Magnets that never touch can still create friction - and it breaks a 300-year-old law

Can two objects that never touch still experience friction between them?

The answer, according to a team at the University of Konstanz, is yes. And the friction they produce does not behave the way three centuries of physics said it should.

In a study published March 18 in Nature Materials, physicists Hongri Gu, Anton Luders, and Clemens Bechinger describe a tabletop experiment where two layers of permanent magnets generate a measurable friction force despite zero physical contact between them. More striking still, this magnetic friction does not increase steadily as the layers are pressed closer together. Instead, it peaks at an intermediate distance, then drops off - a direct violation of Amontons' law, one of the most venerable empirical rules in all of physics.

What Amontons said in 1699, and why we believed it

Guillaume Amontons formulated his friction law in 1699, and for most practical purposes, it has held up remarkably well. The rule is intuitive: friction between two surfaces increases proportionally with the load pressing them together. Push a heavy desk across the floor and you need more force than for a light chair. Double the weight, roughly double the friction.

The physical explanation developed over subsequent centuries centers on surface contact. When two solids are pressed together, their microscopic surface features - tiny bumps and ridges called asperities - deform slightly under load. Greater load means more asperities make contact, increasing the effective contact area and therefore the friction force. This framework works well for everyday materials: metals on metals, rubber on concrete, wood on wood.

But the framework rests on an assumption that the Konstanz team set out to test. Classical friction involves small surface deformations that do not fundamentally alter the internal structure of the materials. What happens when the act of sliding forces dramatic internal reorganization? Specifically, what happens when the material in question is magnetic, and motion forces its magnetic order to rearrange?

Two magnetic layers, zero contact, real friction

The experiment is conceptually simple. The team built a two-dimensional array of small permanent magnets mounted on pivots, allowing each magnet to rotate freely. This upper layer sat above a second, fixed layer of magnets. The two layers never touched. The only interaction between them was the magnetic field coupling their respective magnetic moments.

When the researchers slid one layer relative to the other, the rotating magnets in the upper layer responded to the changing magnetic field landscape beneath them. Their orientations shifted as they moved, and this continuous reorientation dissipated energy. That energy dissipation is, by definition, friction - even though no surfaces were in contact.

By adjusting the vertical distance between the two layers, the team could continuously tune the effective coupling strength - the magnetic equivalent of changing the load in a conventional friction experiment. Closer spacing meant stronger magnetic interaction, analogous to pressing two surfaces together harder.

Friction peaks where magnetic frustration is greatest

Here is where Amontons' law breaks down. At large separations, where the magnetic coupling between layers was weak, friction was low. The upper magnets barely responded to the lower layer as they slid past. At very small separations, where the coupling was strong, friction was also low - the strong field locked the upper magnets into a stable configuration aligned with the lower layer, and they moved smoothly.

But at intermediate distances, something different happened. At this middle range, the magnetic field from the lower layer favored one arrangement - parallel alignment of magnetic moments - while interactions within the upper layer itself favored the opposite: antiparallel alignment, with neighboring magnets pointing in opposite directions. These two competing preferences created what physicists call frustration: the system could not satisfy both demands simultaneously.

The result was dynamic instability. As the layers slid past each other, the upper magnets were repeatedly forced to flip between incompatible configurations. Each flip dissipated energy through magnetic hysteresis - the phenomenon where a system's current state depends on its history, and switching between states costs energy. The effect was dramatic. Friction spiked to a pronounced maximum at this intermediate coupling strength, then fell off on both sides.

This non-monotonic friction - rising, peaking, then falling with increasing load - is the opposite of what Amontons' law predicts. Amontons says more load equals more friction, always. The magnetic system says: not necessarily.

Friction without wear, surfaces, or roughness

What makes this result conceptually clean is the absence of everything that normally complicates friction studies. There is no surface roughness. No wear. No material transfer. No adhesion. No lubricant films. No plastic deformation. The friction arises entirely from the collective dynamics of magnetic moments responding to a changing energy landscape as the layers slide.

Anton Luders, who developed the theoretical framework for the experiment, points out that this makes the system almost uniquely interpretable. In conventional friction experiments, multiple mechanisms operate simultaneously and are difficult to isolate. In this magnetic system, there is exactly one source of energy dissipation: the hysteretic reorientation of magnetic rotors. The breakdown of Amontons' law is not an anomaly or a measurement artifact - it is a direct, calculable consequence of magnetization dynamics during sliding.

Clemens Bechinger, who supervised the work, emphasizes the purity of the mechanism. Dissipation is generated solely by collective magnetic rearrangements. Nothing else contributes.

From macroscopic magnets to atomic-scale devices

The physics described in this experiment is scale-free, meaning the underlying mechanisms do not depend on the size of the magnets used. Similar effects could, in principle, occur in atomically thin magnetic materials - two-dimensional magnets where even tiny mechanical displacements can switch magnetic ordering. This opens potential applications in micro- and nanoelectromechanical systems (MEMS and NEMS), where conventional friction and wear limit device lifetimes.

The team envisions future applications including tunable frictional interfaces that can be adjusted remotely and reversibly using external magnetic fields. Concepts like frictional metamaterials - engineered surfaces whose friction can be programmed - adaptive vibration dampers, and contactless control elements all become conceivable when friction can be generated and tuned without physical contact.

More broadly, the work forges a new link between two fields that have historically had little to do with each other: tribology (the study of friction, wear, and lubrication) and magnetism. Mechanical measurements of sliding friction, it turns out, can probe the collective behavior of magnetic spin systems - a connection that was not previously appreciated.

Where the limits lie

The experiment used centimeter-scale permanent magnets - macroscopic objects whose behavior is well described by classical electromagnetism. Extending the results to nanoscale or atomic-scale magnetic systems involves quantum mechanical effects (spin-orbit coupling, exchange interactions, thermal fluctuations) that the current experiment does not address. Whether the non-monotonic friction behavior persists at atomic scales is a prediction, not yet an observation.

The system is also two-dimensional and highly ordered. Real magnetic materials have defects, grain boundaries, and three-dimensional complexity. How these factors modify the friction landscape remains unexplored.

Still, as a proof of concept, the experiment is unambiguous. Friction can exist without contact, it can arise purely from internal magnetic dynamics, and when it does, it does not follow the rule Amontons wrote down more than three hundred years ago. That is a clean result, and a rare one.