Fractal patterns can be found everywhere from snowflakes to lightning to the jagged edges of coastlines. Beautiful to behold, their repetitive nature can also inspire mathematical insights into the chaos of the physical landscape.
A new example of these mathematical quirks has been discovered in a type of magnetic substance known as spin ice, and it could help us better understand how a quirky behavior called a magnetic monopole emerges from its troubled structure.
Spin ices are magnetic crystals that follow similar structural rules to water ice, with unique interactions determined by the spins of their electrons rather than the pushing and pulling of charges. As a result of this activity, they do not have any low energy states of minimal activity. Instead, they almost buzz with sound, even at insanely low temperatures.
Out of this quantum buzz emerges a strange phenomenon – features that act like magnets with only one pole. While they’re not quite the hypothetical monopole magnetic particles that some physicists think exist in nature, they behave in ways that make them worth studying.
So an international team of researchers recently turned their attention to a spider ice called dysprosium titanate. When small amounts of heat are applied to the material, the typical magnetic rules break and monopoles appear, with the north and south poles separating and acting independently of each other.
Several years ago, a team of researchers identified distinctive magnetic monopole activity in the quantum hum of a dysprosium titanate spin ice, but the results left a few questions about the exact nature of these monopole motions.
In this follow-up study, physicists realized that the monopoles were not moving in three dimensions with complete freedom. Instead, they were confined to a plane of 2.53 dimensions within a fixed grid.
The scientists created complex atomic-scale models to show that the monopole motion was confined to a fractal pattern that was erased and rewritten depending on conditions and previous motions.
“When we incorporated this into our models, fractals immediately appeared,” says University of Cambridge physicist Jonathan Hallén.
“The configurations of the spins created a network that the monopoles had to move. The network branches out like a fractal with just the right dimension.”
This dynamic behavior explains why conventional experiments had previously missed the fractals. It was the noise created around the monopoles that ultimately revealed what they were actually doing and the fractal pattern they followed.
“We knew something very strange was going on,” says physicist Claudio Castelnovo of the University of Cambridge in the UK. “The results of 30 years of experiments were wrong.”
“After several failed attempts to explain the noise results, we finally had a eureka moment, when we realized that the monopoles must live in a fractal world and could not move freely in three dimensions, as had always been assumed.”
Breakthroughs like this could lead to incremental changes in the capabilities of science and how materials such as spin ice could be used: perhaps in spintronics, an emerging field of study that could offer a next-gen upgrade to the electronics we use today.
“In addition to explaining several puzzling experimental results that have long challenged us, the discovery of a mechanism for the emergence of a new type of fractal has led to a completely unexpected pathway for unconventional motion in three dimensions,” says theoretical physicist Roderich Moessner of the Max Planck Institute for the Physics of Complex Systems in Germany.
The research has been published in Science.