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Imaging of Magnetic Phase Transitions in Artificial Kagome Spin Ice

For the first time, PSI scientists have perceived how minute magnets in a distinct layout arrange themselves exclusively because of temperature variations. This view into procedures that occur within so-called artificial spin ice could have a crucial role to play in the creation of unique high-performance computers. The findings were published recently in the journal Nature Physics.

Imaging of Magnetic Phase Transitions in Artificial Kagome Spin Ice.
(a) Scanning electron micrograph of the lithographically generated artificial kagome spin ice showing the nanoscale permalloy magnets asymmetrically connected by magnetic bridges. The smallest bridges are only 10 nanometers wide. (b) The resulting magnetic order is imaged with a photoemission electron microscope at the Swiss Light Source SLS. The magnetic configuration can be determined from the light-dark contrast and compared with computer simulations. Image Credit: Kevin Hofhuis

When water turns into form ice, the water molecules, with their oxygen and hydrogen atoms, align themselves in an intricate structure. Ice and water are different phases, and the change from water to ice is termed a phase transition.

In the lab, crystals can be created wherein the elementary magnetic moments, the so-called spins, develop structures akin to ice. That is why scientists also call these structures spin ice.

"We have produced artificial spin ice, which essentially consists of nanomagnets that are so small that their orientation can only change as a result of temperature," explains physicist Kevin Hofhuis, who recently completed his doctoral thesis at PSI and currently is employed at Yale University, USA.

In the material the scientists employed, the nanomagnets are aligned in hexagonal structures — a pattern that is seen in the Japanese art of basket weaving called kagome.

Magnetic phase transitions had been theoretically predicted for artificial kagome spin ice, but they have never been observed before. The detection of phase transitions has only been made possible now thanks to the use of state-of-the-art lithography to produce the material in the PSI clean room as well as a special microscopy method at the Swiss Light Source SLS.

Laura Heyderman, Head of Laboratory for Multiscale Materials Experiments, PSI

Laura Heyderman is also a professor at ETH Zurich.

The Trick: Tiny Magnetic Bridges

For their samples, the scientists used a nickel-iron compound known as permalloy, which was applied as a thin film on a silicon substrate. They used a lithography process to repetitively form a small, hexagonal pattern of nanomagnets, with each nanomagnet being around half a micrometer (millionths of a meter) long and one-sixth of a micrometer wide. But that is not all.

"The trick was that we connected the nanomagnets with tiny magnetic bridges," says Hofhuis. "This led to small changes in the system that made it possible for us to tune the phase transition in such a way that we could observe it. However, these bridges had to be really small, because we didn't want to change the system too much."

The physicist is still astonished that this task succeeded. With the formation of the nanobridges, he was pushing up against the boundaries of the technically possible spatial resolution of present-day lithography approaches. Some of the bridges are just 10 nm (billionths of a meter) across.

The orders of magnitude in this experiment are certainly remarkable, says Hofhuis: "While the smallest structures on our sample are in the nanometre range, the instrument for imaging them – SLS – has a circumference of almost 300 metres."

Heyderman adds: "The structures that we examine are 30 billion times smaller than the instruments with which we examine them."

Microscopy and Theory

At the SIM beamline of SLS, the researchers used a dedicated technique known as photoemission electron microscopy that made it viable to view the magnetic state of each nanomagnet in the array. They were enthusiastically supported by Armin Kleibert, the expert in charge of SIM.

"We were able to record a video that shows how the nanomagnets interact with each other as we change the temperature," summarizes Hofhuis.

The novel images just contain black and white contrast that switched occasionally. From this, the scientists could infer the configuration of the spins, that is, the arrangement of the magnetic moments.

"If you watch a video like this, you don't know what phase you're in," explains Hofhuis.

This demanded theoretical consideration, which was provided by Peter Derlet, PSI physicist and adjunct professor at ETH Zurich. His simulations revealed what should hypothetically take place at the phase transitions. Only the evaluation of the recorded images with these simulations established that the processes viewed under the microscope truly are phase transitions.

Manipulating Phase Transitions

The new research is another accomplishment in the analysis of artificial spin ice that Laura Heyderman's team has been involved in for more than 10 years. "The great thing about these materials is that we can tailor them and see directly what is happening inside them," the physicist says.

"We can observe all sorts of fascinating behaviour, including the phase transitions and ordering that depend on the layout of the nanomagnets. This is not possible with spin systems in conventional crystals." Although these analyses are still in the fundamental early stages, the scientists are already looking at probable applications.

"Now we know that we can see and manipulate different phases in these materials, new possibilities are opening up," says Hofhuis.

Manipulating diverse magnetic phases could be stimulating for unique types of data processing. Scientists at PSI and in different places are exploring how the intricacy of artificial spin ice could be used for unique high-speed computers with minimal power consumption.

"The process is based on the information processing in the brain and takes advantage of how the artificial spin ice reacts to a stimulus such as a magnetic field or an electric current," explains Heyderman.

Journal Reference;

Hofhuis, K., et al. (2022) Real-space imaging of phase transitions in bridged artificial kagome spin ice. Nature Physics.

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