nomenclature: electron paramagnetic resonance (epr ... · 01/08/17 prof. dr. christopher w. m. kay...

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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)

Prof.Dr.ChristopherW.M.Kay01/08/17

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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.


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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


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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, 1O2 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


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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 ; Mn2+

•  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


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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 〈S2〉 = {S(S + 1)} ½ !. (2S + 1) components of angular momentum mS ! where mS = S, (S – 1), ..., –S. Hence, there are two components, with mS = ±½.


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Electron Transfer Reactions

Singlet S = 0

MS = 0

Doublet S = ½

MS = ±½

Triplet S = 1

MS = ±1, 0

Quartet S = 3/2

MS = ±3/2, ±½, 0

Quintet S = 2

MS = ±2, ±1, 0

For electrons, the spin quantum number, S = ½. The total angular momentum of magnitude 〈S2〉 = {S(S + 1)} ½ !. (2S + 1) components of angular momentum mS ! where mS = S, (S – 1), ..., –S. Hence, there are two components, with mS = ±½.


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Which Elements are Important for EPR?


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Which species has an unpaired electron in its outer orbital and hence has an EPR signal?

1.  Ca2+

2.  Cu1+ 3.  Cu2+

4.  Ti4+

5.  Zn2+


Seite Prof.Dr.ChristopherW.M.Kay 1301/08/17

Transition Metals with Unpaired Electrons

The energies of the d-orbitals are rendered non-degenerate by the presence of ligands

S = 0 S = 5/2 S = ½ S = 2

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Electron Zeeman Interaction

The analogous quantum mechanical expression (Hamiltonian) with the magnetic field in the z direction (taking the Sz component of S):

The magnetic moment of the electron:

where is the Bohrmagneton

The interaction of the magnetic moment and an external magnetic field, B0, is given by:

For electrons S = ½, so there are two basis states with mS = ±½. These are labelled |αe⟩ and |βe⟩, and may be represented by column vectors:


Seite Prof.Dr.ChristopherW.M.Kay1501/08/17


The allowed energies are found using the complete Hamiltonian in the Schrödinger equation:

In order to find the eigenvalues we need expressions for the quantum mechanical operators representing Sx, Sy and Sz. These are the Pauli spin matrices multiplied by a factor of ½:

By matrix multiplication, we can see that |αe⟩ and |βe⟩ are eigenstates of Sz. The eigenvalues are:



The Hamiltonian: HEZ = ge µβ SZ • Bo

Selection Rule: ΔS = ±1


Boltzmann Populations at Equilibrium


At 9.5 GHz & 298 K


Electromagnetic Radiation


Frequencies, Wavelengths & Magnetic fields


EPR Spectrometer design

Helmholtz Coil



Waveguide



Resonator Mode



1

2

3

5

4 1.  Microwave Source 2.  Attenuator 3.  Circulator 4.  Detector 5.  Amplifier 6.  Resonator 7.  Helmholtz Coil Magnet

7

6


EPR Spectrometer design – modulation


EPR Spectrum of a one electron system strong pitch



Important Nuclei (I ≠ 0) for NMR/EPR

Element Isotope Spin Number of lines

Gyromagnetic ratio [ MHz / T ]

Abundance [ % ]

Electron — ½ — 176085.98 —

Hydrogen 1H ½ 2 267.51 99.985

2H 1 3 41.06 0.015

Carbon 13C ½ 2 67.26 1.11

Nitrogen 14N 1 3 19.32 99.63

15N ½ 2 –27.11 0.37

Fluorine 19F ½ 2 251.67 100

Phosphorus 31P ½ 2 108.29 100

Vanadium 51V 7/2 8 70.32 99.76

Manganese 55Mn 5/2 6 66.18 100

Iron 57Fe ½ 2 8.65 2.19

Cobalt 59Co 7/2 8 63.12 100

Nickel 61Ni 3/2 4 23.95 1.134

Copper 63Cu 3/2 4 71.07 69.1

65Cu 3/2 4 76.05 30.9

Molybdenum 95Mo 5/2 6 -17.09 15.7

97Mo 5/2 6 -17.88 9.46

Bismuth 209Bi 9/2 10 44.92 100


Nuclear Zeeman Interaction

The Hamiltonian: HNZ = −gN µβ IZ • Bo

Selection Rule: ΔI = ±1


Electron-Nuclear Hyperfine Interaction

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:

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:

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:

where


Description of a 1 electron, 1 proton system

S = ½; mS = ±½ I = ½; mI = ±½

The Hamiltonian: H = HEZ + HNZ + HHF

Pauli Spin Matrices



S = ½; mS = ±½ I = ½; mI = ±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



S = ½; mS = ±½ I = ½; mI = ±½




S = ½; mS = ±½ I = ½; mI = ±½


Hig

h-fie

ld a

ppro

xim

atio

n


Silicon doped with Phosphorus @ 10 K

S = ½; mS = ±½ I = ½; mI = ±½


Hig

h-fie

ld a

ppro

xim

atio

n

9.7GHz


EPR Spectrum of N@C60 @ 9 GHz


S = 3/2 mS = 3/2, ½, –½ ,–3/2 I = 1 mI = 1, 0, –1


EPR Spectrum of Mn2+ @ 94 GHz


S = ½ mS = ±½ I = 5/2 mI = ±5/2, ±3/2, ±½


Silicon doped with Bismuth @ 9.7 GHz


Bi

S = ½ I = 9/2 mI = ±9/2, ±7/2, ±5/2, ±3/2, ±½ A = 1.4754 GHz

9.7GHz


Silicon doped with Bismuth @ 9.7 GHz


Bi S = ½ I = 9/2 A = 1.4754 GHz

S = ½ I = ½ A = 117.1 MHz

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


EPR Spectrum of the perinaphthenyl radical


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


Lineshapes: Homogeneous & Inhomogeneous Broadening


Pulse Scheme for a 2-pulse sequence Hahn Echo

pulsed EPR is a useful method to measure relaxation (T1 & T2)

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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, 1O2 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



Group V Dopants in Silicon: Remarkably long relaxation times

pulsed EPR is a useful method to measure relaxation (T1 & T2)

G. Morley et al. Nature Materials (2010,2012)

The Hamiltonian: H = HEZ + HNZ + HHF S = ½; mS = ±½ I = ½ or 9/2;


Group V Dopants in Silicon: Remarkably long relaxation times


Bi

S = ½ I = 9/2 mI = ±9/2, ±7/2, ±5/2, ±3/2, ±½ A = 1.4754 GHz

9.7GHz

28Si:I=0;95.3%29Si:I=½;4.7%


ENDOR: Electron-Nuclear Double Resonance

Determination of the hyperfine couplings (a) between the electron and nucleii


G. Feher Phys. Rev. 103 (1956)


Continuous-wave ENDOR


Pulse (Davies) ENDOR

Davies, Phys. Lett. A 47, 1 (1974)


Pulse (Davies) ENDOR

pulsedENDORofBi@Siat13K,9GHz

S. Balian et al, Physical Review B 2012

2 3 4 5 6 7 8 9 10 11Radio Frequency / MHz

line 10

line 9

line 8

line 7

line 6


0 1 2 3 4 5 6 7 8 9 10 11 12Radio frequency (MHz)

568.7

479.9

396.8

321.6

256.7

203.7

162.6

131.7

108.9

91.8

11.358.328.02

4.81

2.882.49 2.00

0.51

X1

X28.02

2.49

4.8111.35X28.32

1.65 2.881.33

X1

Isotropic superhyperfine couplings (MHz)

11�10

Magnetic

field,B

(mT)

12�9

13�8;

14�7;

15�6;

16�5;

17�4;

18�3;

19�2;

20�1; EPRTransition;



0 1 2 3 4 5 6 7 8 9Radio Frequency (MHz)

0

3

6

9

Line 9 ENDOR at 9.755 GHzFitted GaussiansSum of Gaussians

015304560

B = 0.1888 TB = 0.4799 T

Extrapolated GaussiansSi nuclear Zeeman frequency29

Inte

nsity

(a.u

.)



0

3

6

9


015304560

B = 0.1888 TB = 0.4799 T


Inte

nsity

(a.u

.) *

HyperfineStructureofBi@Si

SilicondopedwithBismuthat10K,9.720844GHz

Bi

Balian et al. PRB (2012)

HyperfineStructureofBi@Si


0

3

6

9


015304560

B = 0.1888 TB = 0.4799 T


Inte

nsity

(a.u

.)


*

EPRstudiesofbismuthdopantsinnaturalsilicon

cw-EPRofBi@Siat42K,4GHz

G. Morley et al, Nature Materials 2013

RelaxationofBi@Siat8K,4GHzpotentialQubits


RabioscillationsofBi@Siat8K,4GHz



Lineshapes: Inhomogeneous Broadening due to Anisotropy


Lineshapes: Inhomogeneous Broadening due to Anisotropy

63Cu 69.15% 65Cu 30.85% S = ½; mS = ±½ I =3/2; mI = ±3/2, ±½


Copper tetraphenylporphyrin


Detection of Triplet States by EPR

Zero-field splitting and anisotropic ISC are fingerprints for a triplet state

The spin Hamiltonian: H = HZFS

Tensor is traceless




The spin Hamiltonian: H = HZFS + HEZ


Time–resolved EPR


Time–resolved EPR

direct-detection – 10 ns time-resolution (no magnetic field modulation)


Time–resolved EPR



Time–resolved EPR


The spin Hamiltonian: H = HZFS + HEZ g, |D|, |E|, Px, Py, Pz

nomenclature: electron paramagnetic resonance (epr ... · 01/08/17 prof. dr. christopher w. m. kay...

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