University of Southern California Dissertations and Theses

High-frequency electron-electron double resonance techniques and applications

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High-frequency electron-electron double resonance techniques and applications

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Content HIGH-FREQUENCY ELECTRON-ELECTRON DOUBLE RESONANCE TECHNIQUES AND APPLICATIONS by Zaili Peng A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (CHEMISTRY) May 2021 Copyright 2021 Zaili Peng This dissertation is dedicated to my parents Qianlu and Guilan for their unconditional love and support. ii Acknowledgements First, I deeply thank my supervisor Dr. Susumu Takahashi for his constructive advice, support and patience. I could not be able to complete this dissertation work without his guidance. I would also thank my defense committee members, Dr. Andrey Vilosov, Dr. Vitaly Kresin and my qualifying committee members Dr. Alex Benderskii and Dr. Travis Williams for their invaluable feedback and support. I thank supports from the Chemical Measurement and Imaging program in the Na- tional Science Foundation (NSF), (CHE-2004252 (with partial co-funding from the Quantum Information Science program in the Division of Physics) and CHE-1611134) and the NSF Condensed Matter Physics program (DMR-1508661). I would like to thank my former colleagues, Dr. Chathuranga Abeywardana, Dr. Rana Akiel and Dr. Victor Stepanov for their supervision from the beginning of my time in the group until their leave. And I thank the current lab members, Benjiamin Fortman, Laura Mugica, Michael Coumans and Ana Gurgenidze and wish them good luck with their graduate studies and future. Finally, I would like to thank my family and friends for their love and support. Espe- cially, I would like to express my wholehearted gratitude to my parents for their tremen- dous support - both emotionally and financially. I could not be able to celebrate this moment today without their unstinting love and support. Thank you! iii Table of Contents Dedication ii Acknowledgements iii List of Tables vii List of Figures viii Abbreviations xxii List of Physical Constants xxv List of Units xxvi List of Symbols xxvii Abstract xxix Chapter 1:Introduction 1 Chapter 2:Fundamental of Electron Paramagnetic Resonance 8 2.1 Static spin Hamiltonian . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.1.1 Electron Zeeman interaction . . . . . . . . . . . . . . . . . . . 9 2.1.2 Nuclear Zeeman interaction . . . . . . . . . . . . . . . . . . . 11 2.1.3 Hyperfine interaction . . . . . . . . . . . . . . . . . . . . . . . 13 2.1.4 Dipolar interaction . . . . . . . . . . . . . . . . . . . . . . . . 14 2.1.5 Quadruple interaction . . . . . . . . . . . . . . . . . . . . . . . 16 2.2 Continuous-wave (cw) EPR spectroscopy . . . . . . . . . . . . . . . . 17 2.2.1 Bloch model-magnetization and relaxation . . . . . . . . . . . . 17 2.2.2 cw EPR spectral analysis . . . . . . . . . . . . . . . . . . . . . 21 2.3 Pulsed EPR spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.3.1 Rabi oscillations . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.3.2 Free induction decay . . . . . . . . . . . . . . . . . . . . . . . 30 iv 2.3.3 Electron spin echo . . . . . . . . . . . . . . . . . . . . . . . . 33 2.3.4 Inversion recovery . . . . . . . . . . . . . . . . . . . . . . . . 38 2.3.5 Simulated echo decay . . . . . . . . . . . . . . . . . . . . . . . 38 2.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 Chapter 3:HF EPR Instrumentation 40 3.1 Instrumentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 3.1.1 HF EPR spectrometer . . . . . . . . . . . . . . . . . . . . . . . 41 3.1.2 HF MW bridge setup . . . . . . . . . . . . . . . . . . . . . . . 43 3.1.3 Installation of IQ mixer . . . . . . . . . . . . . . . . . . . . . . 43 3.2 Characterization of HF EPR microwave bridge . . . . . . . . . . . . . . 44 3.2.1 Dynamic range . . . . . . . . . . . . . . . . . . . . . . . . . . 44 3.2.2 Power stability . . . . . . . . . . . . . . . . . . . . . . . . . . 45 3.3 Implementation of shaped pulses . . . . . . . . . . . . . . . . . . . . . 47 3.3.1 Phase-modulated chirped pulses . . . . . . . . . . . . . . . . . 47 3.3.2 Amplitude-modulated pulses . . . . . . . . . . . . . . . . . . . 51 3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 Chapter 4:ELDOR-detected NMR Spectroscopy 55 4.1 Fundamentals of EDNMR and ENDOR . . . . . . . . . . . . . . . . . 56 4.1.1 EDNMR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 4.1.2 Comparison with ENDOR . . . . . . . . . . . . . . . . . . . . 63 4.2 Materials and methods . . . . . . . . . . . . . . . . . . . . . . . . . . 64 4.2.1 BDPA sample . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 4.2.2 HF EPR/EDNMR spectroscopy . . . . . . . . . . . . . . . . . 65 4.2.3 HF ENDOR spectroscopy . . . . . . . . . . . . . . . . . . . . 65 4.3 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 65 4.3.1 Pulse efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . 69 4.3.2 Excitation bandwidth in the detection scheme . . . . . . . . . . 71 4.3.3 Comparison between EDNMR and ENDOR spectra of BDPA . 72 4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 Chapter 5:Investigation of Near-Surface Defects of Nanodiamonds by High- Frequency EPR and DFT Calculation 75 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 5.2 Materials and methods . . . . . . . . . . . . . . . . . . . . . . . . . . 78 5.2.1 Diamond samples . . . . . . . . . . . . . . . . . . . . . . . . . 78 5.2.2 HF EPR/EDNMR spectroscopy . . . . . . . . . . . . . . . . . 78 5.2.3 X-band EPR spectroscopy . . . . . . . . . . . . . . . . . . . . 79 5.3 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 80 5.3.1 HF EPR spectroscopy: Detection and characterization of near- surface defects . . . . . . . . . . . . . . . . . . . . . . . . . . 80 v 5.3.2 HF EDNMR spectroscopy: Investigation of near-surface impu- rity structures . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 5.3.3 DFT calculation: Identification of near-surface impurities . . . . 89 5.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 Chapter 6:Reduction of Surface Spin-induced Electron Spin Relaxations in Nanodiamonds 95 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 6.2 Materials and methods . . . . . . . . . . . . . . . . . . . . . . . . . . 98 6.2.1 Nanodiamond . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 6.2.2 Air annealing . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 6.2.3 Dynamic light scattering . . . . . . . . . . . . . . . . . . . . . 99 6.2.4 HF EPR spectroscopy . . . . . . . . . . . . . . . . . . . . . . . 99 6.3 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 100 6.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 Chapter 7:Conclusion 112 Chapter A:Calibration 115 A.1 Power dependence of HF EPR intensity on P1 centers . . . . . . . . . . 115 A.2 Frequency dependence of 250-nm ND EPR . . . . . . . . . . . . . . . 115 A.3 Spin relaxation times (T 1 andT 2 ) of P1 and X spins in NDs . . . . . . . 117 A.4 EPR spectral analysis in NDs . . . . . . . . . . . . . . . . . . . . . . . 117 Chapter B: AFM Characterization of NDs 120 Chapter C:Calculation of EPR Parameters Using DFT 126 Chapter D:T 1 andT 2 Analysis 128 D.1 Determination of the spin relaxation times (T 1 andT 2 ) . . . . . . . . . 128 D.2 T 1 analysis: Determination of C, s , the s improvement factor and their errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 D.3 T 2 analysis: Determination of the meanT 2 , theT 2 improvement factor and their errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 Chapter E: DLS Data Analysis Using Constrained Regularization Method 133 Bibliography 136 G.1 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 vi List of Tables 1.1 Comparasion of three commonly used EPR-based hyperfine spectroscopes. 5 5.1 Calculated g tensors for vacancy-related defects, isolated N-impurities (P1 centers) and NV-centers in ’shell-only’ NDs (cf. Fig. 5.2) compared with the experimental value for the X spins. . . . . . . . . . . . . . . . 91 6.1 Summary ofT 1 analyses. For the s analysis, Eq. 6.1 andC = 2:96 10 10 (s 1 K 5 ) were used. T 1 and s are shown with three significant figures. The errors inT 1 represent the standard error of the mean. The errors in s were calculated as the 95% confidence interval. . . . . . . . 104 6.2 Summary ofT 2 analyses. T 2 andT 2 are represented by three significant figures. The errors inT 2 represent the standard error of the mean. The errors inT 2 were calculated as the 95% confidence interval. . . . . . . . 107 A.1 Spin relaxation times (T 1 andT 2 ) of P1 and X spins. . . . . . . . . . . . 117 C.1 DFT-calculated EPR-parameters compared with experiment for spin cen- ters in diamond bulk (216-atom supercell, 333 k-point sampling; other technical settings same as for the nanodiamonds): the negative vacancy (V ),NV , the (excited *)NV 0 and the P1 center (N 0 ). Be- sides the g tensor and the zero-field splitting (D and E values for S = 1) 14 N-related hyperfine splittings are given (for the N-related defects). . . 127 vii List of Figures 1.1 Demonstration of enhanced spectral resolution at high magnetic field. (a) EPR spectrum ofCu 2+ at X band. (b) EPR spectrum ofCu 2+ at 230 GHz. Spin parameters are: 61 g x;y = 2.064,g z = 2.277,A x;y = 70 MHz, A z = 490 MHz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 (a) Demonstration of enhanced spin polarization at high magnetic field and low temperature. The x axis is the temperature in Kelvin (K) and y axis is the spin polarization calculated by the the equation shown in the inset. The spin populationN i for each state is calculated based upon Boltzmann distribution (assume amplitude of B 1 is not sufficiently high to alterN). Simulation parameters are:S = 1/2,g iso = 2.0028, B = 8 T. (b) Demonstration of possibility to investigate high spin system. Simu- lation parameters: S = 1, D = 200 GHz, g = 2.0028. The arrow indicates the transition from state 1 to state 2 atB 0 = 2 T, and the transition energy is 144.4 GHz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Advanced EDNMR spectroscopes. (a) Enhanced detection sensitivity by using echo trains. The top shows the EDNMR pulse sequence used in the experiment, where detection scheme is CPMG instead of spin echo. The experiment was performed on 1 mM TEMPOL in isopropanol at 50K. The bottom two EDNMR spectra were taken with N = 1 (black) and N = 4 (red) respectively. The inset in bottom figure shows the SNR gain as a function of N. (Reprint figure with permission from Mentink et al. 114 Copyright 2021 by Elsevier.) (b) THYCOS measurement to iden- tify coordination mode ofMn 2+ in ATP, ADP and AMPPNP. The top shows the THYCOS pulse sequence. The bottom left present the THY- COS spectra of Mn 2+ in ATP, ADP and AMPPNP. The bottom right shows three coordination modes ofMn 2+ in ATP ((a)Mn 2+ coordinates to both Nitrogen and phosphate. (b)Mn 2+ coordinates to phosphate. (c) Mn 2+ coordinates to Nitrogen.). (Reprint figure with permission from Litvinov et al. 100 Copyright 2021 by Elsevier.) . . . . . . . . . . . . . . 6 viii 2.1 Plot of Eqn. 2.25 as a function oft. The x axis is thet ins, and y axis is intensity in arbitrary unit. In the simulation, e = 28 GHz/T,w 0 w = 0, B 1 = 0.01 Gauss, T 1 = 500s, T 2 = 1s, initiallyM x =M y = 0, M z = 1. The black solid line is the time-dependence ofM z , blue solid line is the time-dependence ofM y , red solid line is the time-dependence ofM x . The inset shows the zoom in ofM x andM y change in a shorter time range. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.2 Plot of Eqn. 2.26b as a function ofB 1 . The x axis is theB 1 in Gauss, and y axis is EPR intensity in arbitrary unit. In the simulation, e = 28 GHz/T, w 0 w = 0, B 1 = 0.01 Guass. The black solid line is the simulation whenT 1 = 500s,T 2 = 1s, blue solid line is the simulation whenT 1 = 50s,T 2 = 1s, red solid line is the simulation whenT 1 = 500s,T 2 = 100 ns. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.3 cw EPR demonstration. (a) the energy diagram of two level system sub- ject to the external magnetic fieldB 0 , and the resonance condition is met where MW frequency is the same as energy differenceE. (b) Illustra- tion of field modulation in conventional cw EPR experiment. The static magnetic field is modulated between the limits B i and B j . The corre- sponding detected signal is then modulated betweenI i andI j , which is approximately the first derivative of the absorption signal. . . . . . . . . 23 2.4 Plot of Eqn. 2.44 as a function of t p . The x axis is the t p in ns, and y axis is P . In the simulation, = 5 MHz. The black solid line is oscillation of P when = 0MHz, the red solid line is oscillation of P when = 2:5MHz and the blue solid line is oscillation ofP when = 12:5MHz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.5 Demonstration of Inversion recovery pulse technique. (a) Pulse sequence used in the inversion recovery measurement. (b) Recovered magnetiza- tion change as a function of time delayT . . . . . . . . . . . . . . . . . 39 2.6 Stimulated echo pulse sequence used to measureT 1 relaxation time. . . 39 3.1 Block diagram of HF EPR spectrometer at USC. . . . . . . . . . . . . . 41 3.2 Block diagram of HF EPR microwave bridge at USC. . . . . . . . . . . 42 3.3 Dynamic range characterization. (a) Charaterization of dynamic range at 115 GHz. The x axis is the attenuation given by variable attenuator before MC, which gives a range of 2.5 dB, and y axis is the attenuation after MC, which has dynamic range of> 40 dB. And the inset shows a zoom-in dynamic range. (b) Charaterization of attenuation range given by variable attenuator at 230 GHz. The x axis is the attenuation given by variable attenuator before MC, which gives a range of 2.5 dB, and y axis is the attenuation after MC, which has dynamic range of> 60 dB. And the inset shows a zoom-in dynamic range. . . . . . . . . . . . . . . 45 ix 3.4 Power stability characterization. (a) Jitter analysis at 115 GHz. The x axis is the attenuation in dB (after MC, the same as y axis in Fig. 3.3) and y axis is jitter in nanosecond (ns). (b) Serial data analysis at 115 GHz. The x axis is the attenuation in dB and y axis is the error in % (see the main text for details). The inset shows the transient single pulse captured by oscillope. The pulse length is 1 s and pulse amplitude around 70 mV . Where three arrows point to the three position taken for power stability characterization. And the same approach for 230 GHz. (c) Jitter analysis at at 230 GHz. (d) Serial data analysis at 230 GHz. . . 46 3.5 (a) Typical linear chirped pulse trace captured by oscilloscope at 230 GHz. The pulse length is 1s, and the frequency sweeping range is 5 MHz to 10 MHz. (b) FFT of Q component, which clearly shows the pronounced frequency component in the range of 5MHz to 10 MHz as indicated by the inset, where blue solid lines are FFT from experimental data and red solid line indicates the frequency range of 5 MHz to 10 MHz. 49 3.6 Summary of one application of chirped pulse in hole-burning experi- ments. (a) The hole buring experiment based on BDPA free radical samples at 115 GHz. The pulse sequence is - T - - - =2 - - echo, where first pulse can be realized by utilizing either conventional rectangular pulse or linear chirped pulse. T is time decay before ap- plying regular spin echo sequence to detect the inversion efficiency. The blue spectrum is the echo detected magnetic resonance (EDMR) without the initial pulse (Ref), and black spectrum is obtained with an initial pulse realized by a linear chirped pulse (CP). Linear chirped pulse is generated with 3 us length and 10 MHz bandwidth. (b) Inversion profile obtained by normalizing the signal (CP) with the reference (Ref), and simulated inversion profile based on spin dynamics agrees reasonably well with the experimental data. (c) Hole burning experiment based on BDPA free radical samples. The blue spectrum is the echo detected mag- netic resonance without the initial pulse (Ref), and black spectrum is the one obtained using a 3-s conventional rectangular hard pulse (HP). (d) Inversion profile obtained by normalizing the signal (HP) with the reference (Ref), and simulated inversion profile based on spin dynamics agrees reasonably well with the experimental data. . . . . . . . . . . . 50 x 3.7 Summary of generation of amplitude-modulated pulse at 230 GHz. (a) A amplitude-modulated pulse captured by oscilloscope without feedback correction. Pulse parameters: I and Q with amplitude range of 0.01-0.04 V , Gaussian width is 500 ns. (b) A amplitude-modulated pulse captured by oscilloscope based on feedback loop control. The modulating signal is a Gaussian shape with 1 s width. x axis is the time in s and y axis is the amplitude in the V . The black solid line is the I component, green solid line is the Q component of the pulse and blue solid line is the magnitude. (c) Diagram of feedback loop control. A custom Labview program is developed to store the pulse captured by oscilloscope and utilized as feedback, and evaluate the captured pulse with the expected pulse. New I and Q files will be generated if the current captured pulse did not meet the criteria. The criteria is defined as: error = P N i=1 jy 0 i y i j > threshold = 0.1, wherey 0 i andy i are the amplitude of expected pulse and observed pulse at each time point respectively. The whole processes will repeat until the criteria is met. . . . . . . . . . . . . . . . . . . . . 52 3.8 Simulation of amplitude modulation with arbitrary frequency offset. (a) A Gaussian pulse multiply by a cos modulating pulse. x axis is the time ins and y axis is the amplitude in V . In the simulation, Gaussian pulse has a width of 500 ns, an amplitude of 0.1 V and a modulating frequency of 5 MHz. (b) Fourier transform of pulse in (a). x axis is the frequency in MHz and y axis is the amplitude in mV . . . . . . . . . . . . . . . . . 53 4.1 (a) Energy levels for an electron spin 1/2 coupling to nuclear spin 1/2 system with the weak coupling wherejAj < j2 n j. There are four energy levels and six possible transitions associated with the system. (b) EDNMR pulse sequence. EDNMR technique consists of two pulse sequences: high turning angle (HTA) pump pulse with sweeping fre- quency 2 applied to inver populations on a EPR forbidden transition, which reduces the population difference on the corresponding EPR al- lowed transition and detected with fixed 1 . . . . . . . . . . . . . . . . 57 xi 4.2 (a) Simulated EDNMR intensity whenMW frequency is resonant with transition connectingj1i andj4i with HTA pulse strengthB 1 = 0.03 mT. The inset at top right shows the Population evolution curves ofj1i to j4i indicated by black solid line, red solid line, blue solid line and green solid line respectively. The inset at bottom right shows the Population evolution curves ofj1i toj4i from 0 to 200s. (b) Simulated EDNMR intensity whenMW frequency is resonant with transition connectingj1i andj4i with HTA pulse strengthB 1 = 0.01 mT. The inset shows the Pop- ulation evolution curves of four states. (c) Simulated EDNMR intensity whenMW frequency is resonant with transition connectingj1i andj4i with HTA pulse strengthB 1 = 0.1 mT. The inset at top right shows the Population evolution curves ofj1i toj4i indicated by black solid line, red solid line, blue solid line and green solid line respectively. The inset at bottom right shows the Population evolution curves ofj1i toj4i from 0 to 200s. Simulation parameters:g e = 2.0025,g n = -5.590,A = 27.5 MHz, B = 22.5 MHz, B 0 = 4.0 T,T 2 = 10s, T 1 = 1 ms, T = 300 K. The simulation is done with the assumption that all EPR allowed and forbidden transitions have same relaxation timeT 2 and noT 1 relaxation for EPR forbidden transition. There are no relaxations associate with NMR transitions. (d) Central blind spot linewidth with different HTA amplitude. x axis is the frequency offset in MHz. Experiment parame- ters are: t HTA = 800s, 2 = 250 ns, = 350 ns, = 1.2s, repetition time = 20 ms, T = 200 K, data were taken with 64 shots and 5 scans. . . 61 4.3 (a) Energy levels for an electron spin 1/2 coupling to nuclear spin 1/2 system with the weak coupling wherejAj < j2 n j. There are four energy levels and six possible transitions associated with the system. (b) Davies-ENDOR pulse sequence. ENDOR technique consists of two pulse sequences: an initial MW pulse (t p ) with fixed frequency 0 applied to invert electron spin population, and an RF pulse (t R ) with sweeping frequency is applied to recover spin population along EPR allowed transition before detected through spin echo pulse sequence. In the pulse sequence, all parameters are fixed except. . . . . . . . . . . 64 xii 4.4 (a) cw spectrum of BDPA in polystyrene with 0.01 wt. %. The inset shows the molecular structure of BDPA. Experimental data was taken with the following conditions: F = 115 GHz, modulation field = 0.002 mT, modulation frequency = 20 kHz, room temperature. Two vertical black dashed lines mark the peak-peak linewidth1 mT in the cw spec- trum. (b)T 2 measurement. In the main figure, transient signal of spin echo decay is indicated by green solid line while the fitting is indicated by red dashed line. The inset shows temperature dependence ofT 2 . (c) T 2 as a function of BDPA concentration in polystyrene. x axis is weight concentration in %, y axis is T 2 in ns. The data was taken at room temperature. (d) T 1 measurement. The inset shows the T 1 values as a function of temperature in K. The experimental data is fitted by a single exponential function. Experiment parameters are: =2 = 250 ns, = 350 ns, = 650 ns, repetition time = 20 ms. . . . . . . . . . . . . . . . 66 4.5 EDNMR spectrum of BDPA. The x axis is frequency offset in MHz and y axis is the EDNMR intensity (normalized spin echo intensity). The blue solid line represents experimental spectrum. Red dashed line denotes simulated EDNMR spectrum with contributions from protons on the BDPA molecules (cyan solid line) and matrix protons (light gray solid line). Experimental data was taken with the following conditions: t HTA = 500s, = 3.33 MHz,=2 = 250 ns, = 350 ns, = 650 ns, repetition time = 20 ms, T = 250 K, 128 shots and 3 scans. Simulation parameters of BDPA: g x = 2.00262, g y = 2.00260, g z = 2.00257; two sets of hyperfine couplings are used in MHz: A x1 = 1.0,A y1 = 1.0,A z1 = 1.26;A x2 = 7.7,A y2 = 5.3,A z2 = 2.0;T 2 = 1.87s,T 1 = 700s, T = 250 K. The matrix signal is simulated by a single Gaussian line (width = 500 kHz) and intensity is adjusted to match the observed intensity. . . 68 xiii 4.6 (a) EDNMR intensity versus temperature. The EDNMR spectra were taken at 200 K (top) and 250 K (bottom). Other experimental parame- ters: t HTA = 500s, = 3.33 MHz,=2 = 250 ns, = 350 ns, = 1.2 s, repetition time = 20 ms, 64 shots and 3 scans. (b) EDNMR inten- sity versust HTA . From bottom to top, EDNMR spectra were taken with t HTA = 10s,t HTA = 100s,t HTA = 500s andt HTA = 800s, respec- tively. Other experimental parameters: T = 200 K, = 3.33 MHz,=2 = 250 ns, = 350 ns, = 1.2s, repetition time = 20 ms, 64 shots and 3 scans. (c) EDNMR intensity versus HTA amplitude . The EDNMR spectrum were taken at = 3.33 MHz (top) and = 2.46 MHz (bottom). Other experimental parameters: T = 200 K,t HTA = 500s,=2 = 250 ns, = 350 ns, = 1.2s, repetition time = 20 ms, 64 shots and 3 scans. (d) Transient spin echo signal when SE detection scheme is employed. The full integration window is marked by two vertical red dashed lines, which is 1.3s. (e) Transient FID signal when FID detection scheme is employed. The full integration window is marked out by two vertical red dashed lines, which is 2.5s. (f) EDNMR spectral resolution ver- sus detection methods. Top spectrum was taken by recording full spin echo (1.3 s). Bottom spectrum was taken by recording full FID (2.5 s). Experimental parameters are: T = 200 K,t HTA = 500s, = 3.33 MHz, =2 = 3 s, repetition time = 20 ms, 64 shots and 3 scans. All simulated spectra with the contribution of matrix signals by adjusting intensity to match the observed intensity. . . . . . . . . . . . . . . . . . 70 xiv 4.7 (a) EDNMR spectrum of 0.01 wt. % BDPA sample. The x axis is fre- quency offset in MHz and y axis is the EDNMR intensity (normalized spin echo intensity). Experimental data was taken with the following conditions: T = 250 K,t HTA = 500s, = 3.33 MHz, =2 = 250 ns, = 350 ns, = 650 ns, repetition time = 20 ms, 128 shots and 3 scans. Simulation parameters: g x = 2.00262,g y = 2.00260,g z = 2.00257; two sets of hyperfine couplings are used in MHz: A x1 = 1.0,A y1 = 1.0,A z1 = 1.26; A x2 = 7.7, A y2 = 5.3, A z2 = 2.0; T 2 = 1.87s, T 1 = 700s, T = 250 K. (b) 1 H Davis ENDOR spectrum of 0.01 wt. % BDPA sample. x axis is the hyperfine coupling ( RF - H ) in MHz and y axis is the EN- DOR intensity with arbitrary unit. Experimental data was taken with the following conditions: T = 100 K,t R = 10s, power = 300 W,t p = 200 ns, =2 = 50 ns, = 100 ns, = 300 ns, repetition time = 20 ms, 100 shots and 80 scans. The simulation detail is described in the main text, and the signal from matrix protons is indicated by black dashed arrow. The inset shows Davis ENDOR pulse sequence which consists of three parts: initialt p preparation pulse creates population inversion, then RF pulset R applied on resonance with NMR transition to recover popula- tion, the effectiveness of population recovery is detected by spin echo at the end. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 5.1 230 GHz cw EPR spectra of the diamond samples. (a) (Left) (100) single crystal diamond. The external magnetic field (B 0 ) was applied along the h100i axis of the diamond. (Right) Diamond powder with 10-m mean diameter. The signal is the so-called powder spectrum of P1 center. (b) EPR spectra of all sizes of NDs. (Left) The experimental and simulated spectra on NDs. (Right) The experimental and simulated EPR spectra on 550-nm, 100-nm and 50-nm NDs. The partial contributions from P1 and X spins are indicated by the red dashed lines. All measurements were performed at room temperature. The EPR spectrum analysis was done by Easyspin. 169 (Reprint figure with permission from Peng et al. 134 Copyright 2020 by the AIP Publishing LLC.) . . . . . . . . . . . . . . 81 xv 5.2 Size dependence of EPR linewidth and intensity of P1 centers and X spins. (a) Linewidth of P1 centers as a function of the diamond size. Lorentzian linewidth (red diamond) was obtained from the fit. (b) Linewidth of X spins as a function of the diamond size. The V oigt function was used in the fit and the peak-to-peak Lorentzian (red diamond) and Gaus- sian (blue square) linewidths were obtained. (c) Intensity ratio of P1 centers and X spins as a function of the diamond size. The relative in- tensity ratio of P1 centers and X spins from 230 GHz EPR is shown by the black solid squares. The green and purple solid circles represents the intensity ratio data obtained from X-band and 115 GHz spectra, respec- tively. The blue solid curve shows the fit result using a simple surface model (P1=X intensity diameter) while the red solid curve shows the fit result using the core-shell model. Overall, the core-shell model gives a better fit. (Reprint figure with permission from Peng et al. 134 Copy- right 2020 by the AIP Publishing LLC.) . . . . . . . . . . . . . . . . . 83 5.3 EPR spectra on 50-nm ND taken by the X-band and 230 GHz EPR spec- trometers. (a) EPR spectrum taken at 9 GHz (X-band EPR). The peak- to-peak linewidth is 0.24 mT. (b) EPR spectrum taken at 230 GHz. The peak-to-peak linewidth is 1.00 mT. The x-ranges of both data are 0.01 Tesla. (Reprint figure with permission from Peng et al. 134 Copyright 2020 by the AIP Publishing LLC.) . . . . . . . . . . . . . . . . . . . . 84 xvi 5.4 Proton EDNMR experiment using X spin. (a) Overview of EDNMR experiment. EDNMR pulse sequence consists of pulses with two mi- crowave frequencies. A high turning angle (HTA) pump pulse at the frequency of 2 induces the population inversion of the cross transition. A change of the population is detected via the spin echo sequence at the frequency of 1 . (b) Echo detected EPR on 50-nm NDs taken at room temperature. The black arrow points the echo signal from X spins. The pulse parameters are=2 = 150 ns, = 200 ns, = 320 ns and repetition time = 10 ms. (c) EDNMR experimental data of X spins (blue solid line) and the simulated EDNMR spectrum of H1 defects (red dashed line). The x axis is frequency offset ( 2 1 and the y axis is EDNMR intensity normalized by the echo intensity without the HTA pulse. Experimental parameters are=2 = 150 ns, = 200 ns, = 320 ns, HTA pulse amplitudew 1 = 3:33 MHz, HTA = 100s and repeti- tion time = 10 ms. The simulation parameters areA x;y =5:5 MHz, A z = 27:5 MHz, w 1 = 3:33 MHz, T 2 = 153 ns and HTA = 100 s. (d) The simulated EDNMR peak intensity as a function of the hyperfine coupling constants. The ranges ofA z andA x;y are10 to 30 MHz and 10 to 10 MHz, respectively. The hyperfine couplings of H1 and H2 defects are indicated by black dots. The inset shows a zoom-in image of (d) where the range ofA z andA x;y are from - 1 to 1 MHz. The two white dashed lines indicates the hyperfine couplings corresponding to the observed noise level (0:2 %) in the experiment. (Reprint figure with permission from Peng et al. 134 Copyright 2020 by the AIP Publishing LLC.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 5.5 14 N EDNMR. (a) EDNMR experimental data. The noise level was es- timated to be 0.8 %. Experimental parameters are =2 = 150 ns, = 200 ns, = 320 ns,w 1 = 3:33 MHz, HTA = 100s and repetition time = 10 ms. (b) Simulated EDNMR intensity as a function of the hy- perfine couplings. The hyperfine constants of P2 and N3 were indicted in the figure. The inset shows the simulated EDNMR for hyperfine cou- pling below 0.05 MHz. EDNMR signal corresponding to the intensity of < 0.8 % (the noise level) is indicated by the white dashed line. (Reprint figure with permission from Peng et al. 134 Copyright 2020 by the AIP Publishing LLC.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 5.6 Isosurfaces of the calculated spin densities. The EPR properties arises from the magnetization densitym(r) =n " (r)n # (r). (a) The negative vacancy V in a minimum-size ND. (b) Substitutional N C (the usual P1). (c) Substitutional N C in the more stable N + C +e configuration where the unpaired electron is transferred to the surface. (Reprint figure with per- mission from Peng et al. 134 Copyright 2020 by the AIP Publishing LLC.) 90 xvii 6.1 Overview of the air annealing experiment. (a) The normalized weight as a function of the annealing duration with annealing at 550 C. The red solid line shows a linear fit to obtain the rate of weight reduction. The weight reduction rate was 0:12 hour 1 . Each sample was weighed five times. The error bar represents the standard deviation of the measure- ments. (b) DLS results for the size characterization of the ND samples before and after the annealing for 5, 7 and 9 hours. The diameter at the maximum in the distribution (d peak ) is indicated. The obtained polydis- persity index (PDI) were 0.11, 0.07, 0.06 and 0.08 for the no-annealing sample and the annealing for 5, 7 and 9 hours samples, respectively. (c) d peak as a function of the annealing duration. The red solid line rep- resents the result of a linear fit. The error bar represent the standard deviation (calculated byd peak p PDI). (Reprint figure with permission from Peng et al. 135 Copyright 2020 by the AIP Publishing LLC.) . . . . 101 6.2 cw EPR analysis of 50-nm NDs before and after the air annealing. (a) Signal intensity as a function of magnetic fields in Tesla with no an- nealing, annealing for 5 hours and 7 hours. The solid green lines rep- resent the experimental data. The inset on the top right shows contri- butions of P1 and surface spins (S) on the EPR spectrum, which were extracted from the EPR spectral analysis. Drawings representing NDs under the annealing process are also shown in the inset. The red arrows in the drawing represent the P1 centers, and the blue arrows represent surface spins. (b) The EPR intensity ratio I s =I P 1 as a function of the diameter (d peak ). The blue solid circles with error bars representI s =I P 1 obtained from EPR spectral analysis. The details of the EPR spectral analysis is described in Sect. A.4 in Appendix A. The gray dashed line is the simulated (I s =I P 1 ) coreshell . The green dashed line is the simu- lated (I s =I P 1 ) surface . (Reprint figure with permission from Peng et al. 135 Copyright 2020 by the AIP Publishing LLC.) . . . . . . . . . . . . . . 102 xviii 6.3 Temperature dependence ofT 1 andT 2 of P1 centers in NDs. (a) TheT 1 measurement using the inversion recovery measurement. The measure- ment was performed at 200 K. The pulse sequence isP TP =2 P echo whereP =2 andP are=2- and-pulses, respectively, is a fixed evolution time and an evolution timeT is varied in the mea- surement. In the measurement, the pulse lengths of P =2 and P were 300 ns and 500 ns, = 1:2s and the repetition time was = 10 ms. The inset shows the spin echo measurement at 200 K to obtainT 2 . The pulse sequence isP =2 P echo where is varied in the measure- ment. The pulse parameters for theT 2 measurement wereP =2 = 300 ns,P = 500 ns and the repetition time = 10 ms. The errors associated withT 1 andT 2 were obtained by computing the standard error. (b) Tem- perature dependence of 1=T 1 on various sizes of NDs. The solid circles are experimental data and the solid lines are fits using Eq. (6.1). (c)T 2 on various sizes of NDs. The error bars are smaller than the dots repre- senting theT 2 value. (Reprint figure with permission from Peng et al. 135 Copyright 2020 by the AIP Publishing LLC.) . . . . . . . . . . . . . . 105 6.4 Temperature dependence ofT 1 andT 2 of P1 centers in the annealed ND samples (initial diameter = 50 nm). (a)T 1 of the annealed ND samples as a function of temperature. Experimental data points are indicated by blue circles and red triangles for air annealing at 550 C for 5 hours and 7 hours, respectively. The blue and red solid lines are corresponding fits utilizing Eq. (6.1). T 1 data with no annealing (gray solid line) and the data of a bulk diamond (green solid line) are shown. The arrow represents the reduction of s . (b) s as a function of the ND diameter. The red solid line shows the fit result to the s =d 4 model for NDs without annealing. The green solid line shows the s =d 4 line simulated for the annealed NDs. The orange arrow represents the reduction of s . The error bar in the s is included and obtained by computing the 95 % confidence interval. (c) T 2 as a function of temperature for the non- annealed and annealed samples. (Reprint figure with permission from Peng et al. 135 Copyright 2020 by the AIP Publishing LLC.) . . . . . . . 109 A.1 Peak-to-peak EPR intensity of P1 centers as a function of the microwave power. The blue circles represent experiment data points. The red dashed line is the linear fit. The microwave power used in the cw EPR experiments (Fig. 1 in the main text) is indicated by the black arrow. . . 116 A.2 Peak-to-peak EPR intensity of P1 centers as a function of the microwave power. The blue circles represent experiment data points. The red dashed line is the linear fit. The microwave power used in the cw EPR experiments (Fig. 1 in the main text) is indicated by the black arrow. . . 116 A.3 EPR spectral analysis of 50-nm NDs (non-annealed). . . . . . . . . . . 119 xix B.1 Characterization of 50-nm NDs. (a) AFM image. ND particles used in the analysis were marked by the yellow dashed circle. (b) Relative height of ND1 as a function of x-position. (c) The size distribution pro- file. The bar graph represents the data taken by the AFM measurement. The blue dashed line represents the data provided from Engis corp. . . 121 B.2 Characterization of 30-nm NDs. (a) AFM image. ND particles used in the analysis were marked by the yellow dashed circle. (b) The size distribution profile. The bar graph represents the data taken by the AFM measurement. The blue dashed line represents the data provided from Van Moppes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 B.3 Characterization of 60-nm NDs. (a) AFM image. ND particles used in the analysis were marked by the yellow dashed circle. (b) The size distribution profile. The bar graph represents the data taken by the AFM measurement. The blue dashed line represents the data provided from Van Moppes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 B.4 Characterization of 100-nm NDs. (a) AFM image. ND particles used in the analysis were marked by the yellow dashed circle. (b) The size distribution profile. The bar graph represents the data taken by the AFM measurement. The blue dashed line represents the data provided from Engis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 B.5 Characterization of 160-nm NDs. (a) AFM image. ND particles used in the analysis were marked by the yellow dashed circle. (b) The size distribution profile. The bar graph represents the data taken by the AFM measurement. The blue dashed line represents the data provided from Van Moppes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 B.6 Characterization of 250-nm NDs. (a) AFM image. ND particles used in the analysis were marked by the yellow dashed circle. (b) The size distribution profile. The bar graph represents the data taken by the AFM measurement. The blue dashed line represents the data provided from Engis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 B.7 Characterization of 550-nm NDs. (a) AFM image. ND particles used in the analysis were marked by the yellow dashed circle. (b) The size distribution profile. The bar graph represents the data taken by the AFM measurement. The blue dashed line represents the data provided from Van Moppes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 B.8 Characterization of 10-m NDs. (a) Optical image. Diamond particles used in the analysis were marked by the blue dashed circle. (b) The size distribution profile. The bar graph represents the data taken by the AFM measurement. The blue dashed curve (not normalized) is the size distribution profile provided by Engis (Beckman Coulter, Multisizer 3 3.51). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 xx D.1 T 1 andT 2 measurement of the 5-hour annealed NDs at 200 K. (a) The result of the inversion recovery measurement. (b) The result of the spin echo measurement. The blue points are experimental data while the red solid lines are fittings based upon a monoexponential function. . . . . . 129 D.2 T 1 andT 2 measurement of the 7-hour annealed NDs at 200 K. (a) The result of the inversion recovery measurement. (b) The result of the spin echo measurement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 E.1 DLS analysis result using constraint regularization method. (a) Second- order correlation data. The black solid is experimental data while the red dashed line is fitting based on Eqn. E.8. Experimental details: the sam- ple is nanodimaond particles suspended in pure methanol, DLS mea- surement was performed with a 632 nm incident laser and 163:5 of detection angle. In the analysis, a of 0.001 was used. (b) Analysed results obtained based on Eqn. E.8. x axis is the diameter in nm, y axis is the intensity %, which is x in Eqn. E.8. Three peaks are obtained cen- tering at 33.6 nm, 147.6 nm and 3382.8 nm for peak1 (pk1), peak2 (pk2) and peak3 (pk3) respectively. . . . . . . . . . . . . . . . . . . . . . . 135 xxi Abbreviations AC Alternating Current AF Amplitude Modulation AFM Atomic Force Microscopy AOM Acoustic Optic Modulator APD Avalanche Photodiode AWG Arbitrary Waveform Generator BDPA ; -BisDiphenylene--PhenylAllyl CPMG Carr-Purcell-Meiboom-Gill CVD Chemical Vapor Deposition CW Continuous Wave DC Direct Current DD Dynamic Decoupling DEER Double Electron Electron Resonance DFT Density Functional Theory DLS Dynamic Light Scattering DQ Double Quantum EDMR Echo Detected Magnetic Resonance EDNMR Electron Electron Double Resonance detected-NMR ELDOR Electron Electron Double Resonance ENDOR Electron Nuclear Double Resonance EPR Electron Paramgentic Resonance xxii ESEEM Electron Spin Echo Envelop Modulation ESR Electron Spin Resonance FID Free Induction Decay FFT Fast Fourier transform FL Fluorescence FM Frequency Modulation FWHM Full Width at Half Maximum HF High Frequency, High Field HPC High Performance Computing HPTH High Pressure High Temperature IF Intermediate Frequency LF Low Field LHe Liquid Helium LNA Low Noise Amplifier LO Local Oscillator LP long Pass MC Multiplication Chain MD Molecular Dynamics MR Magnetic Resonance MRI Magnetic Resonance Imaging MW Microwave ND NanoDiamond NMR Nuclear Magnetic Resonance NV Nitrogen Vacancy ODMR Optically Detected Magnetic Resonance OU Ornstein-Uhlenbeck PAF Principle Axis Frame PL Photoluminescent PM Phase Modulation xxiii PP Peak To Peak PSD Particle Size Distribution RF Radio Frequency RO Readout SE Spin Echo SNR Signal to Noise Ratio SOMS Semi-occupied Atomic Or Molecular Orbital TLS Two-Level System TTL Transistor Transistor Logic ZFS Zero Field Splitting ZQ Zero Quantum xxiv List of Physical Constants h 6.6260695710 34 kgm 2 s 1 or J s Plank constant k B 1.380648810 23 kgm 2 s 2 K 1 or JK 1 Boltzmann constant 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 xxv List of Units A Ampere dB Decibel g gram GHz Gigahertz (=110 9 Hz) Hz Hertz (=1 cycle.s 1 ) J Joule (=1 m 2 kg) K Kelvin kHz Kilohertz (=110 3 Hz) ppm Parts per million (=110 6 %) m Meter mg Milligram (=110 3 g) MHz Megahertz (=110 6 Hz) ms Millisecond (=110 3 s) mT Millitesla (=110 3 T) mW Milliwatt (=110 3 W) ns Nanosecond (=110 9 s) s Second T Tesla m Micrometer (=110 6 m) s Microsecond (=110 6 s) xxvi List of Symbols A hyperfine interaction tensor (Eqn. 2.14) A k parallel component of an axial symmetric hyperfine tensor A ? perpendicular component of an axial symmetric hyperfine tensor B 0 externally applied static magnetic field B 1 oscillating magnetic field produced by the microwave excitation C constant used for fitting temperature dependence ofT 1 (Eqn. 6.1) D zero filed splitting tensor (Eqn. 2.8), or identity operator (Eqn. E.7) g electron g-tensor (Eqn. 2.3) resonance offset (Eqn. 2.41) w bandwidth of the chirp pulse (Eqn. 3.1) g electron g-value full width at half maximum (Eqn. 2.34), or decay constant ing 1 () s 1=T 1 contribution from surface spins (Eqn. 6.1) g 1 () first-order correlation function in dynamic light scattering measurement (Eqn. E.3) g 2 () second-order correlation function in dynamic light scattering measurement (Eqn. E.1) ^ H 0 general static Hamiltonian (Eqn 2.1) ^ H zm electron Zeeman term in spin Hamiltonian (Eqn 2.2) ^ H nzm nuclear Zeeman term in spin Hamiltonian (Eqn 2.7) ^ H zfs zero-field splitting term in spin Hamiltonian (Eqn 2.8) ^ H hf hyperfine interaction term in spin Hamiltonian (Eqn 2.14) ^ H dd dipolar interaction term in spin Hamiltonian (Eqn 2.15) xxvii ^ H qd electric quadruple interaction term in spin Hamiltonian (Eqn 2.18) ^ H MW microwave excitation perturbation term in spin Hamiltonian (Eqn 2.37) HTA high turning angle pump pulse in EDNMR pulse sequence angle between the direction ofA k and B 0 I nuclear spin value ^ I nuclear spin angular momentum vector operator (components ^ I x , ^ I y , ^ I z ) k chirp sweep rate (Eqn. 3.1) M spin magnetization vector (componentsM x ,M y ,M z ) M I nuclear magnetic spin quantum number M S electron magnetic spin quantum number Rabi frequency (Eqn. 2.41) ^ ^ R dissipation superoperator representing spin relaxations (Eqn. 4.10) Q nuclear quadrupole interaction value (Eqn 2.18) ^ density operator (Eqn. 4.10) S electron spin value ^ S electron spin angular momentum vector operator (components ^ S x , ^ S y , ^ S z ) t time T temperature, microwave excitation pulse spacing between the first- and/2-pulse in the inversion recovery pulse sequence, or pulse separation in double electron electron resonance or EDNMR or ENDOR T 1 spin lattice relaxation time (or longitudinal relaxation time) T 2 spin spin relaxation time (or transverse relaxation time) t p general pulse length magnetic moment operator w microwave frequency microwave excitation pulse spacing between/2- and-pulse in the spin echo sequence xxviii Abstract Electron paramagnetic resonance (EPR) is a powerful spectroscopic technique widely used to electronic and magnetic properties of various spin systems. However, practically conventional EPR can easily reach its limitations for large spin systems. For instance, EPR spectrum of disordered sample at low field (LF) is often too broad to be resolved, and detail information of the spin magnetic parameters and molecular structures can be easily hidden in the broadened EPR spectrum. With the advances in instrumentation, such as the realization of high magnetic field (HF) and high frequency microwave (MW) radiation, EPR spectroscopy gains more powerful capabilities. Compared with LF, HF EPR attains the following appealing advantages: 1) Enhanced spectral resolution; 2) Enhanced spin polarization; 3) Possibility to investigate high spin systems; 4) Possibility to investigate field-dependent phenomena. Additionally, multi-frequency pulse EPR techniques complement the EPR spec- troscopy and provides much more potentialities. Among them, electron electron double resonance (ELDOR) technique has been widely used to determine distance between a pair of electron spins, measure polarization transfer to another region of the spectrum, measure weak couplings between electron spins, etc. Moreover, hyperfine coupling between electron spins with nearby nuclear spins is often too weak to be resolved in xxix a continuous-wave (cw) EPR spectrum. To obtain the details of weak hyperfine cou- pling, hyperfine spectroscopes (most of them are type of ELDOR technique) are often employed. This dissertation is dedicated for investigation of HF ELDOR techniques and appli- cations. The investigation is conducted on a home-built HF EPR spectrometer. And the dissertation is organized as the following: in Chap. 1, current progress on HF EPR and ELDOR techniques and their applications are over viewed, and the motivation for this dissertation is discussed. Fundamentals of EPR spectroscopy are explained in Chap. 2, including static magnetic interactions as well as cw and pulsed EPR spectroscopes. In Chap. 3, characterization of a 115 GHz/230 GHz EPR spectrometer and implemen- tation details of shaped pulse capabilities in the HF EPR spectrometer are discussed. In Chap. 4, a thorough investigation of HF EDNMR spectroscopy based on BDPA free radicals is discussed, including EDNMR fundamentals, experimental strategies and data analysis. Chapter 5 discusses the study of defect and impurity contents in various sizes of diamond crystals using HF (230 GHz and 115 GHz) and 9 GHz cw and pulsed EPR spectroscopy, and DFT calculation. Finally, Chapter 6 describes the investigation of the relation between surface spins andT 1 andT 2 of single-substitutional nitrogen impurity (P1) centers in NDs using HF EPR spectroscopy. xxx Chapter 1: Introduction Electron paramagnetic resonance (EPR) is a powerful spectroscopic technique widely used to investigate the structural and dynamic information of various types of materials, including biological molecules, 20, 21, 86, 131, 133 polymers 15, 74, 78, 85, 175 and nano- materials. 24, 155, 157, 192 For instance, the structure of biological molecules is often ob- tained by probing dipolar couplings between a pair of spin labels. 86 And dynamic infor- mation down to a nanosecond regime is amenable to EPR. 153, 194 However, practically conventional EPR can easily reach its limitations for large spin systems. For instance, EPR spectrum of disordered sample at low field (LF) (MW fre- quencies up to 35 GHz, and magnetic fields up to 2 T) is often too broad to be resolved, and detail information of the spin magnetic parameters and molecular structures can be easily hidden in the broadened EPR spectrum. 194 With the advances in instrumentation, such as the realization of high magnetic field (HF) and high frequency MW radiation, EPR spectroscopy gains more powerful capabilities. Compared with LF, HF EPR attains the following appealing advantages: 1) Enhanced spectral resolution. 2) Enhanced spin polarization. 3) Possibility to investigate high spin systems. 4) Possibility to investigate field-dependent phenomena. 1 (a) (b) gz gx,y Magnetic field (mT) X band 230 GHz 200 250 300 350 400 EPR intensity (arb.units) EPR intensity (arb.units) Magnetic field (mT) 7200 7400 7600 7800 8000 Figure 1.1: Demonstration of enhanced spectral resolution at high magnetic field. (a) EPR spectrum ofCu 2+ at X band. (b) EPR spectrum ofCu 2+ at 230 GHz. Spin parameters are: 61 g x;y = 2.064,g z = 2.277,A x;y = 70 MHz,A z = 490 MHz. For advantage 1), high spectral resolution originates from field-dependent interac- tions in the spin Hamiltonian. For instance, electron Zeeman interaction, the often pre- dominant term in the spin Hamiltonian, has a linear dependence of external magnetic field B 0 and electron Zeeman factor g. And small g difference could be potentially differentiated at HF. 194 Figure 1.1 shows the enhanced spectral resolution of Cu 2+ at 230 GHz compared withX band, whereg anisotropy (g x;y = 2.064,g z = 2.277) is well isolated in the 230 GHz EPR spectrum. High spectral resolution is beneficial in dif- ferentiation of spin systems holding similar g. 88, 134, 194 In addition, HF EPR enhances orientational selectivity in disordered samples. For instance, at HF, even with small g-anisotropy, the relative orientation of spin labels and therefore the structure of bio- logical molecules are accessible by HF double electron electron resonance spectroscopy (ELDOR). 42, 61, 86, 150 For advantage 2), as shown in Fig. 1.2(a), especially at low tem- perature, nearly 100% of thermal spin polarization has been achieved. And by fully polarizing the spin bath, decoherence of probe spins has been completely eliminated. 174 Moreover, at HF and low temperature, high-temperature approximation is no more valid. 2 Polarization Temperature (K) 0 50 100 150 200 250 300 0 100 80 60 40 20 N1 N2 dE = E2 - E1 B P = (N1-N2) / (N1+N2) (a) (b) E1 E2 E3 Energy (GHz) 400 300 200 100 0 Magnetic field (T) 0 2 4 6 8 1 2 D = 200 GHz Figure 1.2: (a) Demonstration of enhanced spin polarization at high magnetic field and low temperature. The x axis is the temperature in Kelvin (K) and y axis is the spin polarization calculated by the the equation shown in the inset. The spin populationN i for each state is calculated based upon Boltzmann distribu- tion (assume amplitude of B 1 is not sufficiently high to alterN). Simulation parameters are:S = 1/2,g iso = 2.0028, B = 8 T. (b) Demonstration of possibility to investigate high spin system. Simulation parameters: S = 1, D = 200 GHz, g = 2.0028. The arrow indicates the transition from state 1 to state 2 atB 0 = 2 T, and the transition energy is 144.4 GHz. The simplest consequence of this effect would be the predominant spin population of the lowest electron spin level. ForS > 1/2 spin system, drastic change on the EPR spec- tra may be expected by varying the sample temperature at high field. Therefore, this property provides an approach to differentiate between free radicals and their clusters, etc. 99 As shown in Fig. 1.2(b), for advantage 3), high spin systems often have large zero-field splittingD, which is only amenable to study at HF. 4, 181 For example, due to the partly occupiedd orbitals, a large amount of transition metal complexes are param- agnetic and hold high spins. There have been many HF EPR studies on various types of transition metal ions and their zero-field splitting parameters, includingD andE, have been obtained with tremendous accuracy. 95, 96, 110, 181, 199 For advantage 4), the availabil- ity of wide range of magnetic field provides the possibility to investigate field-dependent phenomena. It has been reported that bothT 1 andT 2 relaxation times show strong de- pendence of measured frequency. 10, 25, 84, 139 For instance, T 1 of Gd 3+ ion (often used 3 as magnetic resonance imaging (MRI) contrast agents by shortening predominatelyT 1 relaxation time of neighbouring water protons.) exhibits strong field dependence, which was interpreted as being due to modulation of zero-field splitting. 115, 139 Furthermore, line broadening as well as motional dynamics of free radicals in liquid phase often dis- play field-dependence, and detail dynamic information can be obtained from field de- pendence study. 10, 104 Nevertheless, there are many opportunities for further applications of HF EPR spectroscopy. 10, 99, 150, 194 Besides the HF EPR development, multi-frequency pulse EPR techniques comple- ment the EPR spectroscopy and provides much more potentialities. Among them, elec- tron electron double resonance (ELDOR) technique, also known as double electron elec- tron resonance (DEER), 98, 111, 116, 117, 183 utilizes two separate MW frequencies configured for probing dipolar interactions of a pair of spins. 86, 111, 194 And ELDOR has been widely used to determine distances between two electron spins, measure polarization transfer to another region of the spectrum, measure weak couplings between electron spins, etc. 153 Moreover, hyperfine coupling between electron spins with nearby nuclear spins is often too weak to be resolved in a cw EPR spectrum. To obtain the details of weak hyperfine interaction, hyperfine spectroscopes (most of them are type of ELDOR tech- nique) are often employed. 153, 194 Hyperfine spectroscopy is extremely useful to measure nuclear magnetic resonance (NMR) spectrum from nuclear spins hyperfine coupling to electron spins. 4, 152, 153, 194 There are two widely used hyperfine spectroscopic tech- niques: electron spin echo envelope modulation (ESEEM) and electron-nuclear double resonance (ENDOR). In ESEEM, NMR signal is measured from the frequency of mod- ulations in spin echo signals. ESEEM measurement requires only spin echo detection. For a spin system with a long coherence, ESEEM is powerful and measurable using many EPR spectrometers. On the other hand, the intensity of the ESEEM modulation 4 Table 1.1: Comparasion of three commonly used EPR-based hyperfine spec- troscopes. Spectroscopes Description Pro Con ESEEM One MW pulse, detection on EPR, modulation in spin echo signal Easy to implement low signal sensitivity, spectral resolution may be limited on short coherence sample, difficult to measure broad lines HF ENDOR MW and RF pulses, detection on EPR, population recovery by NMR transition high spectral resolution low sensitivity on sample with short electron spinT 1 , hyperfine-specific blind spots HF EDNMR Two MW pulses, detection on EPR, excitation on EPR forbidden transition high signal sensitivity, high spectral resolution, sensitive to number of nuclei spectral resolution may be limited on short coherence sample is maximized when the hyperfine coupling strength is equal to the nuclear Larmor fre- quency. ESEEM spectroscopy is therefore usually performed in a low magnetic field and it is often challenging to obtain a high spectral resolution in the NMR signals. EN- DOR is a double resonance technique where NMR signal is detected by measuring a population change on an EPR transition induced by an excitation of a NMR transition. ENDOR is as sensitive as EPR and is applicable to various kinds of nuclei. The popula- tion change in the NMR transition depends onT 1n , therefore the signal sensitivity tends to be smaller for low- ( is nuclear gyromagnetic ratio) nuclei with which a long NMR pulse is required. In addition, an ENDOR signal also exhibits spectral artifacts including intensity modulation due to hyperfine enhancement 4, 152 and suppression effect. 43, 153 Electron-electron double resonance (ELDOR)-detected nuclear magnetic resonance (EDNMR) is another double resonance-based hyperfine spectroscopy where a NMR signal is detected through a population change on an EPR transition induced by exci- tation of an EPR forbidden transition. 34, 35, 65, 151, 186 Although EDNMR was not widely used before, it has recently been popular because of the advent of high-frequency pulsed EPR spectrometers. 30, 70, 77, 119, 121 The availability of high field is necessary to conquer 5 (a) (b) Figure 1.3: Advanced EDNMR spectroscopes. (a) Enhanced detection sensi- tivity by using echo trains. The top shows the EDNMR pulse sequence used in the experiment, where detection scheme is CPMG instead of spin echo. The ex- periment was performed on 1 mM TEMPOL in isopropanol at 50K. The bottom two EDNMR spectra were taken with N = 1 (black) and N = 4 (red) respectively. The inset in bottom figure shows the SNR gain as a function of N. (Reprint fig- ure with permission from Mentink et al. 114 Copyright 2021 by Elsevier.) (b) THYCOS measurement to identify coordination mode ofMn 2+ in ATP, ADP and AMPPNP. The top shows the THYCOS pulse sequence. The bottom left present the THYCOS spectra ofMn 2+ in ATP, ADP and AMPPNP. The bottom right shows three coordination modes ofMn 2+ in ATP ((a)Mn 2+ coordinates to both Nitrogen and phosphate. (b)Mn 2+ coordinates to phosphate. (c)Mn 2+ coordinates to Nitrogen.). (Reprint figure with permission from Litvinov et al. 100 Copyright 2021 by Elsevier.) the problem of overlapping between NMR signals with central blind spot, where pump frequency sweeping through probe frequency giving a wide spectral spread. Compared with ESEEM and ENDOR, HF EDNMR has much higher sensitivity due to less sen- sitivity to fast T 1 relaxation time. On the other hand, HF EDNMR often exhibits a few limitations. First, the spectral bandwidth is generally less than that of HF EN- DOR, because EDNMR requires a wide microwave bandwidth which may be limited by the microwave resonator bandwidth. In addition, the EDNMR spectral resolution 6 is less satisfactory than that of ENDOR spectrum since the intrinsic linewidth is deter- mined byT 2 , andT 2 of NMR transition is usually much longer than the corresponding EPR transition. HF EDNMR spectroscopy has been successfully employed to study various spin systems including spin-labeled biological systems, metalloproteins, nano- materials. 5, 9, 11, 16, 33, 35, 55, 67, 101, 120, 124–126, 141, 142, 158 With broad bandwidth, W-band ED- NMR spectroscopy was applied to detect in site NMR signals from 55 Mn, 31 P, 1 H, 39 K, 35 Cl, 23 Na and 14 N nuclei surrounding cellular Mn 2+ , which gave details about the ex- tended structures and environments of Mn 2+ centers. 19 Moreover, EDNMR was used to measure 15 N- 31 P correlations for phosphates and a nitrogen coordination in Mn-ATP. 100 Furthermore, as shown in Fig. 1.3, EDNMR was expanded for multi-dimension corre- lation spectroscopy 90, 138 and was combined with Carr-Purcell-Meiboom-Gill (CPMG) sequence to improve the EDNMR sensitivity. 114 HF EDNMR is significantly powerful but relatively new, and its potentiality has not been fully investigated. Therefore, this dissertation mainly aims to investigate HF EDNMR and applications. Specifically, a thorough investigation of EDNMR technique based on a 115 GHz / 230 GHz EPR spectrometer was conducted in this dissertation, including experimental strategies and applications made on solid state systems, such as nanodiamonds. 7 Chapter 2: Fundamental of Electron Paramagnetic Resonance In this thesis, high field EPR is the main tool to investigate the electron-electron double resonance technique and its application, and understanding the basics of EPR is necessary to interpret EPR and EDNMR results. Therefore, fundamentals of EPR spectroscopy are presented in this chapter, including essential magnetic interactions as well as continuous-wave and pulsed EPR spectroscopes analysis. 2.1 Static spin Hamiltonian For a spin system subject to environment, there often exist various types of spin in- teraction. And in EPR, essential spin interactions include electron Zeeman interaction ( ^ H zm ), nuclear Zeeman interaction ( ^ H nzm ), hyperfine interaction ( ^ H hf ), dipolar inter- action ( ^ H dd ), zero-field splitting ( ^ H zfs ), and Quadruple interaction ( ^ H qd ) when nuclear spin quantum number1. And total static spin Hamiltonian ( ^ H 0 ) is the summation of all interaction components, namely, ^ H 0 = ^ H zm + ^ H nzm + ^ H zfs + ^ H hf + ^ H dd + ^ H qd ; (2.1) 8 2.1.1 Electron Zeeman interaction A spin angular momentumS has (2S + 1)-fold degeneracy, and an externally applied static magnetic field B 0 lifts the degeneracy. Electron Zeeman interaction describes the interaction between electron spin magnetic moment e (relating to spin angular mo- mentum by gyromagnetic ratio e , e = e ^ S~) and B 0 . The Hamiltonian describing the energy of this interaction in the unit of angular frequency is, ^ H zm =g B =~B 0 ^ S = e B 0 ^ S; (2.2) whereg is electron Zeemang factor, or generally g tensor of the spin system; B = e~ 2me is Bohr magneton (e is the electronic charge, m e is the electron mass), ~ is reduced Planck constant, and ^ S is electron spin operator. Each paramagnetic species has its own unique g tensor, or a range of g tensor (e.g., g-strain). The deviation of g tensor from the free electron g factor ( 2.0023193) is due to the local magnetic field either permanently exists or induced by B 0 , such as the orbital motion of the unpaired electron induced by B 0 . The orbital angular momentum L is quenched for a non-degenerate ground state through interaction with electrostatic field (crystal field). However, spin-orbit interaction admixes ground state and certain excited states and results in a small amount of orbital angular momentum in the ground state. Therefore, g tensor can be expressed by the following expression, 194 g =g e 1 + 2 (2.3) 9 where 1 is a 33 unit matrix, is the spin-orbit coupling constant and the symmetric tensor consists of the following elements, ij = n6=0 h 0 jL i j n ih n jL j j 0 i 0 n ; (2.4) where L i and L j are orbital angular momentum operators appropriate to the x, y and z direction. Each element ij describes the interaction between the a semi-occupied atomic or molecular orbital (SOMO) ground state 0 with energy 0 and thenth excited state n with energy n . Based on Eqn. (2.4), the small energy difference between two states leads to large spin-orbital coupling, and therefore large deviation of g tensor fromg e . A simple example to explain the experimentally observedg values based on Eqn. 2.4 isV 1 (O 1 ) defect centers inMgO. V 1 center has a tetragonal symmetry and therefore has only diagonal elements in its principle axis frame. AsL z couples only states of the sameM l value, z = 0 andg z =g k =g e . And experimentalg k = 2.0033, which is very close tog e . On the other hand,g ? =g e - 2/ with calculated from x;y , which is also in a good agreement of observedg ? = 2.0386. 130, 197 Since both spin operator ^ S and the external magnetic field B 0 are explicitly orientation-dependent, g has the general form of a tensor with all 9 components in any arbitrary Cartesian coordinate systemx,y,z fixed in the crystal, g = 0 B B 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 C C A ; (2.5) 10 The tensor in the Cartesian frame can be transformed to an Eigen frame containing only diagonal terms (in the following, x, y, z are three axes of g tensor frame, normally coincides with molecular frame, which is defined based on local symmetry of system), g = 0 B B B B B B @ g x 0 0 0 g y 0 0 0 g z 1 C C C C C C A ; (2.6) For instance, if the paramagnetic system has an uniaxial symmetry,g x =g y =g ? ,g z = g k . In a solid state system, g with largely different components manifests itself in the splitting of EPR peaks. For example, transition metal ion Cu 2+ is a S = 1=2 system withg x =g y =2.064,g z =2.277, two peaks corresponding tog x (g y ) andg z are clearly distinguished in the EPR spectrum, especially at highB 0 . On the other hand, in a liquid state, due to rapid random tumbling of molecules, g tends to be averaged out and a single effectiveg value is often obtained from EPR spectrum. 2.1.2 Nuclear Zeeman interaction Similar to electron Zeeman interaction, Nuclear Zeeman interaction describes the in- teraction between nuclear spin magnetic moment n and B 0 . And the Hamiltonian de- scribes the energy of this interaction in the unit of angular frequency is as follows, ^ H nzm = g n n =~B 0 ^ I = n B 0 ^ I; (2.7) where g n is g tensor of nuclear spin; n = jej~ 2mn (m n is the proton mass) is the nuclear magneton; n is gyromagnetic ratio of nuclear spin, and ^ I is the nuclear spin operator. Nuclear Zeeman interaction is much smaller than electron Zeeman interaction as the 11 mass of proton is almost three orders of magnitude larger than that of electron. In regular EPR allowed transitions, nuclear spin remains unexcited. Nuclear Zeeman interaction shifts the energy of both electron spin states to either positive or negative side without affecting the overall energy difference. However, nuclear Zeeman interaction plays an important role in some advanced pulse techniques, such as EDNMR discussed in a later chapter. Zero-field splitting, S> 1/2 system For S > 1 2 spin system, spin-spin interaction induces zero-field splitting ^ H zfs , which has a simplified form of following (x,y,z are three axes of D tensor frame), ^ H zfs = ^ SD ^ S =D x ^ S 2 x +D y ^ S 2 y +D z ^ S 2 z ; (2.8) where S is the total spin angular momentum, D is the zero field splitting tensor withD x , D y andD z components. As D is traceless, only two independent energy parameters,D andE, are required, namely, D = 3 2 D z ;E = 1 2 (D x D y ) Therefore, Eqn. (2.8) can be rewritten as, ^ H zfs =D( ^ S 2 z 1 3 ^ S 2 ) +E( ^ S 2 x ^ S 2 y ); (2.9) D and E strongly reflects the local symmetry of the spin system. For instance, cubic symmetry has D = E = 0, axial-symmetry has E = 0 and D6= 0, lower than axial- symmetry hasD6= 0 andE6= 0. 12 2.1.3 Hyperfine interaction Hyperfine interaction describes the interaction between electron spin magnetic mo- ment and nuclear spin magnetic moment. There are isotropic hyperfine coupling and anisotropic hyperfine coupling. Isotropic hyperfine coupling term takes the following form, 194 ^ H iso =A iso ^ S T ^ I = 2 0 3 g e n j 0 j 2 ^ S T ^ I; (2.10) where isotropic coupling constantA 0 is defined as, A 0 = 2 0 3 g e n j 0 j 2 ; (2.11) which measures the magnetic interaction energy between electron and nucleus. And j 0 j 2 is the probability of the electron wavefunction at the nucleus. The sign ofA 0 indi- cates whether the electron spin magnetic moments and nuclear spin magnetic moments tend to align parallel or anti-parallel. And EPR spectrum is unaffected by the sign of A 0 . One of the mechanism responsible to this isotropic hyperfine coupling is called Fermi contact interaction, which requires the electron occupying an s-orbital (non-zero electron density at the nucleus). 194 On the other hand, dipolar coupling between electron magnetic dipole and nuclear magnetic dipole is responsible for the anisotropic part of hyperfine coupling, which takes the form of dipolar coupling discussed in the next section. Classically, the energy of interaction between two point-magnetic dipoles~ 1 and~ 2 separated by distancer is given by, ^ H hf = 0 4 ( ~ 1 ~ 2 r 3 3 (~ 1 ~ r)(~ 2 ~ r) r 5 ); (2.12) 13 where 0 is the permeability of free space, ~ r is the inter-spin vector connecting two point-magnetic dipoles. Quantum mechanically, the interaction energy is expressed as dipole coupling Hamiltonian in angular frequency unit (rad:s 1 ), ^ H hf = 0 1 2 ~ 4 ( ^ S ^ I r 3 3 ( ^ S~ r)( ^ I~ r) r 5 ); (2.13) By expanding the vectors and averaging the Hamiltonian over the electron distribution, Eqn. 2.13 is then rewritten by the following expression (x,y,z are three axes of A tensor frame), ^ H hf = 0 1 2 ~ 4 = ( ^ S x ^ S y ^ S z ) 0 B B B B B B @ h r 2 3x 2 r 5 i h 3xy r 5 i h 3xz r 5 i h r 2 3y 2 r 5 i h 3yz r 5 i h r 2 3z 2 r 5 i 1 C C C C C C A 0 B B B B B B @ ^ I x ^ I y ^ I z ) 1 C C C C C C A = S T T I (2.14) Where matrix T is symmetric about its main diagonal and is traceless. Overall, hyper- fine tensor is the summation of both isotropic component and anisotropic component, namely, A =A 0 1+ T, where 1 is a 33 unit matrix. 2.1.4 Dipolar interaction Hamiltonian of dipolar interaction between two electron spin magnetic dipoles in angu- lar frequency unit (rad:s 1 ) is, ^ H dd = 0 1 2 ~ 4 ( ^ S 1 ^ S 2 r 3 3 ( ^ S 1 ~ r)( ^ S 2 ~ r) r 5 ); (2.15) 14 By expanding the vectors and averaging the Hamiltonian over the electron distribution, the following expression can be obtained (x,y,z are three axes of D tensor frame), ^ H dd = 0 1 2 ~ 4 = ( ^ S x ^ S y ^ S z ) 0 B B B B B B @ h r 2 3x 2 r 5 i h 3xy r 5 i h 3xz r 5 i h r 2 3y 2 r 5 i h 3yz r 5 i h r 2 3z 2 r 5 i 1 C C C C C C A 0 B B B B B B @ ^ S x ^ S y ^ S z ) 1 C C C C C C A = S T D S (2.16) where 1 and 2 are gyromagnetic ratio of spin 1 and 2 respectively. Dipolar interaction strength scales asr 3 . The first order contribution to the spin system energy is the term commuting with the electron Zeeman term, namely, ^ H dd =d ^ S 1z ^ S 2z (2.17) where d = 0 1 2 ~ 4 3 cos 2 1 r 3 is the dipolar coupling strength, which has a dependence of the distance (r) connecting two magnetic dipoles and the angle () between external magnetic field and the principle axis of the spin system. If dipolar coupling strength is large enough, it manifests itself in the splitting of EPR peaks. However, weak dipolar coupling often results in the broadening of EPR transitions. On the other hand, fluctua- tion of nearby spins having weak dipolar coupling to a central spin is often considered as one of the major decoherence sources for the central spin. Various applications can be realized by detection though dipolar interaction. For instance, structural information of biological samples is often obtained by probing dipolar couplings between two spin labels with distance up to several nanometers. 86 15 2.1.5 Quadruple interaction In general, to describe the charge distribution, such as protons in a nucleus, a proper description requires expanding the charge distribution function as a series of multipoles. The zeroth order of multipole gives the total charge while first-order of multiple gives the electric dipole, and the next highest term is the electric quadrupole moment. All nuclei with a spinI > 1 2 necessarily possess an electric quadrupole momenteQ, where e is the proton charge. eQ is constant for a given nuclear species. The Quadruple interaction describes the interaction between electric quadrupole moment and electric field gradient, and takes the following form (in angular frequency unit), 47 ^ H qd = eQ 6I(2I 1)~ Ieq I; (2.18) where the tensoreq describes the traceless electric field gradient. In a case where the electric field gradient has axial symmetry, for instance Li 1:0 TiS 2 provides an axially symmetric electric field gradient atLi site, 17 the quadrupolar Hamiltonian may be ex- pressed to first order in the applied field B 0 , ^ H qd = 3 8I(2I 1) (3 cos 2 1)(3 ^ I 2 z ^ I 2 ); (2.19) where is the angle between the principalz axis of the electric-field gradient tensor and B 0 , quadrupole coupling constant is defined as from the principle values of the electric field gradient tensor = e 2 q PAF zz Q ~ . Quadrupolar interaction usually contributes to the diagonal as well as the transverse components of Hamiltonian matrix. 16 2.2 Continuous-wave (cw) EPR spectroscopy Conventional cw EPR spectroscopy is a type of steady-state spectroscopy, where spin polarization at thermal equilibrium is detected. In a typical cw EPR measurement, spec- trum is obtained by sweeping external magnetic fieldB 0 while fixingw. 2.2.1 Bloch model-magnetization and relaxation To model the spin dynamics in cw EPR, Bloch equation is often employed. Bloch equa- tion is a classical (non-quantum mechanical) method to help understand the behavior of ensemble spin magnetization where phenomenological spin relaxations can be easily introduced. Total spin magnetization vector M (defined as total spin magnetic moments per volumeV , namely P N i=1 u i V ) in a sample withM x ,M y andM z components, fixes in an arbitrary Cartesian coordinate system in the absence of external magnetic field B 0 . When subject to B 0 applied along laboratoryz axis, M experiences a torque and tends to align with B 0 . As the net torque on a body determines the rate of change of the body’s angular momentum, therefore, dM dt = 0 B B B B B B @ dMx dt dMy dt dMz dt 1 C C C C C C A = e M B (2.20) 17 When subject to additionalB 1 field from MW excitation along laboratoryx ory axis, then the total field experienced by M is, B = 0 B B B B B B @ B x B y B z 1 C C C C C C A = 0 B B B B B B @ B 1 coswt B 1 sinwt B 0 1 C C C C C C A ; (2.21) wherew is the MW frequency. And after simple linear algebra, Eqn. (2.20) is rewritten as, dM dt = e ^ z(M x B 1 sinwtM y B 1 coswt)+ e ^ y(M x B 0 +M z B 1 coswt) + e ^ x(M y B 0 M z B 1 sinwt) (2.22) And three differential equations are obtained accordingly, dM x dt = e (M x B 1 sinwtM y B 1 coswt) (2.23a) dM y dt = e M x B 0 + e M z B 1 coswt (2.23b) dM z dt = e (M y B 0 M z B 1 sinwt) (2.23c) Phenomenological spin-lattice relaxation timeT 1 and spin-spin relaxation timeT 2 can be introduced in the Bloch equation, where bothT 1 andT 2 relaxations are assumed to follow the first-order processes and therefore single exponential decay is often utilized, dM x dt = e (M x B 1 sinwtM y B 1 coswt) M x T 2 (2.24a) dM y dt = e M x B 0 + e M z B 1 coswt M y T 2 (2.24b) dM z dt = e (M y B 0 M z B 1 sinwt) + M 0 z M t z T 1 (2.24c) 18 Mx Mx My Intensity (Arb.Units) Time (us) 0 400 1600 800 1200 2000 0.0 0.2 0.8 0.4 0.6 1.0 My Mz 0 10 0.00 0.05 Figure 2.1: Plot of Eqn. 2.25 as a function oft. The x axis is thet ins, and y axis is intensity in arbitrary unit. In the simulation, e = 28 GHz/T,w 0 w = 0, B 1 = 0.01 Gauss, T 1 = 500 s, T 2 = 1 s, initially M x = M y = 0, M z = 1. The black solid line is the time-dependence of M z , blue solid line is the time-dependence ofM y , red solid line is the time-dependence ofM x . The inset shows the zoom in ofM x andM y change in a shorter time range. As M is continuously rotating along B 0 with Larmor frequencyw 0 = e B 0 , it is easier to visualize the time-dependence of M in a rotating frame. If we choose a rotating frame rotating at a frequency ofw and rotating axis is the same as B 0 , the rotating x-axis is along B 1 , then time-dependent components in Eqn. 2.24 are removed, and the following Bloch equations expressed in a rotating frame are obtained, dM x dt =(w 0 w)M y M x T 2 (2.25a) dM y dt = (w 0 w)M x + e B 1 M z M y T 2 (2.25b) dM z dt = e B 1 M y + M 0 z M t z T 1 (2.25c) Figure 2.1 shows the time-dependence of three components of M. Given the current simulation parameters shown in the figure caption,M z (population difference) decreases 19 from 1 (initial magnetizationM 0 z ) to0.7 with a decay rate determined by 1=T 1 , and achieves a steady-state thereafter. And the steady-stateM z as well asM x andM y does not depend on the initial values of three magnetization components. M y increases from 0 to0.03 at a rate of 1=T 2 (and the maximumM y is determined by 1=T 2 ), and then decreases to0.02 with a decay rate of 1=T 1 , and achieves a steady-state thereafter.M x remains zero all the time. Steady-state solutions are obtained by setting three linear coupled differential equa- tions Eqn. 2.25 to zeros, M x =M 0 z e B 1 (w B w)T 2 2 1 + (w B w) 2 T 2 2 + 2 e B 2 1 T 1 T 2 (2.26a) M y = +M 0 z e B 1 T 2 1 + (w B w) 2 T 2 2 + 2 e B 2 1 T 1 T 2 (2.26b) M z = +M 0 z 1 + (w B w)T 2 2 1 + (w B w) 2 T 2 2 + 2 e B 2 1 T 1 T 2 (2.26c) where the response of M x is in phase with B 1 while M y is 90 out of phase. M x and M y are much smaller than M z . In a typical cw EPR measurement, B 1 is usually set to be small, and M y (detected in EPR measurement) will vanish if B 1 increases significantly large. This is so-called power saturation ( the term 2 e B 2 1 T 1 T 2 becomes very large) one should avoid when perform cw EPR experiment. And due to this reason, the total magnetization is not conversed ( from figure 2.1 and Eqn. 2.26a, Eqn. 2.26b, Eqn. 2.26c). Figure 2.2 shows the simulated EPR signal intensity as a function ofB 1 with different relaxation times. It is clearly that whenT 1 andT 2 is longer, the smaller B 1 will result in power-saturation. 20 B1 (Gauss) 0 0.05 0.10 EPR intensity (Arb.Units) 0.15 0.10 0.05 0.00 T 2 = 1ms, T 1 = 500ms T 2 = 100ns, T 1 = 500ms T 2 = 1ms, T 1 = 50ms Figure 2.2: Plot of Eqn. 2.26b as a function of B 1 . The x axis is the B 1 in Gauss, and y axis is EPR intensity in arbitrary unit. In the simulation, e = 28 GHz/T, w 0 w = 0, B 1 = 0.01 Guass. The black solid line is the simulation whenT 1 = 500s,T 2 = 1s, blue solid line is the simulation whenT 1 = 50s, T 2 = 1s, red solid line is the simulation whenT 1 = 500s,T 2 = 100 ns. 2.2.2 cw EPR spectral analysis In this section, cw EPR spectral analysis using aS = 1 2 system is discussed. To simply, a static Hamiltonian ( ^ H 0 ) containing only a single Zeeman term with isotropic g value (g iso ) is employed, namely, ^ H 0 =g iso B B 0 ^ S =g iso B (B x ^ S x +B y ^ S y +B z ^ S z ) (2.27) 21 whereB x ,B y andB z are three projections of magnetic field vector B 0 in the molecular frame. And three spin operators constructed in the Zeeman basis (jm s = 1 2 i = 0 B B @ 1 0 1 C C A , jm s = 1 2 i = 0 B B @ 0 1 1 C C A ) are, ^ S x = 1 2 0 B B @ 0 1 1 0 1 C C A ; ^ S y = 1 2 0 B B @ 0 i i 0 1 C C A ; ^ S z = 1 2 0 B B @ 1 0 0 1 1 C C A ; (2.28) And the matrix representation of Eqn. 2.27 is therefore, ^ H 0 = 1 2 g iso B 0 B B @ B z B x iB y B x +iB y B z 1 C C A (2.29) By diagonalizing the above matrix, two Eigen values are obtained, E 1 = g iso B 2 q B 2 x +B 2 y +B 2 z (2.30a) E 2 = g iso B 2 q B 2 x +B 2 y +B 2 z (2.30b) And two corresponding Eigen vectors are, j1i = 0 B B @ B z + p B 2 x +B 2 y +B 2 z B x +iB y 1 C C A (2.31a) j2i = 0 B B @ B x iB y B z p B 2 x +B 2 y +B 2 z 1 C C A (2.31b) 22 Magnetic field B0 (arb.units) Energy (arb.units) |1> |2> MW dE=E 1 -E 2 = hv EPR absorption Detected 20 kHz signal 20 kHz modulation field B i B j B m 20 kHz detector output I i I j B 0 (a) (b) Figure 2.3: cw EPR demonstration. (a) the energy diagram of two level system subject to the external magnetic field B 0 , and the resonance condition is met where MW frequency is the same as energy differenceE. (b) Illustration of field modulation in conventional cw EPR experiment. The static magnetic field is modulated between the limitsB i andB j . The corresponding detected signal is then modulated betweenI i andI j , which is approximately the first derivative of the absorption signal. Figure 2.3(a) shows the energy diagram of the two level system as a function of external magnetic fieldB 0 . Eigen valueE 1 increases linearly with respect to theB 0 while Eigen value E 2 decreases linearly with respect to the B 0 . Therefore, the energy difference between two levelsE is also proportional toB 0 . In cw EPR experiment, EPR spectrum 23 is obtained by either sweeping B 0 with fixed MW frequency or vice versa. MW is absorbed when resonance condition satisfied where matchesE, h =E 1 E 2 =g iso B q B 2 x +B 2 y +B 2 z =g iso B B 0 )g iso = h B B 0 (2.32) Therefore,g iso can be easily obtained from the cw EPR spectral analysis. In conventional cw EPR experiment, field modulation is commonly used to improve the signal to noise ratio (SNR). In field modulation, the maindc magnetic field is mod- ulated with a small-amplitude sinusoidal field modulation. As shown in Fig. 2.3(b), a modulation frequency of 20 kHz and a typical amplitude of 0.02 Gauss are used in our HF EPR spectrometer. Under the field modulation, the regular absorption spectrum turns into first-derivative like signal when the modulation field amplitude is smaller than EPR linewidth. This technique allows the incorporation of the signal into a fixed fre- quency usingac technique and therefore amplifies cw EPR signal significantly. More explicitly, the EPR signal buried in noise is multiplied with the 20 kHz reference sig- nal generated from the same lock-in amplifier. And the multiplied signal is then time averaged. As the EPR signal has the same frequency as reference signal, EPR signal will have a time-averaged intensity dependent on its amplitude and phase difference be- tween the reference. For instance, if two signals are 180 degree out of phase, the output intensity is minimum, and if they are exactly in phase, then the output intensity is max- imum. And the noise is time-averaged out to zero. Clearly, drastic gain is obtained by amplifying the averaged signal. Therefore, this phase-sensitive detection technique sig- nificantly improvesSNR of EPR signal by rejecting all frequency components except those in a very narrow band ( 1 Hz) about modulation frequency 20 kHz. Further- more, the larger excitation bandwidth determined by larger modulation field strength 24 can significantly increase signal intensity as the EPR intensity proportional to the slope of absorption spectrum, although potential spectrum distortion may appear. EPR intensity is proportional to the transition probability connecting two states, which is calculated by the following equation, P =jh1j ^ H 1 j2ij 2 ; (2.33) where ^ H 1 = g iso B B 1 ^ S is the MW excitation term, with B 1 usually applied along lab- oratory x axis. For any arbitrary molecular frame, the correct representation of B 0 and B 1 vectors can be easily obtain through Euler rotation matrix. Next, lineshape should be considered as EPR peaks are often broadened either by dy- namic effects (relaxation) or static effects (imhomogeneous magnetic field, unresolved hyperfine couplings A, anisotropy g, etc). Depending on broadening mechanism, two major lineshapes are often considered: Lorentzian lineshape and Gaussian lineshape. In some cases, V ogit function where convolution of two lineshapes is also utilized. And EPR signal commonly follows an exponential decay due to the relaxation, Lorentzian function is often used as the intrinsic lineshape. And the EPR signal obtained in the absence of MW power saturation can be expressed as the following, L(B 0 ;; ) 1 (g iso B B 0 h) 2 + 2 (2.34) where = 1=(2T 2 ) is the full-width at half maximum (FWHM) of an intrinsic lineshape given by Lorentzian function, and the peak-peak linewidth ( pp ) is related to FWHM by pp = = p 3. On the other hand, Gaussian lineshape is used when the peak broadening 25 arises from the inhomogeneous broadening mechanism, such as the inhomogeneous ex- ternal magnetic field and unresolved hyperfine structures. By considering the lineshape, the cw EPR signal is then rewritten as, I(B 0 ;; )/L(B 0 ;; )P (2.35) Next, in the ensemble measurement, when considering many spins with random molec- ular orientations, Eqn. 2.35 should be integrated over all possible polar () and azimuthal angles () to obtain so-called powder-averaged EPR spectrum, I powder cw / Z 2 0 Z 0 L(B 0 ;; )P (;) sin()dd (2.36) 2.3 Pulsed EPR spectroscopy EPR spectroscopy has capabilities to investigate the structural and dynamic information of molecules. For instance, the molecular structure of biological molecules can be ob- tained by probing dipolar coupling between two spin labels with distance up to several nanometers. And dynamic information down to a nanosecond regime can also be in- vestigated. 153 However, those compelling potentialities of EPR spectroscopy cannot be fully achieved with conventional cw EPR spectroscopy due to its limitation of spectral resolution and time resolution. Specially designed pulse techniques are often required to separate weak interactions and therefore obtain the detail information of weak in- teraction. For instance, weak hyperfine coupling between electron spins with nearby nuclear spins is unlikely to be resolved in a cw EPR experiment. However, hyperfine interaction information can be obtained with tremendous accuracy by utilizing hyperfine 26 spectroscopy. T 1 andT 2 relaxation times down to a nanosecond scale is accessible by specially designed relaxation pulse techniques. In a pulsed EPR experiment, often short MW pulses are employed. Depending on the MW power and spin system, a pulse of 500 ns is common at our high field of 230 GHz and spin half system (T 1 ,T 2 ). 29 MW is commonly applied along x axis of lab frame, and MW excitation is often treated as time-dependent perturbation, and therefore takes the form of following Hamiltonian, ^ H MW = e B 1 ^ S x cos (wt) (2.37) And the total Hamiltonian is therefore, ^ H(t) = ^ H 0 + ^ H MW (2.38) And we need to deal with the time-dependent Schr¨ odinger equation, ^ H(t) =i~ @ @t (2.39) In the following sections, a simple two-level system (TLS) is utilized to explain the prin- ciple of some fundamental pulsed techniques. And the static Hamiltonian ( ^ H 0 ) contains a single Zeeman interaction where a spin half system subject to an external magnetic fieldB 0 (the interactions between spins are ignored) namely, ^ H 0 = e B 0 ^ S z (2.40) 27 First, numerical diagonization is applied to transform static Hamiltonian ^ H 0 to a rotating frame by unitary operator ^ U d = exp(iw ^ S z t) (rotating frequencyw is often set to be the same as MW frequency, and rotating axis is laboratoryz axis), ^ H = ^ U y d ( ^ H 0 + ^ H MW ) ^ U d w ^ S z = S x + ^ S z ; (2.41) where = e B 1 is Rabi frequency, = (w 0 w) is the resonance offset. And time- dependent component in the Hamiltonian Eqn. 2.39 is removed. 2.3.1 Rabi oscillations Rabi measurement is conducted at a fixed frequency w and Rabi frequency while varying pulse length t p . And Population on each state is calculated by solving time- dependent Schr¨ odinger equation Eqn. 2.39. The total Hamiltonian takes the form of Eqn. 2.41, and during the application of MW, the unitary operator operating on spin system expressed in theji and ji basis is, ^ R(t p ) = exp(i ^ Ht p ) = exp(i ( ^ S z + ^ S x )t p ) = 0 B B @ cos( R tp 2 )i R sin( R tp 2 ) i R sin( R tp 2 ) i R sin( R tp 2 ) cos( R tp 2 ) +i R sin( R tp 2 ) 1 C C A ; (2.42) wheret p is the MW pulse length, R p 2 + 2 . When this operator operates on an initial stateji = 0 B B @ 0 1 1 C C A , the final statej f i = ^ R(t p ) 0 B B @ 0 1 1 C C A , 28 j f i = 0 B B @ cos( R tp 2 )i R sin( R tp 2 ) i R sin( R tp 2 ) i R sin( R tp 2 ) cos( R tp 2 ) +i R sin( R tp 2 ) 1 C C A 0 B B @ 0 1 1 C C A = 0 B B @ i R sin( R tp 2 ) cos( R tp 2 ) +i R sin( R tp 2 ) 1 C C A =i R sin( R t p 2 )ji + (cos( R t p 2 ) +i R sin( R t p 2 ))ji (2.43) Then the population on stateji = 0 B B @ 1 0 1 C C A (P ) is calculated by the following, P (t p ) =jhj f ij 2 = ( R ) 2 sin 2 ( R t p 2 ) = 1 2 ( R ) 2 (1 cos( R t p )) (2.44) And the population on stateP (t p ) = 1P (t p ). The plot of Eqn. 2.44 is shown in Fig. 2.4. When there is no resonance offset ( = 0 MHz),P (0) is zero, and followed by oscillating between a maximum of 1 and a minimum of 0 at Rabi frequency . While when increases, the maximum probability ofP is reduced and the oscillation frequency increases as well. In general, population on each state oscillates as well as decays with a decay rate of 1=T 2 . To simplify, the total Rabi oscillation becomes the Eqn. 2.44 multiplied by an exponential decay function, P (t p ) = ( R ) 2 sin 2 ( R t p 2 )t p ) exp(t p =T 2 ) (2.45) 29 Pa 1.0 0.8 0.6 0.4 tp (ns) 0 500 1000 d = 0 MHz 0.2 0.0 d = 2.5 MHz d = 12.5 MHz Figure 2.4: Plot of Eqn. 2.44 as a function oft p . The x axis is thet p in ns, and y axis isP . In the simulation, = 5 MHz. The black solid line is oscillation of P when = 0MHz, the red solid line is oscillation ofP when = 2:5MHz and the blue solid line is oscillation ofP when = 12:5MHz. 2.3.2 Free induction decay Free induction decay (FID) is a simple pulsed measurement in which a=2 pulse is ap- plied to rotate initial spin magnetization, which originates from the thermal polarization, into x-y plane. After spin magnetization rotated in the y axis (x axis) when MW applied along x axis (y axis), spin magnetization will remain along the same axis if there is no resonance offset and no change of total magnetic field experienced. However, in reality, even with fixed external B 0 , each spin has a different paramagnetic environment due to random configuration of paramagnetic impurities in lattice. This difference leads to different total magnetic field experienced by each spin in the spin ensembles. As each spin having different Larmor frequency rotating along the z axis, the total transverse component of spin magnetization decays over time. Moreover, bath spins either interact with each other through dipole-dipole interaction (spin flip flop process) or interact with 30 the lattice phonons (single spin flip), the magnetic field experienced by central spins is generally time-varying. In the following, the analytical expression of FID signal is derived for a TLS. When =2 pulse operates on an initial stateji, new state becomesj i i = ^ R(t p )ji. As this pulse is a resonant=2 pulse ( R t p = =2), based on Eqn. 2.43, j i i = 1= p 2(ji iji). After a =2 pulse, spins are subject to a fluctuating magnetic field, which is generally a time-varying function ~ b(t), and the free evolution operator becomes, ^ U(t) = exp(i Z t 0 b(t 0 ) ^ S z dt 0 ) (2.46) Therefore, the final statej f i becomes, j f i = exp(i Z t 0 b(t 0 ) ^ S z dt 0 )j i i = 1= p 2 exp(i Z t 0 b(t 0 ) ^ S z dt 0 )jii= p 2 exp(i Z t 0 b(t 0 ) ^ S z dt 0 )ji = 1= p 2 exp(i=2 Z t 0 b(t 0 )dt 0 )jii= p 2 exp(i=2 Z t 0 b(t 0 )dt 0 )ji (2.47) where the power series is applied to the exponential function in the last step to combine the eigen value of ^ S z to the argument of the exponential function. Once final state 31 obtained, the transverse componentsm x andm y of a single spin are computed by the following expression, m x (t) =h f j ^ S x j f i =h f j1=(2 p 2) exp(i=2 Z t 0 b(t 0 )dt 0 )jii=(2 p 2) exp(i=2 Z t 0 b(t 0 )dt 0 )jii = i 4 exp(i Z t 0 b(t 0 )dt 0 ) + i 4 exp(i Z t 0 b(t 0 )dt 0 ) = 1 2 sin( Z t 0 b(t 0 )dt 0 ) (2.48) And, m y (t) =h f j ^ S y j f i =h f ji=(2 p 2) exp(i=2 Z t 0 b(t 0 )dt 0 )ji + 1=(2 p 2) exp(i=2 Z t 0 b(t 0 )dt 0 )jii = 1 4 exp(i Z t 0 b(t 0 )dt 0 ) + 1 4 exp(i Z t 0 b(t 0 )dt 0 ) = 1 2 cos( Z t 0 b(t 0 )dt 0 ) (2.49) If we denote the initial magnetization as m 0 , which is the spin polarization originates from the thermal equilibrium, the following expressions can be obtained, m x (t) =m 0 sin( R t 0 b(t 0 )dt 0 ) (2.50a) m y (t) =m 0 cos( R t 0 b(t 0 )dt 0 ) (2.50b) For ensemble average FID signals, b(t) is commonly treated as a stochastic Ornstein- Uhlembeck (OU) process with zero mean (hb(t)i = 0) and correlation function 32 hb(t)b(0)i t = exp(t= c ), where and c are the variance and correlation time of b(t) process, respectively. Averaging Eqn. 2.50 over the OU process results in the fol- lowing equations, 76, 93 m x (t) = 0 (2.51a) m y (t) =m 0 exp[ 2 2 c ( t c +e t=c 1)] (2.51b) FID signals are usually decay by a decay rate of = 1=T 2 , and therefore transverse spin magnetization (m xy = p m 2 x +m 2 y ) based on Eqn. 2.51 takes the following form, m xy (t) =m 0 exp((t=T 2 ) ); (2.52) where factor characterizes the noise type, and takes a value between 1 and 2. In an ensemble measurement, electrons spins in crystal lattice distribute randomly and have different environments. An ensemble FID signal is obtained by averaged over all possible positions and spin states of bath spins, 118 FID ensemble (t) =m 0 exp( r 2 2 0 2 B g 2 n 9 p 3~ t); (2.53) wheren is the concentration of bath spins in lattice, and the decay rate for ensemble is q 2 2 0 2 B g 2 n 9 p 3~ . 2.3.3 Electron spin echo FID signals decay due to both static magnetic field as well as time-varying magnetic field. In a typical spin echo (SE) measurement, the pulse sequence is=2, where additional pulse is used to invert spin magnetization, and SE signal is formed 33 after the same free evolution time. Therefore, the decay due to static magnetic field experienced is removed in SE measurement, only the time-varying magnetic field causes the SE decay. Spins in the sample are usually divided into two types, excited A spins and non-excited B spins. And the SE decay is mainly due to the following two reasons: the dipolar interaction between A spins even if there are no random flips, which is called instantaneous diffusion due to MW pulse; and spectral diffusion, where the resonance frequency of A spins is randomly shifted due to the random flip of B spins (spin flip flop process or single spin flip) during the experiment time window. 149 In the following, the analytical expression of SE signal for TLS is derived. The final state after SE pulse sequence is calculated by, j f i = ^ U() ^ R ^ U() ^ R =2 j i i (2.54) where the unitary operator during first free evolution time is ^ U() = exp(i R 0 b(t 0 ) ^ S z dt 0 ), and during second free evolution time is ^ U() = exp(i R 2 b(t 0 ) ^ S z dt 0 ). To calculate the final state, we follows the similar procedures described in FID. Initially the state is, and the state j 2 i after first=2 pulse and first free evolution time is the same as Eqn. 2.47, j 2 i = 1= p 2 exp(i=2 Z 0 b(t 0 )dt 0 )jii= p 2 exp(i=2 Z 0 b(t 0 )dt 0 )ji (2.55) 34 Next, a resonant applied ( = 0, and R t p = ), based on Eqn. 2.42, the matrix representation of ^ R is, ^ R = 0 B B @ 0 i i 0 1 C C A =2i ^ S x ; (2.56) Applying ^ R on j 2 i, the statej 3 i is obtained, j 3 i =1= p 2 exp(i=2 Z 0 b(t 0 )dt 0 )jii= p 2 exp(i=2 Z 0 b(t 0 )dt 0 )ji (2.57) Finally, the second free evolution operator ^ U(t) is applied on Eqn. 2.57 and the final statej fse i is obtained, j fse i = exp(i Z 2 b(t 0 ) ^ S z dt 0 ) (1= p 2 exp(i=2 Z 0 b(t 0 )dt 0 )jii= p 2 exp(i=2 Z 0 b(t 0 )dt 0 )ji) =1= p 2 exp(i=2( Z 2 b(t 0 )dt 0 ) Z 0 b(t 0 )dt 0 ))ji+ i= p 2 exp(i=2( Z 0 b(t 0 )dt 0 ) Z 2 b(t 0 )dt 0 ))ji =1= p 2 exp(i)jii= p 2 exp(i)ji (2.58) where = 1=2( R 2 b(t 0 )dt 0 ) R 0 b(t 0 )dt 0 ) is the total phase accumulated by a single spin during total free evolution time 2. Once the final state after spin echo sequence is 35 obtained, the transverse components of the spin magnetizationm x andm y are calculated by the following, m x (2) =h fse j ^ S x j fse i =h f j 1=(2 p 2) exp(i)jii=(2 p 2) exp(i)jii = i 4 exp(2i) + i 4 exp(2i) = 1 2 sin(2) (2.59) And, m y (2) =h fse j ^ S y j fse i =h f ji=(2 p 2) exp(i)ji + 1=(2 p 2) exp(i)jii = 1 4 exp(2i) 1 4 exp(2i) = 1 2 cos(2) (2.60) when usingm 0 to represent the thermal spin polarization from thermal equilibrium and substitutes, the following two expressions can be obtained, m x (2) =m 0 sin( Z 2 b(t 0 )dt 0 Z 0 b(t 0 )dt 0 ) (2.61a) m y (2) =m 0 cos( Z 2 b(t 0 )dt 0 Z 0 b(t 0 )dt 0 ) (2.61b) Total spin echo signal is p m 2 x +m 2 y . Here ifb(t) is static,m x (2) = 0, and onlym y (2) will contributing to the SE signal, which remains along y-axis without losing coher- ence. However, a typically SE decays due to the time-varying ~ b(t). And ~ b(t) is often treated as classical noise field, and is modeled by O-U process with zero mean value (<b(t)> t = 0) and a correlation function<b(t)b(0)> t =b 2 exp(t= c ), whereb 2 and 36 c are variance and correlation time of ~ b(t), respectively. Therefore, SE decay subjected to O-U process is given by, 94 SE(2) =m 0 exp[(b c ) 2 (2= c 3e 2=c + 4e =c )]; (2.62) In the quasistatic limit where b c 1, indicates slow spin bath dynamics, SE(2) = m 0 exp[b 2 (2) 3 =(12 c )] =m 0 exp[(2=T 2 ) 3 ]; while in the motional-narrowing limit where b c 1, indicating fast spin bath dynamics, SE(2) = m 0 exp[b 2 c (2)] = m 0 exp[(2)=T 2 ]. Next, the relation between spin concentration and 1=T 2 is discussed. The typical distance between two spins may be obtained by utilizing the Poisson dis- tribution by setting the probability exp((4nr 3 =3)) of finding no other spins within a distancer of a spin placed at the origin to be 1=2, wheren is the spin concentration, 79 which results in r/ 0:549n 1=3 . As dipolar coupling strength b/ 1=r 3 , b/ n, and variance b 2 / n 2 . In addition, c / 1=n. Therefore, in the quasistatic limit, 1=T 2 = (b 2 =(12 c )) 3 /n, and this linear dependence has been observed experimentally. 12, 168 In the motional-narrowing limit, 1=T 2 =b 2 c /n. Furthermore, SE decay of ensemble spins due to spectral diffusion from B spins is described by the following analytical expression, 149 SE(2) = exp(g Az g Bz 2 B ~ 1 C B J B (2W B )=2W B ) (2.63) whereg Az andg Bz are the g-tensor components of A and B spins along the direction of the external magnetic fieldB 0 ;C B is the concentration of B spins;W B is the spin-flip rate of B spins;J B is the universal function with dimensionless variable 2W B . 37 2.3.4 Inversion recovery Inversion recovery is a type of pulsed technique widely used to measure spin lattice relaxation time T 1 . The pulse sequence is shown in fig. 2.5(a), an initial pulse ap- plied to inverse magnetization and recovered thermal magnetization (M z ) is detected through either FID or SE. In the experiment, time delay T between first pulse and detection pulse sequence is varied, within this interval, inverted magnetization couples to the environment and gradually relaxes back to positive-z axis. The measured recov- ered magnetization often follows an exponential function with decay rate determined by 1=T 1 , namely, M z (T ) =M 0 (1e (T=T 1 ) ); (2.64) where M 0 is the thermal magnetization. The above discussion is based on one relax- ation mechanism. If there are more than one mechanisms govern relaxation process, bi-exponential function, for instance, may be used to fit the experimental data to obtain the two corresponding relaxation times. 2.3.5 Simulated echo decay Besides inversion recovery experiment, stimulated echo decay experiment is another widely used pulse technique to measureT 1 relaxation time. As shown in Fig. 2.6, the pulse sequence is=2 - -=2 -T -=2 - - echo. The first two=2 pulses generate polarization, and the non-equilibrium polarization decays due to spin lattice relaxation duringT . The final=2 generates stimulated echos, and stimulated echo intensity de- creases asT increases. Therefore,T 1 can be determined by measuring stimulated echo intensity as a function ofT . 38 t /2 Echo T t T (arb.units) M z M 0 (a) (b) 0 T 1 Figure 2.5: Demonstration of Inversion recovery pulse technique. (a) Pulse sequence used in the inversion recovery measurement. (b) Recovered magneti- zation change as a function of time delayT . /2 Echo t /2 T t /2 Figure 2.6: Stimulated echo pulse sequence used to measure T 1 relaxation time. 2.4 Summary In this chapter, essential static spin Hamiltonian is explained, and spin Hamiltonian formalism is discussed to interpret cw and pulsed EPR experimental data. 39 Chapter 3: HF EPR Instrumentation As described in Chap. 1, compared with low field, HF EPR spectroscopy gains a large amount of advantages. In the aspect of instrumentation, HF EPR requires highB 0 and high MW frequency w. And advances in instrumentation, such as the realization of high magnetic field and high frequency MW radiation provide aforementioned HF EPR advantages. To date, the highest all-superconducting magnet field of 32 Tesla has been obtained at National High Magnetic Field Laboratory. 193 On the other hand, to generate high frequency MW radiation, it is often starting with a stable low-frequency oscillator and a nonlinear frequency multiplier circuit is utilized to up-convert the low frequency to the expected high frequency efficiently. 137 However, high frequency MW often does not have high power due to the conversion loss and lack of efficient amplifier working at high frequency. In this chapter, implementation details of shaped pulse capabilities in a 115 GHz/230 GHz HF EPR spectrometer are discussed. First, a wide dynamic range after MC at both 115 GHz and 230 GHz has been detected. To characterize the power stability, we further conducted the jitter analysis and serial data analysis at both frequency operating modes. Last, the implementation of shaped pulses, including phase-modulated chirped pulse and amplitude-modulated pulse, is discussed in detail. 40 Quasioptical system 12.1 T superconducting magnet Sample Corrugated waveguide Liquid hellium crystat Local oscillator LNA PC Control Corrugated horns 9-11 GHz synthesizer x8/x4 frequency multiplier PIN switch Power combinar x3 Isolator PIN switch 216-240 /108-120 GHz Frequency multiplication chain (MC) TTL 8-10 GHz synthesizer Fixed ATTN Fixed ATTN Var ATTN VDI Tx Ex. Sig. 2-20 GHz synthesizer x12/x6 frequency multiplier Var ATTN IQ mixer Direct Coup From Tx From Rx x24/x12 frequency multiplier Phase shifter Amplifer I Q cw exp. pulse exp. 3GHz Ref 3GHz IF Direct Coup Var ATTN Oscillo- scope Lock-in amplifier f TTL Subharmonically- pumped mixer Figure 3.1: Block diagram of HF EPR spectrometer at USC. 3.1 Instrumentation 3.1.1 HF EPR spectrometer HF EPR spectrometer was developed in our lab at USC. As shown in Fig. 3.1, the system employs a high frequency high-power solid-state source consisting of two MW synthe- sizers, directional couplers, isolators, attenuators, pin switches, microwave amplifiers and frequency multipliers. For EDNMR measurement, a variable attenuator is imple- mented to control the power of the second HF microwave. The output power of the source system is 100 mW at 230 GHz and 480 mW at 115 GHz. The HF microwaves 41 AWG: Keysight 33600A I Q 8-10 GHz synthesizer 9-11 GHz synthesizer Direct Coup Direct Coup Fixed ATTN PIN switch TTL x8/x4 frequency multiplier Power combinar x3 Isolator 216-240 /108-120 GHz Frequency multiplication chain (MC) TTL Variable ATTN PIN switch L3Harris Narda-ATM AF866-10 P 0 P 1 AWG Figure 3.2: Block diagram of HF EPR microwave bridge at USC. are propagated in free-space using a quasioptical bridge and then coupled to a corru- gated waveguide. A sample placed on a metallic end-plate at the end of the waveguide, and then placed on at the center of 12.1 T cryogenic-free superconducting magnet. EPR signal is isolated from the excitation using an induction mode operation. 161 For EPR experiment, we employ a superheterodyne detection system in which 115 GHz and 230 GHz is down-converted into 3 GHz of intermediate frequency (IF), and then down- converted again to in-phase and quadrature components ofDC signals. Details of the system have been described elsewhere. 29, 30 42 3.1.2 HF MW bridge setup Figure 3.2 shows the diagram of the 115 GHz and 230 GHz MW bridge. The IQ mixer is installed at base frequency (8-10 GHz) before MC. And theI andQ components used for pulse shaping are generated by AWG (Keysight 33600A). To explicitly control the MW power at this transmission line, a variable attenuator is installed right after the MW synthesizer (highlighted in green color in Fig. 3.2). The shaped pulse at low frequency is then amplified and guided into MC, and multiplied by 12X or 24X to obtain 115 GHz or 230 GHz high frequency output respectively. 3.1.3 Installation of IQ mixer Low MW power at high field leads to limitation of MW excitation bandwidth, and re- sults in difficulty to conduct some pulse experiments requiring well-controlled excita- tion profiles, such as double electron electron resonance at high field. An increased pulse length without increasing MW power can be used to compensate pulse bandwidth limitation. However, long pulse imposes a limitation on the spin systems with short relaxation times. To potentially solve this problem, shaped pulse is introduced by in- corporating IQ mixer and arbitrary wave generator (AWG) into EPR spectrometer. The common way to implement AWG at low frequency (e.g. X band) is to mix the out- put of AWG with carrier frequency at or close to operating frequency using IQ mixer. And amplifier is employed after mixer to compensate the power loss due to insertion loss. Imperfection in the resonator response can be corrected by using a simple transfer function. 45, 92, 164 However, there is no efficient MW amplifier working at high frequency (> 100 GHz), and the implementation is often done at base frequency before frequency multiplication chain (MC). For example, it has been reported that shaped pulses (e.g. 43 amplitude-modulated and phase-modulated pulses) have been generated at 200 GHz by implementing fast AWG at 12 GHz base frequency. And nearly one order of magnitude improvement in the excitation bandwidth has been achieved when compared with the conventional rectangular pulse. 89 On the other hand, because of the nonlinearity of MC, it has been shown that signifi- cant difficulty exists in the generation of amplitude-modulated pulse at high frequency. 89 Possible approach to generate desired amplitude-modulated pulse at high frequency is to correct the pulse distortion based on some calibration tables of nonlinear MC response. Furthermore, it has been reported that a closed-loop feedback control was successfully incorporated to numerically optimize MW pulse. And the pulse distortion introduced by the instrument was then compensated. 66 3.2 Characterization of HF EPR microwave bridge 3.2.1 Dynamic range First, the nonlinear property of MC is characterized. A sensitive power detector (Agilent Keysight 33330C detector) is utilized to measure the power before (P 0 ) and after (P 1 ) MC at various power levels, and the power level is controlled by the variable attenuator at a 9 GHz base frequency (Figure 3.2). And the measured power is converted to decibel (dB, defined as 10 log (P f =P i ) 10 , whereP i is the initial power at the MW synthesizer,P f is P 0 orP 1 ). As shown in Fig. 3.3 (a), a narrow dynamic range of 2.5 dB before MC results in a much larger dynamic range of> 40 dB after MC at 115 GHz. An an even larger dynamic range of> 60 dB after MC at 230 GHz is detected. This large difference in dynamic range before and after MC is attributed to the nonlinearity of MC. High input power causes MC saturation, and MC will start to response drastically only when input 44 (a) (b) Output power P 1 (dB) Input power P 0 (dB) 0 5 10 15 Input power P 0 (dB) 0 5 10 15 0 10 20 30 40 13 15 0 40 Output power P 1 (dB) 0 20 40 60 13 15 0 60 Figure 3.3: Dynamic range characterization. (a) Charaterization of dynamic range at 115 GHz. The x axis is the attenuation given by variable attenuator before MC, which gives a range of 2.5 dB, and y axis is the attenuation after MC, which has dynamic range of> 40 dB. And the inset shows a zoom- in dynamic range. (b) Charaterization of attenuation range given by variable attenuator at 230 GHz. The x axis is the attenuation given by variable attenuator before MC, which gives a range of 2.5 dB, and y axis is the attenuation after MC, which has dynamic range of > 60 dB. And the inset shows a zoom-in dynamic range. power is reduced under certain level. These calibration results provide the possibility to control the MW power at operating frequency. 3.2.2 Power stability Next, power stability at 115 GHz and 230 GHz are characterized based on commonly used analysis methods, including jitter analysis and serial data analysis. To avoid ad- ditional noise coming from mixing at high frequency due to different MW power, both variable attenuator and rotating wire-grid polarizer are used to assure similar MW power 45 Figure 3.4: Power stability characterization. (a) Jitter analysis at 115 GHz. The x axis is the attenuation in dB (after MC, the same as y axis in Fig. 3.3) and y axis is jitter in nanosecond (ns). (b) Serial data analysis at 115 GHz. The x axis is the attenuation in dB and y axis is the error in % (see the main text for details). The inset shows the transient single pulse captured by oscillope. The pulse length is 1 s and pulse amplitude around 70 mV . Where three arrows point to the three position taken for power stability characterization. And the same approach for 230 GHz. (c) Jitter analysis at at 230 GHz. (d) Serial data analysis at 230 GHz. sent to spectrometer. An oscilloscope is used to capture the transient I and Q compo- nents, and the inset of Fig 3.4 (b) shows a typical single pulse trace. To obtain the sta- tistical meaningful information, a significantly large number of pulse traces (typically 300) are captured and stored for further jitter analysis and serial data analysis. Jitter is obtained by calculating standard derivation of the time at the middle of rising edge of the pulse trace, and analysis results are summarized in Fig 3.4 (a) and (c). Clearly, different 46 jitters are observed at disparate attenuation levels at a given frequency, and variation pattern at 115 GHz and 230 GHz behaves differently as well. At 115 GHz, while jitter stays below 1 ns at most attenuation levels, a high jitter of 2.5 ns is observed when the attenuation is 6 dB. On the other hand, jitter stays above 1 ns at all attenuation levels at 230 GHz. 1-5 ns of magnitude instability is normal for this high-frequency multiplier-based system. To achieve the minimum duration of jitter, it is likely that the jitter will hit a minimum across a narrow range20 dB. It is within this range that the nonlinearity turns on characteristic of the multiplier. As shown in Fig 3.4(b), in serial data analysis, three positions on the trace are tracked. Amplitude of each position is used to construct a histogram. Standard devi- ation is obtained by fitting the histogram with a normal function and then represented as percentage error (= standard deviation / amplitude mean). As shown in Fig 3.4 (b) and (d), the percentage error at 115 GHz and 230 GHz differs significantly. At 115 GHz, percentage error stays below 5 % at all attenuation levels. While at 230 GHz, percentage errors of> 5 % are obtained at most attenuation levels and a percentage error of 50 % is observed at10 dB. Therefore, based on jitter and serial data analysis results, 115 GHz operating mode achieves a higher power stability than 230 GHz operating mode. 3.3 Implementation of shaped pulses 3.3.1 Phase-modulated chirped pulses With the IQ modulator, pure amplitude modulation (AM), pure phase modulation (PM, which is closely related to frequency modulation (FM)), or combined amplitude and 47 phase modulation can be generated. 54 During IQ modulation, IQ modulator modu- lates both I and Q signals and adds them together, and any arbitrary output ampli- tude and phase can be selected. Mathematically, before addition,i(t) = I cos(2f 0 t), q(t) = Q sin(2f 0 t). After addition, the output of mixer is y(t) = i(t) + q(t) = p I 2 +Q 2 cos(2f 0 t +(t)), where f 0 is the carrier frequency and phase (t) = tan 1 (Q=I). In this study, to generate phase-modulated chirped pulses (where the fre- quency changes linearly with respect to time and pulse magnitude is constant), IQ mixer is utilized to mix carrier waveform with I and Q components generated by AWG. The amplitude of I and Q components are carefully designed to assure the magnitude of pulse is constant and the first derivative of phase (= frequency) has a linear dependence of time at the same time. In general, the phase profile(t) of a linear chirp pulse with arbitrary offsetw offset with respect to the carrier frequency is, (t) = ((w offset w 2 )t + kt 2 2 ); (3.1) where w is the bandwidth of the chirp pulse with half frequency below carrier fre- quency and another half above carrier frequency,k is the chirp sweep rate andt is the time. By taking the first derivative of (t) with respect to time t, frequency w(t) is obtained accordingly, w(t) = d(t) dt =w offset w 2 +kt One thing to note is that in the linear chirped pulse, the pulse amplitude is constant. Therefore, ideally the nonlinear response of the MC should not have an effect on the generation of chirped pulse. Figure 3.5 summarizes the typical linear chirped pulse ob- tained in our HF EPR spectrometer. To generate the phase-modulated chirped pulse, 48 Frequency (MHz) Intensity 0 60 20 40 80 100 120 0 10 20 30 Intensity (b) Figure 3.5: (a) Typical linear chirped pulse trace captured by oscilloscope at 230 GHz. The pulse length is 1s, and the frequency sweeping range is 5 MHz to 10 MHz. (b) FFT of Q component, which clearly shows the pronounced frequency component in the range of 5MHz to 10 MHz as indicated by the inset, where blue solid lines are FFT from experimental data and red solid line indicates the frequency range of 5 MHz to 10 MHz. the pulse is designed to have a 5 MHz bandwidth with 5 MHz frequency offset, and pulse length is 1s. Therefore, chirp sweep rate is 5 MHz/s, and the frequency of chirped pulse should increase linearly from 5 MHz to 10 MHz within 1s. Figure 3.5 (a) shows the I and Q components captured by oscilloscope at 230 GHz based on the designed pulse. Clearly, the pulse is 1s and frequency increases over sweeping time. Magnitude of the pulse stays relatively stable with small variation observed. To under- stand this pulse, spectrum is obtained by Fast Fourier transforming (FFT) of the pulse. As shown in Fig. 3.5(b), the spectrum clearly displays the frequency components in the range of 5-10 MHz although the intensity of each frequency component varies, which agrees reasonably well the expected spectrum. Therefore, this experiment confirms that the phase-modulated shaped pulse can be successfully generated based on the current configuration. 49 (a) (c) (b) (d) Spin echo intensity Spin echo intensity Ref CP Ref HP Frequency (GHz) 114.96 114.98 115.00 115.02 Frequency (GHz) 114.96 114.98 115.00 115.02 Frequency (GHz) 114.96 114.98 115.00 115.02 Spin echo intensity 1.0 0.8 0.6 0.4 0.2 Spin echo intensity 1.0 0.8 0.6 0.4 0.2 Frequency (GHz) 114.96 114.98 115.00 115.02 Inv Exp. Inv Sim. Inv Exp. Inv Sim. Figure 3.6: Summary of one application of chirped pulse in hole-burning ex- periments. (a) The hole buring experiment based on BDPA free radical samples at 115 GHz. The pulse sequence is -T - - -=2 - - echo, where first pulse can be realized by utilizing either conventional rectangular pulse or linear chirped pulse. T is time decay before applying regular spin echo sequence to detect the inversion efficiency. The blue spectrum is the echo detected magnetic resonance (EDMR) without the initial pulse (Ref), and black spectrum is ob- tained with an initial pulse realized by a linear chirped pulse (CP). Linear chirped pulse is generated with 3 us length and 10 MHz bandwidth. (b) Inver- sion profile obtained by normalizing the signal (CP) with the reference (Ref), and simulated inversion profile based on spin dynamics agrees reasonably well with the experimental data. (c) Hole burning experiment based on BDPA free radical samples. The blue spectrum is the echo detected magnetic resonance without the initial pulse (Ref), and black spectrum is the one obtained using a 3-s conventional rectangular hard pulse (HP). (d) Inversion profile obtained by normalizing the signal (HP) with the reference (Ref), and simulated inversion profile based on spin dynamics agrees reasonably well with the experimental data. 50 Next, to demonstrate the advantage of chirped pulse compared with conven- tional rectangular pulse, a series of hold-burning experiments are conducted on 1,3- bisdiphenylene-2-phenyl-allyl (BDPA) sample. BDPA sample (1% weight concentra- tion, preparation procedures can be found in 4.2.1) was placed in a Teflon sample holder (5 mm diameter) with a typical weight being 5 mg. 29 In a hold-burning experiment, an initial pulse (either chirped pulse or conventional rectangular pulse) is applied to invert spin population before detected by SE. When a chirped pulse is used initially (Figure 3.6 (a)), the spin population inversion profile is much wider and deeper than that created by conventional rectangular pulse (Figure 3.6 (b)). Figure 3.6 (c) and (d) include the sim- ulated inversion profiles based on spin dynamics. Therefore, these experiments clearly support that much wider and higher efficient excitation profile can be obtained by using chirped pulse. 3.3.2 Amplitude-modulated pulses Next, generation of amplitude-modulated pulse is discussed. Amplitude-modulated pulse is the simplest pulse modulation conceptually, where the modulation signal with any kind of form (f(x)) modulates the carrier signal and outputs amplitude-modulated carrier signal. However, due to the nonlinearity of MC in the EPR spectrometer, amplitude-modulated pulse is much harder to obtain than linear chirped pulse experi- mentally. As shown in Fig. 3.3, if the MW sent to EPR spectrometer has a high power, MC is easily saturated and results in a distorted pulse shape. For instance, a Gaussian shape pulse is expected but a large plateau is observed in the output due to power sat- uration (Figure 3.7(a)). On the other hand, if the power is too small, correct Gaussian shape can be obtained but with a sacrifice of pulse amplitude. To deal with this issue, 51 Figure 3.7: Summary of generation of amplitude-modulated pulse at 230 GHz. (a) A amplitude-modulated pulse captured by oscilloscope without feedback correction. Pulse parameters: I and Q with amplitude range of 0.01-0.04 V , Gaussian width is 500 ns. (b) A amplitude-modulated pulse captured by oscil- loscope based on feedback loop control. The modulating signal is a Gaussian shape with 1s width. x axis is the time ins and y axis is the amplitude in the V . The black solid line is the I component, green solid line is the Q component of the pulse and blue solid line is the magnitude. (c) Diagram of feedback loop control. A custom Labview program is developed to store the pulse captured by oscilloscope and utilized as feedback, and evaluate the captured pulse with the expected pulse. New I and Q files will be generated if the current captured pulse did not meet the criteria. The criteria is defined as: error = P N i=1 jy 0 i y i j > threshold = 0.1, where y 0 i and y i are the amplitude of expected pulse and observed pulse at each time point respectively. The whole processes will repeat until the criteria is met. 52 (a) (b) Time (ms) 0 2 4 6 8 10 Amplitude (V) -0.10 -0.05 0.00 0.05 0.10 Amplitude (mV) 0 2 4 6 Frequency (MHz) 0 2 4 6 8 10 Figure 3.8: Simulation of amplitude modulation with arbitrary frequency off- set. (a) A Gaussian pulse multiply by a cos modulating pulse. x axis is the time ins and y axis is the amplitude in V . In the simulation, Gaussian pulse has a width of 500 ns, an amplitude of 0.1 V and a modulating frequency of 5 MHz. (b) Fourier transform of pulse in (a). x axis is the frequency in MHz and y axis is the amplitude in mV . feedback loop control would be the optimal approach, and expected pulse will be ob- tained by iteratively correcting input based on the output from EPR spectrometer until predefined criteria is satisfied. Figure 3.7(c) shows the feedback loop control diagram implemented in this study. A custom Labview program is developed to store the pulse captured by oscilloscope and utilized as feedback, and evaluate the captured pulse with the expected pulse. New I and Q files will be generated if the current captured pulse did not meet the criteria. The whole processes will repeat until the criteria is met. Figure 3.7(b) shows the typical Gaussian pulse obtained at 230 GHz by employing feedback loop control. And any amplitude-shaped pulse can be obtained with the arbitrary starting trail function by using feedback loop control. On the other hand, amplitude-modulated pulse should be obtained with certain fre- quency offset in the current configuration. Based on the property of Fourier transform, to obtain a frequency shift of any real number w offset , the carrier signal in the time 53 domain should multiply a modulating signal with modulation frequency the same as w offset , namely, if f(t) =f(t) cos(2w offset t) then, F (w) =F (ww offset ) As shown in Fig. 3.8, by multiplying a cos modulating pulse with 5 MHz modulation frequency, the spectrum after Fourier transform clearly shows the 5 MHz frequency shift as expected. 3.4 Summary In summary, shaped pulses including both phase-modulated linear chirp pulse and am- plitude modulated pulse have been successfully generated in our HF EPR spectrometer at USC. 54 Chapter 4: ELDOR-detected NMR Spectroscopy In this chapter, we discuss the thorough investigation of HF EDNMR spectroscopy. We show that by carefully adjusting experimental settings, high quality EDNMR spectrum of spin system with weak hyperfine couplings can be obtained on our resonator-free 115 GHz / 230 GHz EPR spectrometer at USC. The EDNMR spectroscopy performance was tested on 1,3-bisdiphenylene-2-phenyl-allyl (BDPA) free radicals diluted in polystyrene (PS) solid matrix. Typical NMR signals from BDPA are observed. In order to ex- plain the signal, we employ a more fundamental density operator treatment to simulate EDNMR intensity. We show that by introducing dissipator operator in the equation of motion to account for both population and phase relaxations, simulated EDNMR spectra agree reasonably well with experimental data. And this simulation method can be easily extended to spin systems more than two levels. We directly compare HF EDNMR and HF ENDOR techniques by collecting NMR spectra on the same BDPA sample, and it shows that EDNMR spectrum indeed gives less distorted NMR spectrum. This chapter is organized in the following order: In the section of Fundamental of EDNMR and EN- DOR, the fundamentals of EDNMR and ENDOR spectroscopes are explained using a simple spin system consisting of electron spin 1/2 coupling to a nuclear spin 1/2 with an isotropicg value and anisotropic hyperfine couplings. BDPA sample preparation and 55 115 GHz / 230 GHz EPR/EDNMR spectrometer are described in the section of Mate- rials and methods. In the Results and discussion section, EPR of BDPA is discussed before presenting EDNMR spectrum obtained and how EDNMR spectrum responded to different experimental settings. Finally, comparison between EDNMR and ENDOR spectra of the same BDPA sample is discussed explicitly. 4.1 Fundamentals of EDNMR and ENDOR 4.1.1 EDNMR Here, we consider an electron spin 1/2 system coupling to a nuclear spin 1/2 with an isotropicg value and anisotropic hyperfine couplings A. The Hamiltonian of the system is given by, ^ H 0 = e ^ S z + n ^ I z +A ^ S z ^ I z +B ^ S z ^ I x : (4.1) where e = e B 0 is the electron Larmor frequency, n = n B 0 is the nuclear Larmor frequency andB 0 is the external magnetic field. A = A k cos 2 +A ? sin 2 andB = (A k A ? ) cos sin, whereA k andA ? are components of an axial symmetric hyperfine tensor and is the angle between the direction ofA k and B 0 . Figure 4.1 (a) displays the energy diagram of the system described by Eqn. (4.1) with a weak hyperfine coupling wherejAj <j2 n j. There are six possible transitions: two NMR allowed transitions NMR() and NMR() ( M I =1; M S = 0), two EPR allowed transitions EPR(a) and EPR(d) (M S =1; M I = 0) and two EPR forbidden transitions DQ (b) and ZQ (c) (M I =1; M S =1). Resonance frequencies associated with the system described by Eqn. (4.1) are, 56 |A|<2|ν N |, weak coupling limit |αβ>=|4> |αα>=|3> |ββ>=|2> |βα>=|1> EPR (d) NMR (β) NMR (α) EPR (a) DQ (b) ZQ (c) Energy HTA Pump (v 2 ) Probe (v 1 ) (a) Detection (b) Figure 4.1: (a) Energy levels for an electron spin 1/2 coupling to nuclear spin 1/2 system with the weak coupling wherejAj <j2 n j. There are four energy levels and six possible transitions associated with the system. (b) EDNMR pulse sequence. EDNMR technique consists of two pulse sequences: high turning an- gle (HTA) pump pulse with sweeping frequency 2 applied to inver populations on a EPR forbidden transition, which reduces the population difference on the corresponding EPR allowed transition and detected with fixed 1 . NMR() : = r ( n + A 2 ) 2 + B 2 4 ; (4.2) NMR() : = r ( n + A 2 ) 2 + B 2 4 ; (4.3) EPR(a) : a = e 1 2 ( ); (4.4) EPR(d) : d = e + 1 2 ( ); (4.5) DQ(b) : b = e 1 2 ( + ); (4.6) ZQ(c) : c = e + 1 2 ( + ): (4.7) 57 WhenMW excitation ( ^ H MW / e B 1 ^ S x = ^ S x ) is applied for a transition between an initial statejii and final statejfi, the transition probability (I if =jhfj ^ H MW jiij 2 ) for the present system is given by, 153 I a;d = j 2 n 1 4 ( ) 2 j ; (4.8) I b;c = j 2 n 1 4 ( + ) 2 j : (4.9) As shown in Eqn. (4.8), the EPR transition probability (I a;d ) is approximately 1 for a small hyperfine coupling. Based on the Eqn. (4.9), I b;c increases linearly with the square of hyperfine anisotropyB 2 . As indicated by the definition ofB, when = 0 or = 90 , B = 0, and when hyperfine couplings are isotropic (A k = A ? ), B = 0. It is easy to verify thatB = 0 leads toI b;c = 0. In addition, maximumI b;c is obtained at exactly cancellation condition whenjAj =j2 n j. Furthermore, forS > 1=2 system, when there are other interactions exist, such as nuclear quadrupole interaction, zero field interaction, they are unlikely to have the same interaction axes and tend to mix nuclear Zeeman states and increase transition probability. Next, we discuss a simulation of EDNMR spectrum. As shown in Fig. 4.1 (b), an EDNMR pulse sequence consists of a high turning angle (HTA) pulse at a frequency of 2 to excite an EPR forbidden transition and a probe pulse sequence at a frequency of 1 to measure a population change on an EPR transition induced by the HTA pulse. Measurements of free-induction decay (FID) and spin echo (SE) are often used for the probe. EDNMR experiment is often performed by sweeping the HTA frequency ( 2 ) while the EPR frequency ( 1 ) is fixed. Now, we consider the time evolution of the states using the following, @ ^ (t) @t =i [ ^ H; ^ (t)] + ^ ^ R ^ (t); (4.10) 58 where H is the total Hamiltonian at a frame rotating at a frequency of !, namely, ^ H = ^ U( ^ H 0 + ^ H MW ) ^ U 1 !S z , ^ H MW = e B 1 ^ Scos(!t). ^ ^ R is a dissipation super- operator representing spin relaxations. Similarly to the Bloch equation for a two-level system, 18, 187 we introduce the population (T 1 ) and phase (T 2 ) relaxations in the present system, namely, ^ ^ R is given by, ^ ^ R ^ (t) = 0 B B B B B B B B B B @ C 2 12 12 2 13 13 2 14 14 2 21 21 D 2 23 23 2 24 24 2 31 31 2 32 32 E 2 34 34 2 41 41 2 42 42 2 43 43 F 1 C C C C C C C C C C A ; (4.11) where C =(1=4) 1 13 (( 11 33 ) ( eq 11 eq 33 )) + (1=4) 1 14 (( 11 44 ) ( eq 11 eq 44 )) + (1=4) 1 12 (( 11 22 ) ( eq 11 eq 22 )) D =(1=4) 1 24 (( 22 44 ) ( eq 22 eq 44 )) + (1=4) 1 23 (( 22 33 ) ( eq 22 eq 33 )) + (1=4) 1 21 (( 11 22 ) ( eq 11 eq 22 )) E =(1=4) 1 31 (( 11 33 ) ( eq 11 eq 33 )) + (1=4) 1 32 (( 22 33 ) ( eq 22 eq 33 )) + (1=4) 1 34 (( 33 44 ) ( eq 33 eq 44 )) F =(1=4) 1 42 (( 22 44 ) ( eq 22 eq 44 )) + (1=4) 1 41 (( 11 44 ) ( eq 11 eq 44 )) + (1=4) 1 43 (( 33 44 ) ( eq 33 eq 44 )) 1 ij = 1=T 1;ij ( 2 ij = 1=T 2;ij ) denotes population relaxation rate associating with tran- sition betweenjii andjji and 1 ij = 1 ji (denotes transverse relaxation rate associating 59 with transition betweenjii andjji and 2 ij = 2 ji ). The definition ofjii is shown in Fig. 4.1 (a). ij =jiihjj denotes element in the density matrix. The thermal equilibrium density operator ( ^ eq ) is given by, ^ eq = e (h ^ H 0 =(k B T )) Tr(e (h ^ H 0 =(k B T ))) ; (4.12) whereh is Planck constant, k B is Boltzmann constant andT is temperature in Kelvin (K). After calculating evolution of the density matrix using Eqn. (4.10), the population is calculated using P j =hjj^ (t=t HTA ) jji. Then, the EDNMR intensity is obtained by calculating a population change on an EPR transition. For instance, when HTA pulse is pumped on transition connectingj1i andj4i and detected on transition betweenj2i and j4i, the EDNMR intensity is then given by, I EDNMR ( 2 ) = 1 (P 2 ( 2 )P 4 ( 2 ))=(P eq 2 P eq 4 ): (4.13) In addition, for powder sample, EDNMR spectrum is calculated by summing all orien- tations, I powder EDNMR = Z 0 Z 2 0 I EDNMR sin()dd: (4.14) Figure 4.2 shows an example of EDNMR spectrum. As shown in Fig. 4.2 (a), MW excitation is applied to excite the forbidden transition betweenj1i andj4i. With the ap- plication of the HTA pulse, the populations ofj1i andj4i change gradually and then goes to an equilibrium state by saturating the transition. On the other hand, changes onj2i andj3i are very small. The calculated EDNMR intensity is shown in Fig. 4.2 (a). And as expected, stronger B 1 will increase the EDNMR intensity achieved. As discussed, the EDNMR intensity depends on population inversion induced by HTA pulse. The flip angle f depends on experimental parameters and spin properties including HTA pulse 60 (d) (b) (c) (a) Frequency offset (MHz) 0 -15 15 δw = 6.66 Population 0.252 0.248 0.250 I_EDNMR 1.0 0.0 0.5 t HTA (μs) 100 200 0 B 1 =0.1 mT B 1 =0.03 mT B 1 =0.005 mT P 1 P 2 P 3 P 4 I_EDNMR 1.0 0.0 0.5 t HTA (μs) 100 200 0 Population 0.252 0.248 0.250 I_EDNMR 1.0 0.0 0.5 t HTA (μs) 100 200 0 Population 0.252 0.248 0.250 1.0 0.5 0.0 t HTA (ms) Figure 4.2: (a) Simulated EDNMR intensity whenMW frequency is resonant with transition connectingj1i andj4i with HTA pulse strengthB 1 = 0.03 mT. The inset at top right shows the Population evolution curves ofj1i toj4i in- dicated by black solid line, red solid line, blue solid line and green solid line respectively. The inset at bottom right shows the Population evolution curves ofj1i toj4i from 0 to 200 s. (b) Simulated EDNMR intensity when MW frequency is resonant with transition connectingj1i andj4i with HTA pulse strengthB 1 = 0.01 mT. The inset shows the Population evolution curves of four states. (c) Simulated EDNMR intensity whenMW frequency is resonant with transition connectingj1i andj4i with HTA pulse strength B 1 = 0.1 mT. The inset at top right shows the Population evolution curves ofj1i toj4i indicated by black solid line, red solid line, blue solid line and green solid line respec- tively. The inset at bottom right shows the Population evolution curves ofj1i to j4i from 0 to 200s. Simulation parameters:g e = 2.0025,g n = -5.590,A = 27.5 MHz,B = 22.5 MHz,B 0 = 4.0 T,T 2 = 10s,T 1 = 1 ms, T = 300 K. The simula- tion is done with the assumption that all EPR allowed and forbidden transitions have same relaxation timeT 2 and noT 1 relaxation for EPR forbidden transition. There are no relaxations associate with NMR transitions. (d) Central blind spot linewidth with different HTA amplitude. x axis is the frequency offset in MHz. Experiment parameters are:t HTA = 800s, 2 = 250 ns, = 350 ns, = 1.2s, repetition time = 20 ms, T = 200 K, data were taken with 64 shots and 5 scans. 61 lengtht HTA , transition probabilityI f , HTA pulse amplitude , off resonance s ,T 1 and T 2 . can be determined by the full width at half maximum (FWHM)w of the signal at 1 2 = 0 (called central blind spot). By considering the application of a rectangular MW pulse with lengtht p can be modeled as a unitary operator, ^ R(t p ) = exp(i ^ Ht p ): (4.15) For a typical EDNMR experiment with long HTA pulse, the lineshape of the central blind spot is then calculated by time averaging of the population inversion probability f(t p ), 124 L( s ) = 1 t HTA Z t HTA 0 f(t p )dt p ; (4.16) where s =! e . By considering application of a rectangular MW pulse with length t p and a two-level system with no spin relaxation, the population inversion function is given by, f = ( R ) 2 sin 2 ( R t p 2 ); (4.17) where R = p 2 s + 2 . Using Eqn. 4.16 and Eqn. 4.17, the lineshape of the central blind spot is therefore given by, L( s ) = ( R ) 2 = 2 2 + 2 s : (4.18) w is therefore independent oft HTA but only the amplitude . By performing EDNMR with HTA pulse frequency sweeping though detection frequency, one can obtainw and therefore at the sample space. Figure 4.2 (d) shows thatw increased from 3.42 MHz to 6.66 MHz by adjusting MW power of HTA pulse. Here, we discuss those parameter dependence using simulation results with Eqn. (4.10). Transition probabilityI f andT 2 62 dominate the flip angle achieved. LargeI f gives larger EDNMR intensity and negligible EDNMR intensity will be ifI f is close to zero. The same argument is applied toT 2 in the case whenT 1 is much longer thanT 2 . Due to either small transition probability or short relaxation time, exponential decay with non-periodic signal will be observed. Spin nutation can be observed only when relaxation rate 1/T 2 is smaller than . Empirically, I EDNMR can also be fitted by the following analytical expression: 124 I EDNMR =K [1 cos(2 t HTA p I f )e t HTA T 2 ]; (4.19) where K is the maximum EDNMR intensity. Optimal pulse length can be found by performing spin nutation experiment when the above condition is satisfied. On the other hand,T 2 not only affects EDNMR intensity, but also determines the intrinsic EDNMR linewidth. Usually NMR transitions have much longerT 2 than the corresponding EPR transitions. A given NMR response therefore has much narrower distribution than EPR response. 4.1.2 Comparison with ENDOR Another well-known EPR based hyperfine spectroscopy is ENDOR, and one of widely used pulsed ENDORs-Davies ENDOR 37 is discussed here based on a simple four-level spin system (Figure. 4.3(a)). Davies ENDOR pulse sequence consists of both MW and RF pulses (Figure. 4.3(b)). Initially, a selective MW pulse (t p ) with fixed frequency 0 applied on resonance with one of EPR allowed transitions, e.g.j1i toj3i, to invert electron spin polarization. The inverted electron spin polarization can potentially be 63 |A|<2|n N |, weak coupling limit |ab>=|4> |aa>=|3> |bb>=|2> |ba>=|1> EPR (d) NMR (b) NMR (a) EPR (a) DQ (b) ZQ (c) Energy (a) (b) t t p/2 p MW (v 0 ) RF(v) t R t p Figure 4.3: (a) Energy levels for an electron spin 1/2 coupling to nuclear spin 1/2 system with the weak coupling wherejAj < j2 n j. There are four en- ergy levels and six possible transitions associated with the system. (b) Davies- ENDOR pulse sequence. ENDOR technique consists of two pulse sequences: an initial MW pulse (t p ) with fixed frequency 0 applied to invert electron spin population, and an RF pulse (t R ) with sweeping frequency is applied to recover spin population along EPR allowed transition before detected through spin echo pulse sequence. In the pulse sequence, all parameters are fixed except . recovered if the selective long RF pulse transfers the corresponding nuclear spin polar- ization, e.g. NMR(). The final electron spin polarization is then detected by applying spin echo pulse sequence. The pros and cons are listed in Chap. 1. 4.2 Materials and methods 4.2.1 BDPA sample BDPA is a stable free radical, which forms a 1:1 complex with benzene. In the present experiment, we used several concentrations of BDPA samples (0.01, 0.20, 0.67 and 1.00 wt. %). For example, to prepare BDPA sample with 0.01 wt. %, 0.03 mg 64 BDPA complex with benzene (1:1) free radical (Sigma-Aldrich) was dissolved into 5 ml toluene (OmniSolv), and then 199.46 mg polystyrene (PS) (Alfa Aesar, MW 13,000) was added. The mixture had been stirred until it became pastry (e.g. one day). After stirring, the mixture was placed on a glass slide and dried in a fume hood ( 2 days). 4.2.2 HF EPR/EDNMR spectroscopy HF EPR and EDNMR experiments were performed using a home-built system at USC. The system employs a high frequency high-power solid-state source consisting of two MW synthesizers, which provides the capabilities to perform double resonance experi- ments. For EDNMR measurement, a variable attenuator is implemented to control the power of the second HF microwave. Details of the system have been described else- where. 29, 30 In the present study, to obtain continuous-wave (cw) EPR spectra of BDPA, the BDPA sample was placed in a Teflon sample holder (5 mm diameter), with a typical weight being 5 mg. 4.2.3 HF ENDOR spectroscopy 130 GHz Davis ENDOR experiments are conducted at UC Davis. Details of the ENDOR system are described elsewhere. 132 4.3 Results and discussion Here we discuss EDNMR spectroscopy of BDPA in polystyrene. The inset of Fig. 4.4 (a) shows the molecular structure of BDPA. Two fluorenyl and phenyl moiety are arranged in a propeller shape. Approximately a half of the -spin density is distributed on the allyl group and another half on the 2,2 0 -biphenylydiyl group. 7 There are two sets of 65 Intensity (arb.u.) Magnetic field (mT) ~1 mT (a) 4100 4102 4104 4106 Fit T 2 =1.88 ± 0.03 ms T (ms) 0.0 (b) (d) Echo intensity (arb.u) 2t (ms) 5.0 10.0 15.0 20.0 Echo intensity (arb.u) T 1 =3.30 ± 0.08 ms 25.0 50.0 Exp. Fit Exp. T 2 (ns) 900 1200 (c) Weight concentration (%) 0.0 0.5 1.0 600 2 3 4 2 3 4 1' 2' 3' 4' 2' 3' 4' 1 1'1 BDPA Temp (K) 100 200 300 T 2 (ms) 2.0 1.5 1.0 Temp (K) 100 200 300 T 1 (ms) 3.6 2.4 1.2 0.0 Figure 4.4: (a) cw spectrum of BDPA in polystyrene with 0.01 wt. %. The inset shows the molecular structure of BDPA. Experimental data was taken with the following conditions: F = 115 GHz, modulation field = 0.002 mT, modu- lation frequency = 20 kHz, room temperature. Two vertical black dashed lines mark the peak-peak linewidth1 mT in the cw spectrum. (b)T 2 measurement. In the main figure, transient signal of spin echo decay is indicated by green solid line while the fitting is indicated by red dashed line. The inset shows temperature dependence ofT 2 . (c)T 2 as a function of BDPA concentration in polystyrene. x axis is weight concentration in %, y axis isT 2 in ns. The data was taken at room temperature. (d) T 1 measurement. The inset shows the T 1 values as a function of temperature in K. The experimental data is fitted by a single exponential function. Experiment parameters are:=2 = 250 ns, = 350 ns, = 650 ns, repetition time = 20 ms. hyperfine couplings to protons. Eight protons at 1,1 0 and 3,3 0 sites give larger hyperfine couplings in MHz: A x1 = 7.7,A y1 = 5.3,A z1 = 2.0. Another eight protons at 2, 2 0 and 4,4 0 sites give smaller hyperfine couplings in MHz: A x2 = 1.0,A y2 = 1.0, A z2 = 1.26. It also shows that the g-factor is slightly anisotropic: g x = 2.00262, g y = 2.00260, g z = 2.00257. 13 Figure 4.4 (a) shows cw EPR of 0.01 wt. % BDPA sample. Due to the hyperfine splitting and the anisotropicg-factor, cw EPR spectrum is a single peak with 1 mT peak-peak linewidth, in which the hyperfine splitting was not resolved. We next 66 measured the spin relaxation times (T 1 and T 2 ) for EDNMR experiment. Figure 4.4 (b) shows spin echo (SE) signal of 0.01 wt. % BDPA sample. The measurement was performed at 100 K. By fitting the SE decay with a single exponential function, we obtainedT 2 to be 1.88 0.03s. TheT 2 experiment was also performed at 250 K and room temperature. As shown in the inset of Fig. 4.4 (b),T 2 are 1-2s in the measured temperature range. Figure 4.4 (c) shows the BDPA concentration dependence onT 2 . We found thatT 2 increases when the concentration decreases and the linear relation between 1=T 2 and spin concentration is discussed in Chap. 2. Figure 4.4 (d) shows a result ofT 1 measurement of the 0.01 wt. % BDPA sample. The measurement was performed using the inversion recovery sequence. As shown in the inset of Fig. 4.4 (d), T 1 10 s at room temperature, and we obtainedT 1 = 3.30 0.08 ms at 100 K. Next, we set the magnetic field at center of EPR of BDPA (B 0 = 4102.95 mT) to perform EDNMR experiment. Figure 4.5 shows EDNMR experiment of 0.01 wt. % BDPA performed at 250 K where we observed the signal in the range between 168 MHz and 182 MHz. To explain the experimental result, we performed simulation using Eqn.(4.10). In the simulation, we used measuredT 1 andT 2 values for the EPR transi- tion. For forbidden transitions, we assumed thatT 2 is same as that of the EPR transition and 1/T 1 = 0. No relaxations was considered for the NMR transitions. As shown in Fig.4.5, simulated EDNMR spectrum from protons in BDPA molecules matches the ob- served power pattern. Two peaks centered at 172.2 MHz and 177.4 MHz represent the contribution from the larger set of the hyperfine couplings (A 1 ), and two peaks centered at 174.1 MHz and 175.2 MHz represent the contribution from the smaller set of the hy- perfine couplings (A 2 ). The broadening of each peak is due to the hyperfine anisotropy. For instance, the protons withA 1 give 5 MHz splitting while the protons withA 2 give 1.5 MHz splitting in the EDNMR spectrum. Because of a wide excitation bandwidth 67 Figure 4.5: EDNMR spectrum of BDPA. The x axis is frequency offset in MHz and y axis is the EDNMR intensity (normalized spin echo intensity). The blue solid line represents experimental spectrum. Red dashed line denotes simulated EDNMR spectrum with contributions from protons on the BDPA molecules (cyan solid line) and matrix protons (light gray solid line). Experimental data was taken with the following conditions:t HTA = 500s, = 3.33 MHz,=2 = 250 ns, = 350 ns, = 650 ns, repetition time = 20 ms, T = 250 K, 128 shots and 3 scans. Simulation parameters of BDPA:g x = 2.00262,g y = 2.00260,g z = 2.00257; two sets of hyperfine couplings are used in MHz: A x1 = 1.0,A y1 = 1.0,A z1 = 1.26;A x2 = 7.7,A y2 = 5.3,A z2 = 2.0;T 2 = 1.87s,T 1 = 700s, T = 250 K. The matrix signal is simulated by a single Gaussian line (width = 500 kHz) and intensity is adjusted to match the observed intensity. of 8 MHz, BDPA with a various orientations contributed to the EDNMR spectrum re- sulting in powder pattern of the spectrum. EDNMR spectra obtained at different EPR positions were virtually identical. On the other hand, there is also contribution from matrix protons centered at the nuclear Larmor frequency. Although the hyperfine cou- plings are very small compared with the coupling strength from protons in the BDPA molecules, the large number of matrix protons could give observable contribution. 6, 195 The matrix signal is simulated by a single Gaussian line with fixed frequency distribu- tion and intensity is adjusted to match the observed intensity. Overall, by considering 68 the contribution from protons both in the BDPA molecules and matrix, the simulated EDNMR spectrum agrees well with the experiment data. To obtain high quality EDNMR spectrum, there are two main experimental param- eters need to be optimized: (1) pulse efficiency: the optimal combination of HTA pulse lengtht HTA and amplitude ; (2) excitation bandwidth in the detection scheme. Next, we demonstrate how those experimental parameters affect EDNMR intensity using 1.00 wt. % BDPA sample. 4.3.1 Pulse efficiency As described in the fundamentals section, HTA pulse length and amplitude significantly affect the effective flip angle can be achieved, and the combination should to be opti- mized. Since central blind spot lineshape depends only on amplitude when a very long HTA pulse is applied, to avoid the derivation of the central blind spot from Lorentzian lineshape,t HTA should be long enough. EDNMR peak linewidth is scaled by p I f , and linewidth can be narrower than central blind spot. To be able to apply longt HTA and reduce the relaxation effect coming from delay between pump and probe pulse due to instrumentation limitation, relaxation timeT 1 should be long enough. With the inver- sion recovery measurements, T 1 = 245 2s at 250 K andT 1 = 521 16s at 200 K, whereT 2 relaxation times were similar. t HTA dependence on EDNMR intensity dis- cussed in the fundamental section is confirmed by the experimental spectra. Whent HTA varied from 10s to 800s, the EDNMR intensity kept increasing, and then stayed the same after approaching maximum intensity. Due to small transition probability, t HTA should be long enough to be able to detect signal above noise level at a fixedMW am- plitude. As shown in Fig. 4.6 (b), witht HTA = 10s, very tiny signal was detected. On the other hand, whent HTA was fixed, large enhanced EDNMR intensity significantly. 69 Figure 4.6: (a) EDNMR intensity versus temperature. The EDNMR spectra were taken at 200 K (top) and 250 K (bottom). Other experimental parameters: t HTA = 500s, = 3.33 MHz,=2 = 250 ns, = 350 ns, = 1.2s, repetition time = 20 ms, 64 shots and 3 scans. (b) EDNMR intensity versust HTA . From bottom to top, EDNMR spectra were taken witht HTA = 10s,t HTA = 100s, t HTA = 500s andt HTA = 800s, respectively. Other experimental parameters: T = 200 K, = 3.33 MHz,=2 = 250 ns, = 350 ns, = 1.2s, repetition time = 20 ms, 64 shots and 3 scans. (c) EDNMR intensity versus HTA amplitude . The EDNMR spectrum were taken at = 3.33 MHz (top) and = 2.46 MHz (bottom). Other experimental parameters: T = 200 K, t HTA = 500 s, =2 = 250 ns, = 350 ns, = 1.2s, repetition time = 20 ms, 64 shots and 3 scans. (d) Transient spin echo signal when SE detection scheme is employed. The full integration window is marked by two vertical red dashed lines, which is 1.3 s. (e) Transient FID signal when FID detection scheme is employed. The full integration window is marked out by two vertical red dashed lines, which is 2.5s. (f) EDNMR spectral resolution versus detection methods. Top spectrum was taken by recording full spin echo (1.3s). Bottom spectrum was taken by recording full FID (2.5 s). Experimental parameters are: T = 200 K, t HTA = 500s, = 3.33 MHz,=2 = 3s, repetition time = 20 ms, 64 shots and 3 scans. All simulated spectra with the contribution of matrix signals by adjusting intensity to match the observed intensity. 70 Figure 4.6 (c) shows that whenMW amplitude increased from = 2.46 MHz to = 3.33 MHz, approximately 5 times enhancement of EDNMR intensity was achieved. The optimal pulse combination depends on the type of nuclear spins investigated. Maximum pulse efficiency can be obtained for one type of nuclear spin while sacrificing intensity of another type of nuclear spin. 4.3.2 Excitation bandwidth in the detection scheme In EDNMR, orientation selection is governed by the detection sequence. As proposed in the original paper, 151 EDNMR spectrum can be obtained by spin echo and FID. When longT 2 is available, a long soft pulse giving narrow excitation bandwidth is possible to detect signal. Narrow excitation bandwidth in the detection pulse, either the single pulse in the FID or first=2 pulse in SE pulse sequence, potentially narrows down EDNMR spectrum. Spin echo detection method requires long to record full spin echo, usually pulse length is a few hundred of nanoseconds whenT 2 is 1s. However, much longer pulse can be applied using FID detection method with the same relaxation rate. The typical FID transient signal is shown in Fig. 4.6 (e). When a pulse length of 3s pulse length was used, the full FID window extended to the same length as the pulse length. Due to the saturation at the beginning of FID signal, 2:5s window was recorded, which was indicated in the Fig. 4.6 (e). As shown in Fig. 4.6 (f), EDNMR spectrum taken by FID was better resolved than the one taken by spin echo and similar signal sensitivity was observed. When employ FID detection pulse, full FID signal should be recorded to avoid any artifacts. Overall, if sample has longT 2 , FID detection scheme can be employed to obtain finer spectral resolution. 71 Figure 4.7: (a) EDNMR spectrum of 0.01 wt. % BDPA sample. The x axis is frequency offset in MHz and y axis is the EDNMR intensity (normalized spin echo intensity). Experimental data was taken with the following conditions: T = 250 K,t HTA = 500s, = 3.33 MHz, =2 = 250 ns, = 350 ns, = 650 ns, repetition time = 20 ms, 128 shots and 3 scans. Simulation parameters:g x = 2.00262,g y = 2.00260,g z = 2.00257; two sets of hyperfine couplings are used in MHz: A x1 = 1.0, A y1 = 1.0, A z1 = 1.26; A x2 = 7.7, A y2 = 5.3, A z2 = 2.0; T 2 = 1.87s,T 1 = 700s, T = 250 K. (b) 1 H Davis ENDOR spectrum of 0.01 wt. % BDPA sample. x axis is the hyperfine coupling ( RF - H ) in MHz and y axis is the ENDOR intensity with arbitrary unit. Experimental data was taken with the following conditions: T = 100 K,t R = 10s, power = 300 W,t p = 200 ns, =2 = 50 ns, = 100 ns, = 300 ns, repetition time = 20 ms, 100 shots and 80 scans. The simulation detail is described in the main text, and the signal from matrix protons is indicated by black dashed arrow. The inset shows Davis ENDOR pulse sequence which consists of three parts: initial t p preparation pulse creates population inversion, then RF pulset R applied on resonance with NMR transition to recover population, the effectiveness of population recovery is detected by spin echo at the end. 4.3.3 Comparison between EDNMR and ENDOR spectra of BDPA To compare HF EDNMR with HF ENDOR spectroscopes, 130 GHz 1 H ENDOR spec- trum on the BDPA sample with 0.01 wt. % concentration was collected at 100 K. Figure 4.7 (b) shows Davis ENDOR spectrum and a pulse sequence used in the mea- surement. Since spin lattice relaxation timeT 1 on many spin systems is short at room temperature, ENDOR is often performed at low temperature. Long T 1 can allow the application of the long and relative lower power of RF to drive NMR transition and 72 avoid power broadening. As shown in Fig. 4.7 (b), Davis ENDOR spectrum of BDPA clearly shows peaks coming from two sets of hyperfine couplings, which center at 2.6 MHz and 0.8 MHz, respectively. However, two peaks centered at 0.8 MHz exhibit smaller intensity than those centered at 2.6 MHz even they have the same number of protons contributing to the signal. This type of observation is intrinsic to Davis ENDOR technique and is explained by a suppression effect, which demonstrates that ENDOR response reduces dramatically when hyperfine coupling A! 0. 153 EPR spectrum has narrow spectral line width when hyperfine couplings are weak. Almost all EPR tran- sitions will be excited simultaneously if a strong and short MW pulse is employed to invert the population during preparation. Due to the overlapping between central and side holes, polarization transfer by theRF pulse becomes incomplete. Therefore, to fit experimental data, Salt function in Easyspin 169 is employed to compute ENDOR spec- trum and resulted spectrum is convoluted with the following detectability function to account for the suppression effect, 43 ENDOR(A;t p )/ 1:4(At p ) 0:7 2 + (At p ) 2 ; (4.20) WhereA is the hyperfine couplings (- 0 ) in MHz,t p is the duration of the preparation pulse ins. On the other hand, matrix protons also give some unpredictable intensity. In the simulation, a single Gaussian function is used to fit the matrix proton signal. Overall, both EDNMR and ENDOR techniques can be used to collect NMR spectrum of BDPA, and similar hyperfine information can be obtained. However, due to suppression effect and matrix proton signal in ENDOR spectrum, careful analysis should be done to avoid misinterpretation. In a other word, EDNMR technique is more likely to relate to the number of nuclear spins contributing to the observed EDNMR intensity. 73 4.4 Summary In summary, HF EDNMR spectroscopy was systematically explored based on 115 GHz EPR spectrometer and BDPA free radicals, including the optimal experimental settings and data analysis. The work presented in this chapter provides fundamentals for the application of HF EDNMR discussed in the following chapter. 74 Chapter 5: Investigation of Near-Surface Defects of Nanodiamonds by High-Frequency EPR and DFT Calculation Materials presented in this chapter can also be found in the article titled Investigation of near-surface defects of nanodiamonds by high-frequency EPR and DFT calculation by Z. Peng, T. Biktagirov, F. H. Cho, U. Gerstmann and S. Takahashi in Journal of Chemical Physics 150, 134702 (2019). 5.1 Introduction Diamond is a fascinating material, hosting nitrogen-vacancy (NV) defect centers with unique magnetic and optical properties. 71, 200 In recent years, remarkable efforts have been put into studying fundamental quantum physics 26, 49, 60, 75, 173, 190 and realizing appli- cations to fundamental quantum information processing 48, 57, 127, 144, 200 as well as mag- netic field sensing 8, 41, 68, 105, 112, 146, 176 using NV centers in diamond. In NV-based mag- netometry, spins inside diamond crystal (e.g., 13 C, single substitutional nitrogen defect 75 centers, and other paramagnetic impurities) 2, 26, 38, 48, 127 as well as external spins in the vicinity of the surface of the diamond (e.g., paramagnetic defects, radicals, 1 H, Gd 3+ , and Mn 2+ ) 68, 69, 91, 97, 102, 107, 108, 165, 166, 172, 178 have been successfully detected. Difficulties in sensing external spins exist due to undesired spin and optical properties of NV centers (e.g., short spin relaxation times and unstable photoluminescence) when NV centers are located close distance to diamond surface. 147, 178, 179 The origin of the undesirable prop- erties is considered to be related to strain on NV centers and paramagnetic impurities existing near the surface. There have been many reports that suggest the existence of specific paramagnetic impurities near surface of various kinds of diamonds. Electron paramagnetic resonance (EPR) investigation of mechanically crushed diamonds revealedg 2 like signals that are attributed to structural damages near the diamond surface due to crushing process 189 or-radicals. 159 EPR measurements of diamond powders produced by detonation pro- cess consistently have also shown g 2 like signals, 46, 81, 154, 162 which are 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). On the other hand, two separate nuclear magnetic resonance (NMR) studies of detonation diamond powders argue that paramagnetic impurities exist in a thin shell (0.6 nm) near the surface, 51 which is not associated with dangling bonds, or may be homogenously distributed throughout the whole volume of diamond crystal. 46 Finally, studies of shallow NV centers in diamond crystals 108, 128, 147 as well as NV centers found in nanodiamond (ND) crystals 91, 178 have shown that these NV centers exhibit different spin properties (e.g., broader linewidth and faster spin relaxation times) compared to deep, stable NV centers in diamond crys- tals, which are often explained by the existence of dense paramagnetic impurities on the surface of hosting diamonds. 76 In this article, we investigate near-surface defects and impurities in NDs. We em- ploy high-frequency (HF) (230 GHz and 115 GHz) and 9 GHz continuous-wave (cw) and pulsed EPR spectroscopy to study defect and impurity contents in various sizes of diamond crystals. HF EPR spectroscopy is highly advantageous to distinguish param- agnetic centers existing in diamond with high spectral resolution. 230 GHz cw EPR spectra show the presence of two major impurity contents; single substitutional nitrogen impurity (P1 center) which is common in diamond, and paramagnetic impurity unique to NDs (denoted as X spin through this paper). Moreover, particle-size dependence of the EPR intensity ratio between P1 and X spins indicates that X is localized in the vicinity of the diamond surface while P1 center is located in the core. We also observe that the linewidth of X is much broader than that of P1 center, and further line broad- ening of X is visible as the electron Larmor frequency is increased from 9 GHz to 230 GHz. We also study composition of X spin using hyperfine spectroscopy. The technique we employ is electron-electron double resonance-detected nuclear magnetic resonance (EDNMR). EDNMR is one of electron-electron double resonance techniques which ex- cites two different electron spin transitions. 151 Compared with commonly used electron nuclear double resonance (ENDOR) spectroscopy which excites electron and nuclear spin transitions, EDNMR has advantage in the signal sensitivity for a spin system with fast electron spin relaxations. HF EDNMR also enables to achieve a high spectral res- olution comparable to ENDOR. With EDNMR investigation on the X spin where no signature of relevant hyperfine couplings are observed, we confirm that the X spin con- sists of neither hydrogen nor nitrogen atom. Furthermore, we utilize a first principle calculation in the framework of density functional theory (DFT) to identify structures of the X spin. The calculation result shows that a negatively charged vacancy-related defect is candidates of the X spin. 77 5.2 Materials and methods 5.2.1 Diamond samples The investigation was performed with a single crystal (1.51.51.0 mm 3 ) type-Ib high- pressure high-temperature (HPHT) synthetic diamond (Sumitomo Electric Industries), micron-size diamond powders (101m) (Engis Corporation), and eight different sizes of NDs (Engis Corporation and L. M. Van Moppes and Sons SA). The mean diameters and standard deviations of NDs specified by the suppliers are 550 100 nm, 250 80 nm, 16050 nm, 10030 nm, 6020 nm, 5020 nm, and 3010 nm. The 10-m and ND powders were manufactured by mechanical milling or grinding of type-Ib diamond crystals where the concentration of nitrogen related impurities in NDs is in the order of 10 to 100 parts per million (ppm) carbon atoms. 5.2.2 HF EPR/EDNMR spectroscopy HF EPR and EDNMR experiments were performed using a home-built system at USC. The system employs a high-power solid-state source consisting two microwave synthe- sizers (8-10 GHz and 9-11 GHz), pin switches, microwave amplifiers, and frequency multipliers. For EDNMR measurement, a variable attenuator is implemented to control the power of the second HF microwave. The output power of the HF source system is 100 mW at 230 GHz and 700 mW at 115 GHz. The HF microwaves are propagated in free-space using a quasioptical bridge and then couple to a corrugated waveguide. A sample placed on a metallic end-plate at the end of the waveguide, and then placed at the center of a 12.1 T cryogenic-free superconducting magnet. In experiments on ND powders, ND powders (5 mg typically) are placed in a teflon sample holder (5 mm 78 diameter) and the teflon sample holder is placed on the end-plate. 27 EPR signals are isolated from the excitation using an induction mode operation. 160 For EPR/EDNMR experiment, we employ a superheterodyne detection system in which 115 GHz and 230 GHz is down-converted into an intermediate frequency (IF) of 3 GHz, and then again down-converted to in-phase and quadrature components of dc signals. Both in-phase and quadrature signals are recorded to obtain the absorption and dispersion signals of EPR. The microwave phase is adjusted to obtain correct shapes in both absorption and disper- sion data. Further details of the HF EPR/EDNMR system are described elsewhere. 27, 28 In the EPR/EDNMR measurements, the HF microwave power and the magnetic field modulation strength are adjusted carefully to maximize the intensity of EPR signals without distortion of the signals (see Sect. A.1 in Appendix A for the power adjust- ment). Typically modulation amplitude of 0.02 mT at modulation frequency of 20 kHz is used. 5.2.3 X-band EPR spectroscopy X-band continuous-wave (cw) EPR spectroscopy was performed using an EMX system (Bruker Biospin). For each measurement, samples were placed in a quartz capillary (inner diameter: 0.86 mm or 0.64 mm), with a typical sample volume being 1-5 L. cw EPR spectra are obtained with optimum microwave power and magnetic field mod- ulation strength which maximize the amplitude of EPR signals without distorting the lineshape. Typical parameter sets are a modulation amplitude of 0.03 mT and a modu- lation frequency of 100 kHz. 79 5.3 Results and discussion 5.3.1 HF EPR spectroscopy: Detection and characterization of near-surface defects First, we discuss the study of paramagnetic impurity contents in the diamond samples using 230 GHz cw EPR spectroscopy. Figure 5.1(a) shows 230 GHz EPR spectra of the single crystal diamond and 10-m diamond powder samples taken using the HF EPR spectrometer. As shown in Fig. 5.1(a), 230 GHz EPR spectrum of the single crystal diamond shows three pronounced signals from P1 centers. The P1 center hasS = 1=2 and the hyperfine coupling to 14 N nuclear spin (I = 1). The spin Hamiltonian of P1 center is given by, H N = B g N B 0 S N +S N $ A I N +P z (I N z ) 2 ; (5.1) where B is the Bohr magneton,g N = 2:0024 is the isotropicg-value of P1 center,B 0 is the external magnetic field, S N and I N are the electron and nuclear spin operators, respectively. $ A is the anisotropic hyperfine coupling to 14 N nuclear spin (A x;y = 82 MHz andA z = 114 MHz). 103, 173 The nuclear quadrupole couplingP z =4 MHz. 31 As shown in Fig. 5.1(a), EPR spectrum of the single crystal diamond was simulated using the P1 spin Hamiltonian (Eq. (5.1)) and we found a good agreement between the observed EPR signal and the simulated spectrum. In addition, EPR spectrum of the 10- m diamond powder is shown in Fig. 5.1(a). The powder sample contains ensembles of diamond crystals which are randomly oriented with respect toB 0 , therefore all the ori- entations of P1 centers were taken into account to obtain so-called powder spectrum. As 80 550-nm 250-nm 160-nm 100-nm 60-nm 50-nm 30-nm Normalized intensity (arb. units) (b) 550-nm P1 X 100-nm P1 X P1 X (a) Intensity (arb. units) Magnetic field (Tesla) Single crystal diamond 8.200 8.204 8.208 8.212 Exp. Sim. 50-nm Magnetic field (Tesla) 8.200 8.204 8.208 8.212 Magnetic field (Tesla) 8.200 8.204 8.208 8.212 10-μm diamond powder Magnetic field (Tesla) Exp. Sim. 8.200 8.204 8.208 8.212 Figure 5.1: 230 GHz cw EPR spectra of the diamond samples. (a) (Left) (100) single crystal diamond. The external magnetic field (B 0 ) was applied along the h100i axis of the diamond. (Right) Diamond powder with 10-m mean diame- ter. The signal is the so-called powder spectrum of P1 center. (b) EPR spectra of all sizes of NDs. (Left) The experimental and simulated spectra on NDs. (Right) The experimental and simulated EPR spectra on 550-nm, 100-nm and 50-nm NDs. The partial contributions from P1 and X spins are indicated by the red dashed lines. All measurements were performed at room temperature. The EPR spectrum analysis was done by Easyspin. 169 (Reprint figure with permis- sion from Peng et al. 134 Copyright 2020 by the AIP Publishing LLC.) 81 shown in Fig. 5.1(a), the simulated powder spectrum also agrees well with the observed EPR signal. Next, we discuss the size dependence of EPR spectra on the ND samples. Fig- ure 5.1(b) shows 230 GHz EPR spectra of NDs with mean diameters from 550 nm to 30 nm. As shown in Fig. 5.1(b), 230 GHz EPR spectroscopy enabled to resolve two EPR signals in the ND samples; (i) one is EPR signal of P1 centers which was also observed in the single crystal diamond and 10-m powder samples. (ii) the other is the EPR signal at 8.2047 Tesla (denoted as X in Fig. 5.1(b)). As shown in Fig. 5.1(b), the EPR intensities of P1 and X spins largely depend on the size of NDs, i.e. for P1 centers, larger the size of NDs is, stronger the EPR intensity is, and, for X spins, smaller the size of NDs is, stronger the EPR intensity is. We also noticed that the X contribution is well represented by a singleS = 1=2 EPR signal. Therefore, in order to simulate the observed EPR spectra of X spins, we considered the spin Hamiltonian forS = 1=2 with g X = 2:0028. By considering EPR spectra for P1 (Eq. (5.1)) and X spins, we found that the observed EPR data can be explained very well for all investigated ND sizes. We also analyzed the EPR intensity of P1 and X spins. The intensity ratios of P1 and X spins were obtained from the fit of the experimental spectrum to calculated EPR spec- tra of P1 and X spins. In the fit, the intensity and linewidths were fitting-parameters, and their errors (95 % confidence interval) were also obtained from the fit. Figure 5.2 shows the result of cw EPR analysis. The analysis shows that the P1 lineshape is dominated by the Lorentzian contribution. As shown in Fig. 5.2(a), the peak-to-peak linewidth of the Lorentzian lineshape is independent of the size of NDs. As shown in Fig. 5.2(b), the lineshape of the X spins is well explained by the V oigt function. From the analysis, we found that the ratio of the contributions is independent of the ND size and their peak- to-peak linewidths in Lorentzian and Gaussian components are still independent of the 82 P1 center linewidth X spins linewidth Diameter (nm) Diameter (nm) Linewidth (mT) Linewidth (mT) (a) (b) 10 100 -0.5 0.0 0.5 1.0 1.5 2.0 0.2 0.4 0.6 10 100 1000 10000 Diameter (nm) P1 /X Intensity ratio 1 0.1 0.01 100 1000 (c) Surface model Core-shell model Figure 5.2: Size dependence of EPR linewidth and intensity of P1 centers and X spins. (a) Linewidth of P1 centers as a function of the diamond size. Lorentzian linewidth (red diamond) was obtained from the fit. (b) Linewidth of X spins as a function of the diamond size. The V oigt function was used in the fit and the peak-to-peak Lorentzian (red diamond) and Gaussian (blue square) linewidths were obtained. (c) Intensity ratio of P1 centers and X spins as a function of the diamond size. The relative intensity ratio of P1 centers and X spins from 230 GHz EPR is shown by the black solid squares. The green and purple solid circles represents the intensity ratio data obtained from X-band and 115 GHz spectra, respectively. The blue solid curve shows the fit result using a simple surface model (P1=X intensity diameter) while the red solid curve shows the fit result using the core-shell model. Overall, the core-shell model gives a better fit. (Reprint figure with permission from Peng et al. 134 Copyright 2020 by the AIP Publishing LLC.) size of NDs. Furthermore, from the result of the lineshape analysis, we extracted the cw EPR intensity ratio between P1 and X spins. Figure 5.2(c) shows the EPR intensity ratio (I P 1 =I X ) as a function of the size of NDs. Observation of strong size dependence on EPR intensity ratio indicates that X is localized in the vicinity of the surface of ND crystals. In order to explain the size dependence, we consider the core-shell model. In the core-shell model, X spins are located in the spherical shell of thicknesst from the near-surface (i.e. shell) region while P1 centers are only located in the core of NDs, therefore,I P 1 =I X [(4=3(rt) 3 )]=[(4=3r 3 4=3(rt) 3 )] wherer is the radius of NDs. The spin concentration ratio between P1 and X spins is assumed to be same for different sizes of NDs. As shown in Fig. 5.2(c), we found good agreement of the size 83 0.328 0.333 0.338 Magnetic field (Tesla) Intensity (arb.units) (a) 9 GHz 50-nm ND (b) Magnetic field (Tesla) 230 GHz 50-nm ND 8.200 8.205 8.210 Intensity (arb.units) 2.0030 2.0020 2.0040 g-value Figure 5.3: EPR spectra on 50-nm ND taken by the X-band and 230 GHz EPR spectrometers. (a) EPR spectrum taken at 9 GHz (X-band EPR). The peak-to- peak linewidth is 0.24 mT. (b) EPR spectrum taken at 230 GHz. The peak-to- peak linewidth is 1.00 mT. The x-ranges of both data are 0.01 Tesla. (Reprint figure with permission from Peng et al. 134 Copyright 2020 by the AIP Publish- ing LLC.) dependence data with the core-shell model. From the fit, we also obtained an estimate of 9 2 nm for the shell thicknesst. Furthermore, we investigated frequency dependence (X-band, 115 GHz and 230 GHz) of EPR spectra with 50-nm and 250-nm NDs. Figure 5.3 shows EPR spectra of the 50-nm ND sample taken at 9.3 GHz and 230 GHz where the EPR signal of the 50- nm ND sample is dominated by X spins. As shown in Fig. 5.3, the EPR linewidths at 9.3 GHz and 230 GHz are clearly different. The observation indicates that the origin of the broadening is related to g X -value, i.e., g-strains. By considering the full-width at half-maximum of the EPR spectrum (Fig. 5.3(b)), we estimated the distribution of theg-value (g X ) to be0:0003, i.e. g X = 2:0028 0:0003. The employment of HF EPR was critical for the identification of X-spins in this experiment because of the small difference in their g-values which causes a significant overlap in X-band spectrum (see Sect. A.2 in Appendix A). The EPR intensity ratio between P1 and X spins was also 84 analyzed using spectra from 50-nm and 250-nm NDs (Fig. 5.3 and Fig. A.2). As shown in Fig. 5.2(c), the result of the size dependence does not depends on the EPR frequency, however, the errors in the 230 GHz EPR analysis are significantly smaller because of the spectral distinction of P1 and X spins at 230 GHz EPR. 5.3.2 HF EDNMR spectroscopy: Investigation of near-surface im- purity structures Next, we discuss HF EDNMR experiment. Identification of the composition of X spin is imperative. Previous studies indicated that there exist dangling bonds and hydrogen and nitrogen-related defects near the diamond surface. 103, 203 Therefore, the aim of the EDNMR experiment is to detect hyperfine couplings from proton and nitrogen nuclear spins. Fundamentals of the EDNMR measurement is described in Fig. 5.4(a) using a S = 1=2 electron spin system coupled to an I = 1=2 nuclear spin with a weak hyperfine interaction (! NMR > A z ). As shown in the pulse sequence of the EDNMR (Fig. 5.4(a)), the experiment is started with a high turning angle (HTA) pulse to excite the cross transition, then EDNMR signal is detected by a change of the echo intensity due to the population inversion induced by the HTA pulse. Since the resonant frequency of the cross transition and effectiveness of the population inversion by the HTA pulse depend on the hyperfine coupling strength, the detection of EDNMR spectrum allows us to probe and measure the hyperfine coupling strengths. In the experiment on NDs, we first performed an echo-detected field sweep mea- surement at 115 GHz to determine the resonance field of the X spin. As shown in Fig. 5.4(b), the data clearly shows the signal from X spins at 4.1017 Tesla. Then, we performed the EDNMR experiment at 4.1017 Tesla (with 1 = 115 GHz). Figure 5.4(c) is the experimental result which shows no visible EDNMR signal. The noise level of 85 A z (MHz) A x,y (MHz) -10 0 10 -10 0 10 0 0.05 0.01 0.02 0.03 20 30 |+, +> Norm. Int. H2 H1 Intensity ≤ 0.002 4.108 4.104 4.100 4.096 Echo intensity (arb. units) (b) ν 2 Cross ν 1 EPR HTA Pump (ν 2 ) Probe (ν 1 ) τ π π/2 τ (a) (c) (d) X Normalized intensity 0.00 0.01 0.02 0.03 Magnetic field (Tesla) 170.0 175.0 180.0 ν 2 −ν 1 (MHz) Exp. H1 (Sim.) Figure 5.4: Proton EDNMR experiment using X spin. (a) Overview of ED- NMR experiment. EDNMR pulse sequence consists of pulses with two mi- crowave frequencies. A high turning angle (HTA) pump pulse at the frequency of 2 induces the population inversion of the cross transition. A change of the population is detected via the spin echo sequence at the frequency of 1 . (b) Echo detected EPR on 50-nm NDs taken at room temperature. The black arrow points the echo signal from X spins. The pulse parameters are=2 = 150 ns, = 200 ns, = 320 ns and repetition time = 10 ms. (c) EDNMR experimen- tal data of X spins (blue solid line) and the simulated EDNMR spectrum of H1 defects (red dashed line). The x axis is frequency offset ( 2 1 and the y axis is EDNMR intensity normalized by the echo intensity without the HTA pulse. Experimental parameters are =2 = 150 ns, = 200 ns, = 320 ns, HTA pulse amplitudew 1 = 3:33 MHz, HTA = 100s and repetition time = 10 ms. The simulation parameters areA x;y =5:5 MHz,A z = 27:5 MHz,w 1 = 3:33 MHz,T 2 = 153 ns and HTA = 100s. (d) The simulated EDNMR peak inten- sity as a function of the hyperfine coupling constants. The ranges ofA z andA x;y are10 to 30 MHz and10 to 10 MHz, respectively. The hyperfine couplings of H1 and H2 defects are indicated by black dots. The inset shows a zoom-in image of (d) where the range ofA z andA x;y are from - 1 to 1 MHz. The two white dashed lines indicates the hyperfine couplings corresponding to the ob- served noise level (0:2 %) in the experiment. (Reprint figure with permission from Peng et al. 134 Copyright 2020 by the AIP Publishing LLC.) 86 the measurement was estimated to be 0:2%. The previous study on the diamond sur- face defects 203 reported two hydrogen-related defects called H1 (S = 1=2,g = 2:0028, I = 1=2 and A x;y = 5:5 MHz and A z = 27:5 MHz) defects and H2 (S = 1=2, g = 2:0028,I = 1=2 andA x;y =2:7 MHz,A z = 17:4 MHz) defects. H1 defect was also observed by other studies. 50, 80, 87, 191 To compare with the experimental result with an expected EDNMR spectrum of H1, we perform simulation of EDNMR signals using Easyspin (the simulation procedure is described elsewhere 32 ). As shown in Fig. 5.4(c), the simulated spectrum for H1 defects has much higher intensity than the observed noise. In addition, the simulated spectrum for H2 defects has even higher EDNMR intensity. Therefore, our analysis strongly suggests that X spin is not hydrogen-related defect Fur- thermore, a contour plot in Fig. 5.4(d) shows the simulated EDNMR peak intensity as a function of hyperfine coupling strengths whereA z andA x;y are considered from10 to 30 MHz and from10 to 10 MHz, respectively. As shown in Fig. 5.4(d), when the hyperfine coupling is zero or isotropic, the EDNMR intensity also becomes zero. On the other hand, the intensity of an anisotropic hyperfine coupling increases, EDNMR intensity also increases. Based on the observed noise level, we estimated detectable hyperfine couplings in Fig. 5.4(d) (the white dashed line in the figure) with which the EDNMR intensity becomes the noise level. Next, we discuss EDNMR experiment to detect a 14 N hyperfine coupling. There exist many nitrogen-related impurities in diamond. 103 Among those impurities, we con- sider the followingS = 1=2 systems because of theirg-values and hyperfine couplings consistent with EPR spectrum of X spin. (1) P2 (consisting of three nitrogen atoms with g = 2:003 0:001, I = 1( 14 N), A x;y = 10:10 MHz, A z = 11:00 MHz for all nitro- gen nuclear spins); (2) N3: (consisting of two vacancies and one nitrogen atom with g = 2:003, I = 1( 14 N), A x;y = 1:50 MHz, A z = 5:10 MHz). In order to detect the 87 (a) Frequency offset (MHz) Normalized intensity (b) A z (MHz) A x,y (MHz) -15 0 15 -15 0 15 0.25 0.15 0.32 30 10 20 Exp. 0 30 40 0.00 0.05 0.10 Norm. Int. 0 P2 N3 Intensity ≤ 0.008 Figure 5.5: 14 N EDNMR. (a) EDNMR experimental data. The noise level was estimated to be 0.8 %. Experimental parameters are=2 = 150 ns, = 200 ns, = 320 ns,w 1 = 3:33 MHz, HTA = 100s and repetition time = 10 ms. (b) Simulated EDNMR intensity as a function of the hyperfine couplings. The hyperfine constants of P2 and N3 were indicted in the figure. The inset shows the simulated EDNMR for hyperfine coupling below 0.05 MHz. EDNMR sig- nal corresponding to the intensity of< 0.8 % (the noise level) is indicated by the white dashed line. (Reprint figure with permission from Peng et al. 134 Copy- right 2020 by the AIP Publishing LLC.) hyperfine couplings of 14 N, we performed EDNMR experiment in the frequency range of 14 N NMR. As shown in Fig. 5.5(a), the experimental result shows noise level 0:8 % and no visible NMR signal from 14 N. Based on the simulated EDNMR spectra with the hyperfine couplings listed above, those two nitrogen centers are expected to give 88 much higher EDNMR intensities than the noise level as indicated in Fig. 5.5(b). There- fore, the EDNMR result excludes nitrogen-related impurities for X spins. Based on the detected noise level of the experiment, detectable hyperfine couplings in the present EDNMR experiment are indicated in Fig. 5.5. Overall, the HF EDNMR experimental results suggest that the X spin is a vacancy-related defect. 5.3.3 DFT calculation: Identification of near-surface impurities Finally, we discuss possible structures of the near-surface vacancy-related defect. For the investigation, we employ a first principles calculation in the framework of density functional theory (DFT) to identify paramagnetic impurities consistent with the ob- served EPR spectrum. A direct ab initio treatment of the entire volume of a nanoparticle, for example, with a diameter of 30 nm, requires a DFT modeling for several ten thou- sands of atoms. Despite the ongoing progress on high performance computing (HPC), the corresponding computational costs for the ND calculations still exceed by far nowa- days available HPC resources. In this work, we therefore focus the investigation on the vicinity of the ND surface (the shell of ND) by considering a small volume with up to 250 atoms. In the calculation, an irregularly formed (’potato’-like) volume containing 200 C atoms is initially cut from the diamond crystal. We next perform molecular dy- namics (MD) calculations under admixture of the diamond lattice and hydrogen atoms to find an optimum shape and surface from the DFT model. As a result, we found that dangling bonds at the diamond surface tend to be passivated by dimerization of car- bon atoms (surface reconstruction) and by hydrogen termination. Additionally, when a single carbon atom exists on the diamond surface, the carbon atom is removed from the diamond surface with formation of CH 4 molecule. After this MD treatment, the 89 (a) (b) (c) Figure 5.6: Isosurfaces of the calculated spin densities. The EPR properties arises from the magnetization densitym(r) =n " (r)n # (r). (a) The negative vacancy V in a minimum-size ND. (b) Substitutional N C (the usual P1). (c) Substitutional N C in the more stable N + C +e configuration where the unpaired electron is transferred to the surface. (Reprint figure with permission from Peng et al. 134 Copyright 2020 by the AIP Publishing LLC.) surface of the resulting NDs are found to be completely terminated by H atoms. Fig- ure 5.6 shows a shell-only ND containing in total 260 atoms, 190 carbon and 70 hy- drogen atoms. Single vacancy and nitrogen-related defects (by taking out selected C atoms and/or substituting them by N atoms) have been already intentionally introduced as shown in Fig. 5.6. In this way, the created structures are fully relaxed in a few differ- ent charge states. We then calculate EPR parameters for the resulting spin-systems using the GIPAW pseudopotential formalism 14, 136 implemented in the Quantum ESPRESSO package 63, 64 (see Appendix C for computational details and comparative data for sin- gle crystal diamond). The resulting DFT-calculated g tensors for the most convenient structures in ND are compiled in Table I. Among calculated vacancy-related defects, Table I contains indeed some defects with theg-values consistent with the experiment (g = 2:0028 0:0003). In particular, the negatively charged vacancies V and V 2 provideg tensors in good agreement with the g-value obtained from the experiment. The averaged g-values and the anisotropy of V and V 2 are close to the experimental value. In both single crystal material and modeled ND, the V defect gives rise to a S = 3=2 high-spin ground state ( g = 90 Table 5.1: Calculated g tensors for vacancy-related defects, isolated N- impurities (P1 centers) and NV-centers in ’shell-only’ NDs (cf. Fig. 5.2) com- pared with the experimental value for the X spins. system g x g y g z g D (MHz) X-center (Exp.) 2.0028 V 2 (S=1) 2.00284 2.00301 2.00310 2.00299 -81 V (S=3/2) 2.00267 2.00278 2.00283 2.00276 -32 V 0 (S=1) 2.00228 2.00241 2.00314 2.00261 6053 P1 center (Exp.) 2.0024 P1 (S=1/2) 2.00230 2.00241 2.00244 2.00238 — N + +e (S=1/2) 2.00232 2.00232 2.00232 2.00232 — NV (S=1) 2.00263 2.00266 2.00297 2.00275 2830 NV 0 (S=1/2) 2.00223 2.00257 2.00388 2.00289 — 2:00276). While the zero-field splitting (ZFS) of V is exactly zero from symmetry reasons in a case of single crystal diamond, in the shell region of NDs, the symmetry is lifted by local strain and anisotropic distortions. A calculated value of ZFS for V is less thanD =30 MHz. The obtainedg- andD-values for V are consistent with the experimentally observed EPR position and linewidth. In contrast, for the twofold negatively charged vacancy V 2 , the g-value of 2.00299 appears slightly too high. In addition, the symmetry reduction within the ND reduces the D-value from143 MHz in single crystal material (V 2 in D 2d symmetry), but the resulting D values of at least80 MHz are still too large to be covered by the observed EPR linewidth of the X spins. In addition, although the defect with the neutral charge state (V 0 ) has ag-value comparable with the experiment ( g = 2:00261), the calculated zero-field splitting showsD = 6:05 GHz which should be clearly visible in the experiment. Therefore, V 0 is no structure of the observed X spin. Additionally, divacancies and trivacancies with various charge 91 states were also considered in the DFT calculation. However, we found that the resulting structures have g values below 2.0025 and too largeg-tensor anisotropies for X spin as well. Therefore, divacancies and trivacancies are also not the structures. Furthermore, we performed DFT calculation on nitrogen-related defects in NDs. Usually, the unpaired electron of substitutional N atoms in diamond tends to remain near the defect. For example, the electronic and magnetic properties of a substitutional nitrogen defect P1 center are predominantly determined by itsp-like unpaired electron, leading to an off-centered position of the nitrogen atom whereby the bond length to one of the four carbon ligands is increased by about 30%. 184 The present DFT method enables to calculate this configuration. The DFT calculated g-value of 2.00238 is in very good agreement with the experimentally observed value for the P1 centers in the core region (see Table C.1). On the other hand, when the N atom is located close to the surface, its unpaired electron tends to be released. It can be transferred to the surface and distributed within an electron cloud located 2 to 4 ˚ A above the surface terminating atoms (see Fig. 5.6(c)), thereby showing free-electron like behavior (isotropicg-tensor withg e = 2:002319). In comparison to the calculated P1-like configuration, about 0.3 eV are gained in the substitutional N defect. Alternatively, the unpaired electron can be trapped by other defects, e.g. vacancies resulting in negatively charged V and V 2 discussed above. In those cases, the substitutional nitrogen defect itself is effectively incorporated in ionized N + form and is not EPR-active anymore. This is consistent with the experimental observation where P1 EPR signal is significantly suppressed in small NDs (see Fig. 2). In parallel, the scenario of electron transfer from ionized P1 to vacancies supports near-surface negatively charged V (V 2 ) as structures responsible for the X spins. 92 Furthermore, we briefly note that NV-type defects have to be ruled out from struc- tures of X spins. ForS = 1 NV center (NV ) in ND, the calculated zero-field splitting (D = 2:83 GHz) is much larger than the observed EPR spectrum shown in Fig. 5.1. For the neutral NV 0 (S = 1=2) in ND, the calculatedg z component (2.00388) is incon- sistent. Furthermore, the calculated 14 N hyperfine constant in NV 0 is 9 MHz, which is two orders of magnitude large than the estimated detection limit of the present ED- NMR experiment and such the hyperfine coupling should be visible (cf. Fig. 5.5(b)). Therefore, both NV 0 and NV have to be ruled out from structures of X spin. 5.4 Summary In summary, we investigated near-surface paramagnetic defects in NDs using HF EPR and EDNMR spectroscopy, and DFT calculation. The HF EPR studies probed near- surface paramagnetic defects in NDs. Theg-value of the near-surface defects was de- termined to be 2.0028(3). With the assumption of the spin concentration ratio between P1 and X spins to be independent of the ND size, the localization of X spins can be well explained by the core-shell model with the shell thickness of 9 2 nm. HF ED- NMR spectroscopy was employed to investigate the physical structures of X spins where no hyperfine coupling with hydrogen and nitrogen nuclear spins was observed. Those results confirmed that X spins are not dominated by hydrogen and nitrogen-related im- purities and most likely they are vacancy-related defects. Furthermore, the DFT study showed that the most probable structure behind the X spins is the negatively charged monovacancies V . Based on the fabrication in which NDs are created by milling of type-Ib crystalline diamond crystals and no NMR signals obtained from EDNMR, we speculate that X-spins are related to lattice defects which are specific to NDs fabri- cated by the milling process. Quantum coherence of NV centers, which is important for 93 NV-based sensing techniques, is often limited by surrounding paramagnetic defects and impurities. The identification of the near-surface paramagnetic defects by the present investigation provides an important clue for improvement of the NV properties in NDs. 94 Chapter 6: Reduction of Surface Spin-induced Electron Spin Relaxations in Nanodiamonds Materials presented in this chapter can also be found in the article titled Reduction of surface spin-induced electron spin relaxations in nanodiamonds by Zaili Peng, Jax Dal- las and Susumu Takahashi in Journal of Applied Physics 128, 054301 (2020) 6.1 Introduction Diamond is a fascinating material in physics, chemistry and biology. For example, a negatively charged nitrogen-vacancy (NV) center in diamond is a promising platform for fundamental sciences and applications of quantum sensing because of its unique magnetic and optical properties as well as a long coherence time at room tempera- ture. 8, 26, 41, 49, 60, 72, 73, 106, 113, 173, 201 Magnetic sensing using a single NV center has been utilized to improve the sensitivity of electron paramagnetic resonance (EPR) spec- troscopy to the level of a single spin. 3, 38, 68, 69, 92, 109, 156, 171, 177 NV-detected EPR allows the detection of external spins existing around the NV center within several nanometers. NV-based sensing is also useful to detect electric field, temperature, strain and pH value 95 in a nanoscale volume. 23, 44, 58, 84 In NV-detected magnetic sensing, a magnetic field is detected through the measurement of the spin relaxation times of NVs such asT 2 and T 1 . For example, in NV-based AC magnetic sensing measurement using a spin echo sequence, the detectable magnetic field is proportional to 1= p T 2 . 176 A small number of Gd 3+ spins has been detected through sensing of fluctuating magnetic fields from Gd 3+ spins. 177 In this case, the detection is achieved by measuring changes ofT 1 relaxation time and the detectable magnetic field is proportional to 1=T 1 . Thus, long T 1 and T 2 times are desired for high detection sensitivity. In NV-based magnetic sensing applications, it is also critical to position the NV cen- ter near a target of the magnetic field sensing. NVs located near the diamond surface and NVs in nanodiamonds (NDs) will therefore be an ideal platform for the applica- tions. However,T 1 andT 2 relaxation times of those NVs are often significantly reduced by surface defects and impurities including dangling bonds, graphite layers and tran- sition metals. ?, ?, ?, 39, 82, 92, 123, 129, 134, 148, 163, 177, 180 For instance, it has been reported that shorterT 1 andT 2 were also observed from shallow NVs. 122, 129 It has also been reported thatT 1 of NVs in NDs is shorter thanT 1 in bulk diamond. The recent study showed that T 1 of NV centers is shorter in a smaller size of NDs and the result implies a decoherence process due to surface impurities although the surface impurities were not measured in the study. 177 Control of the diamond surface enables the determination of spin relaxation mechanisms, subsequently improving the sensitivity of the NV-based magnetic sensing techniques. The recent experiment by Tsukahara et al. showed that air annealing ef- ficiently removes graphite layers compared with tri-acid cleaning and increases theT 2 time 1.4 times longer. 182 In this paper, we investigate the relation between surface spins and T 1 and T 2 of single-substitutional nitrogen impurity (P1) centers in NDs using high-frequency (HF) 96 EPR spectroscopy. Our previous study on NDs suggested that the surface spins are dan- gling bonds located in the surface shell with a thickness of 9 nm. 134 Therefore, the present study aims to remove the surface spins by etching of NDs more than 9 nm and improve the spin relaxation times. AlthoughT 1 andT 2 of NV centers are the primary in- terest for the quantum sensing applications, there are a few advantages to study the spin relaxation on P1 centers over NV centers. First, NV centers are located near P1 centers, shown by the detection of their magnetic dipole coupling via double electron-electron resonance spectroscopy. 3, 38, 168 Therefore, theirT 1 andT 2 times are similar and the re- laxation mechanisms are often common. 173 Second, as shown in the previous study, 134 EPR signals of both P1 and surface spins are observable in the same measurement. This allows us to determine the amount of surface spins and to study the spin relaxations using sample samples. In the experiment, we employ air annealing to etch the diamond surface efficiently. The performance of the air annealing is confirmed by dynamic light scattering (DLS) and 230 GHz EPR experiments. The result of the DLS characterization shows a uniform etching and a linear etching rate of ND samples. We also confirm the reduction of the surface spins after the annealing process with high resolution 230 GHz EPR spectral analysis. Then, we investigateT 1 of P1 centers after the annealing using 115 GHz pulsed EPR spectroscopy. The 115 GHz EPR configuration is advantageous for pulsed EPR experiment because of its higher output power. The temperature and size dependence study elucidates surface spin-inducedT 1 process. From the result, we find that air annealing significantly reduces the presence of surface spins, but a small fraction remains, even after the thickness of NDs is reduced more than 9 nm. We also find that the surface spin contribution onT 1 is suppressed by a factor of 7:5 5:4 after annealing at 550 C for 7 hours. With the same annealing condition,T 2 is improved by a factor of 1:2 0:2. 97 6.2 Materials and methods 6.2.1 Nanodiamond Five different sizes of diamond powders were investigated in the present study. The samples include micron-sized diamond powders (10 1m) (Engis Corporation), and four different sizes of NDs (Engis Corporation and L.M. Van Moppes and Sons SA). The mean diameters of the ND samples specified by the manufacturers are 550 100 nm, 250 80 nm, 100 30 nm, and 50 20 nm. All diamond powders were manufactured by mechanical milling or grinding of type-Ib diamond crystals. The concentration of nitrogen related impurities in the ND powders is in the order of 10 to 100 parts per million (ppm) carbon atoms. 6.2.2 Air annealing The air annealing process was performed using a tube furnace (MTI Corporation) where a sample is positioned in a quartz tube located in the cylindrical access of the furnace. For the preparation of the annealing process, the ND sample was placed in a 5 ml of acetone. The ND sample in acetone was then mixed by utilizing ultrasound sonication for 10 min at room temperature in order to achieve uniform dispersion. After the ul- trasound sonication, the sample solution was placed in a crucible and kept in a fume hood overnight (without application of heating) in order to evaporate acetone from the crucible. In the air annealing process, the temperature of the furnace was first stabilized at the annealing temperature (550 C in the present case), and then the ND sample in the crucible was inserted at the center of the quartz tube. In order to improve homogeneity of the application of the air annealing over the ND powders, the NDs were mixed by a 98 lab spatula periodically during the annealing (typically mixed for 30 seconds every 10 minutes). We also limited the initial amount of ND samples to be approximately 30 mg for the homogeneous application of the air annealing. 6.2.3 Dynamic light scattering The size of a diamond powder sample was characterized by dynamic light scattering (DLS) (Wyatt Technology). A diamond powder sample of 1 mg was suspended in methanol and sonicated for two hours before the measurement of DLS. The DLS measurement was performed with a 632 nm incident laser and 163:5 of detection angle. The second correlation data was analyzed using the constrained regularization method to obtain particle sizes (see Appendix E for details). 6.2.4 HF EPR spectroscopy HF (230 GHz and 115 GHz) EPR experiments were performed using a home-built sys- tem at University of Southern California. The HF EPR spectrometer consists of a high- frequency high-power solid-state source, quasioptics, a corrugated waveguide, a 12.1 Tesla superconducting magnet, and a superheterodyne detection system. The output power of the source system is 100 mW at 230 GHz and 480 mW at 115 GHz, respec- tively. A sample on a metallic end-plate at the end of the corrugated waveguide is placed at the center of the 12.1 Tesla EPR superconducting magnet. Details of the sys- tem have been described elsewhere. 30 In the present study, the diamond powder sample was placed in a Teflon sample holder (5 mm diameter), typically containing the diamond powders of 5 mg. 29 For cw EPR experiments, the microwave power and magnetic field 99 modulation strength were adjusted to maximize the intensity of EPR signals without dis- tortion of the signals. 134 A typical modulation amplitude was 0.02 mT at a modulation frequency of 20 kHz. 6.3 Results and discussion We employed air annealing for the removal of the surface spins in the present study. In the air annealing the surface removal is caused by etching by oxygen where oxygen molecules oxidize carbon and form gaseous CO and CO 2 . We first compared the weight of the ND sample before and after the annealing process. Figure 6.1(a) shows the ND normalized weight as a function of the annealing time. In the experiment, the annealing was done at an annealing temperature of 550 C. The result shows linear reduction in ND weight with increased annealing time. The size of the ND samples was then characterized using DLS. As shown in Fig. 6.1(b), the ND size decreased fromd peak = 53:4 nm to 22.4 nm after the annealing for 9 hours. The observed reduction and narrow distribution of the size indicates a successful and uniform application of the annealing to NDs. Figure 6.1(c) shows the ND size as a function of the annealing duration. We observed a linear relationship between the size reduction and the annealing duration. A reduction rate of 3:5 nm/hour was obtained from the linear fit. Next, we characterized paramagnetic spins existing in NDs using 230 GHz EPR spectroscopy. Figure 6.2(a) shows 230 GHz continuous-wave EPR spectra on 50-nm ND samples before and after the air annealing. The measurements were performed at room temperature. As shown in Fig. 6.2(a), all spectra contain a pronounced and broad EPR signal at 8.206 Tesla and a narrow EPR signal at8.207 Tesla. From the EPR spectral analysis shown in the inset of Fig. 6.2(a), we identified that the EPR signal at 8.207 Tesla is from P1 centers while the signal at 8.206 Tesla is from the surface 100 (a) Normalized weight Annealing duration (hour) 0 2 4 6 8 10 0.8 0.6 0.4 1.0 Number (%) Diameter (nm) 0 50 100 150 200 No annealing 5 hours 7 hours 9 hours d peak = 53.4 nm d peak = 28.5 nm d peak = 26.5 nm d peak = 22.4 nm (b) d peak (nm) Slope = 3.5 nm/hour (c) 0.0 0.2 60 40 20 Annealing duration (hour) 0 2 4 6 8 10 Figure 6.1: Overview of the air annealing experiment. (a) The normalized weight as a function of the annealing duration with annealing at 550 C. The red solid line shows a linear fit to obtain the rate of weight reduction. The weight reduction rate was 0:12 hour 1 . Each sample was weighed five times. The error bar represents the standard deviation of the measurements. (b) DLS results for the size characterization of the ND samples before and after the annealing for 5, 7 and 9 hours. The diameter at the maximum in the distribution (d peak ) is indicated. The obtained polydispersity index (PDI) were 0.11, 0.07, 0.06 and 0.08 for the no-annealing sample and the annealing for 5, 7 and 9 hours samples, respectively. (c)d peak as a function of the annealing duration. The red solid line represents the result of a linear fit. The error bar represent the standard deviation (calculated byd peak p PDI). (Reprint figure with permission from Peng et al. 135 Copyright 2020 by the AIP Publishing LLC.) 101 (b) (a) EPR Intensity (arb.units) d peak (nm) I s /I p1 S P1(5X) Magnetic field (T) 8.200 8.205 8.210 No annealing Annealing for 5 hours Annealing for 7 hours Core-shell model Exp. Surface model Total S P1 40 0 60 20 60 40 20 Figure 6.2: cw EPR analysis of 50-nm NDs before and after the air annealing. (a) Signal intensity as a function of magnetic fields in Tesla with no anneal- ing, annealing for 5 hours and 7 hours. The solid green lines represent the experimental data. The inset on the top right shows contributions of P1 and surface spins (S) on the EPR spectrum, which were extracted from the EPR spectral analysis. Drawings representing NDs under the annealing process are also shown in the inset. The red arrows in the drawing represent the P1 cen- ters, and the blue arrows represent surface spins. (b) The EPR intensity ratio I s =I P 1 as a function of the diameter (d peak ). The blue solid circles with error bars representI s =I P 1 obtained from EPR spectral analysis. The details of the EPR spectral analysis is described in Sect. A.4 in Appendix A. The gray dashed line is the simulated (I s =I P 1 ) coreshell . The green dashed line is the simulated (I s =I P 1 ) surface . (Reprint figure with permission from Peng et al. 135 Copyright 2020 by the AIP Publishing LLC.) 102 spins (dangling bonds). The result is consistent with the previous HF EPR study. 134 As shown in Fig. 6.2(a), the intensity of the EPR signals from the surface spins decreases significantly after the annealing. In general, the EPR intensity is related to the spin population, we therefore analyzed the EPR intensity ratio between the surface spins (I S , where S represents surface spins) and P1 (I P 1 ) to determine their spin population ratio. For example, we obtainedI S =I P 1 to be 61 and 5 with no annealing and 9 hour annealing, respectively. The result from the EPR intensity and DLS analyses was summarized in Fig. 6.2(b). Since our previous HF EPR study of the non-annealed NDs showed the core- shell structure with the shell thickness (t) of 9 nm, 134 we first consider the core-shell model to understand the size dependence of the EPR intensity. In the core-shell model, the EPR intensity ratio (I s =I P 1 ) coreshell = ( X V X )=( P 1 V P 1 ) = X = P 1 [4=3f(d=2) 3 (d=2t) 3 g]=[4=3(d=2t) 3 )], where X ( P 1 ) is the density of the surface spins (P1 spins) andV X (V P 1 ) is the volume of the surface spin (P1 spin) locations. The calculated (I S =I P 1 ) coreshell is shown in Fig. 6.2(b). However, we observed a poor agreement with the experimental data in the range of d < 35. There may be two possible reasons to explain the result. First, as reported previously, 36, 40, 59, 198, 202 the etching rate of the air annealing depends on a crystallographic axis. It has been shown that the etching rate of the (111) plane is a couple of times faster than the (100) plane. 170 However, this can explain only the dependence of EPR, but not the dependence of DLS. Another possible reason is the creation of a small amount of surface spins during air annealing. For instance, it has been reported that dangling bonds were created by air annealing, especially when the surface termination was dominated by C-H bonds. 196 In the latter scenario, the surface spins in the non-annealed NDs (dangling bonds) are located in the shell, and then air annealing removes the dangling bonds in the shell as well as creates a small amount of dangling bonds on the surface (see Fig. 6.2(a)). To take into account 103 the surface spins created by air annealing, we added a contribution from the surface spin model with which (I s =I P 1 ) surface = s = P 1 [4(d=2) 2 ]=[4=3(d=2) 3 )]/ s =d. s is the surface spin density, treating as a constant here. As shown in Fig. 6.2(b), the sum of the core-shell and surface models agrees with the experimental result, supporting the latter case. Table 6.1: Summary of T 1 analyses. For the s analysis, Eq. 6.1 and C = 2:96 10 10 (s 1 K 5 ) were used. T 1 and s are shown with three significant figures. The errors inT 1 represent the standard error of the mean. The errors in s were calculated as the 95% confidence interval. Sample T 1 (ms) s (s 1 ) 100 K 150 K 200 K 250 K 300 K 50 nm 0:581 0:339 0:519 0:341 0:382 0:080 0:132 0:034 0:320 0:020 2430 650 100 nm 1:74 0:12 1:68 0:18 1:19 0:23 1:02 0:15 0:668 0:141 587 63 250 nm 25:6 1:2 19:3 0:7 7:80 0:20 2:14 0:07 1:26 0:03 34:0 16:9 550 nm 84:9 7:4 42:5 2:2 10:3 0:4 2:58 0:03 1:35 0:03 8:12 22:03 10m 1200 580 62:2 5:0 12:0 0:4 3:15 0:06 1:36 0:03 — Annealed (5h) 2:46 0:50 1:41 0:26 1:31 0:35 0:885 0:188 0:679 0:240 531 217 Annealed (7h) 4:37 1:37 1:86 0:48 1:37 0:57 1:06 0:27 0:847 0:595 325 217 Next, we measured the spin relaxation times (T 1 andT 2 ) of the ND samples. The ex- perimental results of the 50-nm ND sample is shown in Fig. 6.3(a). The measurements of the T 1 and T 2 relaxation times of P1 centers were carried out using the inversion recovery and the spin echo sequences, respectively. The T 1 and T 2 measurements of P1 centers were performed at a microwave frequency of 115 GHz and 4.1 Tesla, corre- sponding to the center peak of the P1 EPR spectrum. By fitting the change of the spin echo intensity with a single exponential function, we obtainedT 1 to be 0:382 0:080 ms, and T 2 is 0:413 0:007 s as shown in the inset of Fig. 6.3(a) (see Sect. D.1 in Appendix D for the description of the T 1 and T 2 determination). Moreover, we mea- sured temperature dependence ofT 1 andT 2 . Figure 6.3 (b) and Table A.1 summarize 104 T 2 = 413 ± 7 ns Echo Intensity (arb.units) T 1 = 382 ± 80 ms 1/T 1 (s -1 ) 10 5 10 3 10 1 10 -1 T (ms) 0 5 10 (a) (b) 50-nm ND Temperature (K) 100 200 300 100-nm 50-nm 250-nm 550-nm 10-mm 100-nm 50-nm 250-nm 550-nm 10-mm Temperature (K) 100 200 300 T 2 (ms) 2.0 1.0 0.0 1.5 0.5 (c) Figure 6.3: Temperature dependence ofT 1 andT 2 of P1 centers in NDs. (a) TheT 1 measurement using the inversion recovery measurement. The measure- ment was performed at 200 K. The pulse sequence isP TP =2 P echo where P =2 and P are =2- and -pulses, respectively, is a fixed evolution time and an evolution time T is varied in the measurement. In the measurement, the pulse lengths ofP =2 andP were 300 ns and 500 ns, = 1:2 s and the repetition time was = 10 ms. The inset shows the spin echo mea- surement at 200 K to obtainT 2 . The pulse sequence isP =2 P echo where is varied in the measurement. The pulse parameters for the T 2 mea- surement wereP =2 = 300 ns, P = 500 ns and the repetition time = 10 ms. The errors associated withT 1 andT 2 were obtained by computing the standard error. (b) Temperature dependence of 1=T 1 on various sizes of NDs. The solid circles are experimental data and the solid lines are fits using Eq. (6.1). (c)T 2 on various sizes of NDs. The error bars are smaller than the dots representing the T 2 value. (Reprint figure with permission from Peng et al. 135 Copyright 2020 by the AIP Publishing LLC.) 105 the result of the T 1 measurements as a function of temperature. We observed that T 1 times increase drastically by decreasing temperature. In addition, the temperature de- pendence is strongly correlated with the size of the diamond powder. To understand the temperature dependence, we first considered a contribution of the spin-lattice relaxation observed in bulk diamond. According to the previous studies of T 1 of bulk diamond, the temperature dependence of T 1 is well explained by a spin-orbit induced tunneling model, 143, 173 in which a spin flip event occurs due to the tunneling between P1’s molec- ular axis orientations. Using the spin-orbit induced tunneling model, we write that 1=T 1 is proportional toT 5 , namely, 1=T 1 =CT 5 , where theT -linear term in the spin-orbit in- duced tunneling model 143 is omitted because of its negligible contribution in the present temperature range. By fitting the experimental data of the 10-m diamond to the T 5 model, we ob- tained C = (2:96 0:52) 10 10 s 1 K 5 , which is in a good agreement with pre- vious finding. 143, 173 The result was obtained from a weighted fit analysis in order to take into account the uncertainty inT 1 values (See Sect. D.2 in Appendix D for the de- tails). Furthermore, in cases of smaller diamond samples (from 550-nm to 50-nm NDs in Fig. 6.3(b)), we observed a strong deviation from theT 5 model and found that 1=T 1 at low temperatures highly correlates with the size of NDs. Recent investigation of shallow NV centers as well as NV centers in a single ND showed thatT 1 in NDs is attributed to surface spins. 92, 129, 148, 177 Since the surface spins were also detected from the same ND samples in our experiment, it is likely that the surface spins also influenceT 1 of P1 centers in NDs. In order to take into account relaxation processes from both the surface spins and the spin-orbit induced tunneling, we consider the following for 1=T 1 , 1 T 1 =CT 5 + s ; (6.1) 106 where s is the 1=T 1 contribution from surface spins, originated by fluctuations of the magnetic dipole fields from the surface spins. s is assumed to be independent of tem- perature in a temperature range of the present experiment. In this 1=T 1 model, when temperature increases, the first term (the spin-orbit induced tunneling contribution) in- creases. Therefore, when a sample has a significant contribution from the surface spin relaxation, 1=T 1 will have less pronounced temperature dependence. We performed a weighted fit analysis on 50-nm, 100-nm, 250-nm and 550-nm ND samples to determine their s (See see Sect. D.2 in Appendix D for the details). As shown in Fig 6.3 (b), we found a good agreement between the temperature dependence of 1=T 1 and the model. For example, we obtained that s of the 50-nm ND sample was 2430 650s 1 . Table 6.2: Summary ofT 2 analyses. T 2 andT 2 are represented by three sig- nificant figures. The errors inT 2 represent the standard error of the mean. The errors inT 2 were calculated as the 95% confidence interval. Sample T 2 (s) T 2 (s) 100 K 150 K 200 K 250 K 300 K 50 nm 0:518 0:002 0:440 0:002 0:413 0:007 0:398 0:008 0:211 0:036 0:474 0:060 100 nm 0:756 0:007 0:871 0:011 0:835 0:017 0:942 0:020 1:15 0:01 0:882 0:214 250 nm 1:48 0:01 1:42 0:01 1:36 0:01 1:41 0:01 1:02 0:01 1:34 0:23 550 nm 1:89 0:02 2:03 0:01 2:00 0:01 2:15 0:01 1:98 0:01 2:03 0:10 10m 1:93 0:02 1:84 0:02 1:72 0:01 1:59 0:01 1:53 0:01 1:65 0:17 Annealed (5hr) 0:510 0:091 0:957 0:208 0:341 0:252 0:551 0:208 0:869 0:095 0:675 0:274 Annealed (7hr) 0:520 0:041 0:509 0:036 0:634 0:051 0:604 0:015 0:600 0:023 0:589 0:048 Furthermore, we investigated the temperature- and size-dependence ofT 2 relaxation time of P1 centers. In contrast to the result ofT 1 ,T 2 of P1 centers in the studied NDs does not show noticeable temperature dependence (see Fig. 6.3(c)). Table 6.2 shows the summary of the temperature- and size-dependence of T 2 as well as the mean T 2 (T 2 ) which was obtained from a weighted fit analysis in order to take into account the errors in theT 2 values (See Sect. D.3 in Appendix D for the details of theT 2 analysis). T 2 for 107 50-nm ND and 550-nm samples were 0:4740:060s and 2:030:10s, respectively. Therefore, T 2 of the 50-nm NDs is approximately 4.3 times shorter than that of 550- nm NDs. The result indicates the effect of the surface spins onT 2 . On the other hand, T 2 of 550-nm and 10-m are similar (2 s). This is probably because couplings to neighboring P1 centers dominates theirT 2 processes. Finally, we study the spin relaxation times (T 1 and T 2 ) of the annealed NDs. As shown in Fig. 6.4(a),T 1 times in the annealed diamond became longer after the anneal- ing in the measured temperature range. In addition, as shown in Fig. 6.4(a), theT 1 times of the annealed NDs are still shorter than that of bulk diamond, implying the existence of remaining surface spins. To extract the contribution of the surface spins, we employed Eq. (6.1) to determine s . From the analysis, we indeed found that s in the annealed NDs are smaller than that of the non-annealed samples. The obtained s are 531 217 s 1 and 325 217s 1 for the NDs annealed at 550 C for 5 hours and 7 hours, respec- tively, which are 4.6 2.2 and 7.5 5.4 times smaller than that of the non-annealed 50-nm NDs as shown in Fig. 6.4(b) (see Sect. D.2 in Appendix D for the calculation of the s improvement factor). We next discuss a model of the surface spin-induced T 1 ( s ). As reported previ- ously, 148, 167, 177 by considering fluctuating magnetic fields (B dip ) from surface spins, s is proportional to the variance (hB 2 dip i) and the spin density ( s ). By assuming that sur- face spins cover the whole surface uniformly, B 2 dip ( ! r P 1 )/ R S s b 2 dip ( ! r ! r P 1 )dS, where the radius vectors ( ! r and ! r P 1 ) define the locations of the surface and P1 spins relative to the center of the ND, respectively. b dip ( ! r ) is the magnetic dipole field from the surface spins. By taking into account the quantization axis of P1 and the surface spins along the external magnetic field and considering a spherical shape of NDs and a 108 100 200 300 Temperature (K) (b) 50 nm 5 hours 7 hours (a) 1/T 1 (s -1 ) 10 3 10 2 Non-annealed NDs (d = 50 nm) Bulk T 2 (ms) 1.2 0.6 0.0 0.9 0.3 Temperature (K) 100 200 300 (c) 5 hours 7 hours No annealing Annealing for 5 hours Annealing for 7 hours d peak (nm) 50 100 150 200 Gs (s -1 ) 800 1600 2400 3200 0 d peak (nm) 10 2 10 3 10 4 Gs (s -1 ) 10 -6 10 -1 10 4 10 4 Figure 6.4: Temperature dependence ofT 1 andT 2 of P1 centers in the annealed ND samples (initial diameter = 50 nm). (a)T 1 of the annealed ND samples as a function of temperature. Experimental data points are indicated by blue circles and red triangles for air annealing at 550 C for 5 hours and 7 hours, respec- tively. The blue and red solid lines are corresponding fits utilizing Eq. (6.1).T 1 data with no annealing (gray solid line) and the data of a bulk diamond (green solid line) are shown. The arrow represents the reduction of s . (b) s as a function of the ND diameter. The red solid line shows the fit result to the s =d 4 model for NDs without annealing. The green solid line shows the s =d 4 line simulated for the annealed NDs. The orange arrow represents the reduction of s . The error bar in the s is included and obtained by computing the 95 % con- fidence interval. (c)T 2 as a function of temperature for the non-annealed and annealed samples. (Reprint figure with permission from Peng et al. 135 Copy- right 2020 by the AIP Publishing LLC.) 109 spatially uniform s ,b 2 dip ( ! r ) is proportional to 1=d 6 and the surface integral is propor- tional tod 2 , whered is a diameter of a ND, the magnetic field fluctuations (B 2 dip ( ! r )) is therefore proportional to s =d 4 and s is also proportional to s =d 4 . The s values obtained from the temperature dependenceT 1 in Fig. 6.3(b) were plotted as a function of the ND size in Fig. 6.4(b). We found a good agreement between the obtained s value and the 1=d 4 size dependence. Thus, the result supports theT 1 relaxation mechanism in NDs due the surface spins. Furthermore, as shown in Fig. 6.4(b), s of the annealed NDs are very different from the 1=d 4 line of the non-annealed NDs, indicating significant re- duction of the surface spin density. Using the same model ( s / s =d 4 ), we estimated that s for the annealed NDs is100 times smaller than that of the non-annealed NDs (Fig. 6.4(b)). In addition the T 2 of the annealed diamond was studied. As shown in Fig. 6.4(c), similarly to the non-annealed NDs,T 2 of the annealed diamond showed no temperature dependence. The meanT 2 times were 0:675 0:274s and 0:589 0:048s after the 5 and 7 hour annealing, respectively, showing that the extension ofT 2 by a factor of 1:4 0:6 and 1:2 0:2, respectively (see Sect. D.3 in Appendix D for the calculation of the T 2 improvement factor). This improvement is due to the reduction of the surface spins. The observedT 2 improvement is comparable with the previously reported result. 182 By considering theT 2 results of the non-annealed NDs, we speculate that theT 2 relaxation in the annealed NDs is caused by couplings to residual surface spins and P1 centers. 6.4 Summary In summary, we investigated the relationship between the surface spins and the spin relaxation times (T 1 andT 2 ) of P1 centers in NDs. We reduced the amount of the surface spins using air annealing. The amount of the surface spins was characterized by HF EPR 110 analysis. The pulsed HF EPR experiment extracted the contribution of the surface spins on theT 1 relaxation successfully. We found clear correlation between the amount of the surface spins andT 1 . In addition, the present study showed the improvement ofT 1 and T 2 by removing the surface spins. The finding of the present investigation sets the basis to suppress the spin relaxation process due to the surface spins in NDs which is critical for NV-based sensing applications. The present method is also potentially applicable to improve spin and optical properties of other nanomaterials. 111 Chapter 7: Conclusion In conclusion, this dissertation mainly discussed HF ELDOR techniques and appli- cations. In particular, HF EDNMR was thoroughly investigated and employed to inves- tigate the physical structure of near surface impurities in NDs. Compared with other commonly used hyperfine spectroscopes, HF EDNMR spectroscopy has much higher signal sensitivity to detect weak hyperfine interaction. Chapter 1 overviewed the current progress of HF EPR and ELDOR techniques and their applications. And the motivation to conduct further investigation of HF EDNMR and applications was discussed. Chapter 2 gave an introduction of principles of cw and pulsed EPR spectroscopes. Basic static spin Hamiltonian was introduced to describe different spin interactions of- ten observed in EPR experiments. And spin Hamiltonian formalism was introduced to explain the observed EPR spectra in cw and pulsed EPR experiments. Chapter 3 discussed the implementation of shaped pulse capabilities in our HF EPR spectrometer. First, the 115 GHz / 230 GHz EPR spectrometer and its power stability were explained. The limitation of MW power on the current configuration was dis- cussed. The approach to address power limitation is to implement shaped pulse capabil- ities. And both phase-modulated linear chirped pulses and amplitude-modulated shaped pulses were successfully generated based on our HF EPR spectrometer. 112 Chapter 4 described the details of HF EDNMR spectroscopy. First, the fundamen- tals of EDNMR spectroscopy were explain in details, and brief discussion of ENDOR was also included. Thorough investigation of EDNMR in our HF EPR spectrometer based on BDPA sample was discussed, including the relation between various experi- mental settings and EDNMR spectrum quality, and the EDNMR data analysis. Finally, the comparison between HF EDNMR and ENDOR, including signal sensitivity, spec- tral resolution and spectral distortion, was carefully made based on the NMR spectrum obtained from the same BDPA samples. Chapter 5 discussed the application of HF cw EPR and EDNMR spectroscopes in the investigation of near-surface paramagnetic impurities in HPHT NDs. In NDs, there are various types of paramagnetic impurities. And from our HF cw EPR studies, two major impurities (P1 centers and near-surface spins) were identified, and their relative localization was reasonably explained by a core-shell model. Moreover, HF EDNMR with high signal sensitivity was employed to detect NMR signals from some possible physical structures. And combined with DFT calculation, the candidate for near-surface spins is negatively-charged vacancy-related defect. Chapter 6 investigated the relation between surface spins andT 1 andT 2 of single- substitutional nitrogen impurity (P1) center in NDs using HF EPR spectroscopy. In the experiment, we employed air annealing to etch the diamond surface efficiently. The performance of the air annealing was confirmed by dynamic light scattering (DLS) and 230 GHz EPR experiments. We also confirmed the reduction of the surface spins after the annealing process with high resolution 230 GHz EPR spectral analysis. The temper- ature and size dependence study elucidates surface spin-inducedT 1 process. From the result, we found that air annealing significantly reduced the presence of surface spins, but a small fraction remains, even after the thickness of NDs is reduced more than 9 nm. 113 We also found that the surface spin contribution on T 1 was suppressed by a factor of 7:5 5:4 after annealing at 550 C for 7 hours. With the same annealing condition,T 2 was improved by a factor of 1:2 0:2. 114 Appendix A: Calibration A.1 Power dependence of HF EPR intensity on P1 cen- ters Figure A.1 shows power dependence of HF EPR intensity on P1 centers in the single crystal diamond. P1 centers in bulk diamond was studied. The EPR intensity was determined by the peak-to-peak intensity of the m I = 0 transition (the central signal in Fig. 1). As shown in Fig. A.1, the EPR intensity is linearly proportional to the magnetic component of microwave (B 1 p P MW ). The P1 centers in the single crystal diamond has T 1 = 1.6 0.1 ms and T 2 = 1.31 0.02 s at room temperature. As shown in Table A.1, T 2 times of P1 in NDs are similar to that of the single crystal diamond. The microwave power used in the present cw EPR experiment (Fig. 1 in the main manuscript) indicated by the black arrow shows that the experiments on NDs were performed in the linear regime to avoid saturation effects. A.2 Frequency dependence of 250-nm ND EPR Figure A.2 shows EPR spectra of 250-nm NDs taken at X-band (9.3 GHz), 115 GHz and 230 GHz at room temperature. The EPR signals are originated from P1 and X spins. As 115 EPR intensity (arb. units) Magnetic field (μT) 0.0 0.2 0.4 0.6 0.8 1.0 0.0 Figure A.1: Peak-to-peak EPR intensity of P1 centers as a function of the microwave power. The blue circles represent experiment data points. The red dashed line is the linear fit. The microwave power used in the cw EPR experi- ments (Fig. 1 in the main text) is indicated by the black arrow. Intensity (arb. units) 230 GHz Intensity (arb. units) X-band (c) (a) (b) Intensity (arb. units) 115 GHz Magnetic field (Tesla) 4.100 4.105 4.110 P1 X Magnetic field (Tesla) 0.330 0.335 0.340 P1 X Magnetic field (Tesla) 8.200 8.205 8.210 Exp. Sim. Exp. Sim. Exp. Sim. P1 X Figure A.2: Peak-to-peak EPR intensity of P1 centers as a function of the microwave power. The blue circles represent experiment data points. The red dashed line is the linear fit. The microwave power used in the cw EPR experi- ments (Fig. 1 in the main text) is indicated by the black arrow. shown in Fig. A.1, signals of P1 and X spins are clearly spectrally separated in the 230 GHz EPR while they significantly overlap in the X-band EPR. 116 A.3 Spin relaxation times (T 1 andT 2 ) of P1 and X spins in NDs T 1 andT 2 relaxation times were obtained from three different sizes of NDs by perform- ing the inversion recovery and spin echo measurements at room temperature, respec- tively. As shown in table S1, for P1 spins,T 2 values in those NDs are similar and they are also similar to that of the single crystal diamond (see Sect. A.1). For X spins,T 1 val- ues in the NDs are also similar, they are shorter thanT 1 of the single crystal diamond.T 1 andT 2 of 250-nm ND could not be obtained because the spin echo signal was too small to detect. SinceT 2 is often related to the spin concentration, the result also suggests that the spin populations of P1 and X spins are similar between NDs. Table A.1: Spin relaxation times (T 1 andT 2 ) of P1 and X spins. ND T 1;p1 (s) T 2;p1 (s) T 1;X (s) T 2;X (s) 250-nm 560 220 1.7 0.7 XXX XXX 100-nm 660 270 1.7 0.7 110 40 0.17 0.07 50-nm 400 320 0.9 0.8 120 50 0.15 0.06 A.4 EPR spectral analysis in NDs In this section, we discuss the details of EPR spectral analysis, including EPR intensity ratioI S /I P and its error analysis, based on the EPR spectrum of non-annealing diamond with 50 nm mean diameter. In a typical cw EPR experiment conducted in our EPR spec- trometer, raw experimental data was obtained at a fixed MW frequency while sweeping external magnetic field. And x axis range usually stretched due to the sweeping coil 117 current behaviour. Therefore, magnetic field has to be calibrated first. P1 center in NDs is a type of well known impurity and its EPR peaks are used as references in the cali- bration, the magnetic field is often scaled by a factor of 0:7 1:0 until all P1 peaks match. After the field calibration, we then performed an EPR spectral analysis in which we applied a nonlinear least-square-fit (using Matlab functionlsqnonlin()) by varying the intensities and line width of EPR spectrum of the surface spin (I S ) and P1 spin (I P ), which were calculated from their Hamiltonians, to minimize the chi-square of the sum of the surface spin and P1 EPR spectra and the experimental data. As shown in Fig. A.3, we successfully explained the experimental data by considering contributions of the sur- face spins (denoted as S in Fig. A.3) and P1 centers (denoted as P1 in Fig. A.3). We also obtained their EPR intensities to beI S = 0.624 0.004 andI P = 0.0102 0.0013. The errors in IS and IP were obtained as the 95% confidence intervals. Therefore, the intensity ratio (I S /I P ) was given by 61 8 where the error was computed based on the propagation of random errors, 22 (I S =I P ) = I S I P s ( (I S ) I S ) 2 + ( (I P ) I P ) 2 ; (A.1) where(I S ) and(I P ) represent the errors ofI S andI P . 118 Figure A.3: EPR spectral analysis of 50-nm NDs (non-annealed). 119 Appendix B: AFM Characterization of NDs Sizes of NDs were verified using AFM (Nanobiophysics Core Facility at USC) . 1 For AFM measurements, NDs samples ( 0.5 mg) were first dissolved into 1.0 mL Mini-Q water. Next the mixture was ultra-sonicated for one hour to distribute NDs particles in solution. Then, NDs were spin-coated on a mica substrate (Ted Pella, Inc.). To prepare homogeneous and well-separated NDs, spin-coating with 1000 rpm for 1.5 minutes was applied for NDs with a mean diameter of< 100 nm. For larger size NDs, the spin speed and the spin time were adjusted for each size of NDs. AFM imaging was perform with a tapping mode. The scan rate was set to be 1 Hz and the scan ranges from 5m 5 m to 10m 10m were chosen. The measurement collected the height data as well as the tapping amplitude and the tapping phase. Figure B.1(a) shows an AFM image collected from the 50-nm ND sample. The color contrast of the image represents the relative height extracted from the AFM data. The size of NDs was determined from the height of NDs. For each size of ND samples, AFM imaging was performed at many locations to collect a large amount of the size data (typically > 100 NDs). Isolated NDs used for the size analysis are indicated as ND1 in Fig. B.1(a). Figure B.1(b) shows a relative height of ND1 as a function of the x-position. The height is determined based on the measurements of the maximum height 120 Figure B.1: Characterization of 50-nm NDs. (a) AFM image. ND particles used in the analysis were marked by the yellow dashed circle. (b) Relative height of ND1 as a function of x-position. (c) The size distribution profile. The bar graph represents the data taken by the AFM measurement. The blue dashed line represents the data provided from Engis corp. and the based line. For example, for ND1, the maximum and the baseline for ND1 were measured to be 110 nm and 58 nm, respectively. Therefore, we obtained that the height was 52 nm. Figure B.1(c) shows a summary of the size analysis on the 50-nm ND sample. The summary plot contains a histogram of the ND size obtained from the AFM experimental data. Additionally, we compared the histogram with a size distribution profile provided by the Engis Corporation (blue dashed line). The size distribution data from Engis were measured by a CPS disc centrifuge technique and provided with the sample batch. The data from Engis (the y-axis label is “Relative weight”) are normalized to make the maximum to be 100 %. The distribution data were scaled to compare with the AFM experiment. As shown in Fig. B.1(c), we found a good agreement between the AFM analysis and the provided size distribution. Furthermore, we analyzed the particle size with all other sizes of the ND samples and found a good agreement between the AFM-measured. Figure B.2- B.7 show AFM images (height map) and the size distribution of various sizes of nanodiamonds (NDs). The size distribution data from both Engis and L. M. Van Moppes and Sons SA were measured by a CPS disc centrifuge technique and provided with the sample batch. The 121 Figure B.2: Characterization of 30-nm NDs. (a) AFM image. ND particles used in the analysis were marked by the yellow dashed circle. (b) The size distribution profile. The bar graph represents the data taken by the AFM mea- surement. The blue dashed line represents the data provided from Van Moppes. data from Van Moppes (the y-axis label is “Differential percentiles”) are normalized to make the sum of all percentiles to be 100 %. Those distribution data were scaled to compare with the AFM experiment. Figure B.8 shows optical image of 10-m diamond powders and their size distribution. Each figure contains the size distribution obtained by the experimental result (the black histograms) and the size distribution profiles provided by the companies (the blue dashed line). 122 Figure B.3: Characterization of 60-nm NDs. (a) AFM image. ND particles used in the analysis were marked by the yellow dashed circle. (b) The size distribution profile. The bar graph represents the data taken by the AFM mea- surement. The blue dashed line represents the data provided from Van Moppes. 0.02 0.1 0.3 0.5 0.05 200 (nm) 0 Relative weight 0 50 100 60 30 0 (a) (b) Y (μm) 0 5 X (μm) 0 5 Particle diameter (μm) Frequency count Figure B.4: Characterization of 100-nm NDs. (a) AFM image. ND parti- cles used in the analysis were marked by the yellow dashed circle. (b) The size distribution profile. The bar graph represents the data taken by the AFM measurement. The blue dashed line represents the data provided from Engis. 123 0 0 10 20 30 0.1 0.2 0.3 0.5 0.4 35 40 20 0 Particle diameter (μm) Differential percentiles (a) (b) 1000 (nm) 0 X (μm) 0 5 Y (μm) 0 5 Frequency count Figure B.5: Characterization of 160-nm NDs. (a) AFM image. ND particles used in the analysis were marked by the yellow dashed circle. (b) The size distribution profile. The bar graph represents the data taken by the AFM mea- surement. The blue dashed line represents the data provided from Van Moppes. 0.02 0.1 0.3 0.5 0.05 500 (nm) 0 Relative weight 0 50 100 16 8 0 (a) (b) Y (μm) 0 5 X (μm) 0 5 Particle diameter (μm) Frequency count Figure B.6: Characterization of 250-nm NDs. (a) AFM image. ND parti- cles used in the analysis were marked by the yellow dashed circle. (b) The size distribution profile. The bar graph represents the data taken by the AFM measurement. The blue dashed line represents the data provided from Engis. 124 Figure B.7: Characterization of 550-nm NDs. (a) AFM image. ND particles used in the analysis were marked by the yellow dashed circle. (b) The size distribution profile. The bar graph represents the data taken by the AFM mea- surement. The blue dashed line represents the data provided from Van Moppes. Number X (mm) Y (mm) 0 0 1 1 5 20 60 10 0 1000 2000 8 Particle diameter (μm) 30 15 0 (a) (b) Frequency count Figure B.8: Characterization of 10-m NDs. (a) Optical image. Diamond particles used in the analysis were marked by the blue dashed circle. (b) The size distribution profile. The bar graph represents the data taken by the AFM measurement. The blue dashed curve (not normalized) is the size distribution profile provided by Engis (Beckman Coulter, Multisizer 3 3.51). 125 Appendix C: Calculation of EPR Parameters Using DFT In minimum-size “shell-only” nanodiamonds (< 2 nm diameter) saturated with hydro- gen EPR parameters have been calculated for a large number of spin systems using den- sity functional theory (DFT) as implemented in the Quantum ESPRESSO package. 63, 64 Norm-conserving pseudopotentials and the PBE exchange-correlation functional were used in connection with a plane-wave basis set (energy cutoff of 50 Ry). In a first step, the defect structures were allowed to relax until the forces were below 10 4 Ry/bohr. For the resulting spin systems, we then calculate the full set of EPR parameters: g tensors, hyperfine (hf) splittings, and for systems with S 1 also the zero-field splitting (ZFS) parameters D and E. The calculation of the g tensor was performed using the gauge-including GIPAW formalism 14, 136 implemented in the Quantum ESPRESSO package. The approach has been shown to give reliable estimates for g tensors of defects in various semiconductors, interfaces and surfaces. 62, 145, 188 The application of the approach onto N-related defects in diamond-bulk (see Table S2) shows that its accuracy is even high enough to describe the rather small deviation from the free-electron value g e = 2.002319, as well as the anisotropies of the g tensors sufficiently well, allowing to discriminate between different defect models. The same is true for the zero-field splitting (ZFS) becoming relevant in 126 case of the high-spin states. The calculation of the D value of the ZFS was carried out with the approach described and evaluated in Ref. 14 Note that the corresponding 14 N hyperfine couplings are also in very good agreement with experiment. Table C.1: DFT-calculated EPR-parameters compared with experiment for spin centers in diamond bulk (216-atom supercell, 333 k-point sampling; other technical settings same as for the nanodiamonds): the negative vacancy (V ),NV , the (excited *)NV 0 and the P1 center (N 0 ). Besides the g tensor and the zero-field splitting (D and E values for S = 1) 14 N-related hyperfine splittings are given (for the N-related defects). defect total spin S g x g y g z g av A ? =A k ( 14 N) [MHz] D [MHz] E [MHz] NV 0 1/2 2.00197 2.00234 2.00396 2.00276 6.7, 6.0/ 10.9 XXX XXX NV 3/2 2.00306 2.00306 2.00312 2.00308 17.8 / 27.4 1911 XXX NV 0 (exp.) 53 3/2 2.0029 2.0029 2.0035 2.0031 17.0 / 25.5 1685 0.0 NV 1 2.00274 2.00274 2.00308 2.00284 -2.32 / -1.87 3082 0.0 NV (exp.) 52 1 2.0029 2.0029 2.0031 2.0029 -2.70 / -2.13 2872 0.0 P1 1/2 2.00213 2.00213 2.00208 2.00211 75.8 / 110.0 XXX XXX P1(exp.) 184 1/2 2.0022 2.0022 2.0022 2.0022 81.3 / 114.0 XXX XXX V 3/2 2.00281 2.00281 2.00281 2.00281 XXX 0.0 0.0 V (exp.) 83 3/2 2.0027 2.0027 2.0027 2.0027 XXX 0.0 0.0 127 Appendix D: T 1 andT 2 Analysis D.1 Determination of the spin relaxation times (T 1 and T 2 ) In this section, we discuss the measurements of spin relaxation times (T 1 andT 2 ). We used the inversion recovery (P -T –P =2 – –P - –echo) and the spin echo (P =2 – –P - –echo) sequences for the measurements ofT 1 andT 2 , respectively, where P =2 and P are /2-pulse and -pulse. The data of T 1 and T 2 measurements of the 5-hour and 7-hour annealed NDs taken at 200 K were shown in Fig. D.1 and D.2. The spin echo intensity was recorded as a function ofT and inT 1 andT 2 measurements, respectively. Each data point was taken with 128 averaging. As can be seen in Fig. D.1 and D.2, all experimental data can be well explained by a monoexponential function. From the fit using a monoexponential function, we obtainedT 1 = 1.31 0.35 ms and T 2 = 0.341 0.252s for the 5-hour annealed NDs (Fig. D.1) andT 1 = 1.37 0.57 ms andT 2 = 0.634 0.051s for 7-hour annealed NDs (Fig. D.2). The errors ofT 1 andT 2 were obtained by computing the standard error. In the present experiment, the signal-to- noise ratios (S/Ns) of the inversion recovery and spin echo measurements, especially in the 50-nm and annealed NDs, were limited due to shortT 2 . In addition, a small amount of the annealed NDs obtained from the air annealing process limited S/Ns of the data further. 128 Figure D.1: T 1 and T 2 measurement of the 5-hour annealed NDs at 200 K. (a) The result of the inversion recovery measurement. (b) The result of the spin echo measurement. The blue points are experimental data while the red solid lines are fittings based upon a monoexponential function. Figure D.2: T 1 and T 2 measurement of the 7-hour annealed NDs at 200 K. (a) The result of the inversion recovery measurement. (b) The result of the spin echo measurement. 129 D.2 T 1 analysis: Determination of C, s , the s improve- ment factor and their errors In this section, we discuss the determination of C, s , the s improvement factors and their error analysis. As shown in Eqn. D.1 in the main manuscript, we model the temperature- and size-dependence of 1/T 1 by, 1 T 1 =CT 5 + s ; (D.1) where the first term is a contribution from the spin-orbit induced tunneling relaxation represented by a constant C and T 5 temperature dependence. The second term in Eqn. D.1 is a contribution from the surface spin relaxation represented by a constant s . First the constantC was determined from theT 1 result of the 10m diamond pow- ders since properties of the 10m diamond sample are expected to be very similar to those of a bulk diamond. In order to obtain C, we fit the T 1 result of the 10 m dia- mond sample with Eqn. D.1 with s = 0. The fit analysis was performed by employing a weighted fit to take into account the uncertainty inT 1 . In the fit, the weight was set by 1/ 2 i where 2 i is the square the uncertainty of 1/T 1 at each temperature. The uncertain- ties of 1/T 1 were calculated from the uncertainty ofT 1 . We then used the Levenberg- Marquardt nonlinear least square algorithm for the fit (e.g. “fitnlm“ function in Matlab) and the 95% confidence interval of the fit result was calculated using the result of the fit (e.g. “coefCI“ function in Matlab). As shown in the manuscript, we obtainedC = (2.96 0.52) 10 10 (s 1 T 5 ). 130 Next we determined s for 50-nm, 100-nm, 250-nm, 550-nm and annealed NDs from their temperature dependentT 1 results. In this analysis, we used the fixedC = (2.96 0.52) 10 10 (s 1 T 5 ) and used a weighted fit. Similar to the previous analysis on the 10m diamond sample, the weight was 1/ 2 i where 2 i is the square the uncertainty of 1/T 1 ( 1=T 1 ), which is calculated using the error propagation 22 with the uncertainty ofT 1 ( T 1 ), i.e. 1=T 1 =j T 1 j/((T 1 ) 2 . The nonlinear least square algorithm and the 95% confidence interval were used to obtained s values and their uncertainties. The results were presented in Table I in the main manuscript. Finally, we discussed a s improvement factor, defined by s of the non-annealed (50-nm) ND divided by s of the annealed NDs. Using s = 2430 650 (s 1 ) for the 50-nm ND (with greater significant figures for the analysis), s = 531 217 (s 1 ) for the 5-hour annealed ND and s = 325 217 (s 1 ) for the 7-hour annealed ND, one can obtain the s improvement factors to be 4.6 2.2 and 7.5 5.4 for the 5-hour annealed ND and the 7-hour annealed ND, respectively. The errors were calculated by the following error propagation, 22 = 0 s a s s ( a a s ) 2 + ( 0 0 s ) 2 ; (D.2) where 0 s and a s are s of the 50-nm ND and the annealed ND, respectively. 0 and a are the errors in s of the 50-nm ND and the annealed ND, respectively. 131 D.3 T 2 analysis: Determination of the mean T 2 , the T 2 improvement factor and their errors In this section, we discuss the estimate of the T 2 improvement factors and their error analysis. As discussed in the manuscript, we consideredT 2 to be temperature indepen- dent in the range of 100 K to room temperature. Therefore, we obtained the meanT 2 values ( T 2 ) by fitting the set of the T 2 data by a constant. Moreover, we employed a weighted fit to take into account the errors inT 2 . In practice, we set the weight using the uncertainty ofT 2 , namely, 1/ 2 i where 2 i is the uncertainty inT 2 at each temperature, and used the Levenberg-Marquardt nonlinear least square algorithm (e.g. “fitnlm“ func- tion in Matlab) and the 95% confidence interval based on the fit result was calculated using the result of the fit (e.g. “coefCI“ function in Matlab). As shown in Table II in the main manuscript, from the fit, we obtained that T 2 values and their errors were 0.474 0.060s, 0.675 0.274s and 0.589 0.048s for the non-annealed 50-nm ND (T 0 2 ), the 5-hour annealed ND (T 5h 2 ) and the 7-hour annealed ND (T 7h 2 ), respectively. This gives theT 2 improvement factors for the 5-hour and 7-hour annealed NDs (=T 5h 2 /T 0 2 ) and T 7h 2 /T 0 2 ) of 1.4 0.6 and 1.2 0.2 for the 5-hour annealed ND and the 7-hour annealed ND, respectively. The propagated error of theT 2 improvement factor () was calculated by, 22 = T a 2 T 0 2 s ( a T a 2 ) 2 + ( 0 T 0 s ) 2 ; (D.3) where 0 is the error of the non-annealed ND sample andT 0 a 2 and a areT 2 and its error of the annealed ND sample. 132 Appendix E: DLS Data Analysis Using Constrained Regularization Method In this chapter, DLS data analysis using the constrained regularization method is dis- cussed. DLS is a useful photon correlation technique commonly used to detect particle size distribution (PSD). In the experiment, second-order correlation function data is ob- tained, namely, g (2) () = hI(t)I(t +)i hI(t) 2 i ; (E.1) whereI(t) andI(t+) are the scattered light intensity at timest andt+, respectively, and the braces indicates averaging over t. The first-order (electric field) correlation function isg (1) () is related tog (2) () by Siegert’s relation, 56 g (2) () = 1 +jg (1) ()j 2 ; (E.2) where is an instrumental coherence parameter1, which depends on the experimental geometry. And a PSD can be estimated fromg (1) (), g (1) () = Z 1 0 P () exp()d; (E.3) 133 where P () is the normalized distribution function of the decay constant , and is related to diameter of particles by =k b T=(3d)q 2 . k b is the Boltzmann constant,T is the temperature, is the dynamic viscosity of suspending liquid,d is the diameter of particles detected, and scattering vectorq = (4n=) sin (=2) wheren is the refractive index of the suspending liquid, is the wavelength of incident beam vacuum, and is the scattering angle. In practice, the number of time i is discrete, e.g. i = 1:::M, and the continuous integral in Eqn. E.3 can also be replaced with N discrete decay k in the numeral calcu- lation, namely k = 1...N. Therefore, Eqn. E.3 can be rewritten in a discrete form, g (1) ( i ) = N X k=1 x k Z k k1 exp( i )d;i = 1:::M;k = 1:::N (E.4) Essentially Eqn. E.4 describes a system of M linear equations with N unknown coeffi- cientsx k , wherex k represents the scattered intensity scattered by particle with diameter d k . Matrix form of Eqn. E.4 is as follows, g = Ax; (E.5) And the regularization approaches are often used in this type of problem (involves the inversion of a Fredholm integral of the first kind 185 ) to obtain results with a balance between accuracy and stability. 140 Therefore, Eqn. E.5 can be expressed as functional optimization problems with the following objective function to be minimized, Obj (x;g) =kAx gk 2 + (x); (E.6) 134 (a) (b) Exp. Fit t (ms) 1 10 100 10000 1000 g 2 1.0 1.1 1.2 1.3 1.4 1.5 Intensity (%) Diameter (nm) 10 100 10000 1000 Figure E.1: DLS analysis result using constraint regularization method. (a) Second-order correlation data. The black solid is experimental data while the red dashed line is fitting based on Eqn. E.8. Experimental details: the sam- ple is nanodimaond particles suspended in pure methanol, DLS measurement was performed with a 632 nm incident laser and 163:5 of detection angle. In the analysis, a of 0.001 was used. (b) Analysed results obtained based on Eqn. E.8. x axis is the diameter in nm, y axis is the intensity %, which is x in Eqn. E.8. Three peaks are obtained centering at 33.6 nm, 147.6 nm and 3382.8 nm for peak1 (pk1), peak2 (pk2) and peak3 (pk3) respectively. where (x) is the regularization function often takes a Euclidean norm form, and a iden- tity operator D is used in constrained regularization approach. Andx should subject to the constraints that 0x 1 as non-negative results should be removed. 204 Therefore, in the constrained regularization approach, Eqn. E.6 leads to the following form, Obj (x;g) = 1 2 kAx gk 2 + 2 kDxk 2 ; s.t. 0x 1 (E.7) After reformulation, Eqn. 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Abstract (if available)

Abstract Electron paramagnetic resonance (EPR) is a powerful spectroscopic technique widely used to electronic and magnetic properties of various spin systems. However, practically conventional EPR can easily reach its limitations for large spin systems. For instance, EPR spectrum of disordered sample at low field (LF) is often too broad to be resolved, and detail information of the spin magnetic parameters and molecular structures can be easily hidden in the broadened EPR spectrum. With the advances in instrumentation, such as the realization of high magnetic field (HF) and high frequency microwave (MW) radiation, EPR spectroscopy gains more powerful capabilities. Compared with LF, HF EPR attains the following appealing advantages: 1) Enhanced spectral resolution

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Asset Metadata

Creator Peng, Zaili (author)

Core Title High-frequency electron-electron double resonance techniques and applications

School College of Letters, Arts and Sciences

Degree Doctor of Philosophy

Degree Program Chemistry

Publication Date 01/29/2021

Defense Date 01/15/2021

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag applications,ELDOR,EPR,high frequency,OAI-PMH Harvest,techniques

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Takahashi, Susumu (committee chair), Kresin, Vitaly (committee member), Vilesov, Andrey (committee member)

Creator Email zailpeng@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c89-418919

Unique identifier UC11673098

Identifier etd-PengZaili-9253.pdf (filename),usctheses-c89-418919 (legacy record id)

Legacy Identifier etd-PengZaili-9253.pdf

Dmrecord 418919

Document Type Dissertation

Format application/pdf (imt)

Rights Peng, Zaili

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