Dynamic fractal discovered in clean magnetic crystal

The nature and properties of materials largely depend on the dimension. Imagine how different life would be in a one or two dimensional world from the three dimensions we are used to. With this in mind, it is perhaps not surprising that fractals (objects with fractional dimensions) have attracted significant attention since their discovery. Despite their seeming strangeness, fractals arise in surprising places, from snowflakes and lightning to natural shorelines.

Researchers from the University of Cambridge, the Max Planck Institute for the Physics of Complex Systems in Dresden, the University of Tennessee, and the National University of La Plata have discovered an entirely new type of fractal that appears in a class of magnets called spin ice.

The discovery was surprising because the fractals were seen in a clean three-dimensional crystal, where they would not conventionally be expected. Even more remarkable, fractals are visible in the dynamic properties of the crystal and hidden in the static ones. These characteristics motivated the denomination of “emerging dynamic fractal”.

The findings are published in the journal Sciences on December 15.

The fractals were discovered in crystals of the material dysprosium titanate, where the electron spins they behave like tiny bar magnets. These spins cooperate through ice rules that mimic the constraints experienced by protons in water ice. For dysprosium titanate this leads to very special properties.

Jonathan Hallén of the University of Cambridge is Ph.D. student and the lead author of the study. He explains that “at temperatures slightly above absolute zero, the crystal spins to form a magnetic fluid.” However, this is not an ordinary fluid.

“With small amounts of heat, the rules of the ice break in a small number of places and its north and south poles, forming the inverted gyre, separate from each other traveling as independent magnetic monopoles,” explains Hallén.

The movement of these magnetic monopoles led to the discovery here. As Professor Claudio Castelnovo, also from Cambridge University, 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 magnetic noise from 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 be living in a fractal world and does not move freely in three dimensions, as had always been assumed”.

In fact, this latest analysis of magnetic noise showed the monopoleThe world of ‘s needed to look less than three-dimensional, but in 2.53 dimensions, 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 of the spins themselves could depend on what the neighboring spins were doing.

As Hallén explained, “When we put this into our models, the fractals popped up right away. The spin configurations were creating a lattice that the monopoles had to move in. The lattice was branching out like a fractal with exactly the right dimension.”

But why had this been lost for so long?

Hallén explained that “this was not the kind of static fractal we normally think of. Instead, over longer times, the movement of the 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 National University of La Plata and Alan Tennant of the University of Tennessee, the researchers were able to unravel the meaning of previous experimental work.

“The fact that he fractals they’re dynamic, meaning they didn’t show up in standard neutron and thermal scattering measurements,” Grigera and Tennant said. “It was only because the noise was measuring the motion of the monopoles that it was finally detected.”

Regarding the significance of the results, Moessner explains: “In addition to explaining several puzzling experimental results that have been challenging us for a long time, the discovery of a mechanism for the appearance of a new type of fractal has led to a completely unexpected path.” for unconventional movement that takes place in three dimensions”.

In general, the researchers are interested in seeing what other properties of these materials can be predicted or explained in light of the new understanding provided by their work, including links to intriguing properties like topology. Since spin ice is one of the most accessible cases of a topological magnet, Moessner said: “The ability of spin ice to exhibit such amazing phenomena gives us hope that it promises more amazing discoveries in cooperative dynamics even of many simple topological”. body systems.”