Close
About
FAQ
Home
Collections
Login
USC Login
Register
0
Selected
Invert selection
Deselect all
Deselect all
Click here to refresh results
Click here to refresh results
USC
/
Digital Library
/
University of Southern California Dissertations and Theses
/
Developmnt of high-frequency electron paramagnetic resonance (EPR) spectrometer and investigation of paramagnetic defects and impurities in diamonds by multi-frequency EPR spectroscopy
(USC Thesis Other)
Developmnt of high-frequency electron paramagnetic resonance (EPR) spectrometer and investigation of paramagnetic defects and impurities in diamonds by multi-frequency EPR spectroscopy
PDF
Download
Share
Open document
Flip pages
Contact Us
Contact Us
Copy asset link
Request this asset
Transcript (if available)
Content
DEVELOPMENT OF HIGH-FREQUENCY ELECTRON PARAMAGNETIC RESONANCE (EPR) SPECTROMETER AND INVESTIGATION OF PARAMAGNETIC DEFECTS AND IMPURITIES IN DIAMONDS BY MULTI-FREQUENCY EPR SPECTROSCOPY by Franklin Hyunil Cho A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In partial Fulllment of the Requirements for the Degree of DOCTOR OF PHILOSOPHY (PHYSICS) August 2015 ii c Copyright by Franklin Hyunil Cho 2015 iii I dedicate this to my Father, Yongmin Cho, and Mother, Sunnim Choi, for their unconditional love and support. Abstract Currently, the trend of magnetic resonance study is toward higher frequencies and magnetic elds, and the approach we take in our group utilizes the high-frequency (HF) electron para- magnetic resonance (EPR) spectrometer that has recently been developed. This dissertation aims to identify paramagnetic impurities in diamond and to uncover the relation between impurities and spin relaxation in diamond. The study is performed using a home-built HF EPR spectrometer which is highly advantageous to distinguish impurities in diamond, to probe couplings between spins, and to determine mechanisms of spin relaxations. The dis- sertation is structured as the following: In Chap. 1, an introduction of principles of CW and pulsed EPR spectroscopy including benets of performing EPR spectroscopy at HF is given. In Chap. 2, optical, electrical, and magnetic properties as well as current scientic interests on magnetic resonance study of diamonds are presented. In Chap. 3, details of the development of HF EPR spectrometer with unique experimental capability such as dou- ble electron-electron resonance (DEER) and dynamical decoupling (DD) are explained. In Chap. 4, investigation of spin decohernece in diamonds is demonstrated where HF DEER is used to extract the spin concentration in diamonds. Also extension of spin coherence in dia- monds by HF DD is shown. In Chap. 5, study of surface impurities in nanodiamonds (NDs) by HF CW EPR spectroscopy and HF DEER is shown which reveals that surface impurities exhibit very dierent properties from those found in deep inside ND crystals. Finally, in Chap. 6, study of spin decoherence in NDs by multi-frequency pulsed EPR spectroscopy is described which shows that the longitudinal relaxation times in NDs are signicantly aected and reduced by magnetic noise coming from the surface impurities. iv Acknowledgements There are too many who have helped me in the pursuit of my Ph.D. in Physics, and I wish to thank rst who are unnamed in the acknowledgement. My research could have not been realized without my advisor, Professor Susumu Taka- hashi. I truly appreciate his passion for scientic research, and thank him for his time, patience, support, and advise throughout all of the experiments, measurements, and anal- ysis that I have carried and performed under his guidance. During my time as a graduate student in his group, I have experienced and learned the nuts and bolts of many experimental techniques and tried my best to develop keen insights into scientic problems and establish how to put things into broad perspective. Next, I would like to acknowledge the members of our group. I want to thank Doctor Ekaterina E. Romanova, a past post-doctoral researcher in our group, for her supervision from the beginning of my time in the group until her leave. Countless thanks to current graduate students, Chathuranga Abeywardana, Rana Akiel, and Viktor Stepanov (listed in alphabetical order), for the productive collaborations, erce discussions, and just being good friends in many other circumstances. I believe they will know better how much I appreciate them in my journey. I wish the connections and friendships that I have had to be long-lasting. I also like to show my gratitude to the sta and faculty members of the Department of Physics and Astronomy as well as Chemistry. To name a few that comes to my head: Betty Byers, administrative assistant, Ramon Delgadillo, experimental machinist, G okhan Esirgen, instructional laboratory manager, Professor Stephan Haas, Mary Beth Hicks, administrative assistant, Professor Vitaly Kresin, Lisa Moeller, administrative coordinator, Allan Kershaw, v ACKNOWLEDGEMENTS vi director of advanced instrumentation, Professor Peter Z. Qin, Professor Richard Thompson, Professor Andrey Vilesov, and Don Wiggins, machine shop foreman (listed in alphabetical order). Finally, I want to mention Rick Hapanowicz, national sales manager at Cryogenic Lim- ited, and Steven A. Retzlo, millimeter wave engineer at Virginia Diodes, Inc., for their help and technical assistances in operation of superconducting solenoids, transmitter, and receiver which are essential parts of the home-built HF EPR spectrometer. Contents Abstract iv Acknowledgements v Contents vii List of Figures ix List of Abbreviations xvi List of Physical Constants xviii List of Symbols xix List of Units xxii 1 Introduction 1 1.1 Spin Hamiltonian Formalism . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1.1 Electron Zeeman interaction . . . . . . . . . . . . . . . . . . . . . . . 2 1.1.2 Nuclear Zeeman interaction . . . . . . . . . . . . . . . . . . . . . . . 3 1.1.3 Hyperne interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.1.4 Zero-eld interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.1.5 Nuclear quadrupole interaction . . . . . . . . . . . . . . . . . . . . . 5 1.2 CW EPR spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3 Pulsed EPR spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.4 Advantages of HF EPR spectroscopy . . . . . . . . . . . . . . . . . . . . . . 14 1.4.1 Higher spectral resolution . . . . . . . . . . . . . . . . . . . . . . . . 16 1.4.2 Higher spin polarization and sensitivity . . . . . . . . . . . . . . . . . 16 1.4.3 Better time resolution . . . . . . . . . . . . . . . . . . . . . . . . . . 18 1.4.4 Less susceptible to motional averaging eects . . . . . . . . . . . . . 19 1.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2 Defects and impurities in diamonds 20 2.1 Optical, electrical, and magnetic properties of diamond . . . . . . . . . . . . 20 2.2 Crystallographic defects and impurities in diamond . . . . . . . . . . . . . . 23 2.2.1 Single substitutional nitrogen defect (P1 center) . . . . . . . . . . . . 23 vii CONTENTS viii 2.2.2 Nitrogen-vacancy (NV) center . . . . . . . . . . . . . . . . . . . . . . 29 2.2.3 Surface paramagnetic defects and impurities . . . . . . . . . . . . . . 32 2.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3 Development of HF EPR spectrometer 35 3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.2 High-frequency, high-power transmitter . . . . . . . . . . . . . . . . . . . . . 38 3.3 Quasioptical system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 3.4 Superheterodyne detection system . . . . . . . . . . . . . . . . . . . . . . . . 45 3.5 12.1 T Cryogenic-free superconducting magnet . . . . . . . . . . . . . . . . . 47 3.6 Sample holder congurations and modulation coil designs . . . . . . . . . . . 51 3.7 Liquid helium cryostat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 3.8 Spectrometer control and data acquisition . . . . . . . . . . . . . . . . . . . 55 3.9 Sensitivity of HF EPR spectrometer in pulsed experiments . . . . . . . . . . 56 3.10 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 4 HF DEER and DD to investigate spin decoherence in diamonds 60 4.1 Spin decoherence in type-Ib diamond . . . . . . . . . . . . . . . . . . . . . . 61 4.2 HF DEER to extract spin concentration in diamond . . . . . . . . . . . . . . 64 4.3 HF DD to extend spin coherence in diamond . . . . . . . . . . . . . . . . . . 67 4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 5 HF EPR spectroscopy to identify surface impurities in NDs 70 5.1 Characterization of ND size by DLS . . . . . . . . . . . . . . . . . . . . . . . 71 5.2 HF CW EPR spectra of NDs . . . . . . . . . . . . . . . . . . . . . . . . . . 73 5.3 HF DEER of NDs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 5.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 6 Mechanisms of spin relaxations in NDs 81 6.1 Spin relaxations and surface impurities in NDs . . . . . . . . . . . . . . . . . 82 6.2 T 2 relaxation in NDs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 6.3 T 1 relaxation in NDs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 6.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 7 Conclusion 90 A Performance Specication of High-frequency, High-power Transmitter 93 B Calibration of Calorimetric Power Meter 95 Bibliography 97 List of Figures 1.1 Illustrative gure showing the energy diagram of aS = 1=2 system with isotropic electron g-value and theoretically expected absorption and 1 st derivative CW EPR spectrum, centered at the eld position determined by the resonance condition (see Eqn. 1.18). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.2 CW EPR spectra of BDPA radicals at 115 GHz. As the legend shows, the mea- sured spectrum is shown in solid line and and the simulated spectrum is shown in dotted line. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.3 Illustrative pulse diagram and the magnetization (M) in the Bloch sphere for (a) spin echo sequence and (b) inversion recovery sequence. . . . . . . . . . . . . . 15 1.4 Selected examples demonstrating advantages of HF EPR spectroscopy. (a) En- ergy diagram of two S = 1=2 systems as a function of magnetic eld. The overlapping spectra at lower frequencies well-resolved at higher frequencies. Fig- ure was adapted from Ref. [29] with kind permission from Springer Science and Business Media. Copyright (2009). (b) Simulated spectra showing better reso- lution of g-anisotropies. Figure was adapted from Ref. [30]. (c) Electron spin polarization forS = 1=2 system withg = 2 at two dierent frequencies as a func- tion of temperature, showing higher polarization is achieved by going to higher frequency. (d) Study spin decoherence in a high-spin system (S = 10) where quenching of spin decoherence was demonstrated by use of HF EPR spectroscopy at low temperatures. Adapted by permission from Macmillan Publishers Ltd: Ref. [31], copyright (2011). (e) Simulated spectra showing spectra at HF are less susceptible to motional eects. Figure was adapted from Ref. [30]. . . . . . . . 17 2.1 Selected examples of various applications of diamond. (a) Demonstration of nanoscale magnetic sensing. Adapted by permission from Macmillan Publish- ers Ltd: Ref. [77], copyright (2013). (b) Demonstration of temperature sensing. Figure adapted from Ref. [80], published under the terms of the Creative Com- mons Attribution 3.0 License. (c) Demonstration of nanoscale electric eld sens- ing. Adapted by permission from Macmillan Publishers Ltd: Ref. [78], copyright (2011). (d) Demonstration of entanglement. From Ref. [60]. Reprinted with permission from AAAS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 ix List of Figures x 2.2 (a) Structure of single substitutional nitrogen defect in diamond (P1 center), showing four possible orientations, [111], [ 111], [1 11], and [11 1]. C denotes a carbon atom and N denotes a nitrogen atom. (b) CW EPR spectra of single crystal diamond taken at three dierent orientations of magnetic eld with respect to the crystal for determination of g and A. Reprinted gure with permission from Ref. [87]. Copyright (1959) by the American Physical Society. . . . . . . . 25 2.3 (a) Measured and simulated CW EPR spectra of P1 centers at 230 GHz when B 0 k [100]. (b) Energy diagram of P1 centers as a function of B 0 . (c) E as a function of B 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.4 (a) Simulated absorption spectrum of P1 centers for powder sample showing indi- vidual component of dierent angles of P1 centers. (b) Measured and simulated 1 st derivative CW EPR spectra of P1 centers at 230 GHz for powder sample. . 30 2.5 (a) Structure of NV center in diamond. V denotes a lattice vacancy. (b) Flores- cence emission spectra of single NV centers. Figure was adapted from Ref. [49]. Copyright c [2006] [WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim]. (c) Electronic energy level structure of NV center. Nature of orescence decay de- pends on the spin states of NV center, thus the spin states of NV center can be initialized and read-out by optical illumination and orescence measurement. . 31 2.6 (a) Illustrative gure showing various possible structural defects (dislocations, broken bonds, and grain boundaries). (b) Illustrative gure showing dangling bonds which are proposed as one of possible candidates of paramagnetic defects and impurities near diamond surface. (c) \Core-shell" model. . . . . . . . . . . 33 3.1 Overview of the HF EPR spectrometer. The HF, high-power transmitter and receiver are custom built by Virginia Diodes, Inc., and the quasioptical system consists of corrugated horns, wiregrid polarizers, Faraday rotators, corrugated waveguides (Thomas Keating), and right-angle ellipsoidal mirrors (fabricated by the USC machine shop). EPR signals are rst down-converted to an intermediate frequency (IF) of 3 GHz by the receiver, then amplied by a low-noise amplier (LNA, noise gure of 0.5 dB; MITEQ) and by a second amplier (AML Com- munications). A 3 GHz reference is produced using outputs from the transmitter and receiver synthesizers to down-convert the IF signals to I and Q components of DC signals using an IQ mixer (Marki Microwave). Two lock-in ampliers (Stand- ford Research Systems) and a fast digital oscilloscope (Agilent Technologies) are used to measure I and Q signals for CW and pulsed experiments, respectively. A 12.1 T superconducting magnet (Cryogenic Limited) is employed to apply ex- ternal magnetic eld, and a liquid helium cryostat (Janis Research) is utilized for low temperature measurements. Data acquisition from the lock-in ampli- ers, oscilloscope, magnet, and cryostat is done via general purpose interface bus (GPIB), local area network (LAN), or universal serial bus (USB) connections, and switching of the transmitter and receiver and triggering of the oscilloscope are controlled by transistor-transistor logic (TTL) signals from a pulse genera- tor (SpinCore) via Bayonet Neill-Concelman (BNC) connections, which are all synchronized and programmed using National Instruments LabVIEW codes. . . 37 List of Figures xi 3.2 Circuit diagram of the HF, high-power transmitter. The transmitter consists of two microwave synthesizers (8{10 GHz and 9{11 GHz; Micro Lambda Wireless), isolators (DiTom Microwave), fast PIN switches (American Microwave Corpo- ration), directional couplers (Advanced Technical Materials), a power combiner (Narda Microwave East), a power splitter (Mini Circuits), an analog variable phase shifter (Antenna and Radome Research Associates), an amplier (Mini Circuits), and active and passive frequency multipliers (Virginia Diodes, Inc.). Microwaves up to the rst frequency doubler are connected via subminiature ver- sion A (SMA) connections, and rectangular waveguide connections are used from the output of the doubler to the corrugated horn. (a) Transmitter conguration for double frequency output required in DEER experiments. (b) Transmitter conguration for single frequency output with dual phase required in DD exper- iments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 3.3 Overview of the quasioptical system consisting of the transmitter and receiver stages. Reprinted with permission from Ref. [19]. Copyright [2014], AIP Pub- lishing LLC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 3.4 Calibration measurements of the variable attenuator. A Linearly polarized light with initial magnitude of oscillating electric eldE i propagates through the rotat- ing wiregrid polarizer and the xed-angle wiregrid polarizer where is the angle between the light's initial polarization direction and the axis of the rotating wire- grid polarizer. Magnitude of nal electric eld after the xed-angle wiregrid po- larizer is denoted asE f . (b) Attenuation of excitation waves as a function of the rotating wiregrid polarizer angle. Blue square dots represent measurements and solid line indicates a best-t to Eqn. 3.4. The best-t parameter of . Horizontal error bars represent the accuracy of measuring the angle (1 ), and vertical error bars indicate the standard deviations of three independent readings. For mea- surements, a pyroelectric detector (Eltec Instruments) was used which had been calibrated with a commercial calorimetric power meter from Virginia Diodes, Inc (see Appx. B). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 3.5 Circuit diagrams of the superheterodyne detection system. (a) Circuit diagram of the receiver that receives and down-converts EPR signals to IF. The HF LO consists of a microwave synthesizer (2{20 GHz; Micro Lambda Wireless), a directional coupler (Advanced Technical Materials), a PIN switch (American Microwave Corporation), an isolator (DiTom Microwave), an amplier (Spacek Labs), and active and passive frequency multipliers (Virginia Diodes, Inc.). The outputs of the HF LO are fed into subharmonically-pumped mixers (Virginia Diodes, Inc.) for down-conversion to 3 GHz IF. (b) Circuit diagram of the 3 GHz reference which is composed of a mixer (Marki Microwave), frequency mul- tipliers (Mini Circuits), high-pass lters (Mini Circuits), a variable phase shifter (Advanced Technical Materials), an amplier (Mini Circuits), and an IQ mixer (Marki Microwave). The reference is mixed with 3 GHz IF to produce I and Q of DC signals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 List of Figures xii 3.6 230 GHz CW EPR spectra of P1 centers when the magnetic eld is applied along [100] direction, showing the evidence of the mutual inductance between the main coil and the sweep coil. (a) Measured spectrum taken by ramping the sweep coil at a rate of 0.25 mT/s while the main coil was persisted at 8.15 T. (b) Simulated spectrum. (c) Measured spectrum taken by ramping the main coil at a rate of 0.13 mT/s while the sweep coil was turned o at 0 T. Clear shifts in the resonance eld positions are visible for the spectrum taken by ramping the sweep coil (indicated by vertical dotted lines). For the details of the spin Hamiltonian parameters and simulated spectrum, refer to Sect. 2.2.1. . . . . . . . . . . . . . . . . . . . . . . 49 3.7 Temperature of various points inside the magnet as a function of time as the magnet (a) cools down to its base temperatures from room temperature and (b) warms up back to room temperature from its base temperatures. Typical time frame for cooldown is70 hours and more than a week is needed for the complete warm-up. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 3.8 Overview of various sample holder congurations. Single crystal and thin-lm samples are positioned directly on a conductive end-plate, and powder and aque- ous/frozen solution samples are loaded to cylindrical \buckets" made of Te on. Depending on the dimensions, samples are placed either inside or near the bottom end of the corrugated waveguide. . . . . . . . . . . . . . . . . . . . . . . . . . . 52 3.9 Strength of DC magnetic eld generated by the modulation coil as a function of the amount of current owing through the coil. The magnetic eld at the opening of the coil is measured by the gaussmeter (AlphaLab). Open square dots represent the measurements and solid line is the linear t. . . . . . . . . . . . . 54 3.10 EPR measurements of BDPA radicals in polystyrene at room temperature. (a) CW EPR spectrum of BDPA radicals showing a single EPR signal with 0.9 mT peak-to-peak line width. The spectrum was taken by single scan at the magnetic eld ramp rate of 0.13 mT/s with the xed modulation of 0.05 mT at 20 kHz. (b) A single-shot spin echo signal with 2 = 2:1 s. A =2-pulse of 200 ns and a -pulse of 300 ns were used. The excitation pulses are largely truncated in the plot. The inset shows spin echo intensity as a function of 2. For the spin echo measurement, 256 shots of echo traces with the shot repetition rate of 30 ms were averaged to obtain a single data point. T 2 = 0:62 s was obtained by tting the decay with a single exponential function. Reprinted with permission from [19]. Copyright [2014], AIP Publishing LLC. . . . . . . . . . . . . . . . . . . . . . . 57 4.1 (a) Measurements ofT 2 of P1 centers as a function of volume concentration of P1 centers, showing T 2 is inversely proportional to the volume concentration. Fig- ure was adapted from Ref. [94]. (b) Theoretical investigation of T 2 of NV center surrounded by P1 centers, showing T 2 is inversely proportional to the volume concentration of P1 centers. Reprinted with permission from Ref. [55]. Copy- right (2013) by the American Physical Society. (c) Measurements ofT 2 of P1 and NV centers as a function of temperature, showing the quenching of dipolar uc- tuations of P1 centers from a nearly complete spin polarization. Reprinted with permission from Ref. [51]. Copyright (2008) by the American Physical Society. 62 List of Figures xiii 4.2 (a) 230 GHz echo-detected eld sweep of P1 centers when B 0 k [111] direction. For the spin echo sequence, =2- and -pulses of 300 and 500 ns, respectively, and a xed of 1.5 s were used. The magnetic eld was varied in step size of 0.05 mT, and 16 shots of echo signal were averaged to obtain a single data point with the repetition time of 20 ms. The inset shows the energy diagram of P1 centers. For subsequent DEER measurements,B 0 was xed at 8.2032 T and the P1 centers in the [111] orientation with m I = 1 were chosen as A spins (labeled as 5). B spins were the other four groups of P1 centers at 8.2043 T (P1 centers in the other three orientations with m I = 1; labeled as 4), 8.2072 T (P1 centers in all orientations with m I = 0; labeled as 3), 8.2102 T (P1 centers in the other three orientations with m I = 1; labeled as 2), and 8.2114 T (P1 centers in [111] orientation withm I = 1; labeled as 1). (b) DEER spectrum of P1 centers showing clear reductions of the spin echo intensity of A spins in four regions, centered at 229.771, 229.801, 229.889, and 229.975 GHz, which were due to dipolar couplings toB spins at 1, 2, 3, and 4, respectively. The inset shows the three-pulse DEER sequence used in the experiment where A denotes the resonance frequency of A spins (230 GHz) and B andt denotes the frequency and duration of the-pulse for B spins, respectively. Experimental parameters were =2 = 150 ns, = 250 ns, = 1 s, T = 850 ns, and t = 250 ns. B was varied in step size of 1 MHz, and 64 shots of echo signal were averaged to obtain a single data point with the repetition time of 10 ms. (c) Illustration of the static model of spin baths. (d) Sig DEER as a function of T for Group 1{4. Parameters used for the experiment were =2 = 150 ns, = 250 ns, = 2 s, and t = 250 ns. T was varied in step size of 25 ns, and 64 shots of echo signal were averaged to obtain a single data point with the repetition time of 10 ms. . . . . . . . . . . . . . . . . . . . . . . 65 4.3 (a) Three DD sequences for N = 4. Top: CPMG sequence, middle: two-axis CPMG sequence, and bottom: UDD sequence. -pulses are represented by solid squares and =2-pulses are represented by open squares. Phases of excitation pulses are set with respect to the phase of the reference microwave in the detection system. (b) Application of CPMG, two-axis CPMG, and UDD for N = 8 at 115 GHz. Data with errors are represented by markers with designated shape as shown in the legend and ts to a single exponential function are shown by solid lines. T coh was measured to be 651, 673, and 352 s with CPMG, two- axis CPMG, and UDD, respectively. The inset shows a trace of echo signals with CPMG forN = 4. The echoes are represented with solid lines. (c) Dependence of T coh on N with CPMG sequences at 115 GHz. Data with errors are represented by markers with designated shape as shown in the legend and ts to a single exponential function are shown by solid lines. T coh was measured to be 231, 42.10.5, 48.80.8, 651, 901, 1182, 1683, and 2118 s for N = 1 (spin echo), 2, 4, 8, 16, 32, 64, and 128, respectively. Reprinted with permission from [19]. Copyright [2014], AIP Publishing LLC. . . . . . . . . . . . . . . . . 68 List of Figures xiv 5.1 (a) Second-order autocorrelation curves of NDs obtained by DLS measurements. Data points are represented by open markers with designated shapes as indicated by the legend and ts are shown as solid lines. (b) Comparison of specied size and hydrodynamic diameters obtained from DLS measurements. Data points are represented by square dots and error bars indicate . . . . . . . . . . . . . . . . 72 5.2 230 GHz CW EPR spectra of various sizes of NDs. All spectra were taken at room temperature with eld modulation of 0.02 mT and sweep rate of 0.13 mT/s, and normalized for ease of comparison. Solid and dotted lines represent measured and simulated spectra, respectively. The simulated spectra were obtained by considering a superposition of two separate EPR spectra, P1 center and X. Partial contributions of EPR spectrum of P1 center and X are also shown for 460, 100, and 60 nm NDs. For 50 nm NDs, no trace of P1 center spectrum is visible in the measurement and the simulation is obtained only from X. . . . . . . . . . . . . 74 5.3 9.3 and 230 GHz CW EPR spectra of 50 nm NDs showing signicant line broad- ening from 9.3 to 230 GHz. Line broadenings due to dipolar coupling and g-strain were considered, which resulted in better agreement with the measured spectra compared with single Lorentzian ts. . . . . . . . . . . . . . . . . . . . . . . . 76 5.4 EPR intensity ratio of P1 center to X (I P 1 =I X ) as a function of size of NDs, d. Square dots represent EPR intensity ratio extracted from tting CW EPR spectra. x and y error bars indicate the standard deviations of sizes of NDs and errors associated with numerical simulations of CW EPR spectra, respectively. Dotted line represents a t with surface model and solid line represents a t with the core-shell model. The inset describes the surface model and core-shell model with shell thickness t. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 5.5 HF DEER measurement of 60 nm NDs where A spins were chosen as the central peak of P1 centers (i.e., m I = 0; see Fig. 6.2(a)). Only DEER signal to other groups of P1 centers in m I =1 states were detected and no reduction from dipole coupling to X was observed, which is a supporting evidence of the localized distribution of P1 centers and X in ND crystals presented in Sect. 5.2. . . . . . 80 6.1 Study of T 1 relaxation of single NV centers in NDs as a function of diameter of NDs and illustration of NV center and surface impurities in ND particle. Figure was adapted from Ref. [109]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 6.2 (a) Echo-detected eld-sweep spectrum at taken 115 GHz and 80 K (solid line). 300 ns and 500 ns pulses were used for =2- and -pulses, respectively, and a xed delay time of 1.5 s was used. The simulated spectrum (dotted lines) with contribution of P1 center and X agrees well with the measured spectrum. Arrows indicate resonance positions of P1 centers and X at which all subsequent relaxation measurements were performed. (b) Spin echo measurement and inver- sion recovery measurements of P1 centers, which yielded T P 1 2 of 0.84s andT P 1 1 of 0.93 ms from single exponential ttings shown as solid lines. (c) Spin echo and inversion recovery measurements of X, which yielded T X 2 of 0.32 s and T X 1 of 0.15 ms from single exponential ttings shown as solid lines. For all measure- ments, 64 shots of echo signal were averaged to obtain a single data point with the repetition time of 10 ms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 List of Figures xv 6.3 Summary of temperature, eld, and size dependence study of T P 1 2 in diamonds taken at (a) 9.3 GHz, (b) 115 GHz, and (c) 230 GHz. No strong dependence on temperature, eld, and size was observed. . . . . . . . . . . . . . . . . . . . . . 86 6.4 Summary of temperature, eld, and size dependence study of T P 1 1 in diamonds taken at (a) 9.3 GHz, (b) 115 GHz, and (c) 230 GHz. For the HF EPR spec- trometer, typical lengths of =2- and -pulse used were 500 and 700 ns for 230 GHz and 300 and 500 ns for 115 GHz, respectively, and chosen to maximize echo intensity. For the Bruker X-band spectrometer, typical lengths of =2- and - pulse used were 350 and 650 ns, respectively. (d) Strength of the constant C as a function of ND size. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 A.1 Measured output power of the transmitter as a function of frequency. (a) For 107{120 GHz. (b) For 215{240 GHz. Performance specication is provided by Virginia Diodes, Inc. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 B.1 Calibration measurements of the pyroelectric detector (Eltec Instruments) to a commercial calorimetric power meter (Virginia Diodes, Inc.). . . . . . . . . . . 96 List of Abbreviations AC Alternating Current BNC Bayonet Neill-Concelman BDPA , -BisDiphenylene--PhenylAllyl CPMG Carr-Purcell-Meiboom-Gill CW Continuous-Wave DC Direct Current DD Dynamical Decoupling DEER Double Electron-Electron Resonance DLS Dynamic Light Scattering EPR Electron Paramagnetic Resonance ESR Electron Spin Resonance EZI Electron Zeeman Interaction FWHM Full Width at Half Maximum GPIB General Purpose Interface Bus HF High-Frequency HFI HyperFine Interaction HPHT High-Pressure; High-Temperature I In-phase IF Intermediate Frequency KF Klein Flange LNA Local Area Network LNA Low-Noise Amplier LO Local Oscillator ND NanoDiamond NMR Nuclear Magnetic Resonance NQI Nuclear Quadrupole Interaction NZI Nuclear Zeeman Interaction ODMR Optically Detected Magnetic Resonance PC Personal Computer PP Peak-to-Peak PIN P-I-N Q Quadrature RF Radio Frequency SMA SubMiniature version A TTL Transistor-Transistor Logic xvi LIST OF ABBREVIATIONS xvii UDD Uhring Dynamical Decopuling USB Universal Serial Bus ZFI Zero-Field Interaction List of Physical Constants h 6:6260695710 34 kgm 2 s 1 or Js Planck constant k B 1:380648810 23 kgm 2 s 2 K 1 or JK 1 Boltzmann constant N A 6:0221412910 23 mol 1 Avogadro number 0 410 7 NA 2 or TmA 1 Permeability of free space B 9:2740096810 24 kgm 2 s 2 T 1 or JT 1 Bohr magneton xviii List of Symbols A hyperne interaction tensor (Eqn. 1.6) Attn attenuation (Eqn. 3.1) B proportionality constant used for tting temperature dependence of T 1 (Eqn. 6.1) or baseline constant in dynamic light scattering (Eqn. 5.1) B 0 externally applied static magnetic eld B 1 oscillating magnetic eld produced by the microwave excitation BW pulse excitation bandwidth (Eqn. 3.7) C constant used for tting attenuation of variable attenuator (Eqn. 3.4), tem- perature independent parameter in the ip- op rate equation (Eqn. 4.1), or temperature dependence of T 1 (Eqn. 6.1) E f nal electric eld intensity (Eqn. 3.2) E i initial electric eld intensity (Eqn. 3.2) f fraction of spins that are excited by microwave pulse (Eqn. 3.6) g electron g-tensor (Eqn. 1.2) g electron g-value g 2 () autocorrelation function in dynamic light scattering measurement (Eqn. 5.1) H general spin Hamiltonian (Eqn. 1.1) H EZI electron Zeeman interaction term in spin Hamiltonian (Eqn. 1.2) H HFI hyperne interaction term in spin Hamiltonian (Eqn. 1.6) H NQI nuclear quadrupole interaction term in spin Hamiltonian (Eqn. 1.10) H NZI nuclear Zeeman interaction term in spin Hamiltonian (Eqn. 1.5) H ZFI zero-eld interaction term in spin Hamiltonian (Eqn. 1.8) angle between incident electric eld and wiregrid polarizer I nuclear spin value (n=2 wheren is a positive integer) or nal microwave inten- sity (Eqn. 3.3) ^ I nuclear spin operator in vector form whose elements are ^ I i (i =x, y, and z) ^ I i matrix representation of nuclear spin operators, usually expressed in the Zee- man basis (i =x, y, and z) I f nal signal intensity in calculating attenuation in dB scale (Eqn. 3.1) I i initial signal intensity in calculating attenuation in dB scale (Eqn. 3.1) I 0 initial microwave intensity (Eqn. 3.3) M BDPA molecular weight of BDPA radicals (Eqn. 3.5) m BDPA initial mass of BDPA radicals (Eqn. 3.5) m film mass of polystyrene lm containing BDPA radicals (Eqn. 3.5) m polystyrene initial mass of polystyrene lm (Eqn. 3.5) xix LIST OF SYMBOLS xx m I nuclear spin quantum number m S electron spin quantum number N i relative spin population of i th state N s pins number of electron spins (Eqn. 3.5) n volume concentration of P1 centers (Eqn. 4.2) P electron spin polarization (Eqn. 1.33) Q quality factor of microwave cavity or resonator (Eqn. 1.36) Q nuclear quadrupole interaction tensor (Eqn. 1.10) R(;; ) Rotation with Euler angles , , and (Eqn. 1.4) S electron spin value (n=2 where n is a positive integer) ^ S electron spin operator in vector form whose elements are ^ S i (i =x, y, and z) ^ S i matrix representation of electron spin operators, usually expressed in the Zee- man basis (i =x, y, and z) Sensitivity sensitivity of HF EPR spectrometer in pulsed experiments (Eqn. 3.6) Sig DEER double electron-electron resonance signal (Eqn. 4.2) SNR signal-to-noise ratio (Eqn. 3.6) T temperature (Eqn. 4.1), microwave excitation pulse spacing between the rst - and =2-pulse in the inversion recovery sequence, or pulse separation in double electron-electron resonance experiments (Eqn. 4.2) T Ze Zeeman temperature used in the ip- op equation (Eqn. 4.1) T 1 characteristic recovery time of electron spins in the longitudinal plane of the Bloch sphere measured in spin echo measurement (also known as spin-lattice relaxation time or longitudinal relaxation time) T 2 characteristic decay time of electron spins in the transverse plane of the Bloch sphere measured in inversion recovery measurement (also known as spin deco- herence time, spin-spin relaxation time or transverse relaxation time) T coh coherence time of electron spins in the transverse plane in dynamical decoupling experiments t time symbol used in ring-down equation or t length of -pulse used in the pulse sequence t =2 length of =2-pulse used in the pulse sequence Z partition function (Eqn. 1.34) amplitude of autocorrelation function in dynamic light scattering measurement (Eqn. 5.1) L FWHM full width at half maximum line width of the Lorentzian line shape function (Eqn. 1.23) G PP peak-to-peak line width of the Gaussian line shape function (Eqn. 1.24) res residual relaxation rate in the ip- op rate equation (Eqn. 4.1) 1 rst cumulant of autocorrelation function in dynamic light scattering (Eqn. 5.1) 2 second cumulant of autocorrelation function in dynamic light scattering (Eqn. 5.1) ^ magnetic moment operator (Eqn. 1.25) microwave frequency LIST OF SYMBOLS xxi microwave excitation pulse spacing between =2- and-pulse in the spin echo sequence (also known as free evolution time) or time symbol used in dynamic light scattering (Eqn. 5.1) List of Units A Ampere dB Decibel g Gram GHz Gigahertz (=110 9 Hz) Hz Hertz (=1 cycles 1 ) J Joule (=1 m 2 kg) K Kelvin kHz Kilohertz (=110 3 Hz) ppm Parts per million (=110 6 %) m Meter MHz Megahertz (=110 6 Hz) mA Milliampere (=110 3 s) mbar Millibar (=110 3 bar) mg Milligram (=110 3 g) mol Mole (=6.0221412910 23 molecules) ms Millisecond (=110 3 s) mT Millitesla (=110 3 mT) mW Milliwatt (=110 3 W) ns Nanosecond (=110 9 s) s Second T Tesla m Micrometer (=110 6 m) s Microsecond (=110 6 s) T Microtesla (=110 6 T) xxii Chapter 1 Introduction Electron paramagnetic resonance (EPR) spectroscopy, also referred as electron spin reso- nance (ESR) spectroscopy, is a powerful technique to study electronic and magnetic prop- erties of various systems in solids. Continuous-wave (CW) EPR spectroscopy enables to determine anisotropic g-values and hyperne couplings which re ect structures and symme- tries of spin systems and pulsed EPR spectroscopy enables to measure spin relaxations of the spin system which probes couplings between the spin systems and also their environ- ments. High-frequency (HF) EPR spectroscopy is an emerging technique. In this chapter, an introduction of EPR spectroscopy as well as discussion of advantages of performing EPR spectroscopy at higher frequencies and higher magnetic elds will be given. 1.1 Spin Hamiltonian Formalism In EPR spectroscopy, resonant absorption of electromagnetic eld occurs when the energy separations of electron spin states (E) coincide with the energy of the photons of the electromagnetic eld (h). Using EPR spectroscopy, various static and dynamic properties of a spin system can be measured, e.g., local shielding eects measured by the g-value and interactions to surrounding electron and nuclear spins measured by dipolar and hyperne couplings and spin relaxation times. 1 Chapter 1. Introduction 2 For many spin systems in solids, their spin states are expressed by the following spin Hamiltonian ( ^ H), ^ H = X i ^ H i EZI + ^ H i ZFI + X k ^ H k NZI + ^ H k NQI + X i;k ^ H i;k HFI ; (1.1) where ^ H i EZI and ^ H i ZFI are the electron Zeeman interaction (EZI) and zero-eld interaction (ZFI) of i th electron spin, respectively, ^ H k NZI and ^ H k NQI are the nuclear Zeeman interac- tion (NZI) and nuclear quadrupole interaction (NQI) of k th nuclear spin, respectively, and ^ H i;k HFI is the hyperne interaction (HFI) betweeni th electron spin andj th nuclear spin. The Hamiltonian from the orbital angular momentum is omitted in Eqn. 1.1 because the angular momentum is quenched in the systems discussed here. 1.1.1 Electron Zeeman interaction Often the most dominant term of the spin Hamiltonian in high elds is the electron Zeeman interaction which describes how the magnetic dipole moment arising from an electron spin interacts with the externally applied magnetic eld (B 0 ), ^ H EZI = B h B T 0 g ^ S = B h B x 0 B y 0 B z 0 0 B B B B @ g xx g xy g xz g yx g yy g yz g zx g zy g zz 1 C C C C A 0 B B B B @ ^ S x ^ S y ^ S z 1 C C C C A ; (1.2) where B is the Bohr magneton,B x 0 ,B y 0 , andB z 0 are x-, y-, and z-component of the externally applied magnetic eld, g ij are the elements of g-tensor which characterizes the magnetic moment and gyromagnetic ratio of an electron spin (i;j = x, y, and z), and ^ S x , ^ S y , and ^ S z are the electron spin operators. For an isolated electron spin, the isotropic g-tensor (g e = 2:0023193043617) or electron gyromagnetic ratio (j e j =jejg e =(2m e ) = g e B =h = 28:02495266 GHzT 1 ; e is the elementary charge and m e is the rest mass of an electron) is one of the most precisely determined physical constants (the most recently accepted value Chapter 1. Introduction 3 by the National Institute of Standards and Technology; determined from direct observation of transitions between a trapped free electron and cyclotron in Ref. [1] published in 2006). Possible local magnetic elds and spin-orbit coupling cause anisotropies in the g-tensor, phenomenon known as g-anisotropy, which often re ects structural symmetry. The g-tensor can be transformed into its diagonal form (g diag ) by choosing the x, y, and z-axis to its principal axes, i.e., g diag = 0 B B B B @ g x 0 0 0 g y 0 0 0 g z 1 C C C C A =R 1 (;; )gR(;; ); (1.3) where g x , g y , and g z are the diagonal or principal values of the g-tensor (often referred as g-values of a spin system) andR(;; ) is a rotation with Euler angles, , , and , R(;; ) = 0 B B B B @ c( )c() c()s()s( ) c( )s() + c()c()s( ) s( )s() s( )c() c()s()c( ) s( )s() + c()c()c( ) c( )s() s()s() s()c() c() 1 C C C C A ; (1.4) where c and s are short notations for cosine and sine functions, respectively. 1.1.2 Nuclear Zeeman interaction Similar to the electron Zeeman interaction, the nuclear Zeeman interaction describes how the magnetic dipole of a nuclear spin interacts with the externally applied magnetic eld, ^ H NZI = n g n h B T 0 ^ I = n g n h B x 0 B y 0 B z 0 0 B B B B @ ^ I x ^ I y ^ I z 1 C C C C A ; (1.5) where n is the nuclear Bohr magneton and ^ I x , ^ I y , and ^ I z are the nuclear spin operators. Here the chemical shifts and the chemical shift anisotropies observed in nuclear magnetic Chapter 1. Introduction 4 resonance (NMR) spectroscopy are neglected and only the isotropic nuclear g-factor of a particular nuclear spin (g n ) is considered. 1.1.3 Hyperne interaction When there exists a nuclear spin nearby an electron spin, the dipole-dipole interaction be- tween an electron spin (S) and nuclear spin (I) is known as hyperne interaction, ^ H HFI = ^ S T A ^ I = ^ S x ^ S y ^ S z 0 B B B B @ A xx A xy A xz A yx A yy A yz A zx A zy A zz 1 C C C C A 0 B B B B @ ^ I x ^ I y ^ I z 1 C C C C A ; (1.6) where A ij are the elements of the A-tensor which characterizes the hyperne interaction strengths (i;j = x, y, and z). Anisotropies of hyperne interaction may arise from the dipole-dipole interaction itself and the localized structure of a spin system, but in case of a system with local symmetry, the A-tensor can be transformed into its diagonal form (A diag ) via a rotation, similar to the case of the g-tensor, A diag = 0 B B B B @ A x 0 0 0 A y 0 0 0 A z 1 C C C C A =R 1 (;; )AR(;; ); (1.7) where A x , A y , and A y are the diagonal or principal values of the A-tensor. 1.1.4 Zero-eld interaction In addition, for a spin system with S > 1=2, interaction between electron spins causes split- ting of energy levels even in the absence of the externally applied magnetic eld. Hamiltonian Chapter 1. Introduction 5 of the zero-eld interaction is given by, ^ H ZFI = ^ S T D ^ S = ^ S x ^ S y ^ S z 0 B B B B @ D xx D xy D xz D yx D yy D yz D zx D zy D zz 1 C C C C A 0 B B B B @ ^ S x ^ S y ^ S z 1 C C C C A ; (1.8) where D ij are the elements of the D-tensor (i;j = x, y, and z). The D-tensor is traceless ( P i D ii = 0) and symmetric (D ij =D ji ), and often characterized by two parameters (D and E) in its eigenframe, D diag = 0 B B B B @ D x 0 0 0 D y 0 0 0 D z 1 C C C C A = 0 B B B B @ 1 3 D +E 0 0 0 1 3 DE 0 0 0 2 3 D 1 C C C C A ; (1.9) whereD = 3=2D z andE = (D x D y )=2 (a common convention to choose the principal axes is such thatjD z j>jD y j>jD x j to yield positive E=D). 1.1.5 Nuclear quadrupole interaction Similar to the zero-eld interaction, for a nuclear spin system with I > 1=2, nuclear quadrupole interaction can lift the degeneracy of the energy levels in the absence of the externally applied magnetic eld whose interaction can be written as, ^ H NQI = ^ I T Q ^ I = ^ I x ^ I y ^ I z 0 B B B B @ Q xx Q xy Q xz Q yx Q yy Q yz Q zx Q zy Q zz 1 C C C C A 0 B B B B @ ^ I x ^ I y ^ I z 1 C C C C A ; (1.10) Chapter 1. Introduction 6 where Q ij are the elements of the Q-tensor (i;j = x, y, and z). Similar to D-tensor, the Q-tensor is traceless ( P i Q ii = 0) and symmetric (Q ij =Q ji ), and can also be diagonalized via a similar rotation as in g-, D-, and A-tensor, i.e., Q diag = 0 B B B B @ Q x 0 0 0 Q y 0 0 0 Q z 1 C C C C A = e 2 Qq=h 4I(2I 1) 0 B B B B @ (1) 0 0 0 (1 +) 0 0 0 2 1 C C C C A ; (1.11) where e 2 Qq=h = 2I(2I 1)Q z and = (Q x Q y )=Q z are two parameters used for charac- terizing the diagonal Q-tensor where Q is the electric quadrupole moment of a nuclear spin, eq is the largest component of the electric eld gradient at the nuclear spin, and is the asymmetry parameter. 1.2 CW EPR spectroscopy CW EPR spectroscopy is commonly used to determine parameters in the spin Hamiltonian. Here a method to simulate CW EPR spectrum is introduced brie y. There are also great textbooks that provide spin dynamics in EPR [2{5]. Consider an isolated electron under a magnetic eld whose spin Hamiltonian is expressed with the electron Zeeman term, ^ H = B g iso X i=x;y;z B i 0 ^ S i : (1.12) In principle, any basis can be used for expressing the spin Hamiltonian. However, it is intuitive to write it in so-called Zeeman basis (ji Zeeman i), i.e., j1 Zeeman i =jm S = 1=2i j2 Zeeman i =jm S =1=2i; (1.13) Chapter 1. Introduction 7 and perform rotation on the externally applied magnetic eld with respect to the Zeeman basis. Using the 2 2 matrix representations of the electron spin operators forS = 1=2, i.e., ^ S x = 1 2 0 B @ 0 1 1 0 1 C A ^ S y = 1 2 0 B @ 0 i i 0 1 C A ^ S z = 1 2 0 B @ 1 0 0 1 1 C A ; (1.14) Eqn. 1.12 can be written as, ^ H = B g iso 2 0 B @ B z 0 B x 0 iB y 0 B x 0 +iB y 0 B z 0 1 C A : (1.15) In order to simulate CW EPR spectrum, the eigenstates and eigenvalues of the spin Hamil- tonian are calculated which represent the spin states (jii) and their energies (E i ). It is easy to see that the energies are proportional to the strength of eld, i.e., E 1 = B g iso 2 jB 0 j = B g iso 2 q (B x 0 ) 2 + (B y 0 ) 2 + (B z 0 ) 2 E 2 = B g iso 2 jB 0 j = B g iso 2 q (B x 0 ) 2 + (B y 0 ) 2 + (B z 0 ) 2 ; (1.16) and the eigenstates given as, j1i = 0 B @ B z 0 + q (B x 0 ) 2 + (B y 0 ) 2 + (B z 0 ) 2 B x 0 +iB y 0 1 C A j2i = 0 B @ B x 0 iB y 0 B z 0 q (B x 0 ) 2 + (B y 0 ) 2 + (B z 0 ) 2 1 C A : (1.17) Figure 1.1 shows the energy diagram of a such system as a function of strength of exter- nally applied magnetic eld. The splitting or energy gap betweenj1i andj2i (E =E 1 E 2 ) Chapter 1. Introduction 8 Microwave Magnetic Field Energy Absorption Derivative E 1 E 2 |2> |1> ∆E = E 1 - E 2 = hν Field modulation Figure 1.1: Illustrative gure showing the energy diagram of a S = 1=2 system with isotropic electron g-value and theoretically expected absorption and 1 st derivative CW EPR spectrum, centered at the eld position determined by the resonance condition (see Eqn. 1.18). Chapter 1. Introduction 9 increases linearly to the strength of the eld, and a resonant absorption of microwave occurs and EPR signal can be observed when the frequency of microwave excitations () matches the energy gap (E), i.e., h = E: (1.18) Equation 1.18 is known as the resonance condition. To satisfy the resonance condition, either orB 0 can be varied but is often xed and B 0 is ramped to observe EPR signals as a function of eld because the performance of EPR spectrometer usually depends strongly on . Moreover, it is customary to use magnetic eld modulation technique with CW EPR spectroscopy to improve signal-to-noise (SNR), thus observed CW EPR signals are usually the 1 st derivative of the absorption spectrum (see Fig. 1.1). An approach for simulating the observed EPR spectrum is the following; 1) solving the spin Hamiltonian to nd the resonance condition, 2) calculating the transition probability to determine the EPR intensity, and 3) considering the line shape to build a resembled spectrum. As an example, the CW EPR spectrum of, -bisdiphenylene--phenylallyl (BDPA), aS = 1=2 stable free radical widely used in the eld of EPR spectroscopy and related techniques [6{ 9] is considered here (see Fig. 1.2). The EPR spectrum was taken taken at frequency of 115 GHz in room temperature with applications of external magnetic eld (B 0 ) perpendicular to the 115 GHz microwave elds. As shown in Fig. 1.2, a single EPR peak centered at4.1021 T was observed. The rst step of simulating CW EPR spectrum of BDPA radical is to calculate the resonance magnetic eld position using Eqn. 1.16 and 1.18, i.e., h = E = B h g BDPA iso jB 0 j; (1.19) or, jB 0 j = h B g BDPA iso = 6:62610 34 Js 11510 9 Hz 9:27410 24 JT 1 g BDPA iso : (1.20) The reported isotropic g-value of BDPA radical in the literature is g BDPA iso = 2:003 [10, 11], and this can also be easily extracted from inserting the observed B 0 4:1021 T into Chapter 1. Introduction 10 Meas. Sim. Intensity (Arb. units) Field (T) 4.1 4.102 4.104 4.098 4.106 ≈0.94 mT Figure 1.2: CW EPR spectra of BDPA radicals at 115 GHz. As the legend shows, the measured spectrum is shown in solid line and and the simulated spectrum is shown in dotted line. Chapter 1. Introduction 11 Eqn. 1.20 as, g BDPA iso = h B jB 0 j = 6:62610 34 Js 11510 9 Hz 9:27410 24 JT 1 4:1021 T 2:003: (1.21) Next, EPR signal intensity is the square of the transition moment or transition probability (p ji ) from the initiali th state to the nalj th state caused by microwave excitation (B 1 ). For a given transitionjji!jii, p ji can be expressed as, p ji / hjj ^ H 1 jii 2 ; (1.22) where ^ H 1 = B B T 1 g ^ S=h is the Hamiltonian of excitation microwave containing electron Zeeman interaction terms describing howB 1 interacts with magnetic dipole moments arising from electron spins. The nal step is to consider a shape function of the EPR spectrum. The two most widely used line shape functions are the Gaussian and Lorentzian functions. Relaxations in EPR are often considered as exponentially decaying functions, and Lorentzian line shapes arise from such spin dynamics, thus EPR spectrum will be the 1 st derivative of the normalized Lorentzian function centered at B 0 , 16 (BB 0 ) L FWHM h 4 (BB 0 ) 2 + ( L FWHM ) 2 i 2 ; (1.23) where B is the strength of varying externally applied eld and L FWHM is the full width at half maximum (FWHM) line width of the Lorentzian absorbtion line width. Moreover, an EPR line shape broaden by inhomogeneous B 0 and small hyperne couplings is often well represented by the 1 st derivative of the normalized Gaussian function, 8 r 2 (BB 0 ) ( G PP ) 3 exp 2 BB 0 G PP 2 ! ; (1.24) Chapter 1. Introduction 12 where G PP is the distance between in ection points of the Gaussian absorbtion line shape function (also called as the peak-to-peak (PP) line width of the 1 st derivative Gaussian line shape). Finally there are also cases with non-Lorentzian and -Gaussian line shapes. Examples include broadening due to g- and A-anisotropies and random orientations of spins (e.g., powder spectrum, Sect. 2.2.1) and broadening due to dipolar interactions (Sect. 5.2). For the current example, the Gaussian line shape function obtained with G PP = 0:94 mT yielded a good agreement with the measured EPR spectrum as shown in Fig. 1.2. 1.3 Pulsed EPR spectroscopy While CW EPR spectroscopy is utilized to study static spin properties, pulsed EPR spec- troscopy enables probing the transient spin properties, e.g., various spin relaxation mecha- nisms and spin properties in a transient state, with time resolution of nanoseconds. In pulsed EPR spectroscopy, the intuitive Bloch model is frequently used because of its simple, visual, and intuitive explanation [12]. The model describes the time dependence of the total spin magnetization phenomenologically by the famous Bloch equations. It was mostly developed in the context of NMR, but the basic theoretical framework of spin physics is equally appli- cable to EPR spectroscopy. It starts with the equation of motion from the fundamentals of quantum mechanics, i.e., d^ dt = e ^ B (1.25) where e is the gyromagnetic ratio, ^ is the magnetic momentum operator, and B is the magnetic eld vector. Ensemble averaging of Eqn. 1.25 leads to the basic form of the Bloch equations, dM dt = e MB (1.26) whereM(t) =M x (t)^ x+M y (t)^ y +M z (t)^ z is the time-dependent total, ensemble, or bulk spin magnetization vector of the system. In the laboratory frame with only the static externally Chapter 1. Introduction 13 applied eld along the z-axis, i.e.,B =B L 0 =B 0 ^ z L , Eqn. 1.26 reads, dM x dt = e (M(t)B(t)) x = e B L 0 M y dM y dt = e (M(t)B(t)) y = e B L 0 M x dM z dt = e (M(t)B(t)) z = 0: (1.27) The solutions to Eqn. 1.27 are given as, M x =M i ? cos( e B L 0 ) M y =M i ? sin( e B L 0 ) M z =M i z : (1.28) where M i z is the initial magnetization along the z-direction and M i ? = q (M i x ) 2 + M i y 2 is the initial magnetization in the xy plane. Equation 1.28 reveals thatM precesses about the z-axis. In the thermal equilibrium, the magnetization in a static magnetic eld B = B L 0 will be parallel toB, i.e.,M = M eq ^ z L . This means that the solutions of Eqn. 1.27 as t!1 will need to approach M = M eq ^ z L . Bloch equations incorporate this into Eqn. 1.27 by introducing two empirical relaxation rates as, dM x dt = e (M(t)B(t)) x M x (t) T 2 dM y dt = e (M(t)B(t)) y M y (t) T 2 dM z dt = e (M(t)B(t)) z M z (t)M eq T 1 ; (1.29) whereT 1 is the characteristic relaxation time of the z-component magnetization, also known as longitudinal or spin-lattice relaxation time, and T 2 is the characteristic relaxation time of the x- and y-component magnetization, also known as transverse or spin-spin relaxation time. The x- and y-component magnetization is often combined and expressed as the complex transverse magnetization M trans as, M trans =M x +iM y : (1.30) Chapter 1. Introduction 14 Then, in the frame that is rotating about the z-axis at the angular frequency ! = e B L 0 (often referred as the rotating frame), the solutions of Eqn. 1.29 yield M trans (t) =M i trans exp t T 2 (1.31) M z (t) =M eq M eq M i z exp t T 1 : (1.32) As shown Fig. 1.3(a), the pulse sequence known as the spin echo sequence is employed for measuring T 2 . The pulse sequence consists of a =2- and -pulse where the application of =2-pulse rst ips the magnetization vector into the transverse plane of the Bloch sphere. During the rst half of the sequence, dephasing of the magnetization occurs. By applying -pulse at the middle of the sequence, refocusing of the magnetization occurs, and at the end of the sequence, the magnetization in the transverse plane is detected. By measuring the spin echo intensity as a function of free evolution time 2, the characteristic decay time T 2 is extracted by tting to an exponential function (Eqn. 1.31). Using the spin echo sequence, the pulsed spectrum known as echo-detected eld sweep can also be measured. In this case, 2 is held constant and the echo intensity is recorded as a function of the magnetic eld. For measuring T 1 , the pulse sequence known as the inversion recovery sequence is often employed (see Fig. 1.3(b)). The inversion recovery sequence rst ips the magnetization into the negative z-direction of the Bloch sphere by applying a -pulse. Then the magnetization starts to relax back to its thermal equilibrium, and the degree of relaxation is read out by applying the spin echo sequence. By measuring the spin echo intensity as a function of delay time (T ), the characteristic recovery time T 1 is extracted by tting to an exponential function (Eqn. 1.31). 1.4 Advantages of HF EPR spectroscopy Traditionally, EPR spectroscopy has been routinely carried out at the microwave frequency of9 GHz (X-band) and the magnetic eld of0.3 T. On the other hand, HF pulsed Chapter 1. Introduction 15 X Y Z Dephasing during free evolution Application of π-pulse Refocusing during free evolution Application of π/2-pulse Read-out τ τ Echo π π/2 (a) (b) X Y Z Echo π π T π/2 Relaxing back to thermal equilibrium Application of π-pulse Read-out Figure 1.3: Illustrative pulse diagram and the magnetization (M) in the Bloch sphere for (a) spin echo sequence and (b) inversion recovery sequence. Chapter 1. Introduction 16 EPR is an emerging technique due to recent development of high-frequency high-power mi- crowave transmitters. There exists only several HF pulsed EPR systems in the world [13{19]. Advantages of performing EPR spectroscopy at high frequencies and various spectroscopic techniques have been extensively discussed in the literature [20{29], and a brief overview will be provided here. 1.4.1 Higher spectral resolution Similar to NMR spectroscopy, one advantage of performing EPR spectroscopy at higher frequencies is that it can oer higher spectral resolutions for systems with overlapping spectra and orientational selectivities in systems with g-anisotropies, simply because the energy gap from the electron Zeeman interaction increases proportional to the externally applied magnetic eld (see Eqn. 1.2). As an example, Fig. 1.4(a) shows energy diagram of two systems with close g-values and the overlapping spectra at lower frequencies are clearly separated and well-resolved at higher frequencies. Figure 1.4(b) reveals two CW EPR spectra of a system with g- and A-anisotropies which clearly demonstrates dierent orientations of spins can only be selectively studied with HF EPR spectroscopy. 1.4.2 Higher spin polarization and sensitivity Furthermore, HF EPR spectroscopy benets from higher electron spin polarizations achieved because of higher energy gaps between the states. In EPR spectroscopy, EPR signals are proportional to the population dierence or spin polarization between the two states where the resonant microwave absorption occurs. For a S = 1=2 system, electron spin polarization P is dened as, P = N 1 N 2 N 1 +N 2 ; (1.33) whereN 1 andN 2 are the number of spins in statej1i andj2i, respectively (e.g., see Fig. 1.1). Using the thermal equilibrium populations of states which follows the Maxwell-Boltzmann Chapter 1. Introduction 17 (a) (b) 1 10 100 0.1 1 10 100 Temp (K) Polarization (%) Electron spin polarization 9.5 GHz 230 GHz (c) (d) (e) Figure 1.4: Selected examples demonstrating advantages of HF EPR spectroscopy. (a) Energy diagram of two S = 1=2 systems as a function of magnetic eld. The overlapping spectra at lower frequencies well-resolved at higher frequencies. Figure was adapted from Ref. [29] with kind permission from Springer Science and Business Media. Copyright (2009). (b) Simulated spectra showing better resolution of g-anisotropies. Figure was adapted from Ref. [30]. (c) Electron spin polarization for S = 1=2 system with g = 2 at two dierent frequencies as a function of temperature, showing higher polarization is achieved by going to higher frequency. (d) Study spin decoherence in a high-spin system (S = 10) where quenching of spin decoherence was demonstrated by use of HF EPR spectroscopy at low temperatures. Adapted by permission from Macmillan Publishers Ltd: Ref. [31], copyright (2011). (e) Simulated spectra showing spectra at HF are less susceptible to motional eects. Figure was adapted from Ref. [30]. Chapter 1. Introduction 18 statistics, i.e., N i = 1 Z exp E i k B T ; (1.34) whereN i is the relative population ini th state,E i is the energy ofi th state,k B is the Boltz- mann constant, T is temperature, and Z = P i exp(E i =(k B T )) is the partition function, Eqn. 1.33 becomes, P = exp( E 1 k B T ) exp( E 2 k B T ) exp( E 1 k B T ) + exp( E 2 k B T ) (1.35) Figure 1.4(c) shows a plot of electron spin polarization as a function of temperature at two frequencies, 9.5 and 230 GHz. At 10 K, more than 60% of spins are populated in the lower state at 230 GHz while less than 5% of spins are populated in the lower state at 9.5 GHz. This means that, if all other experimental conditions are the same, EPR signals will be larger at HF. It is also possible to study dierent mechanisms of spin decoherence by employing HF EPR spectroscopy in low temperatures as in Ref. [31] (see Fig. 1.4(d)). Moreover, Ref. [32, 33] reported thatSNR of pulsed EPR spectroscopy theoretically scales proportional to 7=2 from careful comparisons of various experimental conditions. 1.4.3 Better time resolution Unlike CW EPR spectroscopy, higherB 1 is often required in pulsed EPR spectroscopy for driving transitions between states with a short pulses of non-continuous microwave exci- tations. For this purpose, many EPR spectrometers employ various types of microwave or optical cavities and resonators for producing desired high outputs ofB 1 at sample. However, one drawback with employing cavities is that there exists dead time in which measurements cannot take place due to noises from the ringing of the cavity known as \ring-down." The ring-down time of a cavity (r(t)) is typically characterized by [34], r(t)/ exp 2t Q ; (1.36) whereQ is the quality factor of the cavity. For sameQ, it is easy to see that from Eqn. 1.36 that ring-down decays faster for higher so pulsed EPR spectroscopy at HF enables mea- Chapter 1. Introduction 19 surements at earliert, yielding better time resolution. Ref. [35] also provides a discussion of better time resolution of HF EPR spectroscopy in terms of cavity dead time as well as dead times from other sources. 1.4.4 Less susceptible to motional averaging eects For non-rigid systems such as liquid and gas, motional eect of molecules need to be con- sidered in order to obtain correct shape of simulated CW spectra. The degree of rotational motion or tumbling of molecules are often characterized by the reorientational correlation time ( c ). The detailed theory of motional eects is outside of the scope of this disserta- tion, and Ref. [36, 37] provide good background on the subject. CW EPR spectra taken at higher frequencies are intrinsically less susceptible to these eects because of higher pre- cession frequencies of electron spins (see Fig. 1.4(e)), and as a consequence, more precise determinations of c are possible with HF EPR spectroscopy. 1.5 Summary In this chapter, an introduction of CW and pulsed EPR spectroscopy using spin Hamilto- nian formalism and Bloch model was given, and advantages of HF EPR spectroscopy were presented. Chapter 2 Defects and impurities in diamonds In this chapter, current scientic interests of diamonds are discussed, and physical properties as well as crystallographic defects and impurities found in diamonds using EPR and other magnetic resonance techniques are overviewed. 2.1 Optical, electrical, and magnetic properties of diamond Diamond is a fascinating material, appreciated highly for its aesthetic and commercial value. Because of its superb material properties, e.g., extremely high hardness, thermal conductiv- ity, and resistance to high pressure, diamond has found many usages in industrial applica- tions. Various sizes of diamond crystals are available,e.g., bulk single crystals, nanodiamonds (NDs) with averaged diameter of microns to tens of nanometers ground from bulk diamonds and with a few nanometer diameter fabricated by a detonation process [38{42]. The material properties of diamond, e.g., optical, electrical, and magnetic properties, strongly depend on crystallographic defects and impurities in it. Diamonds are often classied into two major types (I and II). In type-I diamonds, the major impurity contents are nitrogen atoms. If nitrogen atoms form a pair or aggregates, the color of diamond is not aected; such diamonds 20 Chapter 2. Defects and impurities in diamonds 21 are classied as type-Ia. Most of naturally occurring diamonds fall into this type. If nitrogen atoms are dispersed homogeneously as a isolated cites, they results in intense yellow (occa- sionally brown tint) and such diamonds are known as type-Ib. Natural diamonds are rarely this type, and synthetic diamonds containing nitrogen atoms are commonly this type. Both type-Ia and b diamonds absorb in the infrared and ultraviolet region of the electromagnetic spectrum with characteristic uorescence and visible absorption spectrum. On the other hand, type-II diamonds contain very few nitrogen atoms, if any. Pure diamonds classied as type IIa are mostly transparent, but can be slightly colored due to small amount of defects and impurities. Type IIb diamonds contain boron atoms which give them blue or gray colors. In addition, for modications of the optical and electronic properties of diamond, various engineering techniques including ion implantations, electron irradiations, and annealing have been investigated extensively. Many types of defects and impurities in diamonds have been found using EPR and other magnetic resonance spectroscopy. Among many defects and impurities in diamond, a negatively-charged nitrogen-vacancy (NV) center has gained tremendous interests in the eld. The point defect has many favorable properties such as photoluminescence, spin-state de- pendent orescence emission leading to possible spin state initialization via optical pumping and orescence-based single spin addressability, and long spin coherence times even in room temperature, and potential applications in the eld of fundamental quantum physics [43{55] as well as quantum information processing [49, 56{66], magnetic eld sensing [67{77], electric eld sensing [78], and temperature sensing [79{82] have been explored and demonstrated (see Fig. 2.1). In addition, biocompatibility of diamond makes it attractive for possible usage in biological settings [64, 81, 83]. Chapter 2. Defects and impurities in diamonds 22 (a) (b) (d) (c) Figure 2.1: Selected examples of various applications of diamond. (a) Demonstration of nanoscale magnetic sensing. Adapted by permission from Macmillan Publishers Ltd: Ref. [77], copyright (2013). (b) Demonstration of temperature sensing. Figure adapted from Ref. [80], published under the terms of the Creative Commons Attribution 3.0 License. (c) Demonstration of nanoscale electric eld sensing. Adapted by permission from Macmillan Publishers Ltd: Ref. [78], copyright (2011). (d) Demonstration of entanglement. From Ref. [60]. Reprinted with permission from AAAS. Chapter 2. Defects and impurities in diamonds 23 2.2 Crystallographic defects and impurities in diamond Here, brief descriptions of selected crystallographic defects and impurities in diamonds that are of interest to this dissertation will be given. See Ref. [49, 84] for a review of some other defects and impurities found in diamond. 2.2.1 Single substitutional nitrogen defect (P1 center) As discussed in Sect. 2.1, nitrogen atom is one of the most abundant defect atoms in diamond. In type-Ib diamonds, the concentration of nitrogen lies in the range of10{100 ppm [85, 86]. Among nitrogen related impurities, the most common impurities is a single substitutable nitrogen, also known as P1 center. Figure 2.2(a) shows the structure of P1 center, which is formed by a single substitutional nitrogen atom ( 14 N) replacing one of carbon atoms ( 12 C) in diamond lattice. Because nitrogen atom has ve valence electrons while carbon atom has only four valence electrons, there exists one excess electron along in one of four carbon-nitrogen bonds, forming a paramagnetic defect center of electron spin-half (S = 1=2) and nuclear spin-one (I = 1) system. The rst experimental observation of P1 center was reported in Ref. [87]. Figure 2.2(b) shows three EPR spectra of P1 centers in diamond as a function of jB 0 j for three dierent orientations ([100], [110], and [111]) ofB 0 with respect to the diamond crystal. While three equally-intense EPR peaks were observed when B 0 k [100], ve EPR peaks were observed whenB 0 k [110] andB 0 k [111], with EPR intensity ratio of 1:1:2 and 1:3:4 (outer side peak to inner side peak to central peak). Moreover, the observed number and spacing of side peaks in EPR spectra proved the tetrahedral symmetry of diamond. When B 0 was applied along [100], all four directions of 12 C- 14 N bonds are identical with respect toB 0 , thus all of P1 centers in diamond crystal yield same hyperne splitting and three equally-intense EPR signals were observed. When B 0 was applied along [110], two directions of four possible orientations of P1 center are identical with respect to B 0 , and Chapter 2. Defects and impurities in diamonds 24 the other two directions of P1 centers are identical with respect toB 0 , yielding two sets of three EPR peaks with dierent spacing between center peak and side peak. As a result, ve EPR signals with 1:1:2 intensity ratio was observed because the position of central peak was overlapping for both sets due to isotropic nature of g-value. Similarly, EPR spectrum whenB 0 was applied along [111] showed ve EPR signals, but the observed intensity ratio was 1:3:4. The reason for this was easily explained with the symmetry of diamond lattice; with respect to [111], three out of four possible orientations of P1 centers were identical. In addition, by analyzing position of the EPR signals as a function of the direction of B 0 , the hyperne interaction strengths were determined as A P 1 x = A P 1 y = 82 MHz and A P 1 z = 114 MHz where the z-axis is along the 12 C- 14 N bond. Moreover, the position of central peak corresponds tojm S =1=2, m I = 0i!jm S = 1=2, m I = 0i transition, which is only aected by the electron Zeeman interaction. And because the position of central peak did not change with applyingB 0 along dierent orientation of the diamond crystal, it was concluded that the g-value of P1 centers is isotropic (g P 1 x =g P 1 y =g P 1 z = 2:0024). Later, more precise measurements of nuclear quadrupole interaction were carried out in Ref. [88{90] by electron nuclear double resonance method which determined Q P 1 x = Q P 1 y =2Q P 1 z = 1:99 MHz. Observations of hyperne interaction to 13 C have been also reported although its contribution to EPR spectrum is small due to its low natural abundance (1.1%). Based on the observed spectra and theory of wave function, Ref. [91] deduced that the excess electron is localized almost entirely on nitrogen and carbon atoms (predominately on carbon atom). And Ref. [87] estimated10% elongated distance for the carbon-nitrogen bond where the excess electron is situated, and this was interpreted as a manifestation of the Jahn-Teller distortion of the degenerate orbital to remove its degeneracy [92] (i.e., the extra electron causes distortion of the orbital on which it is situated such a way that it has a lower energy than the other three). Ref. [84] explained that the g-value is isotropic and close to that of a free electron spin (a small oset arising from spin-orbit coupling) because the unpaired electron's contribution to the orbital magnetic moment is completely quenched. Therefore, Chapter 2. Defects and impurities in diamonds 25 (a) (b) N C [100] [001] [010] S=1/2 N C [111] [111] [111] [111] Figure 2.2: (a) Structure of single substitutional nitrogen defect in diamond (P1 center), showing four possible orientations, [111], [ 111], [1 11], and [11 1]. C denotes a carbon atom and N denotes a nitrogen atom. (b) CW EPR spectra of single crystal diamond taken at three dierent orientations of magnetic eld with respect to the crystal for determination of g andA. Reprinted gure with permission from Ref. [87]. Copyright (1959) by the American Physical Society. Chapter 2. Defects and impurities in diamonds 26 P1 center exhibits a static trigonal Jahn-Teller distortion from Td to C3v symmetry. In addition, spin relaxation measurements of P1 center have been reported in Ref. [51, 93{95] where the main mechanism of spin-lattice (i.e., T 1 ) relaxation was attributed to a phonon- induced tunnelling of the Jahn-Teller barrier accompanied by a reorientation of the electron spin because of the spin-orbit coupling, and the spin-spin (i.e.,T 2 ) relaxation rate depended strongly on the volume concentration of P1 center. In this dissertation, various experimental data of P1 centers will be discussed throughout Chap. 3{6. Spin Hamiltonian of P1 centers is given by, ^ H() = ^ H EZI + ^ H HFI () + ^ H NZI + ^ H NQI () = X i=x;y;z B h B i 0 ()g i ^ S i +A i ^ S T i ^ I i + n g n h B i 0 () ^ I i +Q i ^ I T i ^ I i ; (2.1) Figure 2.3(a) shows 230 GHz EPR spectrum of P1 centers withB 0 along the [100] direction. At8.2 Tesla, the energies of E EZI , E HFI , E NZI , and E NQI are approximately 230 GHz, 100 MHz, 25 MHz, and 2 MHz, respectively, therefore the electron Zeeman term of the spin Hamiltonian dominates the system energy. When the direction ofB 0 is along [100] direction of the diamond crystal lattice, all four sets of P1 centers make an equal angle with respect to B 0 , i.e., for the four orientations = arccos(1= p 3), P1 centers in all four orientations yield overlapping EPR signal. Thus, the CW EPR spectrum of P1 centers in a single diamond crystal whenB 0 k [100] exhibits three pronounced peaks as shown in Fig. 2.3(a). Figure 2.3(b) is the energy diagram of states as a function ofB L 0 . The energy levels were calculated in the same manner outlined by Eqn. 1.12{1.18. In the basis of pure Zeeman states labeled as, j1 Zeeman i =jm S = 1=2; m I = 1i j2 Zeeman i =jm S = 1=2; m I = 0i j3 Zeeman i =jm S = 1=2; m I =1i j4 Zeeman i =jm S =1=2; m I = 1i j5 Zeeman i =jm S =1=2; m I = 0i j6 Zeeman i =jm S =1=2; m I =1i; (2.2) Chapter 2. Defects and impurities in diamonds 27 Field (T) 8.204 8.208 8.212 8.2 Intensity (Arb. units) Meas. Sim. Field (T) 8.204 8.208 8.212 8.2 E (GHz) 115.2 115 114.8 -114.8 -115 -115.2 “Allowed” transitions |1> |2> |3> |6> |5> |4> Detectable “forbidden” transitions Undetectable “forbidden” transitions (a) Field (T) 8.204 8.208 8.212 8.2 ∆E (GHz) 229.8 230.2 230 (p 41 ≈1) |4>→|1> (p 51 ≈2∙10 -3 ) |5>→|1> |6>→|3> (p 36 ≈1) |6>→|2> (p 26 ≈7∙10 -2 ) |5>→|3> (p 53 ≈7∙10 -2 ) |5>→|2> (p 52 ≈1) (p 42 ≈1∙10 -3 ) |4>→|2> (p 43 ≈2∙10 -3 ) |4>→|3> |6>→|1> (p 16 ≈2∙10 -3 ) (c) (b) Figure 2.3: (a) Measured and simulated CW EPR spectra of P1 centers at 230 GHz when B 0 k [100]. (b) Energy diagram of P1 centers as a function of B 0 . (c) E as a function of B 0 . Chapter 2. Defects and impurities in diamonds 28 where m S is the electron spin number and m I is the nuclear spin number, the electron spin operators for S = 1=2 and nuclear spin operators for I = 1 in their 6 6 matrix representations can be written as, ^ S x = 1 2 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 ! ; ^ I x = 1 p 2 0 1 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 1 0 ! (2.3) ^ S y = i 2 0 @ 0 0 01 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 A ; ^ I y = i p 2 0 @ 01 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 01 0 0 0 0 1 0 1 0 0 0 0 1 0 1 A (2.4) ^ S z = 1 2 0 @ 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 01 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 A ; ^ I z = 0 @ 1 0 0 0 0 0 0 0 0 0 0 0 0 01 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 01 1 A : (2.5) Using Eqn. 2.3{2.5, the general 6 6 spin Hamiltonian of P1 centers (i.e., Eqn. 2.1) can be expressed as, ^ H P 1 = 0 B B B B B B B B @ 1 2 B B z 0 g P1 z h + ngnB z 0 h + Az 2 + Qx 2 Qy 2 +Qz 1 p 2 ngnB x 0 h i p 2 ngnB y 0 h 1 p 2 ngnB x 0 h + i p 2 ngnB y 0 h 1 2 B B z 0 g P1 z h +QxQy Qx 2 + Qy 2 1 p 2 ngnB x 0 h + i p 2 ngnB y 0 h 1 2 B B x 0 g P1 x h + i 2 B B y 0 g P1 y h Ax 2 p 2 Ay 2 p 2 Ax 2 p 2 + Ay 2 p 2 1 2 B B x 0 g P1 x h + i 2 B B y 0 g P1 y h 0 Ax 2 p 2 + Ay 2 p 2 Qx 2 + Qy 2 1 2 B B x 0 g P1 x h i 2 B B y 0 g P1 y h 1 p 2 ngnB x 0 h i p 2 ngnB y 0 h Ax 2 p 2 Ay 2 p 2 1 2 B B z 0 g P1 z h ngnB z 0 h Az 2 + Qx 2 Qy 2 +Qz 0 0 1 2 B B z 0 g P1 z h + ngnB z 0 h Az 2 + Qx 2 Qy 2 +Qz Ax 2 p 2 Ay 2 p 2 1 p 2 ngnB x 0 h + i p 2 ngnB y 0 h 1 2 B B x 0 g P1 x h + i 2 B B y 0 g P1 y h Qx 2 + Qy 2 Ax 2 p 2 + Ay 2 p 2 0 1 2 B B x 0 gx h i 2 B B y 0 g P1 y h Ax 2 p 2 + Ay 2 p 2 Ax 2 p 2 Ay 2 p 2 1 2 B B x 0 gx h i 2 B B y 0 g P1 y h 1 p 2 ngnB x 0 h i p 2 ngnB y 0 h Qx 2 + Qy 2 1 2 B B z 0 g P1 z h QxQy 1 p 2 ngnB x 0 h i p 2 ngnB y 0 h 1 p 2 ngnB x 0 h + i p 2 ngnB y 0 h 1 2 B B z 0 g P1 z h ngnB z 0 h + Az 2 + Qx 2 Qy 2 +Qz 1 C C C C C C C C A ; (2.6) where B x 0 , B y 0 , and B z 0 are magnetic eld expressed in the eigenframe of the system, which can be computed by applyingR(;; ) toB 0 with = 0, = arccos(1= p 3), and = 0 Chapter 2. Defects and impurities in diamonds 29 for all four orientations because there is a freedom to choose x- and y-axis of eigenframe due to the axial symmetry. By solving or nding the eigenvalues and eigenstates of Eqn. 2.6 using a numerical computation software, the energy diagram of spin states of P1 centers as a function of B 0 can be obtained as shown in Fig. 2.3(b). And the positions of resonance eld can be easily computed using the resonance condition (Eqn. 1.18) as shown by the vertical dotted lines in Fig. 2.3(b) and (c). Among the nine transitions, there are three strong EPR signals observed at 8.203, 8.207 and 8.210 Tesla for the so-called \allowed" EPR transitions with m S = 1 and m I = 0 (also known as the selection rule). For a purely diagonal spin Hamiltonian, only the \allowed" EPR transitions will be detected. But when the o-diagonal elements of the spin Hamiltonian are non-zero such as the current example, the eigenstates of the spin Hamiltonian will be a mixture of pure Zeeman states, causing nite probabilities of the \forbidden" EPR transitions. Thus, the simulated spectrum from a linear combination of line shape functions at all resonance eld positions, properly weighted by the transition probabilities, agrees well with the exper- imentally observed spectrum as shown in Fig. 2.3(a). When a powder of many small diamond crystals is investigated, so-called \powder" spec- trum needs to be simulated to account for all possible orientations of spins. Figure 2.4(a) shows the simulated absorption spectrum of P1 centers. The broadening of side peaks (e.g., m I =1) due to dierent angular component of the anisotropic hyperne interaction is clearly seen in the spectrum. Figure 2.4(b) shows the measured CW EPR spectrum of di- amond powder sample with average size of10 m, which agrees well with the simulated spectrum in the derivative shape. 2.2.2 Nitrogen-vacancy (NV) center In recent years, a point defect known as NV center has gained great scientic interests due to its unique optical and magnetic properties. As shown in Fig. 2.5(a), NV center is formed by a single substitutional nitrogen atom and a vacancy in diamond lattice. First experimental Chapter 2. Defects and impurities in diamonds 30 Meas. Sim. Field (T) 8.204 8.208 8.212 8.2 Intensity (Arb. units) Field (T) 8.204 8.208 8.212 8.2 Intensity (Arb. units) Sum Individual (b) (a) Figure 2.4: (a) Simulated absorption spectrum of P1 centers for powder sample showing individual component of dierent angles of P1 centers. (b) Measured and simulated 1 st derivative CW EPR spectra of P1 centers at 230 GHz for powder sample. Chapter 2. Defects and impurities in diamonds 31 (a) (c) (b) N C V [100] [001] [010] S=1 -1 1 0 Metastable, non-radiative decay 1 A 3 A D 3 E -1 1 0 m S Optical illumination (532 nm) Flurescence (637-800 nm) Microwave excitation Figure 2.5: (a) Structure of NV center in diamond. V denotes a lattice vacancy. (b) Flores- cence emission spectra of single NV centers. Figure was adapted from Ref. [49]. Copyright c [2006] [WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim]. (c) Electronic energy level structure of NV center. Nature of orescence decay depends on the spin states of NV center, thus the spin states of NV center can be initialized and read-out by optical illumination and orescence measurement. Chapter 2. Defects and impurities in diamonds 32 observations of optical absorption by NV center at 637 nm were reported in Ref. [84, 96] (see Fig. 2.5(b)), and EPR measurements in Ref. [84] indicated that the defect has an elec- tron paramagnetic ground state with electron spin-one (S = 1) with zero-eld splitting of D x =D y =0:96 GHz andD z = 1:92 GHz (axially symmetric due to tetrahedral symmetry of diamond lattice structure; z-axis is along the nitrogen-vacancy bond). The zero-eld split- ting is often characterized by two alternative parameters known asD = 2:88 GHz andE = 0 GHz. Ref. [97] reported observed EPR signal was enhanced upon optical illumination, and Ref. [43] rst demonstrated optically-detected magnetic resonance (ODMR) signal of single NV centers using confocal microscopic technique at room temperature. CW EPR measure- ments with optical illumination in Ref. [98] indicated a possibility of optically reading out the spin state of a single NV center in its ground state. Figure 2.5(c) shows the electronic energy level structure of NV center. Various theoretical and experimental works, e.g., Ref. [86, 97, 99, 100], concluded that the defect center captures additional electron presumably from P1 center and actually becomes negatively-charged. 2.2.3 Surface paramagnetic defects and impurities There have been many reports that suggest the existence of paramagnetic defects and im- purities near surface of various kinds of diamonds. Direct EPR evidences were observed in mechanically crushed diamonds; Ref. [101] attributed the observed single EPR signal (S = 1=2, g 2:003, and line width of 0.55 mT) to structural damages near the diamond surface due to crushing process (see Fig. 2.6(a)) and Ref. [102] observed similar EPR signals (S = 1=2, g 2:003, and line widths of0.2{0.6 mT) but argued these signals arise from -radicals. Also measurements of diamond powders produced by detonation process consis- tently have shown single peak EPR signals (e.g., Ref. [41, 103, 104] reported signals with S = 1=2,g 2:003 and line widths of1{2 mT), which are often claimed to originate from dangling bonds associated with structural defects in the core or within the surface of diamond (i.e., sp 3 -hybridized carbon; see Fig. 2.6(b)). On the other hand, two separate NMR studies Chapter 2. Defects and impurities in diamonds 33 C C C Core Shell (100) surface Grain boundaries (a) (b) (c) Broken bonds Dislocations Diamond surface Excess electrons from dangling bonds Figure 2.6: (a) Illustrative gure showing various possible structural defects (dislocations, broken bonds, and grain boundaries). (b) Illustrative gure showing dangling bonds which are proposed as one of possible candidates of paramagnetic defects and impurities near diamond surface. (c) \Core-shell" model. Chapter 2. Defects and impurities in diamonds 34 of detonation diamond powders argue that paramagnetic impurities exist in a thin-shell near the surface [105], which is not associated with dangling bonds (see Fig. 2.6(c)), or may be homogenously distributed throughout the whole volume of diamond crystal [42]. Finally, studies of shallow NV centers in bulk crystals [106{108] as well as NV centers found in nano- sized crystals [109, 110] have shown that these NV centers exhibit dierent spin properties (e.g., broader line wdith and faster spin relaxation times) compared to deep, stable NV centers in single bulk crystals, which were explained by the existence of dense paramagnetic defects and impurities on the surface of hosting diamonds. No conclusive study has been reported to identify the origin of paramagnetic defects and impurities near the surface of di- amonds, mainly due to a single broad and featureless EPR signal. More discussion of surface paramagnetic impurities will be presented by EPR study of nano-sized diamond powders in Chap. 5 and 6. 2.3 Summary In summary, an overview of optical, electrical, and magnetic properties as well as current scientic interests on magnetic resonance study of diamonds was given, and selected defects and impurities found in diamonds were presented. Chapter 3 Development of HF EPR spectrometer Materials presented in this chapter can also be found in the article titled A high-frequency electron paramagnetic resonance spectrometer for multi-dimensional, multi-frequency, and multi-phase pulsed measurements by Franklin H. Cho, Viktor Stepanov, and Susumu Taka- hashi in Review of Scientic Instruments 85, 075110:1{075110:7 (2014) (Reprinted with permission from Ref. [19]. Copyright [2014], AIP Publishing LLC.) and the book chap- ter titled 230/115 GHz electron paramagnetic resonance/double electron-electron resonance spectroscopy by Franklin H. Cho, Viktor Stepanov, and Susumu Takahashi (accepted in 2015). This chapter describes the home-built HF EPR spectrometer which is the main instru- mentation used for the research presented in this dissertation. Only a few pulsed HF EPR spectrometers above 150 GHz has been constructed around the world. Among the few exist- ing HF pulsed EPR spectrometers, only our system is capable of wide-band electron-electron double resonance (DEER) spectroscopy as well as spin relaxation measurements with time resolution of a few tens of nanoseconds. 35 Chapter 3. Development of HF EPR spectrometer 36 3.1 Overview As shown in Fig. 3.1, the spectrometer consisting of a HF, high-power (peak power of700 and100 mW at 115 and 230 GHz, respectively) solid-state transmitter, a quasioptical system, a superheterodyne phase-sensitive detection system, a 12.1 T cryogenic-free super- conducting magnet, and a liquid helium cryostat operates in frequency range of 107{120 GHz and 215{240 GHz, in magnetic eld range of 0{12.1 T, and in temperature range of 300{1.4 K with unique experimental capabilities such as DEER and dynamical decoupling (DD). CW and pulsed excitations from the transmitter are rst propagated in the quasioptical sys- tem, then propagated through a corrugated waveguide to couple to a sample located at the center of the magnet. The spectrometer employs the induction-mode detection scheme for EPR signal detection where the cross-polarized component of EPR signals is separated from re ections of the incident microwave using a circulator based on a xed-angle wiregrid polar- izer [14, 111{114]. Separated EPR signals are guided to the receiver by quasioptics. In the receiver, the signals are mixed with a HF local oscillator (LO) for the rst down-conversion to an intermediate frequency (IF) of 3 GHz. In the detection system, IF signals are further down-converted to in-phase (I) and quadrature (Q) component of direct current (DC) sig- nals by mixing with a 3 GHz reference, synthesized in the detection system using outputs of the transmitter and receiver synthesizers. In CW measurements, intensities of I and Q signals at a xed magnetic eld modulation frequency (typically 10{100 kHz) are measured using lock-in ampliers. In pulsed measurements, transient responses of I and Q signals are sampled by a fast digital oscilloscope (2 gigasamples/s). A pulse generator, magnet power supplies, data acquisition from the lock-in ampliers and digital oscilloscope are controlled by a personal computer (PC). The details of the spectrometer, including calibrations and operational procedures, are discussed in the following sections. My personal contributions to the development of the spectrometer include testings, cali- brations, adjustments, and alignments of quasioptical system for maximum microwave cou- plings (see Sect. 3.3). Good microwave couplings are essential to achieve high SNR. Also, I Chapter 3. Development of HF EPR spectrometer 37 High-frequency, high-power transmitter Quasioptical system Liquid helium cryostat 12.1 T superconducting magnet PC control Lock-in amplifiers Oscilloscope Corrugated horns Pulse generator IQ mixer 3 GHz IF LO Sig I Q 3 GHz ref Ref 1 Ref 2 Microwave signals (arrowhead indicates direction) Absorber Rotating wiregrid polarizer Ellipsoidal mirror Fixed wiregrid polarizer Faraday rotator Sample LNA Corrugated waveguide Data acquisition via GPIB, LAN, or USB connection Pulse triggering via BNC connection Detection system Receiver Figure 3.1: Overview of the HF EPR spectrometer. The HF, high-power transmitter and receiver are custom built by Virginia Diodes, Inc., and the quasioptical system consists of corrugated horns, wiregrid polarizers, Faraday rotators, corrugated waveguides (Thomas Keating), and right-angle ellipsoidal mirrors (fabricated by the USC machine shop). EPR signals are rst down-converted to an intermediate frequency (IF) of 3 GHz by the receiver, then amplied by a low-noise amplier (LNA, noise gure of 0.5 dB; MITEQ) and by a second amplier (AML Communications). A 3 GHz reference is produced using outputs from the transmitter and receiver synthesizers to down-convert the IF signals to I and Q components of DC signals using an IQ mixer (Marki Microwave). Two lock-in ampliers (Standford Research Systems) and a fast digital oscilloscope (Agilent Technologies) are used to measure I and Q signals for CW and pulsed experiments, respectively. A 12.1 T super- conducting magnet (Cryogenic Limited) is employed to apply external magnetic eld, and a liquid helium cryostat (Janis Research) is utilized for low temperature measurements. Data acquisition from the lock-in ampliers, oscilloscope, magnet, and cryostat is done via general purpose interface bus (GPIB), local area network (LAN), or universal serial bus (USB) con- nections, and switching of the transmitter and receiver and triggering of the oscilloscope are controlled by transistor-transistor logic (TTL) signals from a pulse generator (SpinCore) via Bayonet Neill-Concelman (BNC) connections, which are all synchronized and programmed using National Instruments LabVIEW codes. Chapter 3. Development of HF EPR spectrometer 38 have worked on testings and adjustment methods of the electronics in the detection system for reducing phase noises and maximizing the measured signal responses (see Sect. 3.4), and designed sample holder congurations and calibrated performance of modulation coil (see Sect. 3.6). In addition, the operation of the liquid helium cryostat with liquid nitrogen have been tested and veried, which have made many experiments that do not require tempera- tures below liquid nitrogen temperatures more readily accessible (see Sect. 3.7). Moreover, the existing computer programming codes have been improved, and new codes have been written for triggering microwave excitations from the transmitter, enabling signal detection in the receiver, and synchronizing electronics in the detection system for data acquisition in various pulsed experiments including DEER and DD (see Sect. 3.8). And nally, the sensitivity of the spectrometer in pulsed experiments have been carefully determined (see Sect. 3.9). 3.2 High-frequency, high-power transmitter Figure 3.2 shows a circuit diagram of the HF, high-power solid-state transmitter consisting of two microwave synthesizers, isolators, fast p-i-n (PIN) switches, directional couplers, a power combiner, an analog variable phase shifter, an amplier, and active and passive frequency multipliers. The nal output frequency of the transmitter is tunable in the range of 107{ 120 GHz and 215{240 GHz. As shown in Fig. 3.2, the outputs of the synthesizers are rst connected to the directional couplers, then to the isolators. After the isolators, CW outputs of the synthesizers are gated using the PIN switches for pulse operations where the timings of the switching are controlled by TTL signals from the pulse generator (see Fig. 3.1). Typical rise and fall times of the PIN switches are 12 ns, which makes them possible to produce as short as20 ns pulse. After the switches, the outputs from both synthesizers are subsequently transmitted into an amplier, then to the frequency multiplier chain using a power combiner. The frequency multiplier chain is made up of an active Chapter 3. Development of HF EPR spectrometer 39 Microwave signals via SMA connection Mirocwave signals via rectangular waveguide connection 10 MHz ref 9-11 GHz synthesizer (terminated) 8-10 GHz synthesizer Directional couplers Isolators PIN switches Ref 1 to Detection system TTL trigger signal from pulse generator via BNC connection TTL trigger High-power frequency multiplier chain Final output to corrugated horn 10 MHz ref 9-11 GHz synthesizer 8-10 GHz synthesizer Directional couplers Isolators PIN switches X3 X2 X2 X2 Ref 1 to Detection system 108-120 GHz output 216-240 GHz output TTL trigger TTL trigger Amplifier Active frequency tripler Passive frequency doublers (a) (b) φ Power splitter Power combiner Power combiner Variable phase shifter TTL trigger High-power frequency multiplier chain Final output to corrugated horn X3 X2 X2 X2 108-120 GHz output 216-240 GHz output Amplifier Active frequency tripler Passive frequency doublers Figure 3.2: Circuit diagram of the HF, high-power transmitter. The transmitter consists of two microwave synthesizers (8{10 GHz and 9{11 GHz; Micro Lambda Wireless), isolators (DiTom Microwave), fast PIN switches (American Microwave Corporation), directional cou- plers (Advanced Technical Materials), a power combiner (Narda Microwave East), a power splitter (Mini Circuits), an analog variable phase shifter (Antenna and Radome Research As- sociates), an amplier (Mini Circuits), and active and passive frequency multipliers (Virginia Diodes, Inc.). Microwaves up to the rst frequency doubler are connected via subminiature version A (SMA) connections, and rectangular waveguide connections are used from the output of the doubler to the corrugated horn. (a) Transmitter conguration for double frequency output required in DEER experiments. (b) Transmitter conguration for single frequency output with dual phase required in DD experiments. Chapter 3. Development of HF EPR spectrometer 40 frequency tripler and three passive frequency doublers, and the base synthesizer frequencies are multiplied by 12 and 24 times for the nal microwave output in the range of 107{ 120 GHz and 215{240 GHz, respectively. For example, the synthesizer frequency is set to 115=12 = 230=24 9:583333333 GHz for 115 GHz and 230 GHz output (the frequency step size of the synthesizers is 1 Hz). The output power is200{700 mW in 107{120 GHz (30{100 mW in 215{240 GHz) where the peak power is700 mW at 115 GHz (100 mW at 230 GHz) (see Appx. A). To meet dierent experimental needs, the transmitter can be congured to either single frequency output mode with phase controllability or to double frequency output mode, with minor changes. For DEER experiments, microwave excitations at two dierent frequencies are required so both synthesizers in the transmitter are utilized as shown Fig. 3.2(a). In the single frequency output conguration, one synthesizer is terminated and the output of the other synthesizer is split using a power splitter. Then the phase of microwaves in one arm with respect to the other arm is continuously controlled using the phase shifter with the accuracy of1.2 in 107{120 GHz and2.4 in 215{240 GHz (see Fig. 3.2(b)). This makes the transmitter capable of producing multi-phase pulses (e.g., X (0) and Y (90 )) required for DD experiments (refer to Sect. 4.3 for details). Thus, the transmitter provides a high-power and extremely wide range of tunable frequencies for CW as well as various pulsed EPR experiments. 3.3 Quasioptical system For ecient propagation of excitations (from the transmitter to a sample) and EPR sig- nals (from the sample to the receiver) at HF (e.g., 107{120 GHz and 215{240 GHz), the quasioptical system, composed of corrugated horns, wiregrid polarizers, Faraday rotators, corrugated waveguides, right-angle ellipsoidal mirrors, and transmitter and receiver stages (the mirrors and stages were fabricated by the USC machine shop), is employed as shown Chapter 3. Development of HF EPR spectrometer 41 EPR signals 230/115 GHz pulses Corrugated waveguide (To sample) Transmitter stage Receiver stage Isolation box Monitor port Ellipsoid mirror To mixer Source outputs Faraday rotator Rotating wire-grid polarizer Wire-grid polarizer Corrugated horns Circulator (wire-grid) Figure 3.3: Overview of the quasioptical system consisting of the transmitter and receiver stages. Reprinted with permission from Ref. [19]. Copyright [2014], AIP Publishing LLC. Chapter 3. Development of HF EPR spectrometer 42 in Fig. 3.3. The corrugated horn in the transmitter stage joints a single-mode rectangular waveguide (WR-8.0 and WR-3.4 for 107{120 GHz and 215{240 GHz, respectively) to the corrugated waveguide (HE11 mode) and converts the transmitter outputs to the linearly polarized Gaussian waves (represented by red double-sided arrows in Fig. 3.1). The coupling eciency between the HE11 mode and the Gaussian waves is99%. The quasioptics were designed using a Gaussian mode ray analysis [115]. The Gaussian waves are guided by the right-angle ellipsoidal mirrors with the focal length of 254 mm which focus the Gaussian waves periodically with the period of 508 mm to cancel out the frequency dependence of the quasioptics [115, 116]. The intensity of excitation waves is controlled by a variable attenua- tor based on a rotating wiregrid polarizer and a xed-angle wiregrid polarizer. In addition, a quasioptical isolator made up of a combination of the xed-angle wiregrid polarizer and a Faraday rotator is installed to suppress standing waves in the transmitter stage (as shown in Fig. 3.1, re ections represented by a purple double-sided arrow are directed to an absorber, and Fig. 3.3). Then, the Gaussian waves couple to the corrugated waveguide to excite the sample located at the bottom end of the corrugated waveguide. For detection of EPR signals, the induction-mode detection scheme [14, 111{114] is utilized where a xed-angle wiregrid polarizer separates the circularly polarized EPR signals (represented by blue circular arrows in Fig. 3.1 and Fig. 3.3) from the high-power linearly polarized re ections, then guides the induction signals (represented by blue double-sided arrows in Fig. 3.1) to the receiver (the isolation is30 dB). Similar to those in the transmitter stage, the quasioptics in the receiver stage are also designed as a periodic focusing system with the focal length of 254 mm right- angle ellipsoidal mirrors. The quasioptics in the transmitter and receiver stages are mounted on separate breadboards to adjust their coupling to the corrugated waveguide independently and maximize the coupling ecacy. Finally, the receiver stage is enclosed by an isolation box to reduce possible background noises from scattered re ections from the quasioptics. In order to calibrate the performance of the variable attenuator, the attenuation of the variable attenuator were measured at dierent rotating wiregrid polarizer angles. The at- Chapter 3. Development of HF EPR spectrometer 43 tenuation of a signal is generally expressed as, Attn = 10 log 10 I f I i ; (3.1) whereAttn is the amount of attenuation in dB,I i is the initial signal intensity, andI f is the nal signal intensity. When a linearly polarized microwave is incident on an ideal wiregrid polarizer, the component of electric eld that is parallel to the direction of the wires is re- ected back while the component of electric eld that is perpendicular to the direction of the wires is transmitted through [115]. IfE i represents the magnitude of the incident oscillating electric eld and denotes the angle between the light's initial polarization direction and the axis of the wiregrid polarizer (i.e., along the perpendicular direction to the wires in the wiregrid polarizer; see Fig. 3.4), then the intensity of the electric eld after the wiregrid polarizer (E f ) is given by, E f =E i cos; (3.2) and since intensity of microwave is proportional to the magnitude of electric eld squared (i.e., I 0 E 2 i and IE 2 f ), it follows that I =I 0 cos 2 : (3.3) Using Eqn. 3.3, the resulting attenuation from the combination of the rotating wiregrid polarizer and the xed-angle wiregrid polarizer can be written as, Attn = 10 log 10 cos 4 +C ; (3.4) whereC is the constant that accounts for background noises in the measured power as well as possible leakage through the wiregrid polarizers. From the t of the measured attenuations to Eqn. 3.4, C = (8 2)10 4 was extracted which corresponds to0.01% leakage and the maximum adjustable attenuation of 311 dB at = 90 . For pulsed experiments, highest possible output power is usually desired for fast manipulation and tipping of spins or mag- netization so the rotating wiregrid is set at = 0 . For CW experiments, the output power Chapter 3. Development of HF EPR spectrometer 44 (a) (b) Rotating wiregrid angle (°) Attenuation (dB) 0 20 40 60 80 100 -20 0 -5 -10 -15 -20 -25 -30 -35 Meas. Fit Propagation direction of linearly polarized light Axis of fixed wiregrid polarizer Axis of rotating wiregrid polarizer Incident electric field of magnitude E i Final electric field of magnitude E f θ Figure 3.4: Calibration measurements of the variable attenuator. A Linearly polarized light with initial magnitude of oscillating electric eld E i propagates through the rotating wiregrid polarizer and the xed-angle wiregrid polarizer where is the angle between the light's initial polarization direction and the axis of the rotating wiregrid polarizer. Mag- nitude of nal electric eld after the xed-angle wiregrid polarizer is denoted as E f . (b) Attenuation of excitation waves as a function of the rotating wiregrid polarizer angle. Blue square dots represent measurements and solid line indicates a best-t to Eqn. 3.4. The best-t parameter of . Horizontal error bars represent the accuracy of measuring the angle (1 ), and vertical error bars indicate the standard deviations of three independent read- ings. For measurements, a pyroelectric detector (Eltec Instruments) was used which had been calibrated with a commercial calorimetric power meter from Virginia Diodes, Inc (see Appx. B). Chapter 3. Development of HF EPR spectrometer 45 is often reduced to avoid the distortion of EPR signals due to saturation eect. Attenuation of Faraday rotators was also estimated to be2{3 dB using similar measurements as the calibration of the variable attenuator. 3.4 Superheterodyne detection system The HF EPR spectrometer employs a superheterodyne detection system for phase-sensitive detection of EPR signals (see Fig. 3.5 for detailed circuit diagrams). EPR signals are rst mixed with a HF LO using a subharmonically-pumped mixer (100 dB isolation from LO to signal port) to down-convert to IF of 3 GHz. As shown in Fig. 3.5(a), the HF LO consists of a microwave synthesizer, a directional coupler, a single pole double throw switch, a PIN switch, an isolator, an amplier, an active frequency doubler, two passive frequency doublers, and two passive frequency triplers. For EPR frequency of 115 GHz and 230 GHz, the initial synthesizer frequency of the receiver is set to (115 3)=12 9:333333333 GHz and (230 3)=24 9:458333333 GHz (1 Hz resolution), respectively, to produce the IF signals at 3 GHz. The resulting IF signals are rst amplied by a low-noise amplier and a second amplier. Phase-sensitive detection of EPR signals (e.g., I and Q components of DC signals) are achieved by mixing the IF signals with a 3 GHz reference, produced using transmitter and receiver synthesizers at their base frequencies, a mixer, ampliers, frequency multipliers, a phase shifter, and a variable attenuator (see Fig. 3.5(b)). In the reference circuit, a 250 MHz for 115 GHz (125 MHz for 230 GHz) references, synthesized by mixing Ref 1 from the transmitter transmitter and Ref 2 from the receiver synthesizer, is fed into a frequency multiplier chain with the multiplication factor of 12 for 115 GHz (24 for 230 GHz) to produce the nal reference at 3 GHz. In CW EPR measurements, the power of the IF signals is adjusted by a variable attenuator to optimize the IQ mixer response (not shown in Fig. 3.1 for simplicity), then intensities of the I and Q signals are measured by the lock-in ampliers. In pulsed EPR measurements, transient responses of I and Q signals are Chapter 3. Development of HF EPR spectrometer 46 SMA connection Rectangular waveguide connection 10 MHz ref 2-20 GHz synthesizer Isolator PIN switch Single pole double throw switch X3 X2 X2 X2 TTL trigger signal from pulse generator via BNC connection TTL trigger Amplifier Active frequency doubler Directional coupler Ref 2 to Detection system Passive frequency doubler X3 Passive frequency tripler Passive frequency tripler Subharmonically -pumped mixers Passive frequency doubler IF (3GHz) IF (3 GHz) Sig (115 GHz) Sig (230 GHz) (a) (b) Ref 2 from receiver synthesizer Ref 1 from transmitter synthesizer Mixer X2 X2 X2 X3 φ Variable phase shifter Frequency multiplier chain (x12 for 115 GHz or x24 for 230 GHz) Amplifier High-pass filters 250 MHz for 115 GHz or 125 MHz for 230 GHz For 115 GHz For 230 GHz IQ mixer 3 GHz ref IF (3 GHz) I Q Figure 3.5: Circuit diagrams of the superheterodyne detection system. (a) Circuit diagram of the receiver that receives and down-converts EPR signals to IF. The HF LO consists of a microwave synthesizer (2{20 GHz; Micro Lambda Wireless), a directional coupler (Ad- vanced Technical Materials), a PIN switch (American Microwave Corporation), an isolator (DiTom Microwave), an amplier (Spacek Labs), and active and passive frequency multipli- ers (Virginia Diodes, Inc.). The outputs of the HF LO are fed into subharmonically-pumped mixers (Virginia Diodes, Inc.) for down-conversion to 3 GHz IF. (b) Circuit diagram of the 3 GHz reference which is composed of a mixer (Marki Microwave), frequency multipliers (Mini Circuits), high-pass lters (Mini Circuits), a variable phase shifter (Advanced Technical Ma- terials), an amplier (Mini Circuits), and an IQ mixer (Marki Microwave). The reference is mixed with 3 GHz IF to produce I and Q of DC signals. Chapter 3. Development of HF EPR spectrometer 47 captured simultaneously by the fast digital oscilloscope. 3.5 12.1 T Cryogenic-free superconducting magnet The 12.1 T cryogenic-free superconducting magnet consisting of two superconducting solenoid coils, controlled by separate power supplies. The magnetic has a 89-mm room temperature bore for the sample access. The main coil operates in the range of 0{12 T (corresponding to 0{139.57 A of electric current by the main coil power supply) which can be put into persistent mode for operation of the sweep coil, and the sweep coil is bi-directional and can be ramped in the range of 0{0.1 T (corresponding to 0{42.2 A of electric current by the sweep coil power supply). Dierent ramp rates of the electric currents of the power supplies are available (1.510 3 {1.510 A/s, corresponding to1.310 4 {1.3 T/s, for the main coil, 610 4 {6 A/s, corresponding to1.410 3 {1.410 mT/s, for the sweep coil). Currently, two ways of reading out the values of the magnetic elds produced by the coils are used. One method is to talk to the power supplies and get internal readings in unit of either T or A. The other way is to read out the magnetic elds through signals from analog monitor ports. The monitor ports located in the rear panel of the power supplies provide the voltage across shut resisters in the magnet. The voltage-to-current conversion constants are calibrated by the manufacturer (33.391267 mV/A for the main coil and 2.002283 mV/A for the sweep coil). Because of capability for better precision and faster readout, the monitor ports are usually used to measure the magnetic elds. While the main coil can be ramped in a wide range of magnetic eld, the step size of the magnetic control is relatively large (specication of the power supply is 16-bit resolution of full output current of 150 A for the main coil, corresponding to 150=2 16 0:002 A or 0.2 mT). To achieve ner resolution, the main coil is put into the persistent mode and the sweep coil is used to sweep a small range of magnetic eld (specication of the power supply is 16-bit resolution of full output current of 60 A for the sweep coil, corresponding Chapter 3. Development of HF EPR spectrometer 48 to 60=2 16 0:001 A or 2 T). One potential problem using the sweep coil is that there exists a mutual inductance between the main coil and the sweep coil which gives arise to an articial oset in readout values of magnetic eld. The oset depends on the ramp rate of the sweep coil, which makes it dicult to calibrate the readout. A simple solution to this problem is to use the main coil. Figure 3.6(a) shows the 230 GHz CW EPR spectrum of P1 centers taken by ramping the sweep coil. The measured spectrum reveals an oset of0.32 mT when compared to the simulated spectrum of P1 centers (see Fig. 3.6(b)). When the spectrum was taken by ramping the main coil, no visible oset from the simulated spectrum was observed as shown in Fig. 3.6(c). The cooling system of the magnet is based on a closed-cycle pulse tube cryocooler, which operates at 2.8 K with no load and is surrounded by a radiation shield at 40 K. The cryocooler is specied to operate in the stray eld of the magnet and regular maintenance is required for every 20,000 hours of operation. The magnet comes with seven temperature sensors (e.g., calibrated thermistors) located inside for monitoring the temperature of various regions (e.g., 1st stage, 2nd stage, pang joint plate, support plate, inner magnet, outer magnet, and switch) of the magnet during operation. Figure 3.7 shows the temperatures of magnet as a function of time during cooldown and warm-up process. Before cooling down the magnet, it is pumped below 110 5 mbar using a turbo pumping station with a combination of a turbopump and a roughing pump (Pfeier Vacuum) because of the large volume of the magnet (diameter of 850 mm and height of 1,288 mm). Typical time of cooling down the magnet from room temperature down to its base temperatures is70 hours. The time it takes for the magnet to warm up back to room temperature takes much longer due to little thermal connection due to high vacuum, and more than a week is required for a complete warm-up from the base temperatures. To expedite the process, a small amount of exchange gas can be admitted to the magnet during the warm-up. Chapter 3. Development of HF EPR spectrometer 49 Field offset (mT) Intensity (Arb. units) -4 -2 0 2 4 Meas. (sweep coil) Sim. Meas. (main coil) 3.36 mT 3.36 mT 0.32 mT 0.32 mT (a) (b) (c) Figure 3.6: 230 GHz CW EPR spectra of P1 centers when the magnetic eld is applied along [100] direction, showing the evidence of the mutual inductance between the main coil and the sweep coil. (a) Measured spectrum taken by ramping the sweep coil at a rate of 0.25 mT/s while the main coil was persisted at 8.15 T. (b) Simulated spectrum. (c) Measured spectrum taken by ramping the main coil at a rate of 0.13 mT/s while the sweep coil was turned o at 0 T. Clear shifts in the resonance eld positions are visible for the spectrum taken by ramping the sweep coil (indicated by vertical dotted lines). For the details of the spin Hamiltonian parameters and simulated spectrum, refer to Sect. 2.2.1. Chapter 3. Development of HF EPR spectrometer 50 Time (hour) 0 10 20 30 40 50 60 70 80 Temperature (K) 1 10 100 300 Time (hour) 0 50 100 150 200 250 300 Temperature (K) 1 10 100 300 1 st stage 2 nd stage Pang joint plate Support plate Inner magnet Outer magnet Switch 1 st stage 2 nd stage Pang joint plate Support plate Inner magnet Outer magnet Switch (a) (b) Figure 3.7: Temperature of various points inside the magnet as a function of time as the magnet (a) cools down to its base temperatures from room temperature and (b) warms up back to room temperature from its base temperatures. Typical time frame for cooldown is 70 hours and more than a week is needed for the complete warm-up. Chapter 3. Development of HF EPR spectrometer 51 3.6 Sample holder congurations and modulation coil designs In EPR spectrometers operating below 100 GHz, rectangular and cylindrical cavities are commonly employed to enhance the microwave power experienced by the sample (i.e., the strength of oscillating magnetic eld produced by the microwave excitations). However, one drawback with adapting the cavity design at HF is that the dimensions of the cavities scale proportional to the wavelength of the microwave, which are2.6 mm at 115 GHz and1.3 mm at 230 GHz. Thus, the amount of the sample that can be inserted into the such cavities are very limited in volume. One way to increase the amount of sample volume in HF EPR spectrometers to use Fabry-P erot cavity [7, 14, 18, 111{113, 117{124]. However, the use of Fabry-P erot cavities requires careful tunings (e.g., adjusting the distance between the mirrors to set a resonant frequency of a Fabry-P erot cavity as well as tuning the sample position to maximize EPR signals). For the current HF spectrometer, no microwave cavity is used to measure various forms of samples, e.g., single crystals, thin lms, powders, and aqueous/frozen solutions. Pulsed EPR spectroscopy is also performed without employing any cavity. Figure 3.8 shows various sample holder congurations with a solenoid modulation coil for magnetic eld modulation required for CW EPR measurements, all mounted under the bottom end of the corrugated waveguide. The sample holders are made of Garolite materials (e.g., G10) for low temperature operation. The modulation coil is simply made of a thin cop- per wire, wound around the post several hundred turns. To ensure the mechanical stability of the modulation coil when placed inside a strong magnetic eld (up to 12.1 T), the wound wire is xed with sealing wax. For positioning various forms of samples, single crystals and thin lms are directly placed on a conductive end-plate (e.g., silver-coated mirror) and are placed inside or near the bottom end of the corrugated waveguide for maximum coupling to microwave excitations. For powder and aqueous/frozen solution samples, cylindrical \buck- Chapter 3. Development of HF EPR spectrometer 52 Corrugated waveguide Modulation coil made of thin copper wire Sample mount made of G10 Conductive end-plate (sliver-coated mirror) Single crystal and thin-film samples “Bucket” for powder and aqueous/frozen solution samples Figure 3.8: Overview of various sample holder congurations. Single crystal and thin-lm samples are positioned directly on a conductive end-plate, and powder and aqueous/frozen solution samples are loaded to cylindrical \buckets" made of Te on. Depending on the di- mensions, samples are placed either inside or near the bottom end of the corrugated waveg- uide. Chapter 3. Development of HF EPR spectrometer 53 ets" made of Te on with a nominal volume of 12{527 L are used [9, 125]. Currently three dierent sizes of bucket are available; 12, 25, and 527 L. The nominal diameters are 2.0, 3.0, and 9.4 mm and the nominal heights are 3.8, 4.3, and 7.6, respectively (see Fig. 3.8 for schematic designs). Similar to single crystals and thin lms, the samples loaded into the buckets are placed on the end-plate and are positioned inside or near the bottom end of the corrugated waveguide. Calibration of modulation eld strength can be easily done by directly measuring the eld strength using a gaussmeter. Figure 3.9 shows such calibration plot for one of the modulation coils made in-house. Variable amounts of DC current are sent through the coil using a power supply, and the strengths of magnetic eld generated by the coil at the end-opening of the coil, in the direction of its symmetric axis, are measured. In CW EPR experiments, the current owing through the coil is sinusoidal at a xed frequency (typically 20 kHz) generated from the lock-in amplier. And since the actual modulation eld experienced by the sample placed inside or near the bottom end of the corrugated waveguide may be dierent from the calibration, the optimum amount of modulation eld is often determined from the analysis of the line shape of CW EPR spectrum. 3.7 Liquid helium cryostat As shown in Fig. 3.1, the liquid helium cryostat is placed into the room temperature bore of the magnet for performing EPR experiments in low temperatures. The cryostat is divided into four major sections; vacuum insulation, liquid nitrogen reservoir, liquid helium reservoir, and sample volume. The helium reservoir is protected by the vacuum insulation and the liquid nitrogen reservoir to minimize the thermal conduction and prolong the operation time of the cryostat. The corrugated waveguide is inserted into the sample volume of the cryostat and the sample is cooled by liquid helium vapor where the sample temperature can be controlled continuously from room temperature down to1.4 K by lowering the pressure Chapter 3. Development of HF EPR spectrometer 54 Current (mA) 0 100 200 300 400 Modulation field (mT) 2.5 2.0 1.5 1.0 0.5 0 500 600 Meas. Fit Slope = 0.05 mT/mA Figure 3.9: Strength of DC magnetic eld generated by the modulation coil as a function of the amount of current owing through the coil. The magnetic eld at the opening of the coil is measured by the gaussmeter (AlphaLab). Open square dots represent the measurements and solid line is the linear t. Chapter 3. Development of HF EPR spectrometer 55 of the sample volume using a rotary vane pump (Oerlikon Leybold Vacuum). The opening and closing between the liquid helium reservoir and the sample volume is adjusted by a needle valve, thus controlling the amount of liquid helium vapor ow through the sample volume. The bottom of the cryostat is closed with quartz windows for optical access. Custom probehead adaptors, fabricated by the USC machine shop, are attached to the top end of the corrugated waveguides and ensure proper vacuum-tight sealing needed during pumping of the sample volume. In the custom probehead adaptors, there are two openings with klein ange, one of which is used to apply the magnetic eld modulation. In addition, there are two additional openings for vacuum-tight SMA connections for radio frequency (RF) signal access. For monitoring the temperature at the vaporizer and the sample, two calibrated temperature sensors are used. The temperature of vaporing gas is controlled by an electric heater near the vaporizer. The amount of power to the heater can be set into three zones, 0.5, 5, and 50 W, in order to control the sample temperature in a wide range (Lake Shore Cryogenics). The boiling helium gas from the helium reservoir as well as helium vapor sucked by the pump are collected to a helium liquier system for recycling. The cryostat can also be operated with only liquid nitrogen for experiments from room temperature to80 K. 3.8 Spectrometer control and data acquisition All measurement routines, e.g., generation of TTL signals from the pulse generator for con- trolling microwave excitations as well as data acquisition from various electronic equipment, are all synchronized and programmed using National Instruments LabVIEW software. Chapter 3. Development of HF EPR spectrometer 56 3.9 Sensitivity of HF EPR spectrometer in pulsed experiments In this section, the sensitivity of the HF EPR spectrometer in pulsed EPR experiments is estimated using the spin echo measurement (see Sect. 1.3 for an overview of pulsed EPR spectroscopy). For the estimation, a thin lm (1.61.60.3 mm 3 ) of; -Bisdiphenylene-- phenylallyl (BDPA) complex with benzene (in 1:1 weight %) mixed in polystyrene was used. BDPA is a stable radical and widely used in EPR spectroscopy and related techniques [6{ 9]. Based on the measured weight of the lm (m film = 0:7 0:1 mg), initial weights of BDPA and polystyrene (m BDPA = 6:44 mg andm polystyrene = 618:42 mg), and the molecular weights of BDPA (M BDPA = 495:63 gmol 1 ), the number of electron spins in the lm from BDPA radicals (N spins ), which is equivalent as the number of BDPA molecules in the lm, was calculated as, N spins = m BDPA m BDPA +m polystyrene m film N A M BDPA = 6:44 mg 6:44 mg + 618:42 mg (0:7 0:1 mg) 6:02210 23 mol 1 495:63 gmol 1 810 15 {110 16 electron spins; (3.5) whereN A is the Avogadro constant. Figure 3.10(a) shows the CW EPR spectrum of the lm taken at EPR frequency of 115 GHz in room temperature which is represented by a single peak. Using the spin Hamiltonian parameters of the BDPA radical with adjustment of G PP , the measured spectrum and simulated spectrum with G PP = 0:9 mT are in good agreement (see Sect. 1.2 for details of the simulation). Figure 3.10(b) shows a single-shot spin echo trace captured at the magnetic eld of 4.110 T in room temperature with = 2:1 s. As shown in the inset of Fig. 3.10(b), the characteristic decay time of T 2 = 0:62 s was extracted from the decay of the spin echo signals by varying (refer to Sect. 1.3 for details of the pulse sequence and characteristic decay time). The sensitivity of the spectrometer in pulsed EPR experiments was estimated Chapter 3. Development of HF EPR spectrometer 57 (a) (b) Time (μs) 3 4 5 6 2τ (μs) T 2 = 0.62 μs ) s t i n u . b r a ( y t i s n e t n i R P E ) s t i n u . b r a ( y t i s n e t n i l a n g i S Figure 3.10: EPR measurements of BDPA radicals in polystyrene at room temperature. (a) CW EPR spectrum of BDPA radicals showing a single EPR signal with 0.9 mT peak- to-peak line width. The spectrum was taken by single scan at the magnetic eld ramp rate of 0.13 mT/s with the xed modulation of 0.05 mT at 20 kHz. (b) A single-shot spin echo signal with 2 = 2:1 s. A =2-pulse of 200 ns and a -pulse of 300 ns were used. The excitation pulses are largely truncated in the plot. The inset shows spin echo intensity as a function of 2. For the spin echo measurement, 256 shots of echo traces with the shot repetition rate of 30 ms were averaged to obtain a single data point. T 2 = 0:62 s was obtained by tting the decay with a single exponential function. Reprinted with permission from [19]. Copyright [2014], AIP Publishing LLC. Chapter 3. Development of HF EPR spectrometer 58 using the following equation [8, 18], Sensitivity = N spins f SNR exp 2 T 2 ; (3.6) wheref is the fraction of the spins that were being excited by the spin echo sequence, SNR is the signal-to-noise ratio of spin echo signal, and is the pulse separation between =2- and -pulse in the spin echo sequence. Based on the intensity of spin echo signal and the electronic noises coming from the detection system and oscilloscope, SNR of the single-shot spin echo signal was calculated to be14. The fraction of the spins that were being excited by the pulses was computed by considering the ratio of the pulse excitation bandwidth (BW ) to the observed CW EPR line width. In the single-shot spin echo measurement, a -pulse of 300 ns (t ) was used which corresponds to the pulse excitation bandwidth of, BW = 1 t h B g = 1 30010 9 s 6:62610 34 Js 1 11510 9 Hz 9:27410 24 JT 1 2:003 0:12 mT; (3.7) where h is the Planck constant, B is the Bohr magneton, and g is the g-value of BDPA radical. f can be computed as f = BW= G PP 0:1. Thus, the sensitivity of the HF EPR spectrometer at 115 GHz in pulsed EPR experiments was estimated to be, Sensitivity (810 15 {110 16 electron spins) 0:1 14 exp 22:1 s 0:62 s 210 12 {310 12 electron spins; (3.8) Chapter 3. Development of HF EPR spectrometer 59 in room temperature whereP of electron spins from BDPA radicals is given as (see Eqn. 1.35), P = N 1 N 2 N 1 +N 2 = exp E 1 k B T exp E 2 k B T exp E 1 k B T + exp E 2 k B T = 1 exp E k B T 1 + exp E k B T = 1 exp 9:27410 24 JT 1 2:0034:110 T 1:38110 23 JK 1 300 K 1 + exp 9:27410 24 JT 1 2:0034:110 T 1:38110 23 JK 1 300 K 0:009 or 0:9%: (3.9) This sensitivity corresponds to210 10 {310 10 electron spins at 2 K where the spin polar- ization is88%. From similar measurements and analysis, the sensitivity of the HF EPR spectrometer at 230 GHz in pulsed EPR experimetns was estimated to be510 11 {610 11 and910 9 {110 10 electron spins at room temperature and 2 K where the spin polarization is1.8% and99%, respectively. 3.10 Summary In this chapter, the development of the home-built HF EPR spectrometer operating in frequency range of 107{120 GHz and 215{240 GHz, in magnetic eld range of 0{12.1 T, and in temperature range of 300{1.4 K with unique experimental capabilities such as DEER and DD was presented. Various calibrations and operational procedures as well as performance of the spectrometer in pulsed experiments were discussed. Chapter 4 HF DEER and DD to investigate spin decoherence in diamonds Materials presented in this chapter can also be found in the article titled A high-frequency electron paramagnetic resonance spectrometer for multi-dimensional, multi-frequency, and multi-phase pulsed measurements by Franklin H. Cho, Viktor Stepanov, and Susumu Taka- hashi in Review of Scientic Instruments 85, 075110:1{075110:7 (2014) (Reprinted with permission from Ref. [19]. Copyright [2014], AIP Publishing LLC.) and the book chap- ter titled 230/115 GHz electron paramagnetic resonance/double electron-electron resonance spectroscopy by Franklin H. Cho, Viktor Stepanov, and Susumu Takahashi (accepted in 2015). Here we demonstrate unique capabilities of our HF EPR spectrometer to improve spin coherence in diamond. In particular, we discuss wide-band DEER to determine the spin concentration accurately which is responsible to the decoherence in diamond and manipula- tion with short/multi-phase pulses to extend the spin coherence signicantly. As discussed in Sect. 2.1, diamond has gained a great interest in recent years for its potential applica- tion in various areas including fundamental quantum physics [43{55], quantum information processing [49, 56{66], magnetic eld sensing [67{77], electric eld sensing [78], and tem- 60 Chapter 4. HF DEER and DD to investigate spin decoherence in diamonds 61 perature sensing [79{82]. The ecacy, gure-of-merit, or sensitivity of the applications is strongly related to and depends on coherence of spins that are utilized in diamond, and longer coherence time is often desired for various manipulations of spins as well as longer exposure to environmental changes for sensing purposes and better read-out sensitivity and delity. In diamond, various studies have indicated that the main source of spin decoherence (i.e.,T 2 relaxation) is strongly related to impurity contents, particularly P1 centers in a case of type-Ib diamonds. Ref. [94] studied T 2 of P1 centers in various diamond crystals as a function of volume concentration of P1 centers, and found that T 2 is inversely proportional to the concentration (see Fig. 4.1(a)). Our recent theoretical study of spin decoherence of a single NV center in a type-Ib diamond veried this where they showed T 2 of the NV center is also inversely proportional to the volume concentration of P1 centers surrounding the NV center [55] (see Fig. 4.1(b)). 4.1 Spin decoherence in type-Ib diamond HF EPR is a powerful method for investigating the spin decoherence in various spin systems. A recent HF EPR study at 240 GHz investigated the spin decoherence of ensemble of NV centers in a type-Ib diamond as a function of temperature [51] (see Fig. 4.1(c)). At high magnetic elds, where single spin ips are suppressed, the uctuations in the spin bath of P1 centers are mainly caused by the energy-conserving ip- op processes of P1 centers. The spin ip- op rate in the bath is proportional to the number of pairs with opposite spin, thus it strongly depends on the spin bath polarization [51]. At 240 GHz and 2 K, the polarization of spin bath of P1 centers is99%, which almost completely eliminates the spin ip- op process. This experiment therefore veried that the dominant decoherence mechanism in diamonds is the spin ip- op process of the spin bath of P1 centers. The ip- op rate is modeled by the following equation [51], 1 T 2 = C 1 + exp T Ze T 1 + exp T Ze T + res (4.1) Chapter 4. HF DEER and DD to investigate spin decoherence in diamonds 62 (a) (b) (c) Figure 4.1: (a) Measurements of T 2 of P1 centers as a function of volume concentration of P1 centers, showing T 2 is inversely proportional to the volume concentration. Figure was adapted from Ref. [94]. (b) Theoretical investigation of T 2 of NV center surrounded by P1 centers, showing T 2 is inversely proportional to the volume concentration of P1 centers. Reprinted with permission from Ref. [55]. Copyright (2013) by the American Physical So- ciety. (c) Measurements of T 2 of P1 and NV centers as a function of temperature, showing the quenching of dipolar uctuations of P1 centers from a nearly complete spin polariza- tion. Reprinted with permission from Ref. [51]. Copyright (2008) by the American Physical Society. Chapter 4. HF DEER and DD to investigate spin decoherence in diamonds 63 whereC is a temperature independent parameter related to the concentration of P1 centers, T Ze is the temperature corresponding to Zeeman energy and res is a residual relaxation rate. The measuredT 2 data as a function of temperature was tted to Eqn. 4.1 as shown in Fig. 4.1(c). The t yielded T Ze = 15 K, which was in reasonable agreement with the actual Zeeman energy of 11 K. The result conrms the decoherence mechanism of the uctuations of P1 centers. Thus, it is clearly important to know the concentration of impurity spins in diamonds in order to improve spin coherence and achieve successful applications of diamonds. However, determining absolute number of spins from EPR signal intensity is very challenging, if not impossible. To list a few diculties, carefully calibrated sample is needed and it is dicult to have exactly same microwave coupling to the sample between dierent experiments. Measur- ing the infrared absorption spectra have been commonly used to extract the concentration of P1 centers in diamonds [85], but the sensitivity of the measurement is not very high (on the order of 10 ppm). Here, an alternative method of extracting spin concentration using pulsed EPR technique known as DEER is presented. DEER senses small dipole-dipole couplings between diluted spins in a solid, and using this method very accurate determinations of spin concentrations of P1 centers in diamond on the order of 1 ppm or less is shown to be feasible. This technique utilizes the unique experimental capabilities of the HF EPR spectrometer de- scribed in Chap. 3 where the wide bandwidth as well as high microwave excitation power are essential to realize DEER experiment. Moreover, increasing coherence time in diamond is another ingredient required for successful application of diamond. In this regards, another advanced pulsed EPR technique known as DD utilizing high microwave outputs with multi- phases to improve T 2 in diamond is examined. Here, using DD technique, almost an order of magnitude improvement of T 2 of P1 centers from20 to 200 s is demonstrated without use of low temperature to suppress the spin bath uctuations. Although similar approaches have been demonstrated with NV centers in diamonds [62, 65, 82], results presented here is the rst realization of DD at HF. Chapter 4. HF DEER and DD to investigate spin decoherence in diamonds 64 4.2 HF DEER to extract spin concentration in diamond In this section, HF DEER spectroscopy at 230 GHz to probe couplings between P1 cen- ters and extract the spin concentrations is presented. As discussed in Sect. 4.1, P1 centers are known to be responsible for the spin decoherence in diamond. The sample studied here is a single crystal synthetic HPHT type-Ib diamond crystal (Sumitomo Electric In- dustries) having as-cleaved (111) faces on the top and bottom with nominal dimensions of 1.51.51.0 mm 3 (lengthwidthheight). Typical concentration of P1 centers in type-Ib diamonds ranges between10{100 ppm [85, 86], corresponding to average spatial separation of2{5 nm among the impurities under homogenous distribution. Figure 4.2(a) shows the echo-detected eld sweep spectrum of the diamond crystal at 230 GHz with the application of externally applied magnetic eld (B 0 ) along the [111] direction. The measured spectrum shows ve pronounced peaks representing P1 centers in diamond. The ve EPR peaks, la- beled as Group 1, 2, 3, 4, and 5, originate from four principle axes of P1 centers, i.e., [111], [ 111], [1 11], and [11 1] and hyperne interaction to 14 N nuclear spin (see Sect. 2.2.1). The total intensities of the EPR signals are proportional to the population dierence between electron spins with m S = 1=2 and electron spins with m S =1=2 for each group where the ratio of the population dierence among 1{5 can be approximated to 1:3:4:3:1, respectively, in the \high-eld limit" where the electron Zeeman interaction dominates the spin Hamil- tonian. The inset of Fig. 4.2(a) shows the energy diagram of P1 center. With pulsed EPR measurements using the spin echo sequence and inversion recovery sequence [4, 126], the spin decoherence time (T 2 ) and spin-lattice relaxation time (T 1 ) of P1 centers were determined as T 2 1 s and T 1 2 ms, respectively (see Sect. 1.3 for the details of pulse sequence). Next, a three-pulse DEER sequence (also known as 2+1 DEER sequence) [4, 127] was applied to probe dipolar couplings between P1 centers in the diamond. As shown in the inset of Fig. 4.2(b), the applied DEER sequence consists of the spin echo sequence [126] for Chapter 4. HF DEER and DD to investigate spin decoherence in diamonds 65 Echo intensity (arb. units) Magnetic field (Tesla) 8.202 8.206 8.210 (a) ν B (GHz) Normalized echo intensity 229.8 229.9 230 1 0.8 0.6 0.4 0 ν A ν B Reduced echo π/2 π τ τ t π T Echo 0.2 8.2032 T B 0 = 8.2032 T 1 2 3 4 r i θ i σ i = 1/2 B 0 (b) (c) (d) i-th B spin k-th A spin T (μs) 0 0.5 1 1.5 2 Sig DEER 0 0.2 0.4 0.6 0.8 1 1 2 3 4 1 2 3 4 1/2 -1/2 m S 1 -1 0 m I -1 1 0 A z /2 3 4,5 1,2 5 Figure 4.2: (a) 230 GHz echo-detected eld sweep of P1 centers whenB 0 k [111] direction. For the spin echo sequence, =2- and -pulses of 300 and 500 ns, respectively, and a xed of 1.5 s were used. The magnetic eld was varied in step size of 0.05 mT, and 16 shots of echo signal were averaged to obtain a single data point with the repetition time of 20 ms. The inset shows the energy diagram of P1 centers. For subsequent DEER measurements, B 0 was xed at 8.2032 T and the P1 centers in the [111] orientation with m I = 1 were chosen asA spins (labeled as 5). B spins were the other four groups of P1 centers at 8.2043 T (P1 centers in the other three orientations with m I = 1; labeled as 4), 8.2072 T (P1 centers in all orientations with m I = 0; labeled as 3), 8.2102 T (P1 centers in the other three orientations with m I = 1; labeled as 2), and 8.2114 T (P1 centers in [111] orientation with m I = 1; labeled as 1). (b) DEER spectrum of P1 centers showing clear reductions of the spin echo intensity ofA spins in four regions, centered at 229.771, 229.801, 229.889, and 229.975 GHz, which were due to dipolar couplings toB spins at 1, 2, 3, and 4, respectively. The inset shows the three-pulse DEER sequence used in the experiment where A denotes the resonance frequency of A spins (230 GHz) and B and t denotes the frequency and duration of the -pulse for B spins, respectively. Experimental parameters were =2 = 150 ns, = 250 ns, = 1s,T = 850 ns, andt = 250 ns. B was varied in step size of 1 MHz, and 64 shots of echo signal were averaged to obtain a single data point with the repetition time of 10 ms. (c) Illustration of the static model of spin baths. (d) Sig DEER as a function of T for Group 1{4. Parameters used for the experiment were =2 = 150 ns, = 250 ns, = 2 s, and t = 250 ns. T was varied in step size of 25 ns, and 64 shots of echo signal were averaged to obtain a single data point with the repetition time of 10 ms. Chapter 4. HF DEER and DD to investigate spin decoherence in diamonds 66 A spins and a single -pulse for B spins. In the measurement, changes in the spin echo signal occur when the eective magnetic dipolar elds at A spins are altered by ipping B spins with a resonant -pulse. For DEER spectroscopy, P1 centers whose bonds are along [111] and whose nuclear spin quantum number is m I = 1 were used as A spins (denoted as 1 in Fig. 4.2; the electron spin quantum number (m S ) is conserved during the measurement because T 1 T 2 ), and the other P1 centers denoted as 2{4 in Fig. 4.2 were chosen for B spins (see gure caption for detailed description). As shown in Fig. 4.2(b), DEER signals were observed clearly in the spin echo intensity of probe electron spins as a function of the resonant pulse frequency for B spins ( B ). The number of observed DEER signals and the splitting of the peaks matched the spin parameters of P1 centers, which is an indication of a direct observation of the dipolar coupling among P1 centers. The intensity of the observed DEER signal is known to depend on the concentration of target electron spins. By considering the magnetic dipole interactions between A and B spins (see Fig. 4.2(c)), the expression of the DEER signal is derived by [128], Sig DEER = exp n 0 2 B g A g B 9 p 3h T ; (4.2) wheren is the volume concentration of B spins in m 3 , 0 is the permeability of free space, and g A and g B are the g-values of A spins and B spins, respectively. As shown in Eqn. 4.2, Sig DEER is a single exponential function of the delay of the-pulse (T ) andn. Figure 4.2(d) shows Sig DEER of Group 1{4 as a function of T . As expected, Sig DEER depends on which spin group is being excited by B because each group has dierent volume concentration. The concentrations of P1 centers belonging to Group 1{4 were determined by tting the experimental results with Eqn. 4.2, yielding(1.90.1)10 23 , (4.20.1)10 23 , (5.90.1)10 23 , and (5.20.1)10 23 m 3 , respectively. These volume concentrations correspond to 1.10.1, 2.40.1, 3.40.1, and 3.00.1 ppm, which means the total concentration of P1 centers in the diamond is11 ppm. The extracted concentrations fall into typical concentration range (10{100 ppm) of P1 centers in type-Ib diamonds [85, 86]. Chapter 4. HF DEER and DD to investigate spin decoherence in diamonds 67 4.3 HF DD to extend spin coherence in diamond Finally, another way for extending spin coherence using HF EPR spectroscopy is presented. Coherence of spin systems can be extended by reducing couplings between the spins and surrounding noises using advanced pulse sequences such as various DD sequences. The idea of DD can be traced into the spin echo, in which couplings to static and spatially inhomogeneous magnetic eld noises can be suppressed completely by the rephasing pulse in the middle of the elapsing time interval [126]. The ecacy of DD depends on the relationship between the noise spectrum of surrounding spins and the spectrum or lter function of a DD sequence, and when those two spectra overlap largely, spins experience strong decoherence [55, 129, 130]. Here the demonstration of three DD sequences, e.g., Carr-Purcell-Meiboom-Gill (CPMG) [131, 132], two-axis CPMG, and Uhring dynamical decopuling (UDD) [130] sequence, to P1 centers in diamond were tested at EPR frequency of 115 GHz in room temperature. The sample used in the experiments is another single synthetic HPHT type-Ib diamond crystal (Element Six) having polished (100) faces on the top and bottom with nominal dimensions of 0.80.80.4 mm 3 (lengthwidthheight). Spin decoherence time (T 2 ) of P1 centers was rst determined to be 231s by tting a spin echo decay with a single exponential function. Then application of three DD sequences (CPMG, two-axis CPMG, and UDD sequence) were demonstrated. As shown in Fig. 4.3(a), excitation pulses of the sequences consist of a =2- and four -pulses (denoted as N = 4 whereN is the number of-pulses). All of the-pulses in CPMG and UDD sequences have 90 phase (Y ) with respect to the =2-pulse which has 0 phase (X), while the phase of the -pulses in two-axis CPMG sequence alternates betweenX andY . Coherence times (T coh ) of P1 centers for each sequences with dierentN were determined by tting the observed echo decays as a function of total evolution time (see Fig. 4.3(b) and (c)) with a single exponential function. As indicated by the comparison of echo decays with CPMG, two-axis CPMG, and UDD for N = 8 (see Fig. 4.3(b)), a longer T coh was observed from CPMG and two-axis CPMG than that from UDD. Finally, Fig. 4.3(c) shows the echo decays as a function of the Chapter 4. HF DEER and DD to investigate spin decoherence in diamonds 68 b a c CPMG X UDD Y XY Free evolution time Y X echo echo X X echo Y X Y 0 CPMG N = 4 Signals (arb. units) 0 10 Time (μs) Free evolution time (μs) 0 100 200 300 400 Echo intensity (arb. units) Echo intensity (arb. units) 0 10 100 1000 Free evolution time (μs) B = 4.110 T B = 4.110 T Figure 4.3: (a) Three DD sequences for N = 4. Top: CPMG sequence, middle: two-axis CPMG sequence, and bottom: UDD sequence. -pulses are represented by solid squares and =2-pulses are represented by open squares. Phases of excitation pulses are set with respect to the phase of the reference microwave in the detection system. (b) Application of CPMG, two-axis CPMG, and UDD forN = 8 at 115 GHz. Data with errors are represented by markers with designated shape as shown in the legend and ts to a single exponential function are shown by solid lines. T coh was measured to be 651, 673, and 352 s with CPMG, two-axis CPMG, and UDD, respectively. The inset shows a trace of echo signals with CPMG forN = 4. The echoes are represented with solid lines. (c) Dependence of T coh onN with CPMG sequences at 115 GHz. Data with errors are represented by markers with designated shape as shown in the legend and ts to a single exponential function are shown by solid lines. T coh was measured to be 231, 42.10.5, 48.80.8, 651, 901, 1182, 1683, and 2118 s for N = 1 (spin echo), 2, 4, 8, 16, 32, 64, and 128, respectively. Reprinted with permission from [19]. Copyright [2014], AIP Publishing LLC. Chapter 4. HF DEER and DD to investigate spin decoherence in diamonds 69 total evolution time obtained from CPMG sequences with N -pulses. The application of 128 pulses extends T coh to 2118 s, corresponding to 9-fold enhancement compared to T 2 measured by the spin echo sequence. 4.4 Summary In this chapter, the origin of spin decoherence in type-Ib diamond was discussed. In addition, small magnetic dipole coupling between P1 centers was detected in HF DEER and spin concentrations of dierent groups of P1 centers on the order of 1 ppm were successfully extracted. The accurate determination of spin concentrations is important for extending coherence in diamond. Finally, T 2 was extended by almost an order of magnitude using DD at 115 GHz, which was the rst demonstration of the technique at such HF. Chapter 5 HF EPR spectroscopy to identify surface impurities in NDs Materials presented in this chapter can also be found in the article titled Paramagnetic im- purities on nanodiamond surface by Franklin H. Cho, Viktor Stepanov, Rana Akiel, Xiaojun Zhang, and Susumu Takahashi (manuscript in preparation). In this chapter, we aim to determine location, concentration, and structure of impurities in NDs. As discussed in Sect. 2.2.3, there have been various studies pointing the existence of surface paramagnetic impurities in various diamonds [41, 102{104, 106{110]. Moreover, direct EPR studies of detonation NDs showed that the observed EPR signal has g-value close to 2 which overlaps with other paramagnetic impurities commonly found in diamonds. Here, we utilize our HF EPR spectrometer to distinguish surface impurities (denoted as X for convenience) in NDs. Because eective dierence in g-values between X and other spins in NDs (such as P1) is very small (0.0005), the employment of HF EPR is a key for this study. The clear separation of EPR spectrum from X allows us to observe the size dependence of the EPR spectrum which leads to determine the location of X. Moreover, our line shape analysis and DEER measurement also support that the local environment of X is very dierent from that of P1 centers. 70 Chapter 5. HF EPR spectroscopy to identify surface impurities in NDs 71 5.1 Characterization of ND size by DLS In the present study of surface impurities in NDs, eight dierent sizes of commercially avail- able diamond powders from Engis Corporation and L. M. Van Moppes & Sons SA were used. The ND powders were manufactured by mechanical milling or girding of micron-size type-Ib HPHT diamond crystals, which originally contained10{100 ppm nitrogen con- centrations [38, 39]. The mean diameters and standard deviations of NDs specied by the suppliers are 550100, 25080, 16050, 10030, 9030, 6020, 5020, and 3010 nm. In order to verify the size of NDs, in-house dynamic light scattering (DLS) measurements were performed and mean hydrodynamic diameters (d) and standard deviations () of ND powders were extracted from second-order autocorrelation curves of scattered light intensity. Figure 5.1 shows the summary of second-order autocorrelation functions, g 2 (), obtained by DLS measurements on ND powder samples. The autocorrelation curves were analyzed by the cumulant method and tted to, g 2 () =B + exp(2 1 + 2 2 ); (5.1) where B is the baseline constant (ideally B=1), is the amplitude of the autocorrelation function, and 1 and 2 are the rst and second cumulant which describes the average decay rate and the relative variance of the distribution, respectively [133, 134]. The diusion coecient (D) is related to 1 as D = 1 =q 2 , where q = 4n 0 sin(=2)= is the wave vector, is the incident laser wavelength, n 0 is the refractive index of the solution, and is the angle at which the detector is located to monitor the scattered light. d was calculated using the Stokes-Einstein relation: d =k B T=(3D) wherek B is the Boltzmann constant,T is the temperature, and is the dynamic viscosity of the solution. Finally, the polydispersity index (PDI) was computed as PDI = 2 = 2 1 where PDI is related to sigma as PDI = 2 =d 2 in case of particle distribution following the Gaussian function. Through careful analysis of the obtained autocorrelation signals, d and were extracted as 460 130, 290 70, 160 30, 14020, 10020, 8010, 6010, and 5010 nm, which were in close agreements with the Chapter 5. HF EPR spectroscopy to identify surface impurities in NDs 72 460 nm 290 nm 160 nm 140 nm 100 nm 80 nm 60 nm 50 nm τ (s) g 2 (τ) (a) 1.3 1.0 1.2 1.1 10 -3 10 -6 10 -4 10 -5 10 -1 10 -2 (b) Measured diameter (nm) Specified diameter (nm) 10 100 1000 10 1000 100 Figure 5.1: (a) Second-order autocorrelation curves of NDs obtained by DLS measurements. Data points are represented by open markers with designated shapes as indicated by the legend and ts are shown as solid lines. (b) Comparison of specied size and hydrodynamic diameters obtained from DLS measurements. Data points are represented by square dots and error bars indicate . Chapter 5. HF EPR spectroscopy to identify surface impurities in NDs 73 specications (see Fig. 5.1(b) for the comparison of specied sizes and DLS measurements). For all samples, PDI was below 0.09 (i.e., is less than 30% of d), indicating measured samples can well be considered as monodisperse. 5.2 HF CW EPR spectra of NDs Figure 5.2 shows the summary of CW EPR spectra of NDs with mean sizes and standard distributions of460130, 29070, 16030, 14020, 10020, 8010, 6010, and 5010 nm taken at 230 GHz in room temperature. The observed EPR spectra of NDs were well understood by a superposition of two kinds of spectrum. One is from P1 centers, the most common impurity in synthetic type-Ib diamonds (see Sect. 2.2.1). As shown in Fig. 5.2, the other contribution to the observed EPR spectra of NDs was well represented by a single EPR peak, which will be denoted as X from now on for simplicity. Using the methods described in Sect. 1.2 for the simulation of a single EPR peak for a S = 1=2 system, the isotropic g-value and the Lorentzian line width were found as (g X x = g X y = g X z = 2:00288 0:00005) and L PP 1 mT based on the reported g-value of P1 centers and high spectral resolution of HF EPR spectroscopy. The observed line width for X is much broader than that of P1 centers, which is0.24 mT. In addition, the line width of X showed dependence on the EPR frequency. Figure 5.3 shows the EPR spectra of X taken at 9.3 and 230 GHz The observed frequency dependence indicates that the broadening is due to the distribution of g-value of X, e.g., g-strains. In or- der to explain the line broadening, two line width broadening mechanism were considered; 1) dipolar broadening nearby spins due to high concentration of X and 2) Gaussian distribution of g-values known as g-strain. To simulate the eect of dipolar broadening, the approach described in [135] was adapted. Shifts in the resonance position (B shift ) from unperturbed resonance eld (B res ) due to the dipolar eld originating from nearest-neighbor spins were numerically calculated as a function ofr and wherer is the distance to the nearest-neighbor Chapter 5. HF EPR spectroscopy to identify surface impurities in NDs 74 8.2 8.205 8.21 Magnetic field (Tesla) 460 nm 290 nm 160 nm 140 nm 100 nm 80 nm 60 nm 50 nm 8.2 8.205 8.21 Intensity (arb. units) 460 nm P1+X P1 X 8.2 8.205 8.21 Intensity (arb. units) 140 nm P1+X P1 X 8.2 8.205 8.21 Magnetic field (Tesla) Intensity (arb. units) 60 nm P1+X P1 X Figure 5.2: 230 GHz CW EPR spectra of various sizes of NDs. All spectra were taken at room temperature with eld modulation of 0.02 mT and sweep rate of 0.13 mT/s, and normalized for ease of comparison. Solid and dotted lines represent measured and simulated spectra, respectively. The simulated spectra were obtained by considering a superposition of two separate EPR spectra, P1 center and X. Partial contributions of EPR spectrum of P1 center and X are also shown for 460, 100, and 60 nm NDs. For 50 nm NDs, no trace of P1 center spectrum is visible in the measurement and the simulation is obtained only from X. Chapter 5. HF EPR spectroscopy to identify surface impurities in NDs 75 spin and is the relative angle with respect to the external magnetic eld. Then an integral of Lorentzian line shape, centered atB res B shift with a xed width, weighted by a Gaussian distribution of nearest-neighbor distances (valid for uniform distribution of neighbor spins) over the solid angle was computed. For g-strain, simply B res B shift given by oset of g-values were weighted by the Gaussian distribution of width g. It was found that the broadening at 9.3 GHz was dominated by the dipolar broadening which resulted the volume concentration of X as140 ppm and the broadening at 230 GHz was dominated by g-strain which resulted in g = 0:0003. As shown in Fig. 5.3, a better agreements were observed compared with a single Lorentzian ts. From the strong dependence of CW EPR spectra on the size of NDs, the physical location of X is investigated. Figure 5.4 shows the intensity ratios of P1 center to X (I P 1 =I X ) from the simulated spectra as a function of diameter of NDs (d). Because intensities of EPR signals are proportional to the number or density of spins, a possible explanation of the observed size dependence of I P 1 =I X is that the relative density of P1 center to that of X decreases as d decreases. However, since all ND samples were made from synthetic micron-size HPHT type-Ib diamond crystals, the concentrations of P1 centers in dierent sizes of NDs are likely to be similar. And there is no physical reason for the density of X to increase as d decreases because the powders are produced from a simple griding process. Since P1 centers are known to be distributed homogeneously over the whole volume diamond crystals, another possible explanation of the sharp decrease of I P 1 =I X as d decreases in Fig. 5.2 and 5.4 is that the distribution of X is localized in the vicinity of the surface of ND crystals. In order to explain the observed size dependence ofI P 1 =I X , two simple models, the surface and core-shell model, are considered where the shape of NDs is assumed to be perfectly spherical as shown in the inset of Fig. 5.4. In the surface model, P1 centers are considered to be distributed homogeneously over the whole volume of NDs with a volume density P 1 Chapter 5. HF EPR spectroscopy to identify surface impurities in NDs 76 Intensity (arb. units) 0.330 0.335 0.340 Magnetic field (Tesla) Magnetic field (Tesla) 8.200 8.205 8.210 Meas. g-strain+dipolar Lorentzian 230 GHz 9.3 GHz Figure 5.3: 9.3 and 230 GHz CW EPR spectra of 50 nm NDs showing signicant line broadening from 9.3 to 230 GHz. Line broadenings due to dipolar coupling and g-strain were considered, which resulted in better agreement with the measured spectra compared with single Lorentzian ts. Chapter 5. HF EPR spectroscopy to identify surface impurities in NDs 77 P1 P1 Surface model Core-shell model t 100 500 EPR exp. Surface model Core-shell model d (nm) 50 0.01 0.1 1 I P1 /I X (Arb. units) P1 X Figure 5.4: EPR intensity ratio of P1 center to X (I P 1 =I X ) as a function of size of NDs, d. Square dots represent EPR intensity ratio extracted from tting CW EPR spectra. x and y error bars indicate the standard deviations of sizes of NDs and errors associated with numerical simulations of CW EPR spectra, respectively. Dotted line represents a t with surface model and solid line represents a t with the core-shell model. The inset describes the surface model and core-shell model with shell thickness t. Chapter 5. HF EPR spectroscopy to identify surface impurities in NDs 78 and X are considered to be localized at the surface with a surface density X . This yields, I P 1 =I X 4 3 (d=2) 3 4 (d=2) 2 d: (5.2) On the other hand, in the core-shell model, X are considered to be located in the outer spherical shell of the sphere with thicknesst from the surface with a volume density X and P1 centers are considered to be distributed over the inner core of the sphere excluding the shell. This yields, I P 1 =I X 4 3 (d=2t) 3 4 3 (d=2) 3 4 3 (d=2t) 3 : (5.3) From the ttings of the observedI P 1 =I X to Eqn. 5.2 and 5.3, better agreement was observed with the core-shell model as shown in Fig. 5.4. From the t, t was extracted to be 96 nm. 5.3 HF DEER of NDs Finally, another supporting evidence to the local distribution of P1 centers and X is presented by HF DEER of NDs. Figure 5.5 shows HF DEER measurement of 60 nm NDs taken at 115 GHz and 80 K where the dipole coupling between P1 centers were clearly observed, but no coupling from P1 centers to X was detected. As discussed in Sect. 4.2, HF DEER is an unique pulsed EPR experiment that can sense small dipole-dipole coupling between spins and extract the spin concentration in a case of homogeneously distributed diluted spin systems. With the concentration of140 ppm of X from the line width analysis in Sect. 5.2, it would have been more than enough to be detected by the HF DEER measurement if the physical location of X was similar to that of P1 centers as detection of spin concentration on the order of 1 ppm was demonstrated in Sect. 4.2. Thus, the lack of DEER signal from X supports the local distribution model of P1 centers and X suggested by the HF CW EPR spectra. Chapter 5. HF EPR spectroscopy to identify surface impurities in NDs 79 5.4 Summary In this chapter, HF CW EPR spectroscopy was used to successfully identify two major paramagnetic impurity contents (P1 centers and X) in various sizes of synthetic type-Ib diamond powders. Based on the spectral analysis with supporting HF DEER measurement, it was found that the physical location of X was attributed to10 nm shell of ND crystal with the concentration of140 ppm where P1 centers were known to be homogenously located inside the crystal. Chapter 5. HF EPR spectroscopy to identify surface impurities in NDs 80 ν B (GHz) 114.9 115 115.1 115.2 114.8 Sig DEER (Arb. units) Figure 5.5: HF DEER measurement of 60 nm NDs where A spins were chosen as the central peak of P1 centers (i.e.,m I = 0; see Fig. 6.2(a)). Only DEER signal to other groups of P1 centers in m I =1 states were detected and no reduction from dipole coupling to X was observed, which is a supporting evidence of the localized distribution of P1 centers and X in ND crystals presented in Sect. 5.2. Chapter 6 Mechanisms of spin relaxations in NDs Materials presented in this chapter can also be found in the article titled Paramagnetic impurities on nanodiamond surface by Franklin Hyunil Cho, Viktor Stepanov, Rana Akiel, Xiaojun Zhang, and Susumu Takahashi (manuscript in preparation). Here we determine the relation between spin relaxations (e.g.,T 2 andT 1 ) in NDs and im- purities near the surface of ND crystals (X) that have been extensively discussed in Chap. 5. We utilize multi-frequency pulsed EPR spectroscopy at 9.3, 115, and 230 GHz as a function of temperature in order to study various spin relaxation mechanisms that depend on tem- perature and magnetic eld dierently. Although T 2 relaxations in NDs show no signicant variations as a function of temperature nor frequency, T 1 relaxations in NDs signicantly deviate from the previously reported studies of single crystals. Moreover, T 1 in NDs is cor- related with the size of NDs where we observe up to two orders of magnitude shorter T 1 in smaller NDs, but does not depend on magnetic eld. The observation of no eld or frequency dependence from 9.3 to 230 GHz is an important piece of information that allows us to reveal a signicant contribution from X to T 1 relaxation in NDs. 81 Chapter 6. Mechanisms of spin relaxations in NDs 82 6.1 Spin relaxations and surface impurities in NDs It has been known that the surrounding environment signicantly aects the coherence times in diamonds which limits the applications of diamonds. Recent studies of shallow NV centers in bulk crystals [106{108] as well as NV centers found in NDs [109, 110] have shown that these NV centers exhibit dierent spin properties (e.g., broader line width and faster spin relaxation times) compared to deep, stable NV centers in single bulk crystals, which were explained by contributions of dense paramagnetic impurities on the surface. In Ref. [109],T 1 relaxations of single NV centers in NDs were studied as a function of ND particle size, and signicant reductions of T 1 were reported compared to NV centers found in bulk diamonds. The additional reductions were attributed and modeled by a fast dipole uctuations of similar dense surface impurities (see Fig. 6.1). NDs have been proposed for applications in biological settings [81, 83, 110, 136], and precise understanding of spin relaxation mechanisms in NDs is important for successful applications. 6.2 T 2 relaxation in NDs First the investigation of T 2 relaxations in NDs is discussed. Figure 6.2 shows the 115 GHz echo-detected eld-sweep spectrum of 60 nm NDs taken at 80 K. As shown in the measured and simulated spectra, the EPR signals of both P1 centers and X are clearly visible, but the intensity of X is much less pronounced compared to the CW spectra shown in Fig. 6.2(a). The simulation follows the procedure described in Sect. 2.2.1, but the absorption line shape instead of 1 st derivative line shape functions were used due to the nature of the measurement where DC EPR signal intensity is recorded without eld modulation unlike CW EPR spectroscopy. Also the spin relaxation times (T 2 andT 1 ) of P1 centers and X were measured as T P 1 2 = 0:84s, T P 1 2 = 0:93 ms, T X 2 = 0:32s, andT X 1 = 0:15 ms by employing the spin echo sequence (Eqn. 1.31) and inversion recovery sequence (Eqn. 1.32) as shown in Fig. 6.2(b) and (c). The fact thatT X 2 <T P 1 2 explains the observation of the less pronounced Chapter 6. Mechanisms of spin relaxations in NDs 83 Figure 6.1: Study ofT 1 relaxation of single NV centers in NDs as a function of diameter of NDs and illustration of NV center and surface impurities in ND particle. Figure was adapted from Ref. [109]. Chapter 6. Mechanisms of spin relaxations in NDs 84 4.098 4.1 4.102 4.104 4.106 0 Magnetic field (Tesla) Echo intensity (arb. units) 4 6 8 10 Echo intensity (arb. units) 0 2τ (μs) T 2 = 0.84 µs Echo intensity (arb. units) 0 4 6 8 10 2τ (μs) T (ms) 0 2 4 6 8 Echo intensity (a.u.) T 1 = 0.15 ms T 2 = 0.32 µs (a) (b) (c) Echo intensity (a.u.) T 1 = 0.93 ms T (ms) 0 2 4 6 8 Meas. Sim. (total) Sim. (P1) Sim. (X) P1 X P1 X Figure 6.2: (a) Echo-detected eld-sweep spectrum at taken 115 GHz and 80 K (solid line). 300 ns and 500 ns pulses were used for =2- and -pulses, respectively, and a xed delay time of 1.5 s was used. The simulated spectrum (dotted lines) with contribution of P1 center and X agrees well with the measured spectrum. Arrows indicate resonance positions of P1 centers and X at which all subsequent relaxation measurements were performed. (b) Spin echo measurement and inversion recovery measurements of P1 centers, which yielded T P 1 2 of 0.84 s and T P 1 1 of 0.93 ms from single exponential ttings shown as solid lines. (c) Spin echo and inversion recovery measurements of X, which yielded T X 2 of 0.32 s and T X 1 of 0.15 ms from single exponential ttings shown as solid lines. For all measurements, 64 shots of echo signal were averaged to obtain a single data point with the repetition time of 10 ms. Chapter 6. Mechanisms of spin relaxations in NDs 85 signal of X in the echo-detected eld sweep measurement can be explained where the delay time is held constant in the spin echo sequence. Figure 6.3(a){(c) summarizes the temperature, eld, and size dependence study ofT P 1 2 in diamonds, measured by employing the spin echo sequence (Eqn. 1.31). Measurements at 115 and 230 GHz were performed using the HF EPR spectrometer described in Chap. 3, and the commercial X-band spectrometer in the USC Chemistry department (Bruker Elexsys E580) was used for measurements at 9.3 GHz. Although little variations exist in values of T P 1 2 as a function temperature, eld, and size, but no noticeable trends could be extracted. It has been reported by various studies that the main source of T 2 relaxations in diamonds is the dipolar couplings to P1 centers, thus they depend strongly on the average inter-spin distances or concentration of P1 centers in diamonds [51, 55, 94, 95] (see Fig. 4.1(a) and (b)). The origin of the variations in T 2 was therefore attributed to dierent P1 concentrations among dierent samples of NDs. No sign of temperature dependence down to 80 K also agrees with earlier studies by Ref. [51, 95] (see Fig. 4.1(c)). The observation that T 2 of P1 centers are not aected by signicant amounts of X in NDs also agrees well with the proposed local spatial distribution of P1 centers and X in ND crystals. 6.3 T 1 relaxation in NDs Unlike T P 1 2 measurements, values of T 1 in diamonds are expected to exhibit a strong de- pendence on temperature as reported by several studies. Previous ndings attributed the mechanisms of T 1 relaxation of P1 centers to the spin-orbit phonon-assisted tunneling pro- cess [51, 93, 95] (i.e., 1=T 1 =BT 5 forT above 80 K whereB is the proportionality constant), andT 1 relaxation of NV centers to the two-phonon Raman process, two-phonon Orbach pro- cess, and cross-relaxation [97, 137]. And since dierent spin relaxation mechanisms have dierent dependence on temperature as well as magnetic eld (e.g., for a direct process where the lattice vibrations or phonons with matching energies to the spin transition ener- Chapter 6. Mechanisms of spin relaxations in NDs 86 230 GHz 115 GHz 9.3 GHz (a) (b) (c) 100 150 200 250 300 100 150 200 250 300 100 150 200 250 300 T 2 (μs) 0 1 2 3 T 2 (μs) 0 1 2 3 T 2 (μs) 0 1 2 3 Temperature (K) Temperature (K) Temperature (K) Figure 6.3: Summary of temperature, eld, and size dependence study ofT P 1 2 in diamonds taken at (a) 9.3 GHz, (b) 115 GHz, and (c) 230 GHz. No strong dependence on temperature, eld, and size was observed. Chapter 6. Mechanisms of spin relaxations in NDs 87 gies induce direct spin ips, the expected dependence is 1=T 1 B 2 0 T ; for a Raman process where higher frequency lattice phonons induce spin ips with scattering phonons, the ex- pected dependence is 1=T 1 B 0 T 7 ), information obtained from pulsed EPR spectroscopy at multiple magnetic elds or frequencies allows study of dierent spin relaxation mechanisms in NDs. Figure 6.4(a){(c) shows the summary of T P 1 1 relaxation measurements as a function of temperature, eld, and size by employing the inversion recovery sequence (Eqn. 1.32). The temperature dependence of T P 1 1 in the single crystal and 10 m powders was well described by the known spin-orbit phonon-assisted tunneling process, and tting T P 1 1 of single crystal and 10 m powder at all three frequencies (9.3, 115, and 230 GHz) together to the spin- orbit process yielded B = 2:510 10 s 1 K 5 ), which is in good agreement with previously reported values in Ref. [51, 95]. On the other hand, the observed temperature dependence ofT P 1 1 in ND samples deviated from the knownT 5 dependence, and the degree of deviations was larger for smaller sizes of NDs, as shown in Fig. 6.4(a){(c). As mentioned in Sect. 6.1, it has been reported that a dense paramagnetic impurities at or near the diamond surface can yield reductions of T 1 from the magnetic noise caused by fast dipole uctuations of the impurities. The observed size dependence of T P 1 1 also suggests a contribution from defects and impurities near surface (also observed by CW EPR spectroscopy of NDs in Chap. 5). The deviation of T P 1 1 in NDs correlates with the EPR intensity of X, i.e., larger the EPR intensity of X, larger the deviation of T P 1 1 . In order to explain the observed deviation of T 1 in NDs, we extend theT 1 process model to the following, 1 T P 1 1 =BT 5 +C; (6.1) where B = 2:510 10 s 1 K 5 ) is the previously obtained parameter from tting measure- ments of crystal and 10 m powder to the known T 5 dependence and C is a T 1 process specic to NDs due to fast dipole-dipole uctuations from a dense surface impurities [107{ 110]. The temperature dependence of T P 1 1 in NDs were tted to Eqn. 6.1, and as shown Chapter 6. Mechanisms of spin relaxations in NDs 88 (a) (b) (c) (d) Temperature (K) 100 200 300 10 0 10 2 10 4 1/T 1 (s -1 ) 10 0 10 2 10 4 10 0 10 2 10 4 1/T 1 (s -1 ) Temperature (K) Temperature (K) 230 GHz 115 GHz 9.3 GHz Figure 6.4: Summary of temperature, eld, and size dependence study ofT P 1 1 in diamonds taken at (a) 9.3 GHz, (b) 115 GHz, and (c) 230 GHz. For the HF EPR spectrometer, typical lengths of =2- and -pulse used were 500 and 700 ns for 230 GHz and 300 and 500 ns for 115 GHz, respectively, and chosen to maximize echo intensity. For the Bruker X-band spectrometer, typical lengths of =2- and -pulse used were 350 and 650 ns, respectively. (d) Strength of the constant C as a function of ND size. Chapter 6. Mechanisms of spin relaxations in NDs 89 in Fig. 6.4(a){(c), good agreements between the temperature dependence of T 1 and ttings were observed for all sizes of NDs. Figure 6.4(d) shows the summary of the parameter C obtained from the ts. From T P 1 1 in 460, 290, and 140 nm NDs, no eld-dependence of C was visible. Larger C in smaller NDs were observed, and this trend agrees with the model suggested by Ref. [109, 110]. Considering dipole-dipole coupling between surface impurities to a spin located at the center of ND particle, Ref. [109, 110] claimed the relaxation rate scales as d 4 . However, the dependence of C on d scales more like d 2 , and this deviation is believed to come from the nature of theT 1 measurement of P1 centers where ensemble averaging of P1 centers located at dierent positions in the ND particle experience dierent dipole magnetic noise from X. 6.4 Summary In this chapter, T 2 and T 1 relaxations in NDs are studied by multi-frequency pulsed EPR spectroscopy. No strong dependence on size, temperature, and frequency was observed in T 2 measurements of P1 centers which was another supporting evidence that P1 centers and X are located in dierent regions of ND crystals. T 1 of P1 centers depended strongly on temperature and size, but not on frequency or magnetic eld. More than two orders of magnitude dierence inT 1 was observed in NDs compared to bulk and mircon-size powders, and the size dependence ofT 1 indicates additional relaxation mechanism, most probably due to magnetic noises from X. Chapter 7 Conclusion In conclusion, this dissertation was devoted to the development of HF EPR spectrometer and study of paramagnetic impurities in diamond by EPR spectroscopy. In particular, the relation between impurities and spin relaxation in diamond was studied by multi-frequency pulsed EPR spectroscopy. HF EPR spectroscopy was a highly advantageous technique in distinguishing dierent kinds impurities in diamond, probing couplings between impurities, and determining mechanisms of spin relaxations. Chapter 1 gave an introduction of principles of CW and pulsed EPR spectroscopy. Spin Hamiltonian formalism was introduced to explain the observed EPR spectrum in CW EPR spectroscopy and the expressions of the electron Zeeman, zero-eld, nuclear Zeeman, nuclear quadrupole, and hyperne interaction were given. Then a method was overviewed to used to simulate and explain the measured EPR spectra with illustrative examples. For pulsed EPR spectroscopy, the phenomenological Bloch model was introduced to describeT 2 andT 1 relaxations in spin systems. And nally selected advantages of HF EPR spectroscopy were presented. The most important aspect of HF EPR spectroscopy in this dissertation was the high spectral resolution in order to address dierent paramagnetic spin species in diamonds having very g-values. Chapter 2 emphasized current scientic interests on MR study of diamonds with ex- 90 Chapter 7. Conclusion 91 amples of magnetic eld sensing, electric eld sensing, and temperature sensing as well as quantum information processing. Then optical, electrical, and magnetic properties of three paramagnetic defects found in diamonds, NV centers, P1 centers, and surface impurities, were overviewed. NV centers are particularly interesting in the applications of diamonds be- cause the detection of single NV centers is possible via optical methods and they exhibit long coherence times in room temperature. However, the local spin environment in diamond from other paramagnetic spins such as P1 centers and surface impurities have signicant in uence on the ecacy of the applications, thus a good understanding of paramagnetic defects and impurities existing in diamond is important for successful applications of diamonds. Chapter 3 described the details of the development of the HF EPR spectrometer con- sisting of HF, high-power transmitter, quasioptical system, superheterodyne phase-sensitive detection system, 12.1 T cryogenic-free superconducting magnet, and liquid helium cryostat. The spectrometer operates in wide frequency, magnetic eld, and temperature range with unique experimental capabilities including HF DEER for sensing dipole-dipole couplings and HF DD for extending spin coherence. The HF EPR spectrometer was the main and essen- tial instrumentation which made all of the of the presented experiments in this dissertation possible. Chapter 4 discussed the application of HF DEER and DD in study of spin decoherence in type-Ib diamonds. P1 centers were known as the main source of spin decoherence in type-Ib diamonds from previous studies, and by measuring small dipole-dipole coupling existing between homogeneously distributed P1 centers in diamond crystal, the accurate spin concentrations of P1 centers were successfully extracted. HF DEER provided an accurate method to determine the absolute spin concentrations in diamonds, which is important because T 2 in diamonds are known to be inversely proportional to the spin concentration of P1 centers. In addition, HF DD was rst demonstrated and almost an order of magnitude improvement of T 2 of P1 centers in diamond was shown. In Chap. 5, surface paramagnetic impurities (X) existing in NDs were studied by HF CW Chapter 7. Conclusion 92 EPR spectroscopy and HF DEER. Many studies pointed the existence of dense impurities near the diamond surface, but observed EPR signals were broad and had g-value close to 2 which hindered the investigation because there exists many other paramagnetic impurities such as P1 centers that give rise to the overlapping signal. Using HF CW EPR spectroscopy, X were clearly resolved which had only small eective dierence in the g-value compared with P1 centers which are the most abundant paramagnetic defects in type-Ib diamonds. Also a strong EPR intensity ratio between P1 centers and X was observed which was used to extract the spatial location of X only in the thin shell of ND crystals. And from the line shape analysis of X which depended on the magnetic eld, the spin concentration and g-strain of X were determined. Finally, HF DEER measurement on NDs showed no measurable coupling between P1 centers and X, supporting the localized distribution model of P1 centers and X in NDs. Chapter 6 investigated T 2 and T 1 relaxation mechanisms in NDs by multi-frequency pulsed EPR spectroscopy. T 2 did not depend on temperature, frequency, and size of ND crystals, which supported the local distribution model of P1 centers and X proposed in Chap. 5. T 1 in NDs were found to be very dierent from bulk and micron-size powders; in particular, faster T 1 relaxations were seen in smaller ND crystals. The strong size depen- dence, with the fact that the deviations ofT 1 in NDs from bulk and micron-size powder were not correlated with frequency, indicated that the possible mechanism of additional relaxation is likely due to fast dipole-dipole uctuations of X near ND crystal surface which creates magnetic noises at P1 centers located deep inside ND crystal. Appendix A Performance Specication of High-frequency, High-power Transmitter Figure A.1 shows the output power of the high-frequency, high-power transmitter transmitter as a function of frequency for 107{120 GHz and 215{240 GHz. The peak power of the transmitter is around 700 mW for 115 GHz and 100 mW at 230 GHz. 93 Appendix A. Performance Specication of High-frequency, High-power Transmitter 94 (a) (b) Figure A.1: Measured output power of the transmitter as a function of frequency. (a) For 107{120 GHz. (b) For 215{240 GHz. Performance specication is provided by Virginia Diodes, Inc. Appendix B Calibration of Calorimetric Power Meter Figure B.1 shows the calibration measurements of the pyroelectric detector used for var- ious power measurements of microwaves propagated in the quasioptical system. Incident microwave to the pyroelectric detector was modulated at 100 Hz with 90% duty cycle, and output voltage from the detector was measured by a lock-in amplier. 95 Appendix B. Calibration of Calorimetric Power Meter 96 Measured output power (mW) 1000 100 10 1 0.1 Pyroelectric detector reading (mV) 0.1 10 100 0.01 1 Meas. Fit Slope = 14 mW/mV Figure B.1: Calibration measurements of the pyroelectric detector (Eltec Instruments) to a commercial calorimetric power meter (Virginia Diodes, Inc.). Bibliography 1 B. Odom, D. Hanneke, B. D. Urso, and G. Gabrielse, \New Measurement of the Electron Magnetic Moment Using a One-Electron Quantum Cyclotron", Physical Review Letters 97, 030801:1{030801:4 (2006). 2 C. P. Slichter, Principles of Magnetic Resonance, 3rd (Springer Berlin Heidelberg, 1990). 3 C. P. Poole, Electron Spin Resonance: A Comprehensive Treatise on Experimental Tech- niques, 2nd (Dover Publications, 1996). 4 A. Schweiger and G. Jeschke, Principles of pulse electron paramagnetic resonance (Oxford University Press, 2001). 5 J. A. Weil and J. R. Bolton, Electron Paramagnetic Resonance: Elemental Theory and Practical Application, 2nd (John Wiley & Sons, 2007). 6 L. R. Becerra, G. J. Gerfen, R. J. Temkin, D. J. Singel, and R. G. Grin, \Dynamic nuclear polarization with a cyclotron resonance maser at 5 T", Physical Review Letters 71, 3561{3564 (1993). 7 L. R. Becerra, G. J. Gerfen, B. F. Bellew, J. A. Bryant, D. A. Hall, S. J. Inati, R. T. Weber, S. Un, T. F. Prisner, A. E. Mcdermott, K. W. Fishbein, K. E. Kreischer, R. J. Temkin, D. J. Singel, and R. G. Grin, \A Spectrometer for Dynamic Nuclear Polarization and Electron Paramagnetic Resonance at High Frequencies", Journal of Magnetic Resonance, Series A 117, 28{40 (1995). 97 Bibliography 98 8 M. M. Hertel, V. P. Denysenkov, M. Bennati, and T. F. Prisner, \Pulsed 180-GHz EPR/ ENDOR/PELDOR spectroscopy", Magnetic Resonance in Chemistry 173, S248{S255 (2005). 9 S. Takahashi, L.-C. Brunel, D. T. Edwards, J. van Tol, G. Ramian, S. Han, and M. S. Sherwin, \Pulsed electron paramagnetic resonance spectroscopy powered by a free-electron laser", Nature 489, 409{413 (2012). 10 E. L. Dane, T. Maly, G. T. Debelouchina, R. G. Grin, and T. M. Swager, \Synthesis of a BDPA-TEMPO Biradical", Organic Letters 11, 1871{1874 (2009). 11 E. L. Dane and T. M. Swager, \Synthesis of a Water-Soluble 1,3-bis(diphenylene)-2- phenylallyl (BDPA) Radical", The Journal of Organic Chemistry 75, 3533{3536 (2010). 12 F. Bloch, \Nuclear induction", Physical Review 70, 460{474 (1946). 13 C. Kutter, H. P. Moll, J. van Tol, H. Zuckermann, J. C. Maan, and P. Wyder, \Electron- Spin Echoes at 604 GHz Using Far Infrared Lasers", Physical Review Letters 74, 2925{ 2928 (1995). 14 M. R. Fuchs, T. F. Prisner, and K. M obius, \A high-eld/high-frequency heterodyne induction-mode electron paramagnetic resonance spectrometer operating at 360 GHz", Review of Scientic Instruments 70, 3681{3683 (1999). 15 M. Rohrer, O. Br ugmann, B. Kinzer, and T. F. Prisner, \High-eld/high-frequency EPR spectrometer operating in pulsed and continuous-wave mode at 180 GHz", Applied Mag- netic Resonance 21, 257{274 (2001). 16 Y. A. Grishin, M. R. Fuchs, A. Schnegg, A. A. Dubinskii, B. S. Dumesh, F. S. Rusin, V. L. Bratman, and K. M obius, \Pulsed Orotron-A new microwave source for submillime- ter pulse high-eld electron paramagnetic resonance spectroscopy", Review of Scientic Instruments 75, 2926{2936 (2004). 17 H. Blok, J. A. J. M. Disselhorst, H. van der Meer, S. B. Orlinskii, and J. Schmidt, \ENDOR spectroscopy at 275 GHz", Journal of Magnetic Resonance 173, 49{53 (2005). Bibliography 99 18 G. W. Morley, L.-C. Brunel, and J. van Tol, \A multifrequency high-eld pulsed elec- tron paramagnetic resonance/electron-nuclear double resonance spectrometer", Review of Scientic Instruments 79, 064703:1{064703:5 (2008). 19 F. H. Cho, V. Stepanov, and S. Takahashi, \A high-frequency electron paramagnetic resonance spectrometer for multi-dimensional, multi-frequency, and multi-phase pulsed measurements", Review of Scientic Instruments 85, 075110:1{075110:7 (2014). 20 K. M obius, \High-Field EPR and ENDOR on Bioorganic Systems", in EMR of Param- agnetic Molecules, Vol. 13, edited by L. J. Berliner and J. Reuben (Springer US, 1993), pp. 253{274. 21 T. F. Prisner, \Pulsed high-frequency/high-eld EPR", Advances in Magnetic and Optical Resonance 20, 245{299 (1997). 22 A. K. Hassan, L. A. Pardi, J. Krzystek, A. Sienkiewicz, P. Goy, M. Rohrer, and L.-C. Brunel, \Ultrawide Band Multifrequency High-Field EMR Technique: A Methodology for Increasing Spectroscopic Information", Journal of Magnetic Resonance 142, 300{312 (2000). 23 M. Fuhs and M obius, \Pulsed-High Field/High-Frequency EPR Spectroscopy", in High Magnetic Fields, Vol. 595, edited by C. Berthier, L. P. L evy, and G. Martinez, Lecture Notes in Physics (Springer Berlin Heidelberg, 2001), pp. 267{304. 24 O. Y. Grinberg and L. J. Berliner, eds., Very High Frequency (VHF) ESR/EPR, Vol. 22, Biological Magnetic Resonance (Springer US, 2004). 25 T. F. Prisner, \Pulsed High-Frequency EPR", in Very High Frequency (VHF) ESR/EPR, Vol. 22, edited by O. Y. Grinberg and L. J. Berliner, Biological Magnetic Resonance (Springer US, 2004), pp. 249{276. 26 A. Schnegg, A. A. Dubinskii, M. R. Fuchs, Y. A. Grishin, E. P. Kirilina, W. Lubitz, M. Plato, A. Savitsky, and K. M obius, \High-eld EPR, ENDOR and ELDOR on bacterial photosynthetic reaction centers", Applied Magnetic Resonance 31, 59{98 (2007). Bibliography 100 27 K. M obius and D. Goldfarb, \High-Field/High-Frequency Electron Paramagnetic Reso- nance Involving Single- and Multiple-Transition Schemes", in Biophysical Techniques in Photosynthesis, Vol. 26, edited by T. J. Aartsma and J. Matysik, Advances in Photosyn- thesis and Respiration (Springer Netherlands, 2008), pp. 267{304. 28 K. M obius and A. Savitsky, High-Field EPR Spectroscopy on Proteins and their Model Systems: Characterization of Transient Paramagnetic States (The Royal Society of Chem- istry, 2009). 29 A. Savitsky and K. M obius, \High-eld EPR", Photosynthesis Research 102, 311{333 (2009). 30 P. P. Borbat, A. J. Costa-Filho, K. A. Earle, J. K. Moscicki, and J. H. Freed, \Electron spin resonance in studies of membranes and proteins", Science 291, 266{269 (2001). 31 S. Takahashi, I. S. Tupitsyn, J. van Tol, C. C. Beedle, D. N. Hendrickson, and P. C. E. Stamp, \Decoherence in crystals of quantum molecular magnets", Nature 476, 76{79 (2011). 32 P. P. Borbat, R. H. Crepeau, and J. H. Freed, \Multifrequency Two-Dimensional Fourier Transform ESR: An X/Ku-Band and Spectrometer", Journal of Magnetic Resonance 127, 155{167 (1997). 33 T. F. Prisner, M. Rohrer, and K. M obius, \Pulsed 95 GHz high-eld EPR heterodyne spectrometer with high spectral and time resolution", Applied Magnetic Resonance 7, 167{183 (1994). 34 W. Hofbauer, K. A. Earle, C. R. Dunnam, J. K. Moscicki, and J. H. Freed, \High-power 95 GHz pulsed electron spin resonance spectrometer", Review of Scientic Instruments 75, 1194{1208 (2004). 35 G. M. Smith, P. A. S. Cruickshank, D. R. Bolton, and D. A. Robertson, \High-eld pulse EPR instrumentation", in Electron Paramagnetic Resonance, Vol. 21, edited by B. C. Bibliography 101 Gilbert, SPR-Electron Paramagnetic Resonance (The Royal Society of Chemistry, 2008), pp. 216{233. 36 S. Stoll and A. Schweiger, \EasySpin, a comprehensive software package for spectral sim- ulation and analysis in EPR", Journal of Magnetic Resonance 178, 42{55 (2006). 37 M. Fuhs and M obius, \EasySpin: Simulating cw ESR spectra", in ESR Spectroscopy in Membrane Biophysics, Vol. 27, edited by M. A. Hemminga and L. J. Berliner, Biological Magnetic Resonance (Springer US, 2007), pp. 299{321. 38 Private communication, http://www.engis.com. 39 Private communication, http://www.vanmoppes.ch. 40 http://www.sumitomoelectricusa.com. 41 K. Iakoubovskii, M. V. Baidakova, B. H. Wouters, A. Stesmans, G. J. Adriaenssens, A. Y. Vul', and P. J. Grobet, \Structure and defects of detonation synthesis nanodiamond", Diamond and Related Materials 9, 861{865 (2000). 42 M. Dubois, K. Gu erin, E. Petit, N. Batisse, A. Hamwi, N. Komatsu, J. Giraudet, P. Pirotte, and F. Masin, \Solid-State NMR Study of Nanodiamonds Produced by the Detonation Technique", The Journal of Physical Chemistry C 113, 10371{10378 (2009). 43 A. Gruber, A. Dr abenstedt, C. Tietz, L. Fleury, J. Wrachtrup, and C. von Borczyskowski, \Scanning Confocal Optical Microscopy and Magnetic Resonance on Single Defect Cen- ters", Science 276, 2012{2014 (1997). 44 J. Wrachtrup, S. Y. Kilin, and A. P. Nizovtsev, \Quantum Computation Using the 13 C Nuclear Spins Near the Single NV Defect Center in Diamond", Optics and Spectroscopy 91, 429{437 (2001). 45 T. A. Kennedy, J. S. Colton, J. E. Butler, R. C. Linares, and P. J. Doering, \Long coherence times at 300 K for nitrogen-vacancy center spins in diamond grown by chemical vapor deposition", Applied Physics Letters 83, 4190{4192 (2003). Bibliography 102 46 F. Jelezko, T. Gaebel, I. Popa, A. Gruber, and J.Wrachtrup, \Observation of Coherent Oscillations in a Single Electron Spin", Physical Review Letters 92, 076401:1{076401:4 (2004). 47 L. Childress, M. V. G. Dutt, J. M. Taylor, A. S. Zibrov, F. Jelezko, J. Wrachtrup, P. R. Hemmer, and M. D. Lukin, \Coherent Dynamics of Coupled Electron and Nuclear Spin Qubits in Diamond", Science 314, 281{285 (2006). 48 R. Hanson, F. M. Mendoza, R. J. Epstein, and D. D. Awschalom, \Polarization and Readout of Coupled Single Spins in Diamond", Physical Review Letters 97, 087601:1{ 087601:4 (2006). 49 F. Jelezko and J. Wrachtrup, \Single defect centres in diamond: A review", physica status solidi (a) 203, 3207{3225 (2006). 50 R. Hanson, V. V. Dobrovitski, A. E. Feiguin, O. Gywat, and D. D. Awschalom, \Coherent Dynamics of a Single Spin Interacting with an Adjustable Spin Bath", Science 320, 352{ 355 (2008). 51 S. Takahashi, R. Hanson, J. van Tol, M. S. Sherwin, and D. D. Awschalom, \Quenching Spin Decoherence in Diamond through Spin Bath Polarization", Physical Review Letters 101, 047601:1{047601:4 (2008). 52 V. Jacques, P. Neumann, J. Beck, M. Markham, D. Twitchen, J. Meijer, F. Kaiser, G. Balasubramanian, F. Jelezko, and J. Wrachtrup, \Dynamic Polarization of Single Nu- clear Spins by Optical Pumping of Nitrogen-Vacancy Color Centers in Diamond at Room Temperature", Physical Review Letters 102, 057403:1{057403:4 (2009). 53 P. Neumann, R. Kolesov, V. Jacques, J. Beck, J. Tisler, A. Batalov, L. Rogers, N. B. Man- son, G. Balasubramanian, F. Jelezko, and J. Wrachtrup, \Excited-state spectroscopy of single NV defects in diamond using optically detected magnetic resonance", New Journal of Physics 11, 013017:1{013017:10 (2009). Bibliography 103 54 P. Neumann, J. Beck, M. Steiner, F. Rempp, H. Fedder, P. R. Hemmer, J. Wrachtrup, and F. Jelezko, \Single-Shot Readout of a Single Nuclear Spin", Science 329, 542{544 (2010). 55 Z.-H. Wang and S. Takahashi, \Spin decoherence and electron spin bath noise of a nitrogen-vacancy center in diamond", Physical Review B 87, 115122:1{115122:6 (2013). 56 F. Jelezko, T. Gaebel, I. Popa, M. Domhan, A. Gruber, and J.Wrachtrup, \Observation of Coherent Oscillation of a Single Nuclear Spin and Realization of a Two-Qubit Conditional Quantum Gate", Physical Review Letters 93, 130501:1{130501:4 (2004). 57 T. Gaebel, M. Domhan, I. Popa, C. Wittmann, P. Neumann, F. Jelezko, J. R. Rabeau, N. Stavrias, A. D. Greentree, S. Prawer, J. Meijer, J. Twamley, P. R. Hemmer, and J. Wrachtrup, \Room-temperature coherent coupling of single spins in diamond", Nature Physics 2, 408{413 (2006). 58 J. Wrachtrup and F. Jelezko, \Processing quantum information in diamond", Journal of Physics: Condensed Matter 18, S807{S824 (2006). 59 M. V. G. Dutt, L. Childress, L. Jiang, E. Togan, J. Maze, F. Jelezko, A. S. Zibrov, P. R. Hemmer, and M. D. Lukin, \Quantum Register Based on Individual Electronic and Nuclear Spin Qubits in Diamond", Science 316, 1312{1316 (2007). 60 P. Neumann, N. Mizuochi, F. Rempp, P. Hemmer, H. Watanabe, S. Yamasaki, V. Jacques, T. Gaebel, F. Jelezko, and J. Wrachtrup, \Multipartite Entanglement Among Single Spins in Diamond", Science 320, 1326{1329 (2008). 61 B. Smeltzer, J. McIntyre, and L. Childress, \Robust control of individual nuclear spins in diamond", Physical Review A 80, 050302:1{050302:4 (2009). 62 G. de Lange, Z. H. Wang, D. Riste, V. V. Dobrovitski, and R. Hanson, \Universal Dy- namical Decoupling of a Single Solid-State Spin from a Spin Bath", Science 330, 60{63 (2010). Bibliography 104 63 F. Shi, X. Rong, N. Xu, Y. Wang, J. Wu, B. Chong, X. Peng, J. Kniepert, R.-S. Schoenfeld, W. Harneit, M. Feng, and J. Du, \Room-Temperature Implementation of the Deutsch- Jozsa Algorithm with a Single Electronic Spin in Diamond", Physical Review Letters 105, 040504:1{040504:4 (2010). 64 L. M. Pham, D. L. Sage, P. L. Stanwix, T. K. Yeung, D. Glenn, A. Trifonov, P. Cappellaro, P. R. Hemmer, M. D. Lukin, H. Park, A. Yacoby, and R. L. Walsworth, \Magnetic eld imaging with nitrogen-vacancy ensembles", New Journal of Physics 13, 1{13 (2011). 65 N. Bar-Gill, L. M. Pham, C. Belthangady, D. L. Sage, P. Cappellaro, J. R. Maze, M. D. Lukin, A. Yacoby, and R. Walsworth, \Suppression of spin-bath dynamics for improved coherence of multi-spin-qubit systems", Nature Communications 3, 1{6 (2012). 66 S. Arroyo-Camejo, A. Lazariev, S. W. Hell, and G. Balasubramanian, \Room temperature high-delity holonomic single-qubit gate on a solid-state spin", Nature Communications 5, 1{5 (2014). 67 G. Balasubramanian, I. Y. Chan, R. Kolesov, M. Al-Hmoud, J. Tisler, C. Shin, C. Kim, A. Wojcik, P. R. Hemmer, A. Krueger, T. Hanke, A. Leitenstorfer, R. Bratschitsch, F. Jelezko, and J. Wrachtrup, \Nanoscale imaging magnetometry with diamond spins under ambient conditions", Nature 455, 648{651 (2008). 68 C. L. Degen, \Scanning magnetic eld microscope with a diamond single-spin sensor", Applied Physics Letters 92, 243111:1{243111:3 (2008). 69 J. R. Maze, P. L. Stanwix, J. S. Hodges, S. Hong, J. M. Taylor, P. Cappellaro, L. Jiang, M. V. G. Dutt, E. Togan, A. S. Zibrov, A. Yacoby, R. L. Walsworth, and M. D. Lukin, \Nanoscale magnetic sensing with an individual electronic spin in diamond", Nature 455, 644{647 (2008). 70 J. M. Taylor, P. Cappellaro, L. Childress, L. Jiang, D. Budker, P. R. Hemmer, A. Yacoby, R. Walsworth, and M. D. Lukin, \High-sensitivity diamond magnetometer with nanoscale resolution", Nature Physics 4, 810{816 (2008). Bibliography 105 71 G. Balasubramanian, P. Neumann, B. Twitchen, M. Markham, R. Kolesov, N. Mizuochi, J. Isoya, J. Achard, J. Beck, J. Tissler, V. Jacques, P. R. Hemmer, F. Jelezko, and J. Wrachtrup, \Ultralong spin coherence time in isotopically engineered diamond", Nature Materials 8, 383{387 (2009). 72 L. T. Hall, C. D. Hill, J. H. Cole, and L. C. L. Hollenberg, \Ultrasensitive diamond mag- netometry using optimal dynamic decoupling", Physical Review B 82, 045208:1{045208:5 (2010). 73 M. S. Grinolds, P. Maletinsky, S. Hong, M. D. Lukin, R. L.Walsworth, and A. Yacoby, \Quantum control of proximal spins using nanoscale magnetic resonance imaging", Nature Physics 7, 687{692 (2011). 74 N. Zhao, J.-L. Hu, S.-W. Ho, J. T. K. Wan, and R. B. Liu, \Atomic-scale magnetometry of distant nuclear spin clusters via nitrogen-vacancy spin in diamond", Nature Nanotech- nology 6, 242{246 (2011). 75 P. Maletinsky, S. Hong, M. S. Grinolds, B. Hausmann, M. D. Lukin, R. L. Walsworth, M. Loncar, and A. Yacoby, \A robust scanning diamond sensor for nanoscale imaging with single nitrogen-vacancy centres", Nature Nanotechnology 7, 320{324 (2012). 76 L. Rondin, J.-P. Tetienne, P. Spinicelli, C. D. Savio, K. Karrai, G. Dantelle, A. Thiaville, S. Rohart, J.-F. Roch, and V. Jacques, \Nanoscale magnetic eld mapping with a single spin scanning probe magnetometer", Applied Physics Letters 100, 459{463 (2012). 77 M. S. Grinolds, S. Hong, P. Maletinsky, L. Luan, M. D. Lukin, R. L. Walsworth, and A. Yacoby, \Nanoscale magnetic imaging of a single electron spin under ambient conditions", Nature Physics 9, 215{219 (2013). 78 F. Dolde, H. Fedder, M. W. Doherty, T. Nobauer, F. Rempp, G. Balasubramanian, T. Wolf, F. Reinhard, L. C. L. Hollenberg, F. Jelezko, and J. Wrachtrup, \Electric-eld sensing using single diamond spins", Nature Physics 7, 459{463 (2011). Bibliography 106 79 V. M. Acosta, E. Bauch, M. P. Ledbetter, A. Waxman, L.-S. Bouchard, and D. Budker, \Temperature Dependence of the Nitrogen-Vacancy Magnetic Resonance in Diamond", Physical Review Letters 104, 070801:1{070801:4 (2010). 80 D. M. Toyli, D. J. Christle, A. Alkauskas, B. B. Buckley, C. G. V. de Walle, and D. D. Awschalom, \Measurement and Control of Single Nitrogen-Vacancy Center Spins above 600 K", Physical Review X 2, 031001:1{031001:7 (2012). 81 P. Neumann, I. Jakobi, F. Dolde, C. Burk, R. Reuter, G. Waldherr, J. Honert, T. Wolf, A. Brunner, J. H. Shim, D. Suter, H. Sumiya, J. Isoya, and J. Wrachtrup, \High-Precision Nanoscale Temperature Sensing Using Single Defects in Diamond", Nano Letters 13, 2738{2742 (2013). 82 D. M. Toyli, C. F. de las Casas, D. J. Christle, V. V. Dobrovitski, and D. D. Awschalom, \Fluorescence thermometry enhanced by the quantum coherence of single spins in dia- mond", Proceedings of the National Academy of Sciences 110, 8417{8421 (2013). 83 G. Balasubramanian, A. Lazariev, S. R. Arumugam, and D. Duan, \Nitrogen-Vacancy color center in diamond-emerging nanoscale applications in bioimaging and biosensing", Current Opinion in Chemical Biology 20, 69{77 (2014). 84 J. H. N. Loubser and J. A. van Wyk, \Electron spin resonance in the study of diamond", Reports on Progress in Physics 109, 1201{1248 (1978). 85 G. S. Woods, J. A. V. Wyk, and A. T. Collins, \The nitrogen content of type Ib synthetic diamond", Philosophical Magazine Part B 62, 589{595 (1990). 86 Y. Mita, \Change of absorption spectra in type-Ib diamond with heavy neutron irradia- tion", Physical Review B 53, 11360{11364 (1996). 87 W. V. Smith, P. P. Sorokin, I. L. Gelles, and G. J. Lasher, \Electron-Spin Resonance of Nitrogen Donors in Diamond", Physical Review 115, 1546{1552 (1959). 88 R. J. Cook, \Electron nuclear double resonance at 35000 Mc/s", Journal of Scientic Instruments 43, 548{553 (1966). Bibliography 107 89 R. J. Cook and D. H. Whien, \Electron Nuclear Double Resonance Study of a Nitro- gen Centre in Diamond", Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 295, 99{106 (1966). 90 A. Cox, M. E. Newton, and J. M. Baker, \ 13 C, 14 N and 15 N ENDOR measurements on the single substitutional nitrogen centre (P1) in diamond", Journal of Physics: Condensed Matter 6, 551{563 (1994). 91 H. J. Bower and M. C. R. Symons, \Electron Spin Resonance Spectra associated with Nitrogen in Diamonds", Nature 210, 1037{1038 (1966). 92 H. A. Jahn and E. Teller, \Stability of Polyatomic Molecules in Degenerate Electronic States. I. Orbital Degeneracy", Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences 161, 220{235 (1937). 93 I. M. Zaritskii, V. Y. Brutus, V. S. Vikhnin, A. S. Vishnevskii, A. A. Konchits, and V. M. Ustintsev, \SPIN-LATTICE RELAXATION OF NITROGEN JAHN-TELLER CENTER IN DIAMOND", Soviet Physics-Solid State 18, 1883{1885 (1976). 94 J. A. van Wyk, E. C. Reynhardt, G. L. High, and I. Ki awi, \The dependences of ESR line widths and spin-spin relaxation times of single nitrogen defects on the concentration of nitrogen defects in diamond", Journal of Physics D: Applied Physics 30, 1790{1793 (1997). 95 E. C. Reynhardt, G. L. High, and J. A. van Wyk, \Temperature dependence of spin- spin and spin-lattice relaxation times of paramagnetic nitrogen defects in diamond", The Journal of Chemical Physics 109, 8471{8477 (1998). 96 G. Davies and M. F. Hamer, \Optical Studies of the 1.945 eV Vibronic Band in Diamond", Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 348, 285{298 (1976). Bibliography 108 97 D. A. Redman, S. Brown, R. H. Sands, and S. C. Rand, \Spin Dynamics and Electronic States of N-V Centers in Diamond by EPR and Four-Wave-Mixing Spectroscopy", Phys- ical Review Letters 67, 3420{3423 (1991). 98 J. Harrison, M. J. Sellars, and N. B. Manson, \Optical spin polarisation of the N-V centre in diamond", Journal of Luminescence 107, 245{248 (2004). 99 A. Lenef, S. W. Brown, D. A. Redman, S. C. Rand, J. Shigley, and E. Fritsch, \Electronic structure of the N-V center in diamond: Experiments", Physical Review B 53, 13427{ 13440 (1996). 100 A. Lenef and S. C. Rand, \Electronic structure of the N-V center in diamond: Theory", Physical Review B 53, 13441{13455 (1996). 101 G. K. Walters and T. L. Estle, \Paramagnetic Resonance of Defects Introduced Near the Surface of Solids by Mechanical Damage", Journal of Applied Physics 32, 1854{1859 (1961). 102 E. P. Smirnov, O. K. Semchinova, A. M. Abyzov, and D. Umann, \The surface radicals of diamond", Carbon 35, 31{34 (1997). 103 A. I. Shames, A. M. Panich, W. Kempi nski, A. E. Alexenskii, M. V. Baidakova, A. Dideikin, V. Y. Osipov, V. I. Siklitski, E. Osawa, M. Ozawa, and A. Vul', \Defects and impurities in nanodiamonds: EPR, NMR and TEM study", Journal of Physics and Chem- istry of Solids 63, 1993{2001 (2002). 104 A. A. Soltamova, I. V. Ilyin, P. G. Baranov, A. Y. Vul', S. V. Kidalov, F. M. Shakhov, G. V. Mamin, S. B. Orlinskii, N. I. Silkin, and M. K. Salakhov, \Detection and identication of nitrogen defects in nanodiamond as studied by EPR", Physica B: Condensed Matter 404, 4518{4521 (2009). 105 X. Fang, J. Mao, E. M. Levin, and K. Schmidt-Rohr, \Nonaromatic Core-Shell Structure of Nanodiamond from Solid-State NMR Spectroscopy", Journal of the American Chemical Society 131, 1426{1435 (2009). Bibliography 109 106 H. J. Mamin and M. H. S. D. Rugar, \Detecting external electron spins using nitrogen- vacancy centers", Physical Review B 86, 195422:1{195422:8 (2012). 107 B. K. Ofori-Okai, S. Pezzagna, K. Chang, M. Loretz, R. Schirhagl, Y. Tao, B. A. Moores, K. Groot-Berning, J. Meijer, and C. L. Degen, \Spin properties of very shallow nitrogen vacancy defects in diamond", Physical Review B 86, 081406:1{081406:5 (2012). 108 T. Rosskopf, A. Dussaux, K. Ohashi, M. Loretz, R. Schirhagl, H. Watanabe, S. Shikata, K. M. Itoh, and C. L. Degen, \Investigation of Surface Magnetic Noise by Shallow Spins in Diamond", Physical Review Letters 112, 147602:1{147602:5 (2014). 109 J.-P. Tetienne, T. Hingant, L. Rondin, A. Cavaill es, L. Mayer, G. Dantelle, T. Gacoin, J. Wrachtrup, J.-F. Roch, and V. Jacques, \Spin relaxometry of single nitrogen-vacancy defects in diamond nanocrystals for magnetic noise sensing", Physical Review Letters 87, 147602:1{147602:5 (2013). 110 S. Kaufmann, D. A. Simpson, L. T. Hall, V. Perunicic, P. Senn, S. Steinert, L. P. McGuin- ness, B. C. Johnson, T. Ohshima, F. Caruso, J. Wrachtrup, R. E. Scholten, P. Mulvaney, and L. Hollenberg, \Detection of atomic spin labels in a lipid bilayer using a single-spin nanodiamond probe", Proceedings of the National Academy of Sciences 110, 10894{10898 (2013). 111 T. F. Prisner, S. Un, and R. G. Grin, \Pulsed ESR at 140 GHz", Israel Journal of Chemistry 32, 357{363 (1992). 112 G. M. Smith, J. C. G. Lesurf, R. H. Mitchell, and P. C. Riedi, \A high performance MM-wave electron spin resonance spectrometer", in Microwave Symposium Digest, 1995., IEEE MTT-S International, Vol. 3 (1995), pp. 1677{1680. 113 G. M. Smith, J. C. G. Lesurf, R. H. Mitchell, and P. C. Riedi, \Quasi-optical cw mm- wave electron spin resonance spectrometer", Review of Scientic Instruments 69, 3924{ 3937 (1998). Bibliography 110 114 K. M obius, A. Savitsky, A. Schnegg, M. Plato, and M. Fuchs, \High-eld EPR spec- troscopy applied to biological systems: characterization of molecular switches for electron and ion transfer", Physical Chemistry Chemical Physics 7, 19{42 (2005). 115 P. F. Goldsmith, Quasioptical Systems: Gaussian Beam Quasioptical Propogation and Applications (Wiley-IEEE Press, 1998). 116 H. Kogelnik and T. Li, \Laser Beams and Resonators", Applied Optics 5, 1550{1567 (1966). 117 W. B. Lynch, K. A. Earle, and J. H. Freed, \1-mm wave ESR spectrometer", Review of Scientic Instruments 59, 1345{1351 (1988). 118 K. A. Earle, J. H. Freed, and D. E. Budil, \Millimeter Wave Electron Spin Resonance Using Quasioptical Techniques", Advances in Magnetic and Optical Resonance 19, 253{ 323 (1996). 119 J. P. Barnes and J. H. Freed, \A \shunt" Fabry-Perot resonator for high-frequency electron spin resonance utilizing a variable coupling scheme", Review of Scientic Instruments 69, 3022{3027 (1998). 120 K. A. Earle and J. H. Freed, \Quasioptical Hardware for a Flexible FIR-EPR Spectrom- eter", Applied Magnetic Resonance 16, 247{272 (1999). 121 M. Rohrer, J. Krzystek, V. Williams, and L.-C. Brunel, \Fabry-P erot resonator for high- eld multi-frequency ESR at millimetre and submillimetre wavelengths", Measurement Science and Technology 10, 275{284 (1999). 122 J. H. Freed, \The Development of High-Field /High Frequency ESR", in Very High Fre- quency (VHF) ESR/EPR, Vol. 22, edited by O. Y. Grinberg and L. J. Berliner, Biological Magnetic Resonance (Springer US, 2004), pp. 19{43. 123 S. Vasilyev, J. J arvinen, E. Tjukano, A. Kharitonov, and S. Jaakkola, \Cryogenic 2 mm wave electron spin resonance spectrometer with application to atomic hydrogen gas below 100 mK", Review of Scientic Instruments 75, 94{98 (2004). Bibliography 111 124 J. van Tol, L.-C. Brunel, and R. J. Wylde, \A quasioptical transient electron spin reso- nance spectrometer operating at 120 and 240 GHz", Review of Scientic Instruments 76, 074101:1{074101:8 (2005). 125 P. A. S. Cruickshank, D. R. Bolton, D. A. Robertson, R. I. Hunter, R. J. Wylde, and G. M. Smith, \A kilowatt pulsed 94 GHz electron paramagnetic resonance spectrometer with high concentration sensitivity, high instantaneous bandwidth, and low dead time", Review of Scientic Instruments 80, 103102:1{103102:15 (2009). 126 E. L. Hahn, \Spin Echoes", Physical Review 80, 580{594 (1950). 127 A. D. Milov, K. M. Salikov, and M. D. Shirov, \Application of the double resonance method to electron spin echo in a study of the spatial distribution of paramagnetic centers in solids", Soviet Physics, Solid State 23, 565{569 (1981). 128 F. H. Cho, V. Stepanov, C. Abeywardana, and S. Takahashi, \230/115 GHz electron para- magnetic resonance/double electron-electron resonance spectroscopy", Accepted, 2015. 129 J. Bylander, S. Gustavsson, F. Yan, F. Yoshihara, K. Harrabi, G. Fitch, D. G. Cory, Y. Nakamura, J.-S. Tsai, and W. D. Oliver, \Noise spectroscopy through dynamical decou- pling with a superconducting ux qubit", Nature Physics 7, 565{570 (2011). 130 G. S. Uhrig, \Exact results on dynamical decoupling by pulses in quantum information processes", New Journal of Physics 10, 1{22 (2008). 131 H. Y. Carr and E. M. Purcell, \Eects of Diusion on Free Precession in Nuclear Magnetic Resonance Experiments", Physical Review 94, 630{638 (1954). 132 S. Meiboom and D. Gill, \Modied Spin-Echo Method for Measuring Nuclear Relaxation Times", Review of Scientic Instruments 29, 688{691 (1958). 133 D. E. Koppel, \Analysis of Macromolecular Polydispersity in Intensity Correlation Spec- troscopy: The Method of Cumulants", The Journal of Chemical Physics 56, 4814{4820 (1972). Bibliography 112 134 B. J. Frisken, \Revisiting the method of cumulants for the analysis of dynamic light- scattering data", Applied Optics 40, 4087{4091 (2001). 135 H. J. Steinho, N. Radzwill, W. Thevis, V. Lenz, D. Brandenburg, A. Antson, G. Dodson, and A. Wollmer, \Determination of Interspin Distances between Spin Labels Attached to Insulin: Comparison of Electron Paramagnetic Resonance Data with the X-ray Structure", Biophysical Journal 73, 3287{3298 (1997). 136 N. Mohan, C.-S. Chen, H.-H. Hsieh, Y.-C. Wu, and H.-C. Chang, \In Vivo Imaging and Toxicity Assessments of Fluorescent Nanodiamonds in Caenorhabditis elegans", Nano Letters 10, 3692{3699 (2010). 137 A. Jarmola, V. M. Acosta, K. Jensen, S. Chemerisov, and D. Budker, \Temperature- and Magnetic-Field-Dependent Longitudinal Spin Relaxation in Nitrogen-Vacancy Ensembles in Diamond", Physical Review Letters 108, 197601:1{197601:5 (1991).
Abstract (if available)
Abstract
Currently, the trend of magnetic resonance study is toward higher frequencies and magnetic fields, and the approach we take in our group utilizes the high-frequency (HF) electron paramagnetic resonance (EPR) spectrometer that has recently been developed. This dissertation aims to identify paramagnetic impurities in diamond and to uncover the relation between impurities and spin relaxation in diamond. The study is performed using a home-built HF EPR spectrometer which is highly advantageous to distinguish impurities in diamond, to probe couplings between spins, and to determine mechanisms of spin relaxations. The dissertation is structured as the following: In Chap. 1, an introduction of principles of CW and pulsed EPR spectroscopy including benefits of performing EPR spectroscopy at HF is given. In Chap. 2, optical, electrical, and magnetic properties as well as current scientific interests on magnetic resonance study of diamonds are presented. In Chap. 3, details of the development of HF EPR spectrometer with unique experimental capability such as double electron-electron resonance (DEER) and dynamical decoupling (DD) are explained. In Chap. 4, investigation of spin decohernece in diamonds is demonstrated where HF DEER is used to extract the spin concentration in diamonds. Also extension of spin coherence in diamonds by HF DD is shown. In Chap. 5, study of surface impurities in nanodiamonds (NDs) by HF CW EPR spectroscopy and HF DEER is shown which reveals that surface impurities exhibit very different properties from those found in deep inside ND crystals. Finally, in Chap. 6, study of spin decoherence in NDs by multi-frequency pulsed EPR spectroscopy is described which shows that the longitudinal relaxation times in NDs are significantly affected and reduced by magnetic noise coming from the surface impurities.
Linked assets
University of Southern California Dissertations and Theses
Conceptually similar
PDF
High-frequency and high-field magnetic resonance spectroscopy of diamond
PDF
High-frequency electron-electron double resonance techniques and applications
PDF
Development of high-frequency and high-field optically detected magnetic resonance
PDF
Development of nanoscale electron paramagnetic resonance using a single nitrogen-vacancy center in diamond
PDF
Functionalization of nanodiamond surface for magnetic sensing application
PDF
Development of an electron paramagnetic resonance system for a single nitrogen-vacancy center in diamond
PDF
Analysis of amyloid fibrils by site-directed spin labeling and electron paramagnetic resonance
PDF
Diamond surface chemistry for NV quantum sensing
PDF
Temperature-dependent photoionization and electron pairing in metal nanoclusters
PDF
Study of rotation and phase separation in ³He, ⁴He, and mixed ³He/⁴He droplets by X-ray diffraction
Asset Metadata
Creator
Cho, Franklin Hyunil
(author)
Core Title
Developmnt of high-frequency electron paramagnetic resonance (EPR) spectrometer and investigation of paramagnetic defects and impurities in diamonds by multi-frequency EPR spectroscopy
School
College of Letters, Arts and Sciences
Degree
Doctor of Philosophy
Degree Program
Physics
Publication Date
07/30/2015
Defense Date
06/18/2015
Publisher
University of Southern California
(original),
University of Southern California. Libraries
(digital)
Tag
Diamond,double electron-electron resonance,dynamical decoupling,electron paramagnetic resonance,electron spin resonance,high-field,high-frequency,nanodiamond,OAI-PMH Harvest,spin decoherence,spin relaxation,surface impurities
Format
application/pdf
(imt)
Language
English
Contributor
Electronically uploaded by the author
(provenance)
Advisor
Takahashi, Susumu (
committee chair
), Kresin, Vitaly V. (
committee member
), Qin, Peter (
committee member
), Thompson, Richard S. (
committee member
), Vilesov, Andrey F. (
committee member
)
Creator Email
franklhc@usc.edu,franklin.cho87@gmail.com
Permanent Link (DOI)
https://doi.org/10.25549/usctheses-c3-613675
Unique identifier
UC11303905
Identifier
etd-ChoFrankli-3743.pdf (filename),usctheses-c3-613675 (legacy record id)
Legacy Identifier
etd-ChoFrankli-3743-1.pdf
Dmrecord
613675
Document Type
Dissertation
Format
application/pdf (imt)
Rights
Cho, Franklin Hyunil
Type
texts
Source
University of Southern California
(contributing entity),
University of Southern California Dissertations and Theses
(collection)
Access Conditions
The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...
Repository Name
University of Southern California Digital Library
Repository Location
USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA
Tags
double electron-electron resonance
dynamical decoupling
electron paramagnetic resonance
electron spin resonance
high-field
high-frequency
nanodiamond
spin decoherence
spin relaxation
surface impurities