FRACTALS ADD
NEW DIMENSION TO STUDY OF TINY ELECTRONICS
COLUMBUS, Ohio
When it comes to miniature electronics, scientists have
seen the shape of things to come -- and that shape is a fractal.
People most often see fractals in the familiar, irregular
branching shapes of nature -- a leaf, or tree, or snowflake. A repeating
pattern of ever-smaller branches gives these structures a unique profile
that defies classical geometry.
Now a study suggests that magnetic fields can take
the form of fractals, too -- if a magnet is made of plastic molecules
that are stacked in parallel chains.
While the results could influence the design of electronic
devices in the distant future, the work is so new that scientists
are only beginning to consider its implications, said Arthur Epstein,
Distinguished University Professor of chemistry and physics and director
of the Center for Materials Research at Ohio State University.
Epstein and longtime collaborator Joel Miller, professor
of chemistry at the University of Utah, described the study in a recent
issue of the journal Physical Review Letters. Coauthors included graduate
students Stephen Etzkorn at Ohio State and Wendy Hibbs at the University
of Utah.
Using a computer model, the scientists tried to look
ahead to a time when electronic structures can be built so small that
they no longer behave like normal three-dimensional objects.
“The materials currently used in magnetic devices
-- for example, computer hard discs or ID strips on credit cards --
behave like three-dimensional magnets,” explained Epstein. “However,
the decreasing size of these devices may one day require them to be
considered one- or two-dimensional in nature. As the spatial dimensions
decrease, the magnetic dimensions of the materials may take on fractal
values.”
Mathematically, fractals are considered to exist in
partial, or fractional, dimensions. That means if a device produced
a magnetic field that exhibits fractal behavior, the magnetic field
wouldn’t possess dimension equal to a whole number -- such as
one, two, or three dimensions -- but rather a fractional value such
as 0.8 or 1.6 dimensions.
Such a seemingly bizarre existence in fractional dimensions
sounds like the stuff of science fiction, but that’s what Epstein
and his colleagues found when they modeled the behavior of a plastic
magnet.
The model consisted of a hybrid material, a compound
of manganese tetrapheynlporphyrin and tetracyanoethylene. Theoretically,
this compound can form polymer chains that are one-dimensional.
The researchers modeled the behavior of the material
as it was magnetized by an external magnetic field and then cooled
to a critical temperature where it began to behave as a special kind
of glass. At -267ºC (-449ºF), the magnetic field of the
material appeared to exist in 0.8 dimensions. As it cooled a little
further, it gradually became one-dimensional, then finally settled
at 1.6 dimensions at -269ºC (-452ºF).
The “spin” of the molecules -- a quality
that relates to the source of magnetism and magnetic fields in materials
-- appeared to form clusters within the material, with each cluster
pointing its magnetic field in a different direction. Many magnetic
fields sprouted out from the material like branches of a cactus. Tiny
secondary magnetic fields then sprang out from the branches like needles
on a cactus.
Eventually, the cacti-like branches were locked together,
with crisscrossing needles holding them in place. This interlocking
fractal growth gave the magnetic field a unique kind of order, and
as a result, the material would be called a “fractal cluster
glass,” Epstein said.
To explain this behavior, Epstein likened the one-dimensional
polymer chains of this exotic compound to stacks of poker chips. “Imagine
each poker chip is an atom,” he said, “and that many stacks
of chips are immersed in chicken fat.”
“When the fat insulation is thin, the stacks of
poker chips can all ‘see’ each other. When it comes to
orienting their magnetic fields, each stack can look to its neighbor
to see what it should be doing, and all the stacks can orient the
same way,” he said.
“But when the chicken fat insulation is thick
(as for the materials used in this study), it becomes opaque, and
suddenly the stacks of poker chips can’t see each other,”
he continued. “Without knowing what its neighbors are doing,
each stack has to pick a random direction for its magnetic field.”
Spins of different groups of atoms within the stack
may pick different directions at first. Normally, these clusters would
interact with each other in a kind of competition, until the magnetic
fields were all pointing in the same direction.
“Sometimes the atoms don’t have enough energy
to fight with each other. Then the clusters just continue to point
in random directions, and the material is considered a cluster glass,”
Epstein said.
Epstein believes that cluster glasses could play a role
in future electronics, when organic-based magnets could be structurally
tuned to provide magnets of differing dimension.
Until then, scientists will have to probe this fractal
behavior further.
“We’re just now beginning to understand
these exciting phenomena,” Epstein said.
The Department of Energy and the National Science Foundation
supported this work.
#
Arthur J. Epstein, (614) 292-1133; Epstein.2@osu.edu
Written by Pam Frost Gorder, (614) 292-9475; Gorder.1@osu.edu
