Creating a perfect crystal sounds straightforward: Arrange identical building blocks into a repeating, orderly structure.
At the microscopic scale, though, even subtle biases in how particles interact can push them in preferred directions, making it harder to form uniform crystalline materials.
A Rice University-led study offers a way around that problem. Tanaka Tatsuya, a visiting Rice research scientist from Kao Corp. in Japan, has developed a theoretical strategy for eliminating an unintended directional bias that can arise when magnetic particles are assembled using rotating magnetic fields. The work, published in Physical Review Research , shows the solution can be surprisingly simple: rotate the magnetic field slightly more than one full turn before reversing its direction.
“When we rotate the magnetic field, the magnetic response of the particle is always slightly behind,” said Sibani Lisa Biswal , chair of chemical and biomolecular engineering and the William M. McCardell Professor in Chemical Engineering at Rice and the corresponding author of the study. “That tiny delay turns out to matter. It can create a preferred direction for assembly even when the applied field appears perfectly symmetric.”
Researchers can use rotating magnetic fields to guide magnetic particles into organized structures. One common method rotates the field in one direction then reverses it, helping prevent particles and particle clusters from continuously spinning. But the Rice team found that a conventional 360-degree sweep does not treat every direction equally.
The reason is a slight delay, known as magnetic relaxation, between a change in the applied field and the particle’s magnetic response. Because of that lag, some orientations are effectively sampled more than others, creating a preferred axis along which the particles tend to align.
The researchers found that rotating the field slightly beyond 360 degrees before reversing it can compensate for that imbalance. At a precisely calculated sweep angle, the directional preference disappears, allowing two particles to experience the same average interaction regardless of their orientation.
In other words, an extra fraction of a turn can restore isotropic interactions — interactions that are identical in every direction.
The team also derived a general relationship for determining exactly how much additional rotation is needed. The required angle depends on two factors: how quickly a particle’s magnetization responds, known as its relaxation time, and how quickly the magnetic field rotates.
Numerical simulations showed the relationship remains effective even when the researchers accounted for interactions between particles and for the particles’ own physical rotation.
“This result facilitates designing experiments of interacting particles,” said Aldo Spatafora-Salazar , a chemical and biomolecular engineering research scientist in the Biswal lab and one of the authors of this study. “Calculate the extra rotation using the delay time of the particle and the rotational speed of the field. The sweep can then be fixed as an experimental parameter to achieve isotropic interactions.”
“If you want particles to form highly ordered crystals, you first need to understand and eliminate unintended biases in how they interact,” Biswal said. “This gives us a quantitative recipe for doing that.”
The findings provide a new way to precisely tune the forces that govern magnetic self-assembly and could help researchers design more uniform crystalline structures from microscopic particles.
This work was supported in part by Kao Corp. for research conducted at Rice and by the DMREF program of the U.S. National Science Foundation under grant No. DMR-252272.
Physical Review Research
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