AMES, Iowa – Like the surface motif of a bubble bath, the spatial distribution
of a magnetic field penetrating a superconductor can exhibit an intricate,
foam-like structure. Ruslan Prozorov at the U.S. Department of Energy's
Ames Laboratory has observed these mystifying, two-dimensional
equilibrium patterns in lead samples when the material is in its
superconducting state, below 7.2 Kelvin, or minus 446.71 degrees Fahrenheit.
Through innovative research to relate the complex geometry of the
equilibrium patterns to the macroscopic physical properties,
such as magnetism, Prozorov has shown that the shape of the entire
sample determines the pattern topology and overall magnetic
behavior of the system – a significant finding that represents
a major contribution to the field of superconductivity. "You can
have the same volume and same mass, but if you just change the
shape, you get a different type of response from the sample and
a different type of geometry of the equilibrium field pattern,"
he said. "The discovery has reopened the whole field of equilibrium
in type-I superconductors, which had gone dormant because it was
considered closed."
Prozorov's discovery of the complex patterns in superconducting lead
marks a noteworthy departure from the model first proposed by
Russian physicist Lev Landau in the 1930s. Landau's model, which
resembles a labyrinth or laminar pattern, has been the unchallenged
standard in physics textbooks for 70 years.
But Prozorov questions the Landau model and maintains that it's
impossible to deduce the equilibrium patterns of superconductors
from global energy minimization – an established law of physics.
"You can assume a certain geometry or pattern and work with it
to find an optimal configuration, but that doesn't guarantee
that the pattern you've assumed is the one that will turn out as
the absolute minimum energy state in nature," he explained.
Offering an example of the problem he sees with the Landau
model, Prozorov said, "If you assume two patterns, you can
calculate the total energy for each of them, and the one
with the lowest energy may be the equilibrium pattern.
Of course, you can't prove that there isn't another pattern
that has even lower energy. You need to, in point of fact, observe
the patterns and relate them to the actual measured physical properties."
Over the years there have been observations of equilibrium
patterns in superconductors that differ from the labyrinth
model proposed by Landau. However, the unusual patterns were
considered to be defects or fluctuations due to imperfections
in the material under study. No one bothered to relate the patterns
they were observing to macroscopic properties. No one, that is,
until Prozorov.
"It all started with an accidental finding," he said. I was trying to
calibrate a thermometer in my magneto-optical cryostat, so I put
in a very clean, stress-free piece of lead. This is an easy way to
calibrate because lead becomes superconducting at 7.2 Kelvin,
so when I looked at my sample and saw superconductivity,
I knew my thermometer was correct."
But something else wasn't correct, at least not textbook correct.
When Prozorov applied a sufficiently large magnetic field and
looked at the lead sample in the magneto-optics system, he was
surprised to see not the Landau labyrinth pattern but, rather,
a pattern of two-dimensional tube shapes that he describes as
looking like soap foam. "I was shocked because this was totally
unexpected," he said. "So now the big question was which
pattern represents equilibrium?"
Prozorov's experiments showed that, depending on its purity
and macroscopic physical shape, the sample under investigation
displayed either the soap-foam pattern or the Landau laminar
pattern. He knew that samples like disks or slabs that have two
parallel surfaces also have a property known as a geometric barrier.
Only those sample shapes exhibited the Landau pattern, and
only when the magnetic field was reduced. However, Prozorov
discovered that shapes without two flat surfaces, such as spheres,
hemispheres, pyramids and cones, don't exhibit the Landau behavior.
"We observed the foam, or tubular, phase in all of these s
ample shapes, and we don't have the Landau phase at all," he said.
"So it's the foam phase that's the equilibrium state of the system.
Most of the past studies were done on samples with flat surfaces,
that's why people never observed this previously for decreasing
magnetic field."
Emphasizing the difficulty involved in creating these less common
sample shapes, Prozorov said, "To observe this soap-foam phenomenon,
the samples must be very clean and defect-free with a uniformity
of crystal structure. We spent a lot of time trying to make lead
samples in the shapes of hemispheres, cones and pyramids and
finally succeeded. Having access to the materials expertise
available at Ames Laboratory has been a tremendous benefit
in our efforts," he added.
The DOE Office of Science, Basic Energy Sciences Office and
the National Science Foundation funded the above work on
equilibrium patterns in superconductors.
Ames Laboratory, celebrating its 60th anniversary in 2007, i
s operated for the Department of Energy by Iowa State University.
The Lab conducts research into various areas of national concern,
including energy resources, high-speed computer design,
environmental cleanup and restoration, and the synthesis and study
of new materials.
Reference: "Equilibrium Topology of theIntermediate State in
Type-I Superconductors of Different Shapes,"
by Ruslan Prozorov appears in Physical Review Letters, June 22, 2007.
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