Knots in magnetic materials may provide a new direction for next-generation computing architectures to branch out into. To that end, researchers have now created a novel magnetic knot that looks like a tiny magnetized version of a cinnamon twist. And this same magnetic knot—embedded in a magnetic material a little like an electron hole is embedded in a semiconductor lattice—could be one of the factors that breaks the 2D flatland that computing today is stuck in.
In mathematics, the field of topology deals with shapes and the holes in them—a basketball, without holes, is topologically identical to a football, but distinct from a hula hoop, with one hole. Topological properties are remarkable for their robustness: You can’t turn a football into a hula hoop without doing some violence to it. In real materials, topology can be used to describe the shape of magnetization. When magnetic moments inside a crystal twist themselves into topologically complex knots, they cannot easily be unwound, making them desirable as very stable potential carriers of information or data storage. Now, researchers in Germany, China, and Sweden have created a novel magnetic knot inside a material that, unlike previous topological twists, can move in all three dimensions.
“If we look toward the future, most probably to make our devices the most efficient, at some point, we will have to turn towards a three-dimensional architecture. And that’s where the discovery we made in our paper might become useful.”
—Nikolai Kiselev, Peter Grünberg Institute, Jülich, Germany
“In the last decades, electronics basically developed in the paradigm of two-dimensional systems,” says Nikolai Kiselev, a staff scientist at the Peter Grünberg Institute in Jülich, Germany. “Which from a certain point of view is absolutely reasonable because technologically it’s much easier to fabricate and maintain such devices. But if we look toward the future, most probably to make our devices the most efficient, at some point, we will have to turn towards a three-dimensional architecture. And that’s where the discovery we made in our paper might become useful.”
The discovery they made came as a surprise, Kiselev says, even though he and his collaborators have studied magnetic twists and turns inside materials for decades. One such topological excitation, called a skyrmion, has been observed in multiple materials. Skyrmions pop up in disks of certain materials when they are pierced by magnetic fields. They are akin to whirlpools in the magnetic moments of atoms in the sample, going all the way from the bottom of the disk to the top, like a spiraling string that cannot be unwound. These have attracted attention for their computing potential as well. But, because of their string-like nature, they can only move in two dimensions.
The team wanted to create something known as a skyrmion bag—a cylindrical skyrmion with a hole in the middle that may wrap itself around other, regular skyrmions. Instead, they created something else entirely—a hopfion. Instead of stretching from top to bottom of a sample, hopfions close in on themselves, like a transverse whirpool that twists onto itself into a donut. Because of their structure, hopfions can move not only left and right, but also up and down. Hopfions have been predicted theoretically, but they have only been created in one specialized synthetic material. This was the first time they popped up in a regular crystal.
Researchers have discovered magnetic structures in a iron germanium crystal that are called skyrmions, including an inherently 3D object called a hopfion, surrounding three skyrmions (right).Forschungszentrum Jülich/Nature
The crystal was iron germanium, chosen because of its desirable combination of two properties. On the one hand, the atoms inside iron germanium have magnetic moments that tend to want to align with their neighbors. On the other hand, the structure of the crystal itself motivates the magnetic moments to rotate with respect to their neighbors. The interplay of these two effects allows for the interesting magnetic knots to pop up under different conditions.
Just subjecting iron germanium to a magnetic field births skyrmions in the material. To get the hopfion, however, the team had to perform some careful magnetic gymnastics. They turned on a small magnetic field pointing up, then shifted to an even smaller field pointing down, then up again, increasing to its original value. The result was not the expected skyrmion bag, but a 3-D hopfion ring, surrounding several skyrmions.
Since skyrmions are very small compared to traditional memory devices, the magnetic twists could also become the basis of a very high-density memory device.
It might be tricky to wrap one’s mind around a hopfion knot, but they behave basically as if they are particles, maintaining their strange shape as they travel within a material. Kiselev says they can be stimulated to move up and down along the skyrmion strings without any loss of energy at all. And, the skyrmions can be induced to move in two dimensions, dragging the hopfion along with them.
Skyrmions have been proposed as memory devices in a so-called racetrack architecture. By moving the skyrmion from one edge of the racetrack to another, a single bit of information could be stored and transported. Since skyrmions are very small compared to traditional memory devices, the magnetic twists could also become the basis of a very high-density memory device. Other proposals include using a skyrmion’s arrival time at a particular gate to encode multiple bits of information simultaneously, which could potentially be useful for neuromorphic computing. Since hopfions move in 3D, they could potentially encode multiple bits of information in their location or their arrival times across multiple axes. Additionally, hopfions may not be subject to the same technical drawbacks skyrmions are.
“One of the reasons we have trouble with incorporating skyrmions into technological applications is due to the skyrmion Hall Effect,” says Hanu Arava, a staff scientist at Argonne National Laboratory who did not participate in the work. “This effect makes it very difficult to drive skyrmions along straight lines. Such an effect is not expected in hopfions, which means we can send a Hopfion from point A to B in straight lines. So, one can imagine a new brain-inspired computation that may require a Hopfion to move from one location to another.”
Although hopfions move around readily, other aspects of their computing potential is still uncertain. The team used transmission electron microscopy to image the hopfion, and measuring its location more efficiently is an outstanding problem. The team says they plan to look at how these objects respond to electric current, which could help detect and track them. Plus, precise details on the exact ways hopfions might encode information is still an open question.
That said, Kiselev adds, many questions like this don’t yet have answers because there has been no reason to ask them. “We didn’t even think about this kind of object before, it’s very, very fresh and to some extent also very surprising for us, and full of some mysteries and unknown questions.” Arava agrees: “One must consider the result as only a first step, since there are so many open questions. However, this discovery opens up the world of 3D magnetic objects.”
The researchers published their work last month in the journal Nature.
This article appears in the March 2024 print issue as “Magnetic Knots Could Open New Path to 3D Computing.”