Spatial decay of isolated magnetic hopfions in chiral helimagnets

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 the starting point for a simple analytical model, which is asymptotically correct both near the hopfion center and far away from it. The region of equilibrium hopfions on the phase diagram of a helimagnet is computed and material requirements for supporting movable isolated magnetic hopfions on a uniform background are discussed.