# Researchers explore fractal magnetism for storage

COLUMBUS, Ohio — Magnetic polymer materials being studied at Ohio State University could give rise to a new form of magnetism characterized by fractal fields. Plastic molecules stacked in parallel chains exhibit fractal dimensions at the nanoscale, said professor Arthur Epstein, director of the university's Center for Materials Research, who — with Joel Miller, a professor of chemistry at the University of Utah — is attempting to model the polymer's behavior at about - 450°F.

Epstein and Miller earlier this year discovered photo-induced magnetism in a polymer. Now they predict that as the polymer's dimensions shrink, the magnetic dimension of the field will become fractal. The scientists believe these polymers will eventually yield light-controlled magnetic materials for a new breed of electronic storage devices.

In a fractal system, the "volume increase does not simply relate to an integral power of the dimensions," as in rectangles and cubes, Epstein said. "The volume of frozen water in a snowflake increases by a fractional power of the diameter of the snowflake — that is a fractal system," he said.

Magnetic fields exhibiting fractal dimensions would not obey the normal laws of fields, or would be influenced by them only in proportion to their dimensions. According to Epstein and Miller's detailed simulation, a hybrid compound material — manganese tetrapheynlporphy-rin and tetracyanoethylene — has one-dimensional polymer chains, and a bulk material made from it will have fractal dimensions of 0.8 to 1.6.

Epstein and Miller modeled their material as it cooled, after it was magnetized by an external field. At a critical temperature, the material began to behave as a glass rather than as a solid. At - 267°C ( - 449°F) the magnetic field of the bulk material was 0.8; at - 269°C ( - 452°F) it went to 1.6.

"The fractal dimension of our magnetic material describes the 'spins,' or unpaired electrons, as being aligned in fractal patterns. The magnetic fields that result from the fractal order of the spins will have a fractal shape near the fractal-shaped spin cluster," Epstein said. The farther from the spin cluster, "the magnetic fields are no longer fractal in shape."

In nanoscale plastic magnets, the magnetic "spin" of molecules — the direction of which determines the polarity of the field — forms nanoscale clusters within these polymer materials. If the dimensions are small enough, each cluster can point its field in a different direction without affecting other clusters.

When the temperature of the material was lowered, magnetic fields sprouted out of it like branches on a tree, followed by secondary magnetic fields that sprouted like leaves — the classical fractal repeated pattern-within-a-pattern.

The repeating pattern forms an overlapping, crisscrossing growth of interlocked fields, said the researchers. These fields follow the laws of fractal dimensions rather than ordinary physics. "This interlocking fractal growth gives the magnetic field a unique kind of order, and as a result, the material would be called a fractal cluster glass," said Epstein.