Two types of metastable magnetic hopfions

TL;DR

This paper theoretically investigates two distinct stable configurations of magnetic hopfions in bulk magnets, analyzing their stability regions under various magnetic and anisotropic conditions.

Contribution

It introduces the existence of two topologically equivalent stable hopfion configurations and maps their stability regions in parameter space.

Findings

Two stable hopfion configurations exist in certain conditions.

Stability regions depend on magnetic field, anisotropy, and magnetostatic strength.

Both hopfion types can be stable simultaneously under some parameters.

Abstract

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 N\'eel walls in classical magnetism) there are two possible stable configurations of these solitons, 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.