Measuring the Hall Effect at High Temperatures

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Measuring the Hall Effect at High Temperatures

• Steven Moses
• Physics REU Program
• Prof. Ctirad Uher
• University of Michigan- Ann Arbor
• August 2, 2007

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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 500C 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.

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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
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The Hall coefficient an intrinsic property of a
material
The Hall voltage is given by
The Hall voltage is measured in the following way
The Hall coefficient is defined as the ratio
The units for the Hall coefficient are Om/T or,
equivalently, m3/C.
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The Experimental Setup
Cryogen level meter
Sample mount
AC resistance bridge
Magnet power supply
Thermocouple
Temperature controller
Water cooling system for the furnace
Superconducting magnet
Furnace
Solid state relay
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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.

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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

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Some pictures of the sample mount
To resistance bridge
Thermocouple
Sample
Ceramic support platform
The sample is located at the bottom.
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Inside Temperature vs. Outside Temperature for
the two furnaces
The temperature varies greatly with distance
along the axis of the water-cooled furnace.
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Pictures of the furnace tests
These pictures were taken during the initial
tests of the furnace outside of the magnet.
Solid state relay (outputs current from the
temperature controller)
Hoses to water supply
Thermocouple
Temperature controller
Furnace
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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
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The Long Process of Cooling the Magnet
Transfer tube

• First, the magnets 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
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Some initial data

• I was able to measure the Hall effect at room
  temperature, with relatively good results.
• One problem that I encountered was that the
  magnetic field made the signal on the resistance
  bridge very noisy, so obtaining an exact value
  for the resistance was very difficult.

The following data comes from a sample of
Ba0.3Yb0.05Co4Sb12, an n-type skutterudite, at
room temperature.
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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.

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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