What if the magnon Hall effect, which processes information using magnons (spin waves) capable of current-free information transfer with magnets, could overcome its current limitation of being possible only on a 2D plane? If magnons could be utilized in 3D space, they would enable flexible design, including 3D circuits, and be applicable in various fields such as next-generation neuromorphic (brain-mimicking) computing structures, similar to human brain information processing. KAIST and an international joint research team have, for the first time in the world, predicted a 3D magnon Hall effect, demonstrating that magnons can move freely and complexly in 3D space, transcending the conventional concept of magnons.

KAIST (President Kwang Hyung Lee) announced on May 22nd that Professor Se Kwon Kim of the Department of Physics, in collaboration with Dr. Ricardo Zarzuela of the University of Mainz, Germany, has revealed that the interaction between magnons (spin waves) and solitons (spin vortices) within complex magnetic structures (topologically textured frustrated magnets) is not simple, but complex in a way that enables novel functionalities.

Magnons (spin waves), which can transmit information like electron movement, are garnering attention as a next-generation information processing technology that transmits information without using current, thus generating no heat. Until now, magnon research has focused on simple magnets where spins are neatly aligned in one direction, and the mathematics describing this was a relatively simple 'Abelian gauge theory.'

The research team demonstrated, for the first time in the world, that in complex spin structures like frustrated magnets, magnons interact and become entangled in complex ways from various directions. They applied an advanced mathematical framework, 'non-Abelian gauge theory,' to describe this movement, which is a groundbreaking achievement.

This research presents the possibility of future applications in low-power logic devices using magnons and topology-based quantum information processing technologies, indicating a potential paradigm shift in future information technology.

In conventional linear magnetic materials, the value representing the magnetic state (order parameter) is given as a vector. In magnonics research based on this, it has been interpreted that a U(1) Abelian gauge field is induced when magnons move in soliton structures like skyrmions. This means that the interaction between solitons and magnons has a structure similar to quantum electrodynamics (QED), which has successfully explained various experimental results such as the magnon Hall effect in 2D magnets.

< Figure. Schematic diagram of non-Abelian magnon quantum chromodynamics describing the dynamics of three types of magnons discovered for the first time in this study.>

However, through this research, the team theoretically revealed that in frustrated magnets, the order parameter must be expressed not as a simple vector but as a quaternion. As a result, the gauge field experienced by magnons resembles an SU(3) non-Abelian gauge field, rather than a simple U(1) Abelian gauge field.

This implies that within frustrated magnets, there are not one or two types of magnons seen in conventional magnets, but three distinct types of magnons, each interacting and intricately entangled with solitons. This structure is highly significant as it resembles quantum chromodynamics (QCD) that describes the strong interaction between quarks mediated by gluons rather than quantum electrodynamics (QED) that describes electromagnetic forces.

Professor Se Kwon Kim stated, "This research presents a powerful theoretical framework to explain the dynamics of magnons occurring within the complex order of frustrated magnets," adding, "By pioneering non-Abelian magnonics, it will be a conceptual turning point that can influence quantum magnetism research as a whole."

The research results, with Dr. Ricardo Zarzuela of the University of Mainz, Germany, as the first author, were published in the world-renowned physics journal Physical Review Letters on May 6th.
※ Paper title: "Non-Abelian Gauge Theory for Magnons in Topologically Textured Frustrated Magnets," Phys. Rev. Lett. 134, 186701 (2025)
DOI: https://doi.org/10.1103/PhysRevLett.134.186701

This research was supported by the Brain Pool Plus program of the National Research Foundation of Korea.