Berlin 2024 – scientific programme
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MA: Fachverband Magnetismus
MA 46: Poster II
MA 46.67: Poster
Thursday, March 21, 2024, 15:00–18:00, Poster C
Hopf index calculation in micromagnetic finite-element simulations — •Louis Gallard1, Karin Everschor-Sitte2, and Riccardo Hertel1 — 1Université de Strasbourg and CNRS, IPCMS, 67000 Strasbourg, France — 2Faculty of Physics and CENIDE, University of Duisburg-Essen, 47057 Duisburg, Germany
Magnetic Hopfions are complex topological textures that can be regarded as three-dimensional (3D) counterparts of skyrmions. They have recently attracted considerable interest due to their intriguing structure and possible use in spintronic devices. Unlike skyrmions, which are usually easy to spot in magnetic configurations, Hopfions are difficult to identify because of their complex knotted 3D vector field distribution. The difficulty arises even in micromagnetic simulations, where detailed information about the magnetic structure is readily available. The Hopf index, a topological invariant, provides a measure of Hopfions that allows for their quantitative detection. However, in the general case of 3D samples of finite size, calculating the Hopf index usually involves a two-fold volume integral, whose O(N2) scaling makes its evaluation impracticable in large-scale computations. Here, we present an alternative approach which involves solving a partial differential equation by using a hybrid finite-element / boundary-element method. We retain a scaling of nearly O(N), which is suitable for high-performance computing. The method is fast enough to be used during dynamic micromagnetic simulations to monitor the Hopf index’s evolution in time. We demonstrate the application of the method to a Hopfion structure in a cylinder and a torus geometry.
Keywords: Hopfions; Micromagnetic Simulations; Finite Element Method; Topology; Three-dimensional Nanomagnetism