Do the magnetic hopfions have tails?

TL;DR

This paper investigates the spatial localization of magnetic hopfions in chiral magnets, deriving an asymptotic expansion to model their profiles and determine conditions for their stability and mobility.

Contribution

It introduces an asymptotic analytical model for magnetic hopfions, providing insights into their localization strength and stability conditions in helimagnets.

Findings

Derived an asymptotic expansion for hopfion profiles

Identified equilibrium regions in the phase diagram

Discussed material requirements for stable hopfions

Abstract

Magnetic hopfions in chiral magnets are topological solitons, localized in three dimensions. But is their localization strong? To address this question we derive an asymptotic expansion for the isolated hopfion's spatial profile. It becomes starting point for a simple analytical model, which is asymptotically correct both near the hopfion center and far away from it. Region of equilibrium hopfions on the phase diagram of a helimagnet is computed and material requirements for supporting movable isolated magnetic hopfions on uniform background are discussed.