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Research Highlights

Dynamical fractal discovered in clean magnetic crystal

Jonathan N. Hallén, Santiago A. Grigera, D. Alan Tennant, Claudio Castelnovo, and Roderich Moessner

We have uncovered a new type of fractal, appearing in a class of materials called spin ices. This is the first report of the appearance of a fractal pattern in the bulk of a perfect crystal without disorder.

An example of the fractal structures in spin ice is shown, with its structure at five different lenght-scales placed along an arrow. It is displayed together with a famous example of a fractal (the Mandelbrot set). The background is a close-up photograph of water ice.
Example of the fractal structures in spin ice together with a famous example of a fractal (the Mandelbrot set), on top of a photograph of water ice.

The properties and behaviour of physical systems are strongly dependent on their dimensionality. Life in a one-dimensional or two-dimensional world would be very different from the three dimensions that we are commonly accustomed to. With this principle in mind, it is perhaps not surprising that fractals — objects with non-integer dimensions — have attracted significant attention since their discovery, both in academic as well as popular science contexts. Despite their apparent oddity, fractals occur in manifold settings and length scales in nature, ranging from snowflakes and lightning strikes to natural coastlines.

There are two reasons for the novelty of these findings. Firstly, the phenomenon occurs in a clean, perfect three-dimensional crystal, whereas a typical ingredient to induce fractal behaviour is the presence of disorder. Secondly, fractals in spin ice are borne out of the peculiar rules that govern the time evolution of the magnetisation in these systems. These features motivated the appellation of emergent dynamical fractal.

Spin ice materials had already stood out in recent years for the unusual topological nature of their magnetic properties, and their ability to host emergent magnetic monopole excitations. It is indeed the dynamics of these magnetic monopoles, and their interplay with the crystal structure, that brings about the appearance of fractal patterns.

Being dynamical in nature, the fractals are not detectable through measurements of static properties. They do, however, produce a characteristic signal in the response and fluctuations of the magnetisation, which can be measured. Indeed, signatures of these fractals had been observed in experiments, some dating back to nearly two decades ago, and they had remained poorly understood to date. Besides the general interest and scientific curiosity of our findings, we thus also explain several puzzling results that have been challenging the scientific community.

It will be interesting to see what other properties of these materials may be predicted or explained in light of the new understanding provided by our work. The capacity of spin ice to exhibit such striking phenomena holds promise of further surprising discoveries in the cooperative dynamics of even simple topological many-body systems.

Science 378, 1218 (2022)

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