Magnetic nanoparticles known as skyrmions and their antiparticle equivalents can behave very differently, according to new calculations by researchers in Sweden, Germany and France. This unexpected new finding could have important consequences for any potential technologies involving these particles, such as next-generation data storage and information processing devices.

Skyrmions are swirling vortex-like magnetic spin structures that extend across a few nanometres in a material and can be likened to 2D knots in which the magnetic moments rotate about 360° within a plane. They are now known to occur in many materials and were first observed in experiments about 10 years ago. They show much promise as the building blocks for next-generation memory, low-power binary logic operations and magnetic data storage technologies that have a higher density than today’s disk drives. This is because they can be made much smaller than the magnetic domains employed in these devices and be efficiently controlled with spin currents. They might also be used in neuromorphic and stochastic computing schemes.

Before we can understand the importance of the new result, we need to refer back to electronic circuits for a moment. “These rely on the motion of electrons, and according to electrodynamics theory, would work just as well with positrons – the (extremely rare) antiparticle equivalent of electrons,” says Joo-Von Kim of the Université Paris-Saclay, who led this research effort together with Bertrand Dupé of the University of Mainz and Ulrike Ritzmann of Uppsala University. “The only difference is that electrons and positrons respond in opposite directions under electric fields and are deflected in opposite directions in a magnetic field because of the Lorentz force.

“In the same way, skyrmions and antiskyrmions are deflected in opposite directions in response to a force that is described by the so-called Thiele equation,” he explains. “This equation has worked sufficiently well until now to describe phenomena that researchers have observed in hundreds of published studies. Like our colleagues before us, we naturally assumed that the kinematics of antiskyrmions could be described by simply changing the sign of the topological charge in the Thiele equation, but we have found that things aren’t as simple as this.”

Two important deviations

In their study, the researchers calculated the motion of skyrmions and antiskyrmions in an ultrathin ferromagnetic film (1-2 atoms thick) using electrical currents, so providing a torque on the magnetic moments in the material through spin-orbit interactions. “At low applied currents, the film behaves as expected: opposite topological charges in the material are deflected in opposite directions,” says Kim. “However, two important deviations from the Thiele equation occur when we increase the applied current.

“First, the motion of skyrmions and antiskyrmions no longer mirror each other: skyrmions continue to travel in straight lines as before, but antiskyrmions begin to travel along a curved trajectory. As the current is increased further, these trajectories begin to look like trochoids, which are similar to the curve traced out by the pedal of a bicycle being pedalled along a straight path.”

The second deviation occurs when the amount of energy transferred to the system from the applied current is increased, he adds. “We found that the trochoidal motion can create skyrmion-antiskyrmion pairs here. For each pair, the skyrmion created propagates away in a straight line while the antiskyrmion remains close to the point at which it was created thanks to its trochoidal motion.”

New source of skyrmion-antiskyrmion pairs

“To our surprise, we found that each antiskyrmion thus created becomes a new source of skyrmion-antiskyrmion pairs, a process that produces a large number of these particles,” Dupé tells Physics World. “The result? A ‘gas’ of skyrmions and antiskyrmions begins to form. Because of how these particles move and then collide, we generally find an excess of skyrmions in this gas, however. This is remarkable given that the initial state of the system is a single antiskyrmion.

“Again, if we make an analogy with electrodynamics, this would be like firing a single positron through a strong magnetic field and getting a gas of (mainly) electrons in return.”

The results could have important consequences for any potential applications involving skyrmions. “First, our discovery of the existence of trochoidal motion puts an inherent speed limit on how fast skyrmions and antiskyrmions can travel along straight lines – something that has been largely ignored to date,” says Ritzmann. “We believe that any future circuit or device that exploits skyrmions for transmitting information would have to take this limit into account.

“Second, the asymmetry we saw in the dynamics between skyrmions and antiskyrmions, naturally leading to an excess of skyrmions, means that we can readily generate skyrmions with a single antiskyrmion ‘seed’. Being able to produce skyrmions quickly in this way will be an advantage for when it comes to making future devices from these particles.”

How common could such phenomena actually be?

On a more fundamental level, the researchers say that this asymmetry might even provide a clue as to why there is more matter than antimatter in our universe. “If we make a bold analogy beyond electrodynamics that extends to particles and antiparticles in general, then we also have a concrete example here of how an imbalance of antimatter and matter can arise in a physical system,” states Kim. “This imbalance only occurs at high energies, where the pair creation process combined with asymmetric dynamics leads to an excess of skyrmions (matter).”

“It would be premature of us to suggest that the baryogenesis problem might be solved with skyrmions and antiskyrmions, but it is an intriguing result nonetheless,” adds Dupé. It may even provide inspiration to particle physicists and cosmologists working on the topic.”

The team, reporting its work in Nature Electronics 1 451, says that it would now like to study the other more exotic particle states (with a higher topological charge) that exist in the material system they studied. “These states are less stable than skyrmions and antiskyrmions, so it will be more challenging to measure their dynamics,” says Ritzmann. “We also plan to look into additional materials systems and find out how common such phenomena actually are. Ultimately, we hope that our studies will encourage experimentalists to look for antiskyrmions, and skyrmion–antiskyrmion pair creation events in the lab.”