From smartphones to data centers, modern electronics rely on billions of tiny switches that consume electricity every time they turn on or off. As global demand for computing continues to grow, so does the energy required to power it. Scientists are therefore searching for alternatives that can perform the same tasks while using far less energy.
One promising approach uses clusters of tiny magnets, each thousands of times smaller than a grain of sand. A new study led by the U.S. Department of Energy’s (DOE) Argonne National Laboratory, with contributions from the DOE’s Los Alamos National Laboratory and Adolfo Ibáñez University in Chile, has uncovered a geometric rule that determines whether clusters of nanomagnets behave predictably or probabilistically as they relax toward a stable state. The finding challenges standard modeling assumptions and opens new possibilities for ultralow-energy computing.
“What we have identified is a relationship between structure and function,” said Argonne Materials Scientist Hanu Arava, lead author of the study. “In our case, the structure is the geometric arrangement of the magnets with respect to each other, and the function is how energy moves through the system.”
“We’ve shown that geometry alone can determine how energy moves through these magnetic systems and that insight gives us a new way to design computing devices.” - Argonne Materials Scientist Hanu Arava
To help explain the process, Arava compares it to dropping a ball from the top of a mountain. The ball naturally rolls downhill along the easiest route until it reaches the lowest point. Scientists call that route an energy-relaxation pathway - the path a system follows as it moves toward its most stable state. In the nanomagnet system, the magnets interact through their magnetic fields in a more complex way, but they follow the same basic principle: moving step by step toward the lowest-energy configuration.
To uncover this relationship, the researchers studied a simple geometric progression at Argonne’s Center for Nanoscale Materials, a DOE Office of Science user facility. They began with four nanomagnets arranged in a Greek cross or plus sign, then rotated all four simultaneously until they formed a square. At intervals along the way, the team measured how the system relaxed toward its most stable state.
What they found was striking. In the square geometry, the magnets relaxed toward a stable configuration with very high probability. In the cross geometry, the system encountered an energy barrier, and its relaxation became much less predictable, sometimes settling into different outcomes. Between those two extremes, the researchers identified a tipping point.
When the magnets were rotated to the midpoint between the square and plus-sign states, the system reached a balance in which multiple outcomes became equally likely. On either side of that midpoint, the behavior became either more reliable or more uncertain. The same basic pattern held even when the researchers changed the lengths of the magnets.
To understand how the geometry controls the system’s behavior, the researchers used a theoretical model that treated each tiny magnet as an object with internal structure rather than a simple point. That approach revealed hidden interactions at the junctions, showing that simplified models can miss key features of the physics.
For conventional computing technologies, predictability is essential. A device must produce the same result every time it performs a calculation. The new findings suggest that engineers may be able to control that reliability simply by adjusting the arrangement of the magnetic elements.
“If you want to build computing hardware, you typically need the result to be predictable,” Arava said. “One plus one should equal two.”
At the same time, systems that produce multiple possible outcomes could be useful for emerging forms of computing that rely on probability rather than certainty, such as machine learning and optimization.
“The pathway that energy takes determines whether the outcome is reliable or uncertain,” Arava said. “For engineers designing computing devices, that means they may be able to tune the angle of rotation in nanomagnetic clusters to achieve one outcome or the other.”
Although the experiment involved just four nanomagnets, the result has broader implications. In larger magnetic devices, thousands of similar clusters would need to work together. Understanding how a single building block behaves is essential for designing more complex systems. The new findings give engineers a simple design principle: adjust the rotation angle of the magnets to tune how reliably they reach a predictable final state.
Nanomagnetic devices have already demonstrated the potential to operate using extremely small amounts of energy - possibly millions of times less than conventional electronic components. If such systems can be made reliable and scalable, they could help reduce the growing energy demands of computing infrastructure worldwide.
The new research offers a practical step toward that goal.
“We’ve shown that geometry alone can determine how energy moves through these magnetic systems,” Arava said, “and that insight gives us a new way to design computing devices.”