroscopy. In this THz-THz-THz sequence, all field-matter

interactions arise from THz fields. The final signal emission is a THz field ENL detected by EOS...72

Figure 3.7 Schematic representation of the differential chopping detection method...73 Figure 3.8 2D THz spectroscopy experimental setup. Two time-delayed THz pulses are generated by two

time-delayed optical pulses using the tilted-pulse-front method in a LiNbO3 crystal. The THz signals are detected by EOS in a ZnTe crystal. BS: beamsplitter, HWP: half wave-plate, QWP: quarter wave-plate, P: polarizer, WP: Wollaston prism, PM: parabolic mirror, LN: lithium niobate, PD: photodiode, DAQ: data acq u isitio n . ... 7 4

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Figure 4.1 (a) Rotational energy level diagram. The rotational states are represented by the angular momentum quantum number J. The red arrows denote the rotational transitions, with the transition frequencies given byfjj+ = 2Bc(J + 1), where J is an integer. (b) Linear FID signal of CH3CN induced by one THz excitation pulse interacting once with the sample. The signals in the blue dashed boxes are the quantum rotational revivals (enlarged views shown in the insets. Rev,, Rev2 etc. denotes revival 1, 2 etc.).

Water vapor in the THz propagation path outside the gas cell and signals owing to double reflection of the THz pulse in the detection crystal and cell windows are observed, but do not affect the nonlinear responses of interest. (c) Calculated rotational populations of CH3CN at thermal equilibrium at 300 K as a function of

fi,241= 2Bc(J+ 1), overlapped with the spectrum of the THz pulses (blue shaded area) used in the experiments. Each bar represents a rotational transition originating from a distinct rotational J level. (d) Experimental rotational spectrum of CH3CN, Fourier transformed from the FID signal in the red dashed box in (b). Each sharp peak represents a rotational transition from an initial J level to the final J + 1 level. THz absorption by water vapor causes a dip at 0.56 THz in the spectrum ... 83 Figure 4.2 Experimental setup. Two optical pulses with relative time delay T generate two collinearly propagating time-delayed THz pulses A and B which are focused into the sample gas cell. A time-delayed optical pulse detects the transmitted THz and signal electric field profile by EO sampling in the ZnTe crystal. A differential chopping detection scheme is used to extract the nonlinear signal field as a function of delay T and EOS time t. A Teflon sheet is used to block the residual 800 nm pulses for THz generation that transmit th ro u gh th e L N cry stal...84

Figure 4.3 Differential chopping detection pulse sequence. The two optical choppers at 500 Hz and 250 Hz allow the displayed signal sequence to be generated... 86 Figure 4.4 Experimental time-domain signal by differential chopping detection. (a) The time-domain response with either THz pulse A (red, EA) or B (blue, EB) present. THz pulse B is at 0 ps while THz pulse A is at -6 ps, corresponding to -r = 6 ps. The revivals of THz pulse A (RevA) and B (RevB) are at 48.5 and

54.5 ps as marked in the figure. The EOS measurements of the transmitted THz pulses are saturated, but the measurements of the weaker nonlinear THz signal fields are not. (b) The time-domain response with both THz pulses present (black, EAB) and the extracted nonlinear signal (magenta, ENL magnified 20x). Each type of the signal observed is elaborated in the text. The spikes in ENL at the arrival of each THz pulse are due to the shot-to-shot fluctuation of the laser and the saturation in EOS due to the large THz electric field strength. Additionally, when the THz pulses overlap with other signals (for example revival signals and THz reflections), Kerr effect in the EO crystal results in additional signals detected which cannot be subtracted due to the nonlinear (quadratic) dependence of the Kerr signals on the THz field. But this does not affect our exp erim ental resu lt. ... 87 Figure 4.5 THz photon echoes (rephasing, R) and NR signals in the time domain. (a) Experimental time-domain traces ENL(t,r) at selected delays T< Trev/2. THz pulse B is fixed at time zero. The R signals appear at t = T + nTrev (n = 0 and 1 shown) while the NR signals appear at t ='r + nTrev (n = 1 and 2 shown). For r< Trev/2, each R signal appears earlier than its counterpart NR signal. The vertical dashed lines mark the position of pulse B (t = 0) and its first two revivals (r= Tev and 2Trev), where the PP signals appear. (B) Experimental time-domain traces ENL at delays r> Trev/2. Each R signal appears later than the counterpart NR signal. ..89 Figure 4.6 Experimental 2D time-time plot of ENL(t,). THz pulse B is fixed at zero detection time. The delay r was incremented from 3 to 120 ps in 200 fs steps, which provided a time window spanning twice the revival period. The detection time t was scanned from 3 to 220 ps (120 to 220 ps not shown) with 100 fs steps. The photon echo (R) signals appear within the black dashed lines and the NR signals within the magenta lines. The subscripts in Rn indicate echo signal timing as t = r+ nTrev. The weak vertical features are pump-probe signals involving various reflections of the THz fields in the cell windows, and their periodic revivals (the strongest pump-probe signal would appear at detection time t = 0). The weak diagonal line from (t = 72 ps, r = 0 ps) to (t = 0 ps, r = 72 ps) is NR signal involving a reflection. The very weak diagonal line that starts at (t = 38 ps, r = 0 ps) and declines with half the slope of the NR signals is 2Q signal. ... 90

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Figure 4.7 (a) Nonlinear time-domain trace at a delay r of 20 ps. The signal time window extends to 260 ps.

Five sets of nonlinear signals and their revivals are shown. (b) Nonlinear rotational spectrum resulting from numerical Fourier transformation of the signal in (a). Each sharp peak represents a rotational transition....92

Figure 4.8 2D THz rotational magnitude spectrum. It is obtained by taking the absolute value of the 2D

Fourier transformation of the time-domain signal ENL(t,r). The light dashed lines are along v = 0, v = tf,

and v = 2f respectively. The observed third-order spectral peaks include NR, R, PP and 2Q (magnified x8 inside the red dashed area) signals. The spectrum is normalized and plotted according to the color map shown.

... 9 3 Figure 4.9 Experimental 2D THz rotational spectra. NR (a) and R (b, excitation frequency shown as positive)

quadrants of the 2D rotational spectrum of CH3CN. Spectral amplitudes inside the red dashed area are

magnified lOx to bring out the 2Q (a) and 2Q-R (b) signals. The dashed boxes cover rotational transitions

fromf25,26 tof3 7,38. (c) and (d) enlarged views of the spectra within the dashed boxes in the NR quadrant (a) and R quadrant (b) as functions of initial and final j quantum numbers along the vertical and horizontal axes respectively. Third- and fifth-order off-diagonal peaks are separated from the diagonal peaks at J-resolved positions. All the spectra are normalized and plotted based on the color map shown...95

Figure 4.10 Experimental 2Q and 2Q-R spectra. (a) 2Q and (b) 2Q-R normalized magnitude spectra isolated

from the experimental 2D spectra shown in the main text. The amplitudes outside the red dashed lines are set to zero. (c) and (d) 2D J-quantum-number plots, i.e. magnified views of the spectra in the dashed boxes with the initial and final j levels for the transitions indicated along the vertical and horizontal axes respectively. The strongest diagonal peaks are at f = 2BcJ + 1 and v = 2Bc2J + 3, while the strongest off-diagonal

peaks are at f = 2Bc( + 2) and v = 2Bc2J + 3. All the spectra are normalized and plotted according to the

color map shown. The additional features are due to noise... 96 Figure 4.11 Examples of double-sided Feynman diagrams. Diagram (i)-(iii) describes the third-order

diagonal and off-diagonal peaks in the NR quadrant of the 2D spectrum. Diagrams (iv)-(vi) describe the third-order diagonal and off-diagonal peaks in the R quadrant. Diagrams (vii)-(viii) describe two excitation pathways that lead to the PP peaks. Diagrams (ix)-(xii) describe the typical excitation pathways leading to the 2Q and 2Q-R peaks. Diagrams (xii)-(xiv) and (xv)-(xvi) describe the typical excitation pathways leading to the fifth-order NR and R off-diagonal peaks. The bra and ket symbols for the density matrix elements JJ ' are assumed in all the diagrams. The time subscripts denote the number of preceding field interactions. The nonlinear signal emission time period t corresponds to t3 in all third-order processes and t5 for the fifth-order

processes. The inter-pulse delay time -r corresponds to t1 for the R and NR signals (for third- and fifth-order

signals) and to t2 for the PP, 2Q and 2Q -R signals. ... 98

Figure 4.12 Simulated time-domain nonlinear orientation response. (a) The time-domain response of the

derivative of orientation factor with either THz pulse A (red, EA) or B (blue, EB) present. THz pulse B is at 0 ps while THz pulse A is at -6 ps. The revivals of THz pulse A (RevA) and B (RevB) are at 48.5 and 54.5 ps as marked in the figure. THz double reflections are taken into consideration as marked in the figure. (b) Time-domain response of the derivative of orientation factor with both THz pulses present (black, EAB) and the extracted nonlinear signal (magenta, ENL magnified 4x). The photon echo signal (R) appears at 6 ps, and the 2Q-R signal appears at 12 ps (i.e. 6 ps after the R signal). The NR signal appears at RevA, which is 6 ps earlier than RevB. The 2Q signal appears 6 ps earlier than the NR signal. The signal at the arrival of RevB is the PP sig n a l. ... 10 0 Figure 4.13 Simulated time-domain response of the derivative of the orientation factor, dcos~dt, at delays

-< Trev/2 (a) and at delays r > Trev/2. (b). Except for the effects of dephasing which are not accounted for, the

simulations show good agreement with the experimental results in Fig. 4.5. ... 101 Figure 4.14 2D time-domain trace of simulated orientation response. THz double reflections are taken into

consideration, resulting in a series of stimulated nonlinear responses. Amplitudes of orientation signal dcosOdt exceeding 1.5 are saturated in the color map for better contrast of weak signals...102

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Figure 4.15 Simulated 2D THz rotational spectra. NR (a) and R (b) spectra obtained from numerical Fourier transformation of the simulated 2D time-domain rotational response. The excitation frequency of the R spectra is made positive. Amplitudes inside the red dashed area are magnified lOX to bring out the 2Q (a) and 2Q-R (b) signals. The dashed boxes cover rotational transitions fromf25,26 tof37,38. (c) and (d) Enlarged

views of the spectral peaks in the dashed boxes in the NR (a) and R (b) spectra as functions of j quantum nunber. All the spectra are normalized and plotted based on the color map shown. Our simulation reproduces the third- and fifth-order J-resolved spectral peaks...103 Figure 4.16 Simulated 2Q (a) and 2Q-R (b) spectra. The amplitudes outside the red dashed lines are set to zero. (c) and (d) 2D J-quantum-number plots, i.e. magnified views of the spectra in the dashed boxes with the initial and final J levels for the transitions indicated along the vertical and horizontal axes respectively. The strongest diagonal peaks are at f = 2BcJ + 1 and v = 2Bc2J + 3, while the strongest off-diagonal peaks are at f = 2BcU + 2) and v = 2Bc2J + 3. All the spectra are normalized and plotted according to the co lo r m ap sh o w n . ... 10 3 Figure 4.17 Spectral slices from 2D rotational spectra. ID spectral slices along excitation frequency v=

0.589 THz =fi,32 (corresponding to the rotational transition between J = 31 and 32) from the NR (a, c, e)

quadrant and the R quadrant (b, d, f) at 70 torr (high pressure, red), 52 torr (medium pressure, blue) and 23 torr (low pressure, black). As pressure decreases, the linewidths of the rotational spectral peaks are narrower due to less collisional broadening. In both plots the vertical dashed lines represent the positions of each rotational transition frequency ranging fromfi, 2 2 tof4 4,45. The correlation between the rotational coherences

as far apart in frequency as 3132 and 3940 is seen by the most distant off-diagonal peak above the noise flo o r...10 5 Figure 5.1 Experimental setup for THz time-domain EPR spectroscopy. The static magnetic field is oriented either perpendicular (Faraday geometry) or parallel (Voigt geometry) to the sample surface. In both cases, the THz magnetic field is perpendicular to the static magnetic field...118 Figure 5.2 (a) Molecular structure of hemin. The HS Fe(III) is in square pyramidal coordination with five ligands. (b) MO diagram of an HS Fe(III) in a square-pyramidal coordination envionment. ... 120 Figure 5.3 (a) Magnetic sublevels originating from the ZFS of a spin-5/2 system assuming a positive D. The spin states are denoted by the MS quantum number. The magnetic dipole-allowed transitions are denoted by double-sided arrows. (b) Zeeman splitting and shift of the magnetic sublevels in hemin. (c) Magnetic field dependence of the dipole-allowed transition frequencies. In (b) and (c), the red, black and blue lines represent the splitting with Bo parallel to the molecular x, y and z axes respectively...121 Figure 5.4 (a) Time-domain waveform of reference THz pulse (black) and THz pulse transmitting through the sample followed by the FID signal (blue). The FID signal is magnified by 10 for clarity. (b) FT amplitude spectra of the THz reference pulse (black) and the THz pulse transmitting through the sample (black). Two spin resonances are indicated by the arrow s...122 Figure 5.5 (a) Raw absorbance spectrum of hemin at 20 K. Two spin resonances at ~0.4 and ~0.8 THz are indicated by the arrows. (b) Absorbance spectrum after background subtraction (dots) and a fit to two G aussian functions (solid line)...123 Figure 5.6 (a) Temperature-dependent absorbance spectra of hemin. The temperatures are color coded according to the legend. A slight blueshift for the peak at -0.4 THz is noticeable. (b) and (c) ZFS diagrams for positive and negative D. The disappearance of the higher-frequency peak at 3 K indicates D is positive. ... 1 2 3 Figure 5.7 (a) and (b) Experimental absorbance spectra of hemin as a function of the static external magnetic field at 3 K (a) and 20 K (b). (c) and (d) Simulated intensity spectra at 3 K (c) and 20 K (d). The spectra are color-coded based on the magnetic fields indicated in the figure...125

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Figure 5.8 (a) and (b) Experimental difference absorbance spectra (solid lines) and simulated difference

intensity spectra (dashed lines). The spectra are color-coded according to the magnetic fields indicated in the fig u re . ... 12 6 Figure 5.9 (a) Crystal structure of CoX2(PPh3)2. (b) MO diagram of a Co(II) in an ideal tetrahedral coordination environm ent...127

Figure 5.10 (a) Magnetic sublevels originating from the ZFS of a spin-3/2 system assuming a negative D.

The spin states are denoted by the MS quantum number. The magnetic dipole-allowed transition is denoted

by the double-sided arrow. (b) Zeeman splitting and shift of the magnetic sublevels in CoC12(PPh3)2. (c) Magnetic field dependence of the dipole-allowed transition frequencies. Red, black and blue lines represent the splittings with Bo parallel to the molecular x, y and z axes respectively, in (b) and (c). ... 128

Figure 5.11 Zero-field absorbance spectra of CoCl2(PPh3)2 at 6 K (a) and CoBr2(PPh3)2 at 2 K. Strong absorption peaks are due to vibrations. The spin resonance peak in each figure is indicated by the arrow. 129

Figure 5.12 Field-dependent absorbance spectra of CoCl2(PPh3)2 at 6 K (a) and CoBr2(PPh3)2 at 2 K (b). The

spectra all used a hamming apodization function. The color coding of the spectra is based on the magnetic field strengths show n in the legends...129

Figure 5.13 Experimental difference absorbance spectra (solid lines) and simulated difference absorbance

spectra (dashed lines) for CoCl2(PPh3)2 at 6 K (a) and CoBr2(PPh3)2 at 2 K (b). The spectra are color-coded according to the magnetic fields indicated in the figure. Additional features around 1.2 THz in (b) are due to the strong vibrational absorption peak...130

Figure 5.14 (a) Crystal structure of Fe(H20)62+. (b) MO diagram of a HS Fe(II) in an octahedral environment.

... 1 3 1 Figure 5.15 (a) Magnetic sublevels originating from the ZFS of a spin-2 system assuming a positive D. The

spin eigenstates are denoted by cPi. The magnetic dipole-allowed transitions are denoted by double-sided arrows. (b) Zeeman splittings and shifts of the magnetic sublevels in Fe(H20)6(BF4)2. (c) Magnetic field dependence of the dipole-allowed transition frequencies. Red, black and blue lines represent the splittings with Bo parallel to the molecular x, y and z axes respectively, in (b) and (c)...132

Figure 5.16 Absorbance spectra of Fe(H20)6(BF4)2 at 1.8 K (red) and 20 K (blue). A Hamming apodization function is applied to each spectrum. At 1.8 K, two strong peaks are assigned as the spin resonances resulting from two transitions. At 20 K, four peaks are assigned as the spin resonances resulting from six transitions.

... 1 3 3 Figure 5.17 Field-dependent absorbance spectra of Fe(H20)6(BF4)2 at 1.8 K. The two spin resonance peaks show splittings and shifts as a function of the applied magnetic field. The spectra are color-coded according to the m agnetic field strengths in the legend. ... 134 Figure 5.18 Experimental difference absorbance spectra (solid lines) and simulated difference intensity

spectra (dashed lines) for Fe(H20)6(BF4)2 at 1.8 K. The spectra are color-coded according to the magnetic fields indicated in the figure...134

Figure 5.19 (a) Crystal structure of NiCl2(PPh3)2. (b) MO diagram of a Ni(II) in an ideal tetrahedral coordination environm ent...135

Figure 5.20 (a) Magnetic sublevels originating from the ZFS of a spin-I system assuming a positive D. The

spin eigenstates are denoted by Di. The magnetic dipole-allowed transitions are denoted by double-sided arrows. (b) Zeeman splittings and shifts of the magnetic sublevels in NiCl2(PPh3)2. (c) Magnetic field dependence of the dipole-allowed transition frequencies. Red, black and blue lines represent the splitting with Bo parallel to the molecular x, y and z axes respectively, in (b) and (c)...136

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Figure 5.21 Field-dependent absorbance spectra of NiCl₂(PPh₃)₂at 2 K. The two spin resonance peaks show splittings and shifts as a function of the applied magnetic field. The strong absorption peak is likely due to lattice vibrations. The spectra are color-coded according to the magnetic field strengths in the legend...137 Figure 5.22 Experimental difference absorbance spectra (solid lines) and simulated difference intensity spectra (dashed lines) for NiCl2(PPh3)2 at 2 K. The spectra are color coded according to the magnetic fields

indicated in the figure...138

Figure 6.1 Lattice structure and spin order in YFeO₃. The oxygen octahedra in the four unit cells at the bottom are neglected for simplicity. The green dashed lines connect the nearest-neighbor sublattice spins denoted by the red arrow s...14 8 Figure 6.2 (a) The canted AFM order in YFO leads to a net magnetization M along the crystal c axis. S₁and S2 are the Fe

3

' electron spins ordered along the crystal a axis. The AF mode is the amplitude oscillation of

M while the F mode is the precession of M. (b) Single THz pulses transmitted through the sample followed by FID signals from the AF (blue) and F (red) modes. (c) FT magnitude spectra of the FID signals from both magnon modes, showing magnon resonances atfAF = 0.527 THz andfF = 0.299 THz. ... 149

Figure 6.3 (a) Schematic experimental geometry. Two THz pulses delayed by T with magnetic field polarization parallel to M excite the AF mode. At each delay r, BNL copolarized with input THz magnetic fields is measured by EOS as a function of t. Rotating the sample about the crystal a axis by 90' such that M is perpendicular to the THz magnetic fields allows the measurement of the F mode. (b) AF mode magnon signals induced by THz pulse A (BA, blue) and B (BB, red) individually. (c) Magnon signal with the presence of both THz pulses at r = 3.7 ps (BAB, black) and nonlinear signal (BNL magnified 50X, magenta). (d) FT magnitude spectrum of the oscillatory signal in BNL reveals X(3) and (2) peaks atfAF and 2fAF. .-... 151 Figure 6.4 Field dependence of the nonlinear time-domain traces. (a) Time-domain traces of BNL at varying excitation THz magnetic field strengths. The oscillatory signals in the dashed box are the nonlinear magnon responses. (b) Fourier transformation magnitude spectra of the oscillatory signals in (a). Two spectral peaks at the fundamental and second harmonic frequencies of the AF mode are observed. There is also a weak peak at zero frequency. The legend shows the magnetic field strengths for each trace as percentages of the m axim um T H z m agnetic field used...153 Figure 6.5 Dependence of the spectral peaks on input THz magnetic field strength. The peaks at the AF mode fundamental and second harmonic frequencies are fitted with one fit parameter to cubic and quadratic power dependences respectively. The scaling relations with respect to the input peak THz magnetic field strength confirm the orders of the nonlinear signals observed in our experiments. ... 154 Figure 6.6 Normalized 2D time-time plots of BNL(t, T) from the AF (a) and F (b) mode magnons respectively. Amplitudes exceeding 0.8 are saturated in the color map...154 Figure 6.7 2D time-frequency plot IBNL(fr) of AF magnon mode nonlinear response. IBNL(fT)l is generated by a numerical Fourier transformation with respect to t of the 2D time-time plot from the AF mode magnon shown in Fig. 6.6(a). The AF mode fundamental and second harmonic peaks are modulated as the delay r

in cre a se s. ... 15 5 Figure 6.8 (a) Spectral modulation as a function of rat the AF mode frequencyf=fAF. The real part (blue), imaginary part (red) and absolute value (black) of the complex spectral peak are plotted. Oscillations are clearly discernible in the time traces, showing a modulation of the spectral amplitude and phase as a function of r. (b) Fourier transformation of the complex spectral modulation along r in (a) yields the spectrum as a function of v. Four peaks are observed in the spectrum, corresponding to the rephasing (R), nonrephasing (NR), 2-quantum coherence (2Q), and pump-probe (PP) peaks. (c) Spectral modulation as a function of r along f=fAF. The real part (blue), imaginary part (red) and absolute value (black) of the complex spectral modulation are plotted as functions of r. (d) Fourier transformation of the complex spectral peak modulation along r in (c) yields the spectrum as a function of v. (e) Spectral modulation as a function of ratf= 0 THz.

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The real part (blue), imaginary part (red) and absolute value (black) of the complex spectral peak are plotted as functions of r. (f) Fourier transformation of the spectral peak modulation along r yields the spectrum as a fu n ctio n o f v. ... 15 6

Figure 6.9 2D THz magnetic resonance spectra of magnons in YFO. (a) Experimental AF mode 2D

magnitude spectrum. X/) spectral peaks include rephasing (R), nonrephasing (NR), pump-probe (PP) and

2-quantum (2Q) peaks. X2) spectral peaks include second harmonic generation (SHG) and THz rectification

(TR) peaks. (b) Experimental F mode 2D magnitude spectrum showing the full set ofX() spectral peaks. The artifacts are due to the signal double reflections in the sample. Each spectrum is normalized to its maximum value. Amplitudes above 0.5 are saturated in the color map. ... 157 Figure 6.10 Double-sided Feynman diagrams. Double-sided Feynman diagrams show typical excitation

pathways leading to the coherent emission of third-order (a, (i)-(iv)) and second-order (b, (v)-(vi)) nonlinear signals. Each solid arrow denotes a field interaction that induces a transition between magnon populations or coherences denoted by diagonal (00, 11) or off-diagonal (10, 20) density matrix elements respectively. The blue and red arrows represent interactions with THz pulse A and B respectively. The dashed arrows represent the measured signal fields. The time interval subscripts denote the number of preceding field interactions.

... 1 5 9 Figure 6.11 Simulated 2D THz magnetic resonance spectra of magnons in YFO. (a) Simulated AF mode 2D

magnitude spectrum. (b) Simulated F mode 2D magnitude spectrum. Each spectrum is normalized to its m axim um value...162

Figure 6.12 Simulated 2D magnitude spectra of the F mode magnon. (a) and (b) 2D spectra calculated from

the magnetization projections onto crystal b and c axis respectively. Third-order signals show up only in (a) while second-order signals show up only in (b). (c) The sum of 2D spectra in (a) and (b). Each spectrum is normalized to its maximum amplitude and is plotted according to the color map shown. ... 163

Figure 6.13 Temporal evolution of sublattice spins in AF magnon mode. (a) Exaggerated precession of

sublattice spins Si and S2 on the Bloch sphere. The two red arrows denote Si and S2 precessing around their static orientations indicated by the light red lines. The black arrow denotes the net magnetization M. The red dashed ellipses are the trajectories of Si and S2 on the sphere surface. (i)-(iii) The projection of the sublattice spins motion onto crystal ac plane. (i) is the projection with Si and S2 at equilibrium. (ii) and (iii) are the projections with Si and S2 reaching maximum and minimum values respectively along the crystal c axis. Note that under large angle precession, the excursion along the b axis is considerable, and the actual trajectories are distorted ellipses that are no longer planar. (b) Temporal evolution of the deviations from the static projections of Si and S2 along the crystal c axis, ASi,, as a function of time t normalized to the precession period T. The projection along c is periodic with a larger amplitude in the negative direction than in the positive direction (with respect to the projection of the static spin vectors) and results in a DC component in the negative c direction. (c) and (d) Fundamental (c), second harmonic (d, blue) and DC (d, black) components of ASi,c. This temporal evolution of Ai, gives rise to the second harmonic and rectification signals polarized along the crystallographic c axis and radiated by M (t)...166

Figure 7.1 Schematic representation of a generic ferroelectric phase transition. In the high temperature phase,

the crystal is in an isotropic paraelectric phase. As the temperature crosses the Curie temperature Tc, a structural phase transition occurs and the crystal enters a noncentrosymmetric ferroelectric phase. A dipole moment is formed in each unit cell. The long-range parallel order of the dipole moments gives rise to a m acroscopic spontaneous polarization. ... 172 Figure 7.2 Schematic representation of the evolution of the free energy curve based on Landau theory. The

vertical axis represents the free energy G and the horizontal axis represents the order parameter P. In the high-temperature phase, the minimum is at the center of the potential corresponding to order parameter P being zero. In the low-temperature phase, two local minima with nonzero order parameter values +P occur.

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Figure 7.3 Comparison of the lattice potential energy curves at T > Tc between displacive and OD phase transitions. (a) Displacive type transitions. Above Tc the phonon ground state energy Eo is above the potential barrier Vo. As temperature decreases the barrier height increases. The average phonon displacement gradually displaces away from zero in the soft mode coordinate and forms a static dipole. (b) OD type transitions. The transition occurs by the localization of ions to certain potential minima as the thermal-hopping or tunneling motions freeze at Tc ( Vo >> kBTc, where kB is the Boltzmann constant)...174

Figure 7.4 Lattice structure of STO. The unit cell has a perovskite structure. The soft mode in STO is associated with the oscillation of the central Ti ion with respect to the oxygen octahedron. ... 176 Figure 7.5 (a) Dielectric constant of STO as a function of temperature (data plotted after [9]). The horizontal axis is on logarithmic scale. (b) Frequencies of soft mode(s) in STO as a function of temperature (data plotted after [10]). The soft modes in different temperature ranges are labeled according to the symmetry shown in the legend. The black lines are guides for the eye. ... 177 Figure 7.6 (a) Estimated refractive indices (real part nr in blue and imaginary part ni in red) and (b) power absorption coefficients of STO in the TH z region...178 Figure 7.7 THz pump-optical SHG probe setup. Laser pulses are split into two paths by a beamsplitter (BS). The strong laser pulses are used to generate THz pulses in the LiNbO₃crystal. The generated THz pulses are collimated and focused onto the sample. The weak laser pulses are time delayed, attenuated and focused onto the sample. Optical SHG at 400 nm propagate in two directions collinear with the fundamental pulses at 800 nm as phase matching is fulfilled. Here, the SHG reflection is collected by a dichroic mirror (DM) and detected by a photomultiplier tube (PMT) and a data acquisition card at 1 -kHz repetition rate. A pair of wiregrid polarizers is used to vary the THz field strength without affecting the waveform...179 Figure 7.8 (a) THz time-domain profile and (b) FT amplitude spectrum of the pulses used in the experiments.

... ... 1 8 0

Figure 7.9 Schematic pulse sequence in the TFISH measurement. The THz, probe (800 nm), and SHG (400 nm ) pulses are located at ti, t2 and t respectively...182

Figure 7.10 The square of the THz field and TFISH signals from STO at four temperatures. The arrival of the first half-cycle of the THz field is around 0 ps. The SHG signals follow the square of the THz electric field. At 124 K, two cycles of oscillatory signals are discernible. The traces are color-coded according to the le g e n d . ... 18 3 Figure 7.11 The square of the THz field and TFISH signals from STO at five temperatures. The arrival of the first lobe of the THz field is around 0 ps. The instantaneous SHG signals follow the square of the THz electric field. As temperature decreases, more underdamped oscillatory signals are observed. The oscillation period becomes larger at lower temperatures, which is consistent with the temperature dependence of the soft mode frequency. The traces are color-coded according to the legend. The increasing baseline before 0 ps is attrib u ted to H R S ... 18 4 Figure 7.12 TFISH signals from STO at seven temperatures. The arrival of the first lobe of the THz field is around 0 ps. As temperature decreases, the oscillatory signals become more underdamped. The background also shows a more pronounced increase at lower temperatures. The traces are color-coded according to the legend. The increasing baseline before 0 ps is attributed due to HRS...185 Figure 7.13 (a) Oscillatory signals extracted from the TFISH signals at selected temperatures. The oscillatory features on the left hand side of vertical dashed line contain the instantaneous signals. Each trace is vertically offset and is color-coded according to the temperatures shown. (b) Fourier transform (FT) amplitude spectra of the oscillatory signals on the right hand side of the dashed line in (a) at each temperature. Each spectrum is vertically offset and color-coded according to the temperatures shown in (a). (c) Frequencies of the spectral

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peaks in (b) and soft mode frequencies after Ref. [10] as a function of temperature. The symbols are labeled in the legend. The black lines are guides for the eye. ... 187

Figure 7.14 Background SHG signal traces at selected temperatures extracted from the TFISH signal traces

by subtracting the oscillatory signals. The traces are color-coded according to the temperatures shown. .. 188 Figure 7.15 SHG background as a function of temperature. The SHG background level is extracted by taking

the average background intensity at 10 data points located at earlier than -2 ps in the signal trace at each temperature, ensuring that only the background before the arrival of the THz pulse is considered. The uncertainty range is the standard deviation of these averaged SHG intensities. The data below 50 K are fitted to a linear function (black line). The fit gives rise to an extrapolated critical temperature Tc of 72 K. ... 189

Figure 7.16 (a) and (b) Structure of TSCC in the crystal bc and ac planes. Dashed lines indicate hydrogen

bonds between N and Cl ions. A unit cell is indicated in the box with solid lines. The soft phonon vibrates along the crystal b axis. A ferroelectric polarization is formed along the crystal b axis below Tc ~130 K. 192

Figure 7.17 Soft mode frequency as a function of temperature in both ferroelectric and paraelectric phase of TSCC. The B2u soft mode frequency approaches a minimum at Tc = 127 K following a functionJ(T) oc [(T-Tc)/Tc]12

which is shown by the dashed line. Below Tc, the At soft mode frequency recovers to about 0.95 T H z. T he data are plotted after [20]. ... 192 Figure 7.18 (a) Time-domain traces of THz pulses transmitted through the TSCC sample above Tc with each

trace offset relative to the previous one. (b) THz absorbance spectra of TSCC in units of optical density (OD) at various temperatures with each trace offset by OD 2 relative to the next trace. The spectral peaks within the dashed box show the soft phonon at different temperatures. At ~1.65 THz a temperature independent T H z-active m ode is observed. ... 194

Figure 7.19 (a) Time-domain traces of THz pulses transmitted through the TSCC sample below Tc with each trace offset relative to the previous one. (b) THz absorbance spectra of TSCC in units of (OD) at various temperatures with each spectrum offset by OD 2 relative to the previous one. The spectral peaks within the dashed box show the soft phonon at different temperatures. The mode at 1.65 THz split into two below 116 K. Two additional modes at ~1.07 and ~1.32 THz appear below Tc...195 Figure 7.20 (a) ISRS time-domain signals and (b) Raman spectra of TSCC at three temperatures above Tc. The spectrum at 152 K is fitted to two Gaussian functions (red dashed line), which yields two peaks at 1.18 and 1.23 THz. The signals and spectra are offset vertically and are color coded according to the temperatures.

... ... 1 9 6

Figure 7.21 (a) Experimental time-domain traces at room temperature. The red line is the birefringence signal from TSCC and the blue line is the square of the THz electric field measured by electro-optic sampling. (b) Experimental spectra. The red line is the Fourier transformation of the oscillations in (a) after the THz field. The blue line is the THz excitation spectrum from the Fourier transformation of the THz electric field. .. 198 Figure 7.22 (a) Time-domain Kerr signals at four temperatures. (b) Vibrational spectra resulting from Fourier

transformation of the oscillatory signals in (a) excluding the signals during the arrival time of the THz pulse.

... 2 0 0 Figure 7.23 A two-step process describing the mechanism of THz excitation of Raman-active modes in TSCC. (i) THz field drives the soft mode by field-dipole interaction. (ii) At finite soft mode amplitude, the

lattice centrosymmetry is broken. THz field drives a Raman coherence through field-dipole interaction. The Raman coherence scatters the 800 nm probe pulse through a virtual state denoted by the dashed line. ... 201

Figure 8.1 (a) Schematic representation of a dipolar molecule. The n-bridge is functionalized with an electron donor (D) and an acceptor (A) in order to induce an asymmetric electron density distribution. Typical constituents of the 7r-bridge are also shown, where R1and R2 are usually carbon or nitrogen. (b) Molecules

Dynamics of lattice vibrations, molecular rotations and spins studied by terahertz spectroscopy

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Dynamics of molecular rotations, spins and lattice vibrations

studied by terahertz spectroscopy

Abstract

Acknowledgements

Contents

List of Figures