Researchers have found a solution to a thorny experimental mystery. The magnetic excitation in a particular material was not behaving like something moving in three-dimensional space, but neither was it akin to just moving on a plane. It turns out that it was moving in a fractal dimension.
Fractals are peculiar geometrical shapes that continue to arbitrarily small scales. And scaling is a key property for them. If you have a triangle and you double the length of its side, its area increases by four times as areas scale to the power of two. But fractals instead have dimensions with digits beyond the decimal point.
Fractals are seen in many natural environments, from coastlines to snowflakes, from lightning strikes to Romanesco broccoli, and even in the microscopic world. This new research discovered a fractal dysprosium titanate, a substance that is a type of clean magnetic crystal also known as spin ice. The spins of the electrons behave like tiny bar magnets. When these crystals are cooled just above absolute zero, the whole system acquires a whole new state and becomes a magnetic fluid, something we do not experience in our everyday life.
“With tiny amounts of heat the ice rules get broken in a small number of sites and their north and south poles, making up the flipped spin, separate from each other traveling as independent magnetic monopoles,” lead author Jonathan Hallén of the University of Cambridge, said in a statement.
Research on these systems measures the magnetic noise of these monopoles and discovered that for the monopoles the world is not 3D but rather has 2.53 dimensions. Once it is used in the descriptions of the systems, everything else falls into place.
“We knew there was something really strange going on. Results from 30 years of experiments didn’t add up,” Professor Claudio Castelnovo, also from the University of Cambridge, explained. “After several failed attempts to explain the noise results, we finally had a eureka moment, realizing that the monopoles must be living in a fractal world and not moving freely in three dimensions, as had always been assumed.”
The discovery was very much unexpected. The team was not expecting to see fractals in a clean three-dimensional crystal. And the fractals themselves are weird, making the whole thing even more surprising. The fractals only happen when the system is changing not when the system is static. The connection to the dynamical properties has earned this the name of "emergent dynamical fractal".
The findings of this work are published in the journal Science.