Waves on circular paths

At present the transport and control of electrical charges is the basis for the vast majority of electronic components. A major disadvantage of this technology is that the flow of electric currents generates heat due to the electrical resistance. With the immense number of electronic components in use worldwide, this causes gigantic losses of energy.

An energy-efficient alternative may be the use of spin waves to transport and process information, because they do not produce nearly as much waste heat. Such components could also be much more compact. Scientists around the world are therefore looking for materials in which spin waves can be used to transport information.

An international research consortium with significant participation from the Technical University of Munich (TUM) has now taken an important step forward in this search. Their observations of spin waves on circular paths in certain magnetic materials could also represent a breakthrough for those quantum technologies that use waves to transport information.

Propagation of magnetic waves in materials

If you throw a stone into water, you bring the water molecules out of their equilibrium position. They start to oscillate and a circular wave spreads out. In a very similar way, the magnetic moments in some materials can be made to oscillate. In this process, the magnetic moment performs a gyroscopic motion with respect to its rest position. The precession of one moment affects the vibration of its neighbor, and so the wave propagates.

For applications, controlling the properties of these magnetic waves, such as their wavelength or direction, is important. In conventional ferromagnets, in which the magnetic moments all point in the same direction, magnetic waves generally propagate in a straight line.

The propagation of such waves is quite different in a new class of magnetic materials, which, like a box of uncooked spaghetti, consist of a tight arrangement of magnetic vortex tubes. This magnetic order was discovered almost fifteen years ago by a team led by Christian Pfleiderer and Peter Böni at the Technical University of Munich with the help of neutron experiments.

Because of their non-trivial topological properties and in recognition of the theoretical-mathematical developments of British nuclear physicist Tony Skyrme, these vortex tubes are known as skyrmions.

Propagation of magnetic waves on a circular path

Since neutrons carry a magnetic moment, they are particularly well suited for the study of magnetic materials. Like a compass needle they respond sensitively to magnetic fields. As neutron scattering can provide the necessary resolution over very large length and time scales, it proved to be the only technique that could detect the spin waves on circular orbits.

Tobias Weber from the Institut Laue Langevin (ILL) in Grenoble, France, and his team could now prove using polarized neutron scattering that the propagation of a magnetic wave perpendicular to such skyrmions does not occur in a straight line but on a circular path.

The reason for this is that the direction of neighboring magnetic moments, and thus the direction of the axis about which the precessional motion occurs, changes continuously perpendicular to the magnetic vortex tube. Analogously, when the precessional motion propagates from one magnetic moment to the next, the direction of propagation also changes continuously. The radius and the direction of the circular path of the propagation direction of the spin waves depends on the strength and the direction of the tilting of the magnetic moments.

Quantization of circular orbits

"But there is even more to it," says Markus Garst of the Karlsruhe Institute of Technology (KIT), who had developed the theoretical description of spin waves in skyrmions and its coupling to neutrons some time ago. "There is a close analogy between the circular propagation of spin waves perpendicular to a skyrmion lattice and the motion of an electron perpendicular to a magnetic field caused by the Lorentz force."

At very low temperatures, when the circular orbits are closed, their energy is quantized. Predicted almost a hundred years ago by Russian physicist Lev Landau, this phenomenon has long been well-known for electrons as Landau quantization. Here, the influence of the vortex-like character of the skyrmions on the spin waves can be elegantly interpreted by a fictitious magnetic field. That is, the very complicated interplay of the spin waves with the skyrmion structure is actually very simple and may be described just like the motion of electrons transverse to a real magnetic field.

Moreover, the propagation of spin waves perpendicular to skyrmions also displays a quantization of the circular orbits. The characteristic energy of the spin wave is thus also quantized, which promises completely new applications. In addition, the circular orbit is twisted in itself, similar to a so-called Möbius strip. It is topologically non-trivial: Only by cutting and reconnecting the strip can the twisting be removed. All this leads to a particularly stable spin wave motion.

Successful international cooperation

"The experimental determination of spin waves in skyrmion lattices required both a combination of world-leading neutron spectrometers and a massive advancement of the software to interpret the data," explains TUM physicist Peter Böni.

The research team employed instruments of the Institut Laue-Langevin in France, the Swiss spallation source SINQ at the Swiss Paul Scherrer Institute, the UK’s ISIS neutron and muon source, the U.S. Los Alamos National Laboratory, the Karlsruhe Institute of Technology and the Research Neutron Source Heim Maier-Leibnitz (FRM II) at the Technical University of Munich.

Marc Janoschek, meanwhile working at the Paul Scherrer Institute emphasises: "It is simply great to see that, after countless experiments at world-leading spectrometers and the clarification of major experimental and theoretical challenges during my time at Los Alamos, the microscopic detection of Landau quantization at the world's unique beamline RESEDA at TUM's FRM II in Garching closes a circle that began almost fifteen years ago with my first measurements at the Heinz Maier-Leibnitz Zentrum (MLZ) in Garching."

However, the motion of spin waves on circular orbits, which are quantized on top, is a breakthrough not only from the perspective of fundamental research. Christian Pfleiderer, managing director of the newly founded Center for QuantumEngineering at TUM, emphasizes: "The spontaneous motion of spin waves on circular orbits, whose radius and direction arise from the vortex-like structure of skyrmions, opens up a new perspective for realizing functional devices for information processing in quantum technologies, such as simple couplers between qbits in quantum computers."

Text: Based on a press release by Technical University of Munich