Topological Rings: Hopfion structure, Dynamics and Control – TOROID

Topological magnetic structures like domain walls, vortices, and skyrmions are central in modern magnetism. They display several unique properties rendering them attractive for fundamental research and spintronic applications. In parallel to the scientific interest in topological structures, three-dimensional nanomagnetism has emerged in the past few years as a vibrant field of research. Against the backdrop of these developments, magnetic Hopfions structures that are both inherently topological and three-dimensional have recently shifted into the focus of attention. While Hopfions—knotted structures which can be regarded as a three-dimensional generalization of skyrmions—have been studied intensively in the neighboring domain of liquid crystals, they remain exotic and underexplored in magnetic materials, despite a rapidly growing interest. Key questions concern the conditions leading to their formation, their behavior in confined geometries, and the ability to control these structures through external means.
The scientific goal of the TOROID project is to obtain a thorough theoretical understanding of the complex fundamental physics and properties of magnetic Hopfions. The teams of K. Everschor-Sitte (Duisburg-Essen - UDE) and R. Hertel (Strasbourg - IPCMS) will join forces to investigate the structure, stability, and dynamics of magnetic Hopfions by combining analytic theory and micromagnetic simulations. We will study the properties of Hopfions in bulk systems and in three-dimensional confined geometries. Our starting point is to precisely analyze and identify these three-dimensional topological objects characterized by the Hopf index. The first goal is to obtain a thorough understanding of the conditions leading to their stabilization in various host samples. Once we have gained sufficiently detailed knowledge of single Hopfions, we will address the interactions in pairs and arrays of Hopfions, including the analysis of coupled dynamic modes. We will use simulation results to develop analytic models describing the Hopfion dynamics. Finally, we will investigate means to manipulate and control these structures by applied currents and fields. Exploring these aspects could provide essential insight into the applicability of Hopfions in nanomagnetic devices.