Magnetostatic bounds on stability of hopfions in bulk helimagnets

Abstract

Magnetic hopfions are three-dimensional localized topological solitons in the volume of a magnet. In this work, starting with a classical free energy density of a helimagnet, an approximate variational model of hopfions is studied. The hopfion stability regions on the uniaxial anisotropy-external magnetic field phase diagram are computed and their evolution with increasing magnetostatic interaction strength is considered. It is found that magnetostatic interaction destabilizes the hopfions and, above the certain strength (relative to Dzyaloshinskii-Moriya interaction), destroys their stability completely. Numerical estimates for this bound are provided. They can help focus the search for materials, supporting bulk magnetic hopfions.