Numerical Calculation of the Hopf Index for 3D Magnetic Textures
arXiv:2410.22058 · doi:10.1103/PhysRevB.111.134408
Abstract
To gain deeper insight into the complex, stable, and robust configurations of magnetic textures, topological characterisation has proven essential. In particular, while the skyrmion number is a well-established topological invariant for 2D magnetic textures, the Hopf index serves as a key topological descriptor for 3D magnetic structures. In this work, we present and compare various methods for numerically calculating the Hopf index, provide implementations, and offer a detailed analysis of their accuracy and computational efficiency. Additionally, we identify and address common pitfalls and challenges associated with the numerical computation of the Hopf index, offering insights for improving the robustness of these techniques.
References in corpus (18)
- The design and verification of Mumax3
- Knots and Particles
- Reconfigurable knots and links in chiral nematic colloids
- Skyrmion knots in frustrated magnets
- Binding a Hopfion in Chiral Magnet Nanodisk
- How superfluid vortex knots untie
- Three-dimensional dynamics of magnetic hopfion driven by spin transfer torque
- ``Smoke Rings'' in Ferromagnets
- Vortex rings in ferromagnets
- On quantifying the topological charge in micromagnetics using a lattice-based approach
- Unwinding in Hopfion vortex bunches
- Winding Hopfions on R^2 x S^1
- Large-scale magnetostatic field calculation in finite element micromagnetics with H2-matrices
- Magnetic helicity in multiply connected domains
- Spacetime magnetic hopfions: from internal excitations and braiding of skyrmions
- Emergent magnetic field and vector potential of the toroidal magnetic hopfions
- Oersted fields and current density profiles in spin-torque driven magnetization dynamics -- Finite element modelling of realistic geometries
- On lines of constant polarisation in structured light beams