Electron Spin Resonance in a Ferrite B15

ELECTRON SPIN RESONANCE IN A FERRITE

SAFETY ISSUES

THE 100 VOLTS DC POWER SUPPLY FOR THE MAGNET COULD BE LETHAL.

You should not have any need to touch any of the associated wiring.
If you suspect a fault, consult a laboratory technician.

A lot of power is dissipated in the voltage-to-current converter, particularly when set to high currents, so ensure that it is freely ventilated. Reduce the current to small values (but don't keep turning the electronics on and off) when possible.

Objectives

You should achieve an understanding of:

a) the phenomenon of magnetic resonance.

b) electromagnets and use of Hall probes.

c) microwave components.

d) modulation and Phase Sensitive (or Lock-In) Detection

Background

In the presence of a magnetic induction B, the spin-up and spin-down energy levels of a free electron are split by:

Eq. 1

where gs is the free electron g-factor (=2.0023…) and mB is the Bohr magneton, eh/4pm (=9.271024JT-1).

This Zeeman splitting of energy levels was first seen as additional structure in the optical spectra over a century ago; direct transitions between spin-up and spin-down states occur at much lower frequencies and were not observed until the advent of microwave electronics.

In order for there to be a net absorption of photons, the numbers of spin-up and spin-down electrons must be different, i.e., the sample has to be magnetically polarised. Furthermore, for the absorption to be detectable with the fairly simple equipment used here, the excess number of spins has to be rather large.

Both of these conditions can be met by using a ferromagnetic material, such as yttrium iron garnet (Y3Fe5O12), in which the Fe atoms are magnetically aligned. Eq.1 has then to be modified, and gs replaced by geff, the effective g-factor; geff depends on the material, and also the shape of the sample.

Spherical samples of the ferrite provided for this experiment have geff close to 2.

Equipment

Electromagnet

110V 3A power supply with integrated Voltage-to-current converter (VIC)

Hall sensor

2 audiofrequency signal generators

Lock-in amplifier

Chart recorder

Microwave source (Gunn diode) and power supply

Microwave Isolator

Waveguide attenuator.

Wavemeter

Waveguide diode detector and amplifier

Ferrite samples

Experimental Set-up

electromagnet calibration

Inspect the high current connections to the magnet, and ensure that they are as in Fig.1. Turn on the 110V power supply.

Using a Hall sensor, calibrate the magnetic field against magnet current, which can be varied with the offset potentiometer on the Voltage to Current Converter (VIC).

Estimate:

(a)  The accuracy with which you will be able to ascertain the field at the eventual sample position.

(b)  The reproducibility with which you will be able to set that field.

microwave circuit

Connect the microwave components as in Fig.2.

Tune the Gunn diode source by adjusting the micrometer (which alters the length of a resonant cavity), until a large amount of power is seen by the detector.

Measure the microwave frequency with the cavity wavemeter, which when tuned to resonance absorbs a small fraction of the power.

(a)  Find out what range of microwave frequencies can be generated by the source.

The guided wavelength which can be measured with the wavemeter has to obey the following equation

where is the free-space wavelength and the cut-off wavelength (2 x the broad side of the waveguide).

(b)  Estimate the accuracy with which the frequency can be measured.

Measurements (1 unit experiment)

simple detection

Locate a spherical ferrite sample appropriately within the waveguide and magnet. Sweep the magnetic field at a suitable speed using the ramp signal generator (RSG).

(a)  Obtain a (small) resonant signal in the transmitted microwave power as a function of magnetic field.

(b)  Optimise the signal-to-noise of that signal.

(c)  Estimate geff for the material.

(d)  Examine how the signal behaves at one or two more microwave frequencies.

phase sensitive (PSD or lock-in) detection

If you are not already familiar with the purpose and use of PSD’s, it is vital that you read about them.

Ensure that you understand how modulation of the magnetic field yields a signal that is proportional to the derivative of the absorption. Clarify with a demonstrator if necessary.

Connect the detector output to the PSD signal input, and the reference output from the modulator signal generator (MSG) to the PSD reference input. Set the MSG to around 30Hz.

(a)  With the sample that you used for simple detection, set the field to a (fixed) value where you expect the absorption derivative to be large, and monitor the PSD output.
Adjust the MSG modulation amplitude and vary the gain setting on the PSD until you obtain a visible signal on the PSD output.

(b)  Explore the effects of varying the PSD settings, including phase, output time-constant and offset.

(c)  Set the PSD phase correctly (Hint: it is always easier to set a null than a maximum).

(d)  Optimise the signal-to-noise.

(e)  Using the RSG to sweep the field at a suitable speed, plot the absorption derivative signal on the chart recorder.

(f)  Examine the resonance in a small amount of powdered ferrite, measure geff and linewidth.

(g)  Explore a few different microwave frequencies.

(h)  Explore the effect of changing the microwave power level.

Report

Should follow the standard pattern. The description of the equipment should be brief, but sufficient to allow a self-contained explanation of what you have done to set it up optimally.

Ensure that the graphical information is concise and can be referred to easily.

NB, magnetic resonance in a ferromagnetic material is a complicated phenomenon (see e.g. Kittel Introduction to Solid State Physics; you are not expected to understand it in detail, nor to reproduce the theory in your report.

Assessment Criteria

In addition to the standard criteria:

You need to demonstrate that you have understood the principle of modulation combined with phase-sensitive detection, and shown how to maximise the signal-to-noise.

Note that an excess of data is a waste of your time, and will tend to count negatively!

Possible extensions

Other kinds of ferrite sample may be available; check with demonstrator.

Measure the field modulation amplitude at the sample position, and examine changes in the signal shape when the amplitude becomes comparable with the line width.

General References

Microwaves and waveguides:

·  I.S. Grant & W.R. Phillips Electromagnetism or other advanced undergraduate text.

·  Paul Lorrain, Dale Corson Electromagnetic Fields and Waves (1970, W.H. Freeman and Company, New York)

·  John D. Kraus Electromagnetics international edition (1991, McGraw-Hill Book Company, New York)

·  J.D. Jackson Classical Electrodynamics (1975, John Wiley \& Sons, New York)

·  http://www.fnrf.science.cmu.ac.th/theory/waveguide

ESR:

·  H.Haken, H.C.Wolf The Physics of Atoms and Quanta (2001, Springer-Verlag, Berlin)

·  http://en.wikipedia.org/wiki/Electron_spin_resonance

Lock-in-Amplifier:

·  http://www.uni-oldenburg.de/Docs/epkos/Messtechnik.pdf

·  http://www.bentham.co.uk/pdf/Lock-in%20amplifier%20tutorial.pdf

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