Two types of metastable hopfions in bulk magnets

Localized magnetic topological solitons with Hopf index of 1 in an unbounded bulk magnet are studied theoretically, starting with the classical micromagnetic Hamiltonian. It is shown analytically that (like Bloch and Neel walls in classical magnetism) there are two possible stable configurations of these nanoobjects, which are equivalent topologically. Their stability regions are plotted on a phase diagram in the magnetic field - uniaxial anisotropy space for different normalized magnetostatic interaction strengths. For some parameters both types of hopfions can be stable.(c) 2022 Elsevier B.V. All rights reserved.

Automated summary

This paper theoretically studies localized magnetic topological solitons with a Hopf index of 1 in an unbounded bulk magnet, starting with the classical micromagnetic Hamiltonian. It is analytically proven that there are two equivalent topologically stable configurations for these nanoobjects, similar to Bloch and Neel walls in classical magnetism. The stability regions of these solitons are plotted on a phase diagram, showing their distribution in the magnetic field - uniaxial anisotropy space. Both types of hopfions can be stable for certain parameter values.