Introduction to EPR Spectroscopy EPR allows paramagnetic species to be identified and their electronic and geometrical structures to be characterised Interactions with other molecules, concentrations, lifetimes and dynamics Solid state, solution, gas phase Non-destructive Nomenclature: Electron Paramagnetic Resonance (EPR) Electron Magnetic Resonance (EMR) Electron Spin Resonance (ESR) 2
Spectroscopy Magnetic Resonance Probing energy level structure via interaction with electromagnetic radiation. Energy level transitions associated with absorption/emission of EM radiation. Frequency proportional to energy level separation. 3
Outline Applications of EPR Biology & Medicine Chemistry Physics & Geology Materials Science Photosynthesis Metallo-proteins Metallo-enzymes in vivo EPR Oximetry EPR Imaging Spin-labels Irradiation damage in DNA Irradiated food Beer Reactive Oxygen Species Radicals in solution Short-lived paramagnetic compounds Radical pair reactions Fullerenes (C60) Photochemistry Reaction kinetics Excited states Spin trapping Catalysts Metal clusters Organic conductors EPR Dosimetry EPR Dating EPR Microscopy Semiconductors Defects Laser-crystals Ferroelectrics Phase transitions Adsorption of gases oleds Polymers Glasses High temperature superconductors Ceramics Nano-particles Photographic film Transition metal ions in Zeolites Porous Materials Coal Literature Introduction to Magnetic Resonance Carrington & McLachlan Electron Spin Resonance Atherton The Theory of Magnetic Resonance Poole & Farach Principles of Pulse Electron Paramagnetic Resonance Schweiger and Jeschke Electron paramagnetic resonance of transition ions Abragam & Bleaney Electron Paramagnetic Resonance Elementary Theory and Practical Applications Weil, Bolton, and Wertz Biological Magnetic Resonance Vol. 19: Distance Measurements in Biological Systems by EPR, Berliner, Eaton & Eaton 4
Outline Research Papers: Materials 1. Group V donor in Silicon: Quantum control of hybrid nuclear electronic qubits 2. Organic Spintronics: Ordering in thin films and relaxation of Cu-Phthalocyanine 3. Photo-excited Triplet states of Porphyrins: TR-EPR, ENDOR and DFT 4. Light-Activated Antimicrobial Agents: TR-EPR, 1 O 2 production, and DFT 5. Masers I: Pentacene in p-terphenyl Crystals 6. Masers II: NV- Centers in Diamond 7. Singlet Fission in Thin Films of Pentacene in p-terphenyl 5
Outline Theory and Methodology 1. Principles of EPR Unpaired Electrons and Electron Spin Spectrometer Design: Helmholtz Coil ; Modulation ; Waveguide ; Resonators 2. Electron-Nuclear Hyperfine Coupling The Hamiltonian for a system with one electron & one spin ½ Nucleus High-Field Approximation Examples of systems with single Nuclei: P@Si ; Bi@Si ; N@C60 ; Mn 2+ Example of a system with several (symmetry) equivalent nuclei: PNT Line-shapes: Homogenous and Inhomogenous Broadening Relaxation; spin echo experiments on P@Si and Bi@Si Continuous-wave Electron-Nuclear Double Resonance (ENDOR) on PNT Pulse ENDOR on Bi@Si 3. Photo-excited Triplet States Zero-field Splitting Time-resolved EPR 6
Stern Gerlach Experiment (1922) A beam of silver atoms splits in an inhomogeneous magnetic field due to the angular momentum or spin of the unpaired valence electron. For electrons, the spin quantum number, S = ½. The total angular momentum of magnitude S 2 = {S(S + 1)} ½!. (2S + 1) components of angular momentum m S! where m S = S, (S 1),..., S. Hence, there are two components, with m S = ±½. 7
Electron Transfer Reactions Singlet S = 0 M S = 0 Doublet S = ½ M S = ±½ Triplet S = 1 M S = ±1, 0 Quartet S = 3/2 M S = ±3/2, ±½, 0 Quintet S = 2 M S = ±2, ±1, 0 For electrons, the spin quantum number, S = ½. The total angular momentum of magnitude S 2 = {S(S + 1)} ½!. (2S + 1) components of angular momentum m S! where m S = S, (S 1),..., S. Hence, there are two components, with m S = ±½. 8
Which Elements are Important for EPR? 9
Which species has an unpaired electron in its outer orbital and hence has an EPR signal? 1. Ca 2+ 2. Cu 1+ 3. Cu 2+ 4. Ti 4+ 5. Zn 2+ 10
Transition Metals with Unpaired Electrons The energies of the d-orbitals are rendered non-degenerate by the presence of ligands S = 2 S = 0 S = 5/2 S = ½ 13
Electron Zeeman Interaction The magnetic moment of the electron: where is the Bohrmagneton The interaction of the magnetic moment and an external magnetic field, B 0, is given by: The analogous quantum mechanical expression (Hamiltonian) with the magnetic field in the z direction (taking the S z component of S): For electrons S = ½, so there are two basis states with m S = ±½. These are labelled α e and β e, and may be represented by column vectors: 14
Electron Zeeman Interaction In order to find the eigenvalues we need expressions for the quantum mechanical operators representing S x, S y and S z. These are the Pauli spin matrices multiplied by a factor of ½: By matrix multiplication, we can see that α e and β e are eigenstates of S z. The eigenvalues are: The allowed energies are found using the complete Hamiltonian in the Schrödinger equation: 15
Electron Zeeman Interaction The Hamiltonian: H EZ = g e µ β S Z B o Selection Rule: ΔS = ±1 16
Boltzmann Populations at Equilibrium The Hamiltonian: H EZ = g e µ β S Z B o At 9.5 GHz & 298 K 17
Electromagnetic Radiation 19
Frequencies, Wavelengths & Magnetic fields 20
EPR Spectrometer design Helmholtz Coil 21
EPR Spectrometer design Waveguide 22
EPR Spectrometer design Resonator Mode 23
EPR Spectrometer design Resonator Mode 24
EPR Spectrometer design 5 1 7 6 2 4 3 1. Microwave Source 2. Attenuator 3. Circulator 4. Detector 5. Amplifier 6. Resonator 7. Helmholtz Coil Magnet 25
EPR Spectrometer design modulation 26
EPR Spectrometer design 27
EPR Spectrum of a one electron system strong pitch The Hamiltonian: H EZ = g e µ β S Z B o 28
Important Nuclei (I 0) for NMR/EPR Element Isotope Spin Number of lines Gyromagnetic ratio [ MHz / T ] Abundance [ % ] Electron ½ 176085.98 Hydrogen 1 H ½ 2 267.51 99.985 2 H 1 3 41.06 0.015 Carbon 13 C ½ 2 67.26 1.11 Nitrogen 14 N 1 3 19.32 99.63 15 N ½ 2 27.11 0.37 Fluorine 19 F ½ 2 251.67 100 Phosphorus 31 P ½ 2 108.29 100 Vanadium 51 V 7/2 8 70.32 99.76 Manganese 55 Mn 5/2 6 66.18 100 Iron 57 Fe ½ 2 8.65 2.19 Cobalt 59 Co 7/2 8 63.12 100 Nickel 61 Ni 3/2 4 23.95 1.134 Copper 63 Cu 3/2 4 71.07 69.1 65 Cu 3/2 4 76.05 30.9 Molybdenum 95 Mo 5/2 6-17.09 15.7 97 Mo 5/2 6-17.88 9.46 Bismuth 209 Bi 9/2 10 44.92 100 30
Nuclear Zeeman Interaction The Hamiltonian: H NZ = g N µ β I Z B o Selection Rule: ΔI = ±1 31
Electron-Nuclear Hyperfine Interaction The magnetic moments of the electron and nuclei are coupled via two interactions: the isotropic Fermi contact interaction and the anisotropic dipolar coupling giving the Hamiltonian: The magnetic moments of the electron and nuclei are coupled by the Fermi contact interaction. It represents the energy of the nuclear moment in the magnetic field produced at the nucleus by electric currents associated with the "spinning" electron: where There is also a magnetic coupling between the magnetic moments of the electron and nucleus which is entirely analogous to the classical dipolar coupling between two bar magnets: 32
Description of a 1 electron, 1 proton system The Hamiltonian: H = H EZ + H NZ + H HF S = ½; m S = ±½ I = ½; m I = ±½ Pauli Spin Matrices 33
Description of a 1 electron, 1 proton system The Hamiltonian: H = H EZ + H NZ + H HF S = ½; m S = ±½ I = ½; m I = ±½ Direct Product Expansion is a form of matrix multiplication whereby all the elements of one matrix are multiplied by a second matrix in turn. Thus direct product expansion of an n n matrix with an m m matrix results in the formation of an nm nm size matrix 34
Description of a 1 electron, 1 proton system The Hamiltonian: H = H EZ + H NZ + H HF S = ½; m S = ±½ I = ½; m I = ±½ 35
Description of a 1 electron, 1 proton system The Hamiltonian: H = H EZ + H NZ + H HF S = ½; m S = ±½ I = ½; m I = ±½ 36
Description of a 1 electron, 1 proton system The Hamiltonian: H = H EZ + H NZ + H HF S = ½; m S = ±½ I = ½; m I = ±½ 37
Description of a 1 electron, 1 proton system The Hamiltonian: H = H EZ + H NZ + H HF S = ½; m S = ±½ I = ½; m I = ±½ 38
Description of a 1 electron, 1 proton system The Hamiltonian: H = H EZ + H NZ + H HF S = ½; m S = ±½ I = ½; m I = ±½ High-field approximation 39
Description of a 1 electron, 1 proton system The Hamiltonian: H = H EZ + H NZ + H HF S = ½; m S = ±½ I = ½; m I = ±½ High-field approximation 40
Silicon doped with Phosphorus @ 10 K The Hamiltonian: H = H EZ + H NZ + H HF S = ½; m S = ±½ I = ½; m I = ±½ High-field approximation 9.7 GHz 41
EPR Spectrum of N@C60 @ 9 GHz The Hamiltonian: H = H EZ + H NZ + H HF S = 3/2 m S = 3/2, ½, ½, 3/2 I = 1 m I = 1, 0, 1 42
EPR Spectrum of Mn 2+ @ 94 GHz The Hamiltonian: H = H EZ + H NZ + H HF S = ½ m S = ±½ I = 5/2 m I = ±5/2, ±3/2, ±½ 43
Silicon doped with Bismuth @ 9.7 GHz The Hamiltonian: H = H EZ + H NZ + H HF S = ½ I = 9/2 m I = ±9/2, ±7/2, ±5/2, ±3/2, ±½ A = 1.4754 GHz Bi 9.7 GHz 44
Silicon doped with Bismuth @ 9.7 GHz The Hamiltonian: H = H EZ + H NZ + H HF S = ½ I = ½ A = 117.1 MHz Bi S = ½ I = 9/2 A = 1.4754 GHz Given that: Hyperfine coupling gyromagnetic ratio spin density (1) Work out the ratio of spin density for P@Si and Bi@Si. (2) Comment on your result 45
EPR Spectrum of the perinaphthenyl radical The Hamiltonian: H = H EZ + H NZ + H HF Binomial distribution 1 protons gives 2 lines 1:1 2 protons gives 3 lines 1:2:1 3 protons gives 4 lines 1:3:3:1 4 protons gives 5 lines 1:4:6:4:1 5 protons gives 6 lines 1:5:10:10:5:1 6 protons gives 7 lines 1:6:15:20:15:6:1 46
Lineshapes: Homogeneous & Inhomogeneous Broadening 47
Pulse Scheme for a 2-pulse sequence Hahn Echo pulsed EPR is a useful method to measure relaxation (T1 & T2) 49
Outline Research Papers:Materials 1. Group V donor in Silicon: Quantum control of hybrid nuclear electronic qubits 2. Organic Spintronics: Ordering in thin films and relaxation of Cu-Phthalocyanine 3. Photo-excited Triplet states of Porphyrins: TR-EPR, ENDOR and DFT 4. Light-Activated Antimicrobial Agents: TR-EPR, 1 O 2 production, and DFT 5. Masers I: Pentacene in p-terphenyl Crystals 6. Masers II: NV- Centers in Diamond 7. Singlet Fission in Thin Films of Pentacene in p-terphenyl 50
Group V Dopants in Silicon: Remarkably long relaxation times The Hamiltonian: H = H EZ + H NZ + H HF S = ½; m S = ±½ I = ½ or 9/2; G. Morley et al. Nature Materials (2010,2012) pulsed EPR is a useful method to measure relaxation (T1 & T2) 51
Group V Dopants in Silicon: Remarkably long relaxation times The Hamiltonian: H = H EZ + H NZ + H HF S = ½ I = 9/2 m I = ±9/2, ±7/2, ±5/2, ±3/2, ±½ A = 1.4754 GHz Bi 9.7 GHz 28 Si: I = 0; 95.3% 29 Si: I = ½; 4.7% 52
ENDOR: Electron-Nuclear Double Resonance The Hamiltonian: H = H EZ + H NZ + H HF G. Feher Phys. Rev. 103 (1956) Determination of the hyperfine couplings (a) between the electron and nucleii 53
Continuous-wave ENDOR 54
Pulse (Davies) ENDOR Davies, Phys. Lett. A 47, 1 (1974) 55
Pulse (Davies) ENDOR 58
pulsed ENDOR of Bi@Si at 13 K, 9 GHz line 10 line 9 line 8 line 7 line 6 2 3 4 5 6 7 8 9 10 11 Radio Frequency / MHz S. Balian et al, Physical Review B 2012
pulsed ENDOR of Bi@Si at 13 K, 9 GHz Isotropic superhyperfine couplings (MHz) X 1 8.02 8.32 11.35 2.49 2.00 2.49 2.88 1.65 2.88 X 2 1.33 X 2 4.81 0.51 4.81 X 1 8.02 8.32 11.35 11 10 568.7 12 9 479.9 13 8; 14 7; 15 6; 16 5; 17 4; 18 3; 19 2; 20 1; 396.8 321.6 256.7 203.7 162.6 131.7 108.9 91.8 0 1 2 3 4 5 6 7 8 9 10 11 12 Radio frequency (MHz) Magnetic field, B (mt) EPR Transition; S. Balian et al, Physical Review B 2012
pulsed ENDOR of Bi@Si at 13 K, 9 GHz Line 9 ENDOR at 9.755 GHz Fitted Gaussians Sum of Gaussians Extrapolated Gaussians Si nuclear Zeeman frequency 29 * 0 9 B = 0.4799 T 6 3 0 0 1 2 3 4 5 6 7 8 9 Radio Frequency (MHz) S. Balian et al, Physical Review B 2012
Hyperfine Structure of Bi@Si Bi Silicon doped with Bismuth at 10 K, 9.720844 GHz Balian et al. PRB (2012)
Hyperfine Structure of Bi@Si Intensity (a.u.) 60 45 30 15 0 9 6 Line 9 ENDOR at 9.755 GHz Fitted Gaussians Sum of Gaussians Extrapolated Gaussians 29 Si nuclear Zeeman frequency B = 0.1888 T B = 0.4799 T * 3 0 0 1 2 3 4 5 6 7 8 9 Radio Frequency (MHz) S. Balian et al, Physical Review B 2012
EPR studies of bismuth dopants in natural silicon
G. Morley et al, Nature Materials 2013 cw-epr of Bi@Si at 42 K, 4 GHz
G. Morley et al, Nature Materials 2013 Relaxation of Bi@Si at 8 K, 4 GHz potential Qubits
G. Morley et al, Nature Materials 2013 Rabi oscillations of Bi@Si at 8 K, 4 GHz
Lineshapes: Inhomogeneous Broadening due to Anisotropy 71
Lineshapes: Inhomogeneous Broadening due to Anisotropy The Hamiltonian: H = H EZ + H NZ + H HF 63 Cu 69.15% 65 Cu 30.85% S = ½; m S = ±½ I =3/2; m I = ±3/2, ±½ Copper tetraphenylporphyrin 72
Detection of Triplet States by EPR The spin Hamiltonian: H = H ZFS Tensor is traceless Zero-field splitting and anisotropic ISC are fingerprints for a triplet state 73
Detection of Triplet States by EPR The spin Hamiltonian: H = H ZFS + H EZ Zero-field splitting and anisotropic ISC are fingerprints for a triplet state 76
Detection of Triplet States by EPR The spin Hamiltonian: H = H ZFS + H EZ Zero-field splitting and anisotropic ISC are fingerprints for a triplet state 77
Time resolved EPR 82
Time resolved EPR direct-detection 10 ns time-resolution (no magnetic field modulation) 83
Time resolved EPR direct-detection 10 ns time-resolution (no magnetic field modulation) 86
Time resolved EPR The spin Hamiltonian: H = H ZFS + H EZ g, D, E, P x, P y, P z direct-detection 10 ns time-resolution (no magnetic field modulation) 87