According to an empirical law that is over 300 years old, the friction force increases in proportion to the contact pressure. However, it was unclear whether Amonton’s law also applies to magnetic materials. Researchers have now tested this in an experiment with small magnets that are movably attached to a surface – with surprising results: the resistance to movement did not increase steadily as the distance between the surfaces decreased, but rather showed a peak at a medium distance. This refutes Amonton’s law, which is more than 300 years old, and shows what role magnetic interactions and competing orders play in it.
Leonardo da Vinci made his first observations on the laws of friction. But it was only the laws formulated by Guillaume Amonton in 1699 that became the basis for empirical friction research. The first of these Amontons’ laws relates to the friction surface, the second states that the friction force increases in proportion to the contact pressure. In everyday life, this is evident, for example, in the fact that a heavy piece of furniture is less easy to move than a light one. The cause of this behavior is microscopic deformation of the contact surfaces, which increases the number of contact points. This in turn increases resistance to movement. However, it was previously unclear whether Amonton’s law still applies when the movement triggers strong internal rearrangements – for example in magnetic materials. With these, frictional forces can also occur without any contact – due to purely magnetic interactions between the materials.
Maximum in the middle distance instead of a constant gradient
In order to investigate whether Amonton’s law also applies to this contactless, magnetic friction, Hongri Gu from the University of Konstanz and his colleagues have developed a macroscopic test system for the first time. It consists of a lower surface into which numerous mini magnets made of a neodymium-iron-boron alloy are embedded. Each of the small magnetic cubes is four millimeters in size. The upper surface is attached so that it can slide laterally over the lower surface and its distance can be varied. Mini magnets made of neodymium-iron-boron alloy also sit on their surface. However, these are ring-shaped and movable. This allows the magnets to rotate and thus freely adjust their polarity. A camera records the movements and arrangement of these color-coded magnets as the surfaces move at different distances from each other. The magnetic interactions of the magnets in both surfaces generate a clearly measurable friction force.
The measurements showed something surprising: Contrary to expectations, the friction force did not increase steadily as the surfaces got closer. Instead, the result was a clearly curved curve: at small and large distances, the friction was comparatively low. At medium distances between the two magnetic surfaces, however, it reached a maximum. “This is in stark contrast to Amonton’s law, which states that frictional resistance is proportional to contact pressure,” write Gu and his colleagues. In this case, the pressure corresponds to the intensity of the magnetic attractions between the two test surfaces. The experiment shows that the friction force in such a magnetic interaction is shaped by other mechanisms. “From a theoretical perspective, it is particularly remarkable that the friction here does not arise from direct surface contact, but from the collective dynamics of magnetic moments,” explains co-author Anton Lüders from the University of Konstanz, who has developed a theoretical model for this process.
Competing influences
The reason for the deviations from Amonton’s law was revealed by the analysis of the camera recordings and accompanying model simulations. They show that the arrangement of the moving magnets in the upper surface changes in a characteristic way depending on the distance from the lower surface. If the distance is large, the repulsive forces between the moving magnets predominate in the upper surface. This causes them to rotate so that the poles of adjacent magnets are aligned in opposite directions. They are arranged antiparallel or, in physical terms, antiferromagnetic. However, if the distance between the magnetic surfaces is small, the influence of the fixed lower magnetic surface predominates. “Since all rotors are exposed to the same magnetic field, this leads to a collective rotation of the magnets and a ferromagnetic order when sliding,” explains the team. All rotating magnets then point in the same direction.
But when the two surfaces are at a medium distance, this order breaks down. Because the influence of the neighboring magnets and the lower surface are almost equally strong, the system becomes unstable. “If the magnetic inter- and intrasurface interactions are comparable, the individual magnetic rotors switch between ferromagnetic and antiferromagnetic orders in an uncontrolled manner,” report Gu and his team. This constant reorganization during sliding consumes energy and thereby causes the friction maximum at medium distance.
The results thus clarify the question of whether magnetic friction also obeys Amonton’s law. “The amazing thing is that the friction arises entirely from internal reorganization,” says senior author Clemens Bechinger from the University of Konstanz. “There is no wear, no roughness and no direct contact. All dissipation arises solely from collective magnetic rearrangements.” As the physicists explain, similar effects could also occur in atomically thin magnetic materials, in which even the smallest shifts influence the magnetic order. They open up new possibilities for specifically controlling the magnetism and friction of magnetic materials. Potential applications range from micro- and nano-electromechanical systems to magnetic bearings, adaptive dampers and contactless controls.
Source: Hongri Gu (University of Konstanz) et al., Nature Materials, doi: 10.1038/s41563-026-02538-1