Measuring the Hall Effect at High
Temperatures
Steven Moses
Physics REU Program
Prof. Ctirad Uher
University of Michigan- Ann Arbor
August 2, 2007
Summary of the project
• I designed an apparatus which mounts a sample and is then
placed in a superconducting magnet that will enable us to
measure the Hall effect at high temperatures and in strong
magnetic fields (hopefully up to 500˚C and 9 Tesla).
• I worked with many of the other components of the system,
including the furnace, magnet, cryogens, temperature
controller, and water cooling system.
• The goal of this project is to be able to measure the Hall
effect at high temperatures for a wide range of samples, and
thus expand the repertoire of available measurements in the
lab.
A brief summary of the Hall effect
• The Hall effect arises when a
current-carrying sample is
placed in a transverse
magnetic field.
• The Lorentz force in this
diagram is always towards the
front.
• The sign of the potential
difference VH determines the
polarity of the charge carriers
in the sample.
• The Hall effect can also be
used to calculate the carrier
density of the sample and the
drift velocity.
www.eeel.nist.gov/812/images/fig1.jpg
The Hall coefficient: an intrinsic
property of a material
IB
The Hall voltage is given by: VH E H w
nqd
The Hall voltage is measured in the following way:
V H ( B ) V H ( B )
VH
2
The Hall coefficient is defined as the ratio
VH 1
RH
IB / d nq
The units for the Hall coefficient are Ω∙m/T or, equivalently, m3/C.
The Experimental Setup
Cryogen level meter Sample mount
AC resistance bridge
Magnet power
supply
Thermocouple
Temperature
Water cooling controller
system for the
furnace
Superconducting magnet Furnace Solid state relay
Factors that made the design difficult
• Space was the major issue in the design, as the bore
in the magnet is only a little over 8 cm wide.
• It is difficult to design a furnace that can fit in the
small space yet remain cool on the outside when the
inside temperature is 300 to 500˚ C.
• Maintaining a good contact on the sample over a wide
range of temperatures is crucial but difficult to obtain
due to effects like thermal expansion. Using silver
paste or some other adhesive helps to make a good
contact but is sloppy and can be awkward to use in
such cramped conditions; furthermore, silver paste
cannot be used at temperatures over 500˚ C.
The superconducting magnet
• Uses approximately 80 L of
liquid helium and 125 L of
liquid nitrogen to precool
• Operates at a temperature of
4.2 K
• Is capable of generating fields
of up to 9 Tesla
• Has an 8 cm cylindrical bore
that houses the sample mount
and furnace
Some pictures of the sample mount
To resistance bridge
Thermocouple
Sample Ceramic support
platform
The sample is located at the bottom.
Inside Temperature vs. Outside Temperature for
the two furnaces
Original design
Temperature vs. distance at 400 C
300
140
250
inside
temperature (C)
120
200 temperature
temperature (C)
100
150
80
100 temperature
outside
60
50
temperature
40
0
20 Water-cooled furnace
0 2 4 6 8 10 12 14 16 18 20
0
time (minutes) 450
0 2 4 6 8 10 12 14 16 17
distance from bottom of furnace (cm) 400
inside temp.
350
temperature (C) 300
250
maximum
The temperature varies greatly 200 outside temp.
with distance along the axis of 150
100 minimum
the water-cooled furnace. 50
outside temp.
0
0 10 20 30 40 50 60 70 80 90 100
time (minutes)
Pictures of the furnace tests
These pictures were taken during the initial tests Solid state relay (outputs
of the furnace outside of the magnet. current from the
temperature controller)
Hoses to water supply
Thermocouple
Temperature controller
Furnace
Some of the things I did during the last
ten weeks
• I worked in the machine
shop, fixed the temperature
controller setup, tested the
furnaces, and continually
modified the design for the
sample mount.
• I learned how to work with
and transfer cryogens.
• I practiced making several
of the other measurements
in the lab.
A picture of me during the liquid helium transfer
The Long Process of Cooling the Magnet
• First, the magnet’s Transfer tube
outer chamber must be
pumped to a very low
pressure (~10-5 torr).
• Next, the liquid helium
chamber must be pre-
cooled.
• Liquid nitrogen must
then be blown-out.
• Finally, liquid helium
is transferred.
• This whole process
takes about two days.
Cylinder of helium gas used to blow out the liquid helium
Some initial data
The following data comes from a sample of • I was able to measure the
Ba0.3Yb0.05Co4Sb12, an n-type skutterudite, at Hall effect at room
room temperature.
temperature, with relatively
Hall Coefficient good results.
Field Strength (T) Resistance (mΩ)
10-2 cm3 /C
• One problem that I
1.000 -0.0065
-1.000 0.0090
-2.26 encountered was that the
2.000 -0.0115 magnetic field made the
-2.55
-2.000 0.0235 signal on the resistance
5.000 -0.0420
-2.39 bridge very noisy, so
-5.000 0.0400
Average -2.40
obtaining an exact value for
the resistance was very
The value for the Hall coefficient was found previously by
Dr. Xun Shi to be -2.212∙10-2 cm3 /C at 300 K and 1 T. difficult.
What will come next
• As soon as the magnet is ready for operation again, I
will begin to take measurements at high temperatures.
• In the future, I hope to reduce the noise and improve
the accuracy of the measurements.
• I will try to improve the setup to allow measurements
to be made at increasingly higher temperatures.
• Hopefully, my work on this project and the
measurements I make may eventually allow me to
publish a paper based on my results.
Acknowledgments
• I would like to thank Prof.
Ctriad Uher, Dr. Xun Shi,
and Huijun Kong for their
help with my project.
• I would like to thank the
Physics REU Program.
• I would also like to thank
the NSF for funding part of
my stipend.
A picture of my research group