An Electron Spin Resonance Study Using a Toroidal Split Ring Resonator

Transcription

1 An Electron Spin Resonance Study Using a Toroidal Split Ring Resonator AARON CLEMENTS SUPERVISED BY DR. JAKE BOBOWSKI

2 Outline Background: The Zeeman effect the origin of Electron Spin Resonance (ESR) What is a Toroidal Split Ring Resonator? Motivation - Why use a toroidal split ring resonator? Experimental design Magnet with water cooling loop What is DPPH? Lock-in detection method Results Characterization of the resonator s properties Successful observation of ESR spectrum AARON CLEMENTS AN ESR STUDY USING A TOROIDAL SRR 2

3 The Zeeman Effect Electrons have an intrinsic magnetic moment μ s (like tiny bar magnets). The spin-up and spin-down energy states are degenerate when the electrons are in zero magnetic field. In a magnetic field B applied, the energies of the two spin states diverge due to the Zeeman effect. The magnetic moment of an electron aligns either parallel ( spin-up ) or antiparallel ( spin down ) to the field. Parallel Spin up Lower energy Anti-parallel Spin down Higher energy AARON CLEMENTS AN ESR STUDY USING A TOROIDAL SRR 3

4 Magnetic Potential Energy U B = μ B Image: CC BY-SA 3.0, AARON CLEMENTS AN ESR STUDY USING A TOROIDAL SRR 4

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6 Electron Spin Resonance (ESR) Electrons can transition between the two energy states (spin-flip). They must gain or lose just the right amount of energy ( E) to do so. This energy comes in the form of photons: E = hν A electron can transition by absorbing or emitting a photon of the right frequency: hν = g e μ B B μ E μ B E B E = hν = E AARON CLEMENTS AN ESR STUDY USING A TOROIDAL SRR 6

7 ESR - Uses ESR is used to study paramagnetic samples. The sample must contain unpaired electrons (free radicals). Numerous applications across fields of science and industry. Image: Bruker EPR Spectrometer at University of Lethbridge Magnetic Resonance Facility AARON CLEMENTS AN ESR STUDY USING A TOROIDAL SRR 7

8 Split Ring Resonators Images: Bobowski 2013 AARON CLEMENTS AN ESR STUDY USING A TOROIDAL SRR 8

9 Split Ring Resonators The SRR can be modelled as a series LRC circuit, resonant frequency: ω 0 = 1 LC Images: Bobowski 2016 and 2013 AARON CLEMENTS AN ESR STUDY USING A TOROIDAL SRR 9

10 Toroidal SRR: f MHz 1Ghz AARON CLEMENTS AN ESR STUDY USING A TOROIDAL SRR 10

11 Motivation Recall: hν = g e μ B B An ESR experiment requires a suitable sample holder. Cavity size must be equal to radiation wavelength (for resonance). Cavity must be able to accommodate a sample The Toroidal SRR resonates at approximately 1 GHz relatively low. Requires only modest magnetic field strength easy to produce. We were able to demonstrate Electron Spin Resonance using this resonator, with a chemical called DPPH. AARON CLEMENTS AN ESR STUDY USING A TOROIDAL SRR 11

12 Magnet We wound a solenoid to accommodate the resonator. 600 m of wire, 30 cm long, 7.9 cm wide, 2500 turns, 10 layers, 5 kg of copper required. Total resistance = 13.7 Ω Resistive heating: P = I 2 R Peak magnet current in our experiment = 3 A Peak power dissipation = 123 W (as heat) Cooling system required. AARON CLEMENTS AN ESR STUDY USING A TOROIDAL SRR 12

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17 Resonator Characteristics Resonance frequency f MHz Quality factor Q 2200 Very stable when assembled, but: Slight variations can occur during reassembly. Coupling loop depth is important. Heating of the copper resonator changes resistivity. f % Q 9% Magnetic field is not responsible for these shifts. Latex sample holder did not affect characteristics. AARON CLEMENTS AN ESR STUDY USING A TOROIDAL SRR 18

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19 What is DPPH? 2,2-diphenyl-1-picrylhydrzyl A stable radical - chemical compound with one unpaired electron. Our thanks to Dr. Susan Murch, for lending us a bottle! Image: Sigma-Aldrich AARON CLEMENTS AN ESR STUDY USING A TOROIDAL SRR 20

20 Expected Behavior The ratio of electrons in the energy levels is given by MB distribution: n high = exp E high E low n low k b T = exp hν k b T = Thus there are slightly more electrons in the lower energy state and there will be a net absorption of energy by electrons. Set radiation frequency to f 0 of the resonator, scan through B. When hν = g e μ B B is satisfied, electrons will be able to transition. AARON CLEMENTS AN ESR STUDY USING A TOROIDAL SRR 21

21 Challenging to measure! Frequency AARON CLEMENTS AN ESR STUDY USING A TOROIDAL SRR 22

22 Lock-in Detection Need to measure tiny absorption dip within a large signal. Simply measuring P vs. f won t cut it (so, spectrum analyzer). Lock-in amplifier allows us to measure the derivative of our signal. The derivative is very distinct changing sign through the peaks. The frequency f is modulated by the signal generator at a reference frequency f ref. The signal of interest to us will also fluctuate with frequency f ref. AARON CLEMENTS AN ESR STUDY USING A TOROIDAL SRR 23

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24 Frequency AARON CLEMENTS AN ESR STUDY USING A TOROIDAL SRR 25

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