By including weights associated with particles, researchers in the US, South Korea and Germany have generalized significantly the concept of hyperuniformity of multi-particle systems.

Hyperuniformity refers to a structural property in which at large enough length scales there is hidden order. Hyperuniform systems behave like they have no order at small length scales, similar to liquids, but at larger length scales they behave like crystals. This dual character leads to important applications for such materials, and the addition of weights allows for this characterization to extend to cases where additional properties of particles are included – such as a particle’s charge or mass.

The simplest example of a hyperuniform material is a crystal in which atoms or molecules are arranged in a uniform lattice that repeats in all directions. In addition to crystals, there are two classes of hyperuniform structures that are of great interest to physicists: quasicrystals and exotic disordered systems. Quasicrystals have highly ordered structures, but their patterns never repeat – so they are not true crystals.

Exotic disordered systems are of great interest to Salvatore Torquato of Princeton University, who was involved in this latest research on hyperuniformity. He tells Physics World that these systems are especially interesting because “they can behave like perfect crystals in the way they suppress large-scale density fluctuations and yet have characteristics of liquids or glasses at small length scales”.

Omnidirectional mirrors

From an engineering point of view, being both liquid-like and crystal-like is very useful. For example, crystalline materials will transmit light at specific wavelengths and incident angles and reflect light at others. In 2022, Torquato and colleagues showed that these optical “band gaps” should also exist in some exotic disordered systems, but without the restriction on incident angles. They suggest that this property could be used to create omnidirectional mirrors that operate only for light at certain wavelengths — unlike everyday mirrors, which reflect light at all wavelengths.

In their latest work, Torquato and colleagues have extended the theoretical description of hyperuniform systems by assigning “weights” to a material’s particle constituents. These weights can be scalar or vector properties. Examples of scalar properties include the charge or mass of a particle; whereas vector properties include the dipole moment or velocity of a particle.

Toraquato and colleagues discovered that under this more general framework of hyperuniformity, including weights can take a particle system which, without weights, is hyperuniform to one which is not (and vice versa).

Different atomic species

For example, one could begin with a standard hyperuniform system comprising identical particles and then imagine that the particles can have one of several different masses. In the real world this would describe a material made of several different atomic species.

The team’s work is important because it represents a significant expansion in the number and richness of systems that can be studied and potentially classed as hyperuniform. Furthermore, weighting provides engineers with additional degrees of freedom that could be used to fine tune hyperuniformity to create new and useful materials.

Torquato is hugely excited about future directions of this work: “Our generalization of hyperuniformity to weighted many-particle configurations opens up an immense set of problems. Our next steps will be driven by what we find to be the most exciting prospects”.

The research is described in Physical Review X.

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Through new experiments with magnetic materials, physicists in Austria, Hong Kong and Germany have overturned a simple law of friction that has held for over 300 years. Led by Clemens Bechinger at the University of Konstanz, the team’s discovery shows how internal collective dynamics in these materials can cause friction to peak at a certain applied, load before dropping sharply. The effect could prove especially promising in applications where friction needs to be precisely controlled.

In 1699, French physicist Guillaume Amontons published his rediscovery of an effect first observed by Leonardo da Vinci: that the force of friction between two sliding surfaces is proportional to the load pressing them together. He also showed that this relationship is monotonic, meaning friction continues to grow as the load increases, forcing stronger interactions between the surfaces.

Since then, Amontons’ law has held up to close experimental scrutiny. “It is actually quite remarkable that this simple law holds across a wide range of very different materials,” Bechinger says. “At the same time, this classical picture does not account for systems where internal degrees of freedom – such as magnetic order – play an active role.”

Little microscopic insight

For all its success, Amontons’ law offers little insight into the microscopic mechanisms underlying friction. To probe these mechanisms, many studies have turned to atomic force microscopy, which measures the motion of a nanoscale tip as it is scanned across a surface. While powerful, this technique can only capture frictional mechanisms over extremely local regions. As a result, it is less well suited to systems where friction emerges from larger-scale effects.

In particular, magnetic materials host regions of aligned atomic spins that can extend across millimetres. When two magnetic surfaces slide past each other, these spins continuously reorient in response to their changing interactions. However, this reconfiguration isn’t instantaneous.

Famously, magnetic systems can display hysteresis, whereby a material’s response to an external magnetic field depends to the history of its magnetization. For two interacting magnetic surfaces, hysteresis means that spin realignments to lag behind the sliding motion, causing the system to undergo repeated cycles of delayed switching. In the process, the kinetic energy of the sliding motion is partly dissipated, increasing the overall friction experienced by the surfaces.

To explore these effects in more detail, Bechinger’s team developed a new experimental platform that moves beyond the constraints of conventional techniques. Instead of applying a load directly, they varied the interaction strength between two extended magnetic surfaces by precisely controlling their separation distance.

Monitoring magnetization

“Using millimetre-sized rotatable magnets, this allowed us to directly monitor the orientations of their magnetization during sliding, and to correlate these changes quantitatively with the measured friction force,” Bechinger explains.

As the surfaces were brought closer together, the researchers observed that friction initially rose, in line with the expectations of Amontons’ law. However, this trend did not continue indefinitely: at an intermediate separation distance, friction reached a maximum.

“A peak occurs when competing magnetic interactions drive the system into a frustrated state,” Bechinger continues. “This causes repeated, hysteretic switching of magnetic orientations during sliding, which strongly enhances energy dissipation.”

Beyond this point, the effect was weakened by further decreases in separation distance, and friction dropped sharply: a clear departure from the monotonic behaviour predicted by Amonton’s law.

Altogether, the team’s findings show that friction can arise entirely from the internal collective dynamics of the material, rather than from direct mechanical contact alone. As Bechinger explains, the ability to tune these effects could open up new technological possibilities.

“This opens up new possibilities for designing wear-free, contactless frictional systems and suggests that friction itself can serve as a sensitive probe of microscopic ordering,” he says. “Potential applications could range from magnetic sensing to programmable metamaterials.”

The research is described in Nature Materials.

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