The nature and properties of the materials are strongly dependent on the dimension. Imagine how different life in a one-dimensional or two-dimensional world would be from the three dimensions we are commonly used to. With that in mind, it’s perhaps unsurprising that fractals – fractional-dimensional objects – have garnered considerable attention since their discovery. Despite their seeming weirdness, fractals appear in surprising places, from snowflakes and lightning bolts to natural ribs.
Researchers from the University of Cambridge, the Max Planck Institute for the Physics of Complex Systems in Dresden, the University of Tennessee and the Universidad Nacional de La Plata have discovered a brand new type of fractal appearing in a class of magnets called spin ices.
The discovery was surprising because the fractals were seen in clean three-dimensional crystal where they would not normally be expected. More remarkably, fractals are visible in the dynamic properties of the crystal, and hidden in the static properties. These characteristics have motivated the designation of “emergent dynamic fractal”.
The results are published in the journal Science December 15.
Fractals were discovered in crystals of dysprosium titanate, where electron spins behave like tiny magnetic bars. These spins cooperate through ice rules that mimic the stresses experienced by protons in water ice. For dysprosium titanate, this leads to very special properties.
Jonathan Hallén of the University of Cambridge holds a Ph.D. student and the lead author of the study. He explains that “at temperatures slightly above absolute zero, the spins of the crystal form a magnetic fluid”. This is no ordinary fluid, however.
“With small amounts of heat, the rules of ice are broken in a small number of sites and their north and south poles, constituting the reverse spin, separated from each other, traveling as independent magnetic monopoles,” says Hallén.
The movement of these magnetic monopoles led to the discovery here. As Professor Claudio Castelnovo, also from the University of Cambridge, points out, “We knew something really strange was going on. The results of 30 years of experiments didn’t add up.”
Referring to a new study on the magnetic noise of monopoles published earlier this year, Castelnovo continued: “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 moving freely in three dimensions, as had always been assumed.”
In fact, this latest magnetic noise analysis showed that the Monopoly world had to look less three-dimensional, but 2.53-dimensional, to be precise. Professor Roderich Moessner, director of the Max Planck Institute for the Physics of Complex Systems in Germany, and Castelnovo proposed that the quantum tunneling effect of the spins themselves may depend on what neighboring spins were doing.
As Hallén explained, “When we introduced this into our models, fractals immediately emerged. The configurations of the spins created a lattice over which the monopoles had to move. The lattice branched out like a fractal with exactly the right dimension .”
But why had it been missed for so long?
Hallén explained that “it was not the kind of static fractal we normally think of. Instead, at longer moments, the movement of monopoles would actually erase and rewrite the fractal.”
This made the fractal invisible to many conventional experimental techniques.
Working closely with Professors Santiago Grigera of the Universidad Nacional de La Plata and Alan Tennant of the University of Tennessee, the researchers managed to disentangle the meaning of previous experimental work.
“The fact that the fractals are dynamic meant that they did not show up in standard measurements of thermal and neutron scattering,” Grigera and Tennant said. “It was only because the noise was measuring the monopoles movement that it was finally spotted.”
Regarding the significance of the results, Moessner explains: “In addition to explaining several puzzling experimental results that have puzzled 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 for an unconventional movement that unfolds in three dimensions.”
Overall, the researchers are interested in seeing what other properties of these materials can be predicted or explained in light of new insights provided by their work, including links to intriguing properties like topology. Since spin ice is one of the most accessible examples of a topological magnet, Moessner said: “The ability of spin ice to exhibit such striking phenomena gives us hope that it promises further discoveries. surprising in the cooperative dynamics of several even simple topological bodily systems.”
Jonathan N. Hallén, Dynamic Fractal and Anomalous Noise in a Clean Magnetic Crystal, Science (2022). DOI: 10.1126/science.add1644
Provided by the University of Cambridge
Quote: Dynamical fractal discovered in clean magnetic crystal (December 15, 2022) Retrieved December 16, 2022 from https://phys.org/news/2022-12-dynamical-fractal-magnetic-crystal.html
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