Experiment #9: Electron Spin Resonance
You will use electron spin resonance to measure the spin magnetic moment of the electron. (μz,
its z component, to be precise.) A substance (containing electrons) is placed in a magnetic field,
B, which causes a difference in energy between "spin up" and "spin down" of
ΔU = 2μz B
Radio waves are also sent through the area. B is adjusted until ΔU matches the energy of the
radio wave photons. When they match, the photons can be absorbed by flipping electrons from
spin up to spin down. You can tell when this happens, because when the electrons take energy, it
puts a load on the circuit that produces the radio waves. At this time, you know ΔU from the
frequency of the photons (ΔU = hf), and you know B from the current in the coils producing the
field. So, you can solve for μz.
DETAILS:
A material whose molecules have one unpaired
electron outside a closed subshell is placed inside a
small coil carrying an rf (radio frequency) alternating
current. (Interactions with the molecule's other
electrons balance out.) This is placed in a set of larger Helmholtz coils, which produce the
background field, B.
The background field makes the electron precess like a
gyroscope; as time passes, μ, the electron’s spin magnetic
moment vector, traces out a cone over and over. μ's angle
with the z axis can be just one of the two possibilities shown,
similar to how there are just certain allowed directions for the
orbital magnetic moment. Work must be done against the
magnetic torque to turn a magnet in a B field; the work to get
from spin up to spin down is ΔU = 2μz B, as stated above.
The radio waves from the small coil are really just the rapidly
changing magnetic field from the coil's current, and the
electric field it induces. As they build up, the coil's fields gain energy from the circuit; when the
fields decay, much of the energy goes back into the circuit again. However, if the radio waves
are being absorbed by flipping the electrons, the circuit doesn't get the energy back. This load on
the circuit makes the current drop, which is how you detect "resonance" between the radio waves
and the electrons.
To search for resonance, the apparatus slowly varies the current producing B, which varies ΔU
between the spin states. When ΔU reaches the energy of the photons, the sample suddenly starts
absorbing a lot of them, causing resonance.
The absorption signal and the signal powering the Helmholtz coils are applied to an oscilloscope,
- 2 as shown. When the right B for resonance is reached in either
direction (hence a peak on either side of the origin), the
absorption of photons goes up, causing the peaks shown. So, half
the distance between the peaks tells you the current, which tells
you B. A digital display on the ESR apparatus tells you the rf
frequency it's producing, which tells you the ΔU between the two
spin states. From ΔU and B, you can find μz.
PROCEDURE:
1. Calibrate the horizontal scale of the oscilloscope.
(It has no built-in calibration for signals it gets
through EXT X.)
a. Connect the scope to a DC power supply
and a digital voltmeter as shown.
Set time/cm to external x. Adjust brilliance to a minimum to avoid damaging the screen.
Set the switch near the bottom left of the scope on DC.
b. Set the power supply so that the meter reads 5.0 V.
c. Flip the power supply on and off over and over. Adjust x gain until this makes exactly
5 cm difference in the spot's horizontal position. The horizontal axis on the scope is now
calibrated to 1 volt per centimeter. Be
careful not to touch x gain again,
especially when using x shift.
2. Remove the voltmeter and power supply
from the scope, then make the connections
shown. Attach the head to a ring stand and put
its probe (with the rf coil on the end) through a
slot in the side of the Helmholtz coil. Center
the sample in the Helmholtz coil.
3. Get the apparatus working:
a. Turn volts/cm on the scope all the
way to 10 mV. (Time/cm should still be
on EXT X).
b. Turn the ESR system on with the
switch on the base unit.
c. If necessary, adjust the feedback knob on the head unit so that the frequency meter on
- 3 the base unit reads between 25 and 40 MHz.
d. Turn "coil current adjust" on the base unit all the way up (clockwise).
e. If the two resonance peaks discussed earlier are not now visible, set "tuning" on the
head unit for a frequency in the upper 30's of Megahertz (the peaks are largest in this
range) and then adjust feedback until they appear. If the frequency drops to 0, you've
turned feedback too far down.
In stubborn cases, turn the ESR unit off, let it rest a minute or two, then try again.
f. Once the peaks are visible, adjust feedback to make them as large as possible.
g. If the lower peaks don't line up with the upper pair, adjust "phase null" on the base
unit.
4. Observe the magnetic field (current in large coil) necessary for resonance at several different
frequencies:
a. Record the distance between the peaks and the corresponding frequency for a number
of frequencies, spread out over the full range available. Just measure this with a ruler:
Positioning the trace to best read the scale on the scope runs the risk of turning X gain
along with X shift. At lower frequencies, a slight readjustment of feedback may be
necessary to make the peaks show up.
b. Since the peaks are 2Ires apart, divide their separation by 2 to fill in the current column
of the data table. (Things are calibrated such that 1 A in the Helmholtz coils corresponds
to a 1 cm horizontal deflection on the scope).
5. Plot a graph with Ires on the horizontal axis and f on the vertical axis. (Just do it by hand, or if
you prefer the computer, refer back to the photoelectric lab for instructions.) For error bars,
estimate how far off the oscilloscope readings might have been and divide this by 2 also. Fit a
line through these points, and through the origin. (ΔU equals 0 when B equals 0). Find its slope.
Even doing the graph by hand, there shouldn't be much room for error if you remember to
include 0, 0 as one of your data points.
6. Find μz from the slope. Show all steps in the space provided.
a. Into ΔU = 2μzB, substitute ΔU = hf and the fact that the field of the Helmholtz coils is
given by B = .00049 I tesla. .
b. Rearrange that to solve for f/I.
c. Think about where to fill the slope into the expression you just wrote. Solve for μz.
7. Compare to the accepted value of μz is given in your text. (Look for "Bohr magneton" in the
index). If your value has an uncertainty of about ± 5%, does it agree with the accepted one?
- 4 Report on Experiment 9: Electron Spin Resonance
peak to peak
distance (cm)
Calculate slope:
Calculate μz from slope:
Calculate uncertainty:
Accepted value:
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Resonant
current (A)
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f (MHz)
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