Originally published 2019-10-27.
Pete LinForth/Pixabay
In October 2019 a team led by physicist Riccardo Comin at the Massachusetts Institute of Technology reported the first known fractal pattern in a quantum material. Mapping the tiny magnetic regions inside a thin film of neodymium nickel oxide (NdNiO3) with a finely focused X-ray beam, they found that the regions followed the same statistical pattern whether you looked at small scales or large ones. The study, published in Nature Communications, also found that the material "remembers" where its magnetic regions formed, a property that could one day be useful for storing information.
Here is what the team measured, how they did it with a lens design borrowed from lighthouses, what "fractal" means in this context, and why the result interests people working on future electronics.
The discovery in brief
The paper, titled "Scale-invariant magnetic textures in the strongly correlated oxide NdNiO3", appeared on 15 October 2019. Its lead author was Jiarui Li, then an MIT graduate student, and the team included researchers from Brookhaven National Laboratory, the University of Geneva, Purdue University and the University of Zurich. The thin films were grown at the University of Geneva.
The key observations were simple to state. The magnetic regions, called domains, ranged from a few atoms across to tens of thousands of atoms. There were many small domains and progressively fewer large ones, and the way their numbers fell off with size followed a power law: the same relationship held across every scale the team could measure. That scale-invariance is the signature of a fractal. Comin later said the discovery was "completely unexpected"; the team had set out simply to map the domains.
Fractals, from coastlines to crystals
A fractal is a pattern that looks statistically similar at different magnifications. Classic examples include coastlines, river networks, lightning, the branching of trees and lungs, and the frost patterns on a window. The mathematician Benoît Mandelbrot popularised the idea in the 1970s and 1980s, and gave the word its modern meaning.
Fractals turn up in physics too, especially near critical points, the special conditions at which a material is on the edge of changing from one state to another, such as water at its critical point or a magnet at the temperature where it loses its magnetism. Fluctuations at such points have no preferred size, so patterns of every scale appear together. Finding fractal magnetic domains in neodymium nickel oxide suggested to the researchers that the material's magnetic transition is continuous and that it sits close to such a critical point.
What made the 2019 result a first was not that fractals are rare, but that nobody had directly imaged one in the arrangement of magnetic domains in a quantum material, a class of solids whose behaviour is dominated by strong interactions between electrons.
Neodymium nickel oxide: a metal that turns insulator
NdNiO3 belongs to a family called rare-earth nickelates. (Neodymium is the rare-earth element in the compound; the oxide itself is a synthetic crystal grown in thin layers in the laboratory.) At room temperature it conducts electricity like a metal. Cool it below a critical temperature and it abruptly becomes an insulator, and at about the same point it becomes magnetically ordered.
The exact temperature depends on the sample. For the film used in this study, the paper places the metal-to-insulator and magnetic transitions at about 180 kelvin, roughly minus 93 °C. Popular articles at the time often quoted about minus 123 °C; the difference is a reminder that thin films and bulk crystals do not behave identically, so a single "official" figure can mislead.
The magnetic order in this material is antiferromagnetic, meaning neighbouring atomic magnets point in opposing directions rather than all lining up as in a fridge magnet. The domains are patches in which that order has a particular orientation. How such domains form in a material that is simultaneously switching from conductor to insulator was the open question the team wanted to explore.
A lighthouse lens for X-rays
To see domains this small, the team needed a beam of X-rays far narrower than a normal synchrotron beam, which is several hundred microns wide. Their solution borrowed from the Fresnel lens, the design invented in the 1820s to let lighthouses concentrate light into a powerful beam using concentric ridges rather than a single thick piece of glass.
Photopips/iStock
The team built a Fresnel-type lens for soft X-rays about 150 microns across, roughly the width of a human hair or two, and used it at the CSX beamline of the National Synchrotron Light Source II at Brookhaven National Laboratory in New York. The lens focused the beam down to about 70 nanometres. They then scanned it across the film point by point, recording how X-rays scattered from the magnetic order at each spot, and stitched the data into maps of domain size, shape and orientation. Researchers at Purdue developed the statistical methods used to analyse the domain counts.
What the maps showed, and a memory effect
When the researchers plotted the number of domains against their size, the curve sloped steadily downwards in the same way at every scale they could resolve, and the domains had non-integer fractal dimensions. Li summed it up: "Most strikingly, we have found that these magnetic patterns have a fractal nature."
The second surprise came when they heated the film above its transition temperature, wiping out the magnetic order, and then cooled it again. The domains came back in nearly the same places. The team attributed this memory to the domains being pinned by features of the material, so that the pattern is effectively written into the film and can be restored after being erased.
Why it could matter for electronics
Magnetic domains are the basis of the magnetic hard drive, which stores bits as tiny magnetised regions. A material whose domains reliably return to the same places after heating hints at a way of storing information that survives conditions that would scramble it in other materials.
The MIT team also pointed to neuromorphic computing, hardware that imitates the way neurons and synapses work. Materials like NdNiO3 that switch sharply between conducting and insulating states are already being studied as artificial neurons, and understanding their nanoscale textures could help in designing such devices.
These are possibilities rather than products. The measurements were made on carefully grown films at low temperature, using one of the world's most advanced X-ray sources, and turning that into practical technology would take many more steps.
Common misreadings
- "Fractals were never found in nature before." They are everywhere in nature. The novelty was finding one in the magnetic domains of a quantum material.
- "All quantum materials are fractal." The study measured one compound under specific conditions. Its result says something about that material and its transition, not about every quantum system.
- "Neodymium nickel oxide is a rare earth metal." Neodymium is a rare-earth metal; NdNiO3 is an oxide compound containing it.
- "This will be in our phones soon." The work is basic research. It improves understanding of how magnetic order forms, which may inform future devices.
Sources: Li et al., "Scale-invariant magnetic textures in the strongly correlated oxide NdNiO3", Nature Communications 10, 4568 (2019); MIT Physics: Scientists discover fractal patterns in a quantum material. The story was also reported by ScienceAlert. Header image: Pete LinForth/Pixabay; lighthouse image: Photopips/iStock.
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