Skyrmions, increasingly promising magnetic particles for future computers

In the second half of the 19th century^e century, the famous British physicist Kelvin came up with a brilliant idea when he read the work of his German colleague Hermann Helmholtz. The latter showed that the rotating rings of liquid are quite stable, and also that they will exert forces on each other that are reminiscent of the forces of magnetic fields between wires through which an electric current flows. Kelvin concluded that atoms were actually strands of liquid rotating around a central axis, forming different nodes, one for each chemical element. The liquid carrying these threads was interpreted as ether, a material medium whose stresses and waves were supposed to be the source of the electromagnetic field.

Although elegant and attractive, this unitary theory was a failure, as proven by the advances of quantum atomic theory. Physicists, however, held to the idea that discrete stable structures that could be interpreted as particles could arise from nonlinear equations, such as the Navier-Stokes equations, describing continuous fields.

Thus, we know about the existence of solitons, types of stable energy packets in media described by nonlinear partial differential equations. One of the most famous examples can be found in fluid dynamics. It is a tidal wave, a single wave first observed by Scotsman John Scott Russell in the 19th century.^e century, which followed the wave going upstream for several kilometers and did not seem to want to weaken.

Nucleon model

Because of their stable nature, elementary particles have been repeatedly proposed as solitons. Moreover, almost fifty years ago, before the theory of quantum chromodynamics was discovered, the great British theorist Tony Skyrme sought to better understand the nature of nucleons and the strong nuclear force. So he tried to play the same game as Kelvin to explain the existence and properties of nucleons. We already knew that protons and neutrons are half-integer-spin fermions and that they exchange a species of photon, the famous integer-spin Yukawa boson, the pion.

At the same time, Heisenberg also sought to better understand nuclear forces, but went further. He considered a nonlinear fundamental field equation based on the fermion field, which must contain all matter particles and forces known at the time. For example, in this unified theory, photons and gravitons were considered as bunches of fermions. Having their own angular momentum, spin, corresponding values ​​of 1 and 2, they can effectively be bound states of an even number of spin ½ fermions.

Skyrme took a more modest approach (he dealt only with baryons and nuclear forces), but very similar. He also considered a nonlinear equation whose fundamental field was that of a spin-zero boson, the Yukawa pion.

At first glance, the idea seems absurd. How to obtain particles with spin ½ from the composite states of particles with spin zero?

This is where the nonlinear nature of the equation comes into play. Just as stable vortices with angular momentum can form in a liquid, also described by a nonlinear equation (the Navier-Stokes equation), we could consider protons and neutrons as types of vortices in a pion liquid. These configurations, which resemble those of solitons, are today called skyrmions.

The discovery of quarks and the theory of quantum chromodynamics (QCD) eclipsed the Skyrme baryon model (ironically, it later appeared as an approximation of the QCD equations). But several decades later we realized its importance in the field of condensed matter physics.