If you've ever watched a flock of birds move in perfect unison or seen ripples travel across a pond, you've witnessed nature's remarkable ability to coordinate motion. Recently, a team of scientists and engineers at Rice University discovered a similar phenomenon on a microscopic scale, where tiny magnetic particles driven by rotating fields spontaneously move along the edges of clusters driven by invisible "edge currents" that follow the rules of an unexpected branch of physics. The research was published in the journal Physical Review Research .
"When I saw the initial data — with streams of particles moving faster along the edges than in the middle — I said 'these are edge flows!' and we got to work exploring this," said corresponding author Evelyn Tang , assistant professor of physics and astronomy. "What's very exciting is that we can explain their emergence using ideas from topological physics, a field that became prominent due to quantum computers and exotic materials."
In their experiments, the team suspended superparamagnetic colloids — think tiny magnetic beads about a hundred times smaller than a grain of sand — in salty water. They then applied a rotating magnetic field, which caused the particles to form crystals in different shapes: Sometimes they formed dense circular clusters, and other times they spread out in sheets with empty holes or "voids."
The experiment got especially interesting when the particles along the outer edges of these shapes started to move faster than the rest, forming a kind of conveyor belt around the border.
"We call this edge flow," said co-first author Aleksandra Nelson , a former postdoctoral fellow in Tang's lab. "It is basically a current that forms naturally around the boundary without anyone pushing it."
To understand why this occurred, the researchers turned to something called topological physics, which is a way of describing systems where movement or behavior is controlled by the overall shape or layout rather than the exact details.
"Topology is like the highway signs that determines the traffic flow," said co-author Sibani Lisa Biswal , the William M. McCardell Professor in Chemical Engineering. "Even if there are construction or potholes, the traffic still flows the same way because the route is set by the system's shape. That's what topology is — rules that hold up even in messy or noisy conditions."
In this case, the "rules" predicted that rotating magnetic particles would generate movement along the edges of whatever shape they formed — whether it was a cluster or a void. And that's exactly what the team observed under the microscope.
Interestingly, the type of motion depended on the shape. When particles formed free-floating clusters, the edge flow caused the whole cluster to spin like a tiny wheel. But when the particles formed larger sheets with voids, the edges still had movement, but the overall structure didn't rotate.
Tang explained that this phenomenon happened because in clusters, the particles were free to turn together like dancers in a circle. But in sheets with voids, the surrounding material held them in place, so the edge motion had to spread inward instead of rotating. This difference also changed how quickly the entire system reorganized. Clusters could change shape and merge within minutes, while sheets with voids took much longer.
The ability to control how particles move and organize themselves may seem like a niche discovery, but it has broad implications. Understanding how to direct motion in crowded, dynamic systems could inform the design of responsive materials such as targeted drug delivery, adaptive surfaces or swarms of microbots.
"We're learning how to control collective behavior using simple physical principles," said co-first author Dana Lobmeyer , a recent graduate in Biswal's lab. "This is a step toward creating materials that can sense their environment and respond intelligently without needing a computer or instructions."
Although the experiments used synthetic particles, the team sees parallels in biology too. Many cell clusters rotate during development or healing, raising the possibility that similar physical principles are at work inside living organisms.
"This is the beauty of science," Tang said. "We're taking a concept from fundamental math and statistical physics to apply it to everyday materials. It's a reminder that the same elegant rules can show up right in the lab next door."
This research was supported by the National Science Foundation and The Kavli Foundation.
