A new type of fractal has been discovered in magnetic ice – ScienceAlert

Fractal patterns can be found everywhere from snowflakes to lightning bolt on the irregular edges of the coasts. Beautiful to look at, its repetitive nature can also inspire mathematical insights into the chaos of the physical landscape.

A new example of these mathematical curiosities has been discovered in a type of magnetic substance known as spin ice, and it could help us better understand how a peculiar behavior called a magnetic monopole arises from its unstable structure.

Spin gels are magnetic crystals that obey similar structural rules to water gels, with unique interactions governed by the spins of their electrons rather than the push and pull of charges. As a result of this activity, they have no unique low-energy state of minimum activity. Instead, they almost glide along with noise, even at incredibly low temperatures.

From this quantum hum arises a strange phenomenon: features that act like magnets with only one pole. Although they are not entirely hypothetical magnetic monopole particles some physicists think they may exist in nature, behave in a similar enough way that they are worth studying.

So, recently, an international team of researchers turned their attention to a spinning gel called dysprosium titanate. When small amounts of heat are applied to the material, its typical magnetic rules break down and monopoles appear, with the north and south poles separating and acting independently.

Some years ago a team of researchers identified characteristic magnetic monopole activity in the quantum hum of a dysprosium titanate spin gel, but the results left some questions about the exact nature of these monopole motions.

In this follow-up study, the physicists realized that the monopoles were not moving total freedom in three dimensions. Instead, they were limited to a plane of dimensions 2.53 within a fixed lattice.

Scientists created complex atomic-scale models to show that monopole motion was constrained in a fractal pattern that was erased and rewritten based on previous conditions and motions.

“When we introduced this into our models, fractals immediately emerged,” says physicist Jonathan Hallén from the University of Cambridge.

“The configurations of the spins were creating a network where the monopoles had to move. The network was branching out like a fractal with exactly the right dimension.”

This dynamic behavior explains why conventional experiments had previously missed fractals. It was the noise created around the monopoles that finally revealed what they were really doing and the fractal pattern they were following.

“We knew something really weird was going on,” says physicist Claudio Castelnovo from the University of Cambridge in the United Kingdom. “The results of 30 years of experiments did not add up.”

“After several failed attempts to explain the noise results, we finally had a eureka moment, realizing that monopoles must live in a fractal world and not move freely in three dimensions, as had always been assumed.”

These kinds of advances can lead to incremental changes in the possibilities of science and how materials like spin gels can be used: perhaps in spintronicsan emerging field of study that could provide a next-generation upgrade to the electronics we use today.

“In addition to explaining several puzzling experimental results that have challenged us for a long time, the discovery of a mechanism for the emergence of a new type of fractal has led to a completely unexpected route because the unconventional motion occur in three dimensions”. says theoretical physicist Roderich Moessner from the Max Planck Institute for the Physics of Complex Systems in Germany.

The research was published in science.