For the first time, fractal distributions have been demonstrated in a quantum material

Fractals are mathematical objects whose internal patterns are repeated, forming an invariant structure by scaling. From snowflakes to lightning, fractals are found in many natural phenomena. And recently, MIT researchers have demonstrated a fractal distribution of magnetic domains in a material with particular quantum properties.

MIT physicists provided the first known example of a fractal arrangement in a quantum material. The patterns have been observed in an unexpected distribution of magnetic units called "domains", which develop in a compound called nickel-neodymium oxide - a rare earth metal with amazing properties. The study was published in Nature Communications .

A better understanding of these areas and their structures could potentially lead to new ways of storing and protecting digital information. As the physicist Riccardo Comin explains, " the material is not magnetic at all temperatures ".

Geometric distribution of magnetic domains in nickel-neodymium oxide 

The atoms of nickel oxide and neodymium form minute clusters of magnetically oriented particles called domains. The domains come in different sizes and arrangements, depending on the quantum interactions between the electron s and their atoms under certain conditions. But the question was how they emerged in nickel-neodymium oxide, given its nature as a driver.

" We wanted to see how these areas appear and develop once the magnetic phase is reached when cooling the material, " says Comin. Researchers have in the past studied the unique magnetic properties of the material through X-rays. While this showed how the material was distributing its electrons at different temperatures, mapping the size and distribution of its domains under such conditions required more focused approach.

Experimental protocol used by researchers to analyze magnetic domain structures. Credits: Jiarui Li et al. 2019
" We have therefore adopted a special solution that focuses the X-ray beam, so that we can map, point by point, the arrangement of the magnetic domains in this material, " says Comin.

Fresnel lenses are stacked layers of transparent material with ridges, which redirect electromagnetic radiation. The lenses that Comin and his team developed were only 150 microns wide. The end result was an X-ray beam small enough to detect the fine scale of the magnetic domains through a thin neodymium nickel oxide film developed in the laboratory.

Fractal distribution of magnetic domains

Most of these areas were tiny. Scattered among them were bigger ones. But once the data was analyzed and a map was modeled, the distribution of larger domains among the many much smaller domains was strangely similar, regardless of the scale used.

Fractal distribution of magnetic domains in nickel-neodymium oxide. Credits: Jiarui Li et al. 2019

 The schema of the models was difficult to decipher at first, but after analyzing the statistics of the domain distribution, we realized that it had fractal behavior. It was completely unexpected, pure chance, "says Comin. Materials that can be used as both conductors and insulators already play an important role in the world of electronics. Transistors are based on this very principle.

But nickel-neodymium oxide has another property. The same fractal pattern of domains reappears when the temperature drops again, almost as if it had some sort of memory. " Similar to magnetic disks in rotating hard disks, we can consider storing bits of information in these magnetic domains, " concludes Comin.

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