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Topological Characterization of Magnetic Surface Waves
—New Path toward Low-energy Wave-based Computing Technologies—

A magnet is made of billions of trillions of microscopic bar magnets (called magnetic moments). The orientations of these moments can oscillate by a tiny amount, and these oscillations propagate as magnetic waves. It has been long known that magnetic surface waves, which propagate along the surface of magnets, travel significantly longer distances than volume waves propagating inside the magnets. What makes the surface waves more stable than the volume waves? - the answer has remained a "mystery" to date.

In this study, the question has been addressed by using topology to characterize the equations that describe magnetic waves. A suitable choice of mathematical representation of the magnetic waves allowed the researchers to show that magnets with and without surfaces waves have distinct topologies. Once the connection between the presence of magnetic surface waves and topology is established, one can deduce various properties of the surface waves from standard mathematical theorems. For example, the surface waves cannot be converted into volume waves and thus, even if the surface waves get disturbed by either obstacles or external stimuli, they cannot be deflected into the interior of the magnet and will continue to propagate along the surface in a stable manner.

The findings in this study can be applied to materials with various types of magnetism. Aside from their stability, surface waves also possess other unique properties, such as unidirectional propagations. Those properties are suited for, for example, applications in computing devices. The results of this study can be used as criteria for the search for materials with surface waves that are more suitable for data processing, which is an active field of research in materials science.

Because of the slower motion of magnetic waves than that of electrons, their use in data processing in place of electrical circuits will reduce the amount of heat generated during computations, and thus result in energy-savings. In addition, since magnetic waves have multiple amplitudes in different directions, in contrast to ordinary electric signals characterized by a single amplitude, they have the potential to convey more pieces of information at a time and therefore may make a great contribution to the future development of information technology.

Conceptual diagram of magnetic surface waves and volume waves
Surface waves propagate through a longer distance in a more stable manner than volume waves.
The mechanism was revealed by an application of topology.

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